1. No category

DistortionMitigationin
CognitiveRadioReceivers
DISTORTION MITIGATION IN COGNITIVE
RADIO RECEIVERS
Dlovan Hoshiar Mahrof
Members of the dissertation committee:
Chairman:
Prof. Dr.
P.M.G. Apers
University of Twente
Prof. Dr.
P.M.G. Apers
University of Twente
B. Nauta
University of Twente
E.A.M. Klumperink
University of Twente
F.E. van Vliet
Henrik SjÖland
C.H. Slump
P.G.M. Baltus
TNO / University of Twente
Lund University
University of Twente
Eindhoven University of Technology
Secretary:
Promotor:
Prof. Dr. ir.
Assistant Promotor:
Dr. ing.
Members:
Prof. Dr. ir.
Prof. Dr.
Prof. Dr. ir.
Prof. Dr. ir.
This research is supported by the Dutch Technology Foundation
STW, which is part of the Netherlands Organisation for Scientific
Research (NWO) and partly funded by the Ministry of Economic
Affairs (08081).
CTIT Ph.D. Thesis Series No. 15-348
Centre for Telematics and Information Technology
P.O. Box 217, 7500 AE
Enschede, The Netherlands.
Title:
Distortion Mitigation in Cognitive Radio Receivers
ISBN: 978-90-365-3846-6
ISSN: 1381-3617 (CTIT Ph.D. Thesis Series No. 15-348 )
DOI: 10.3990/1.9789036538466
http://dx.doi.org/10.3990/1.9789036538466
Copyright © 2015 by Dlovan Hoshiar Mahrof, Enschede, The Netherlands
DISTORTION MITIGATION IN COGNITIVE RADIO
RECEIVERS
DISSERTATION
to obtain
the degree of doctor at the University of Twente,
on the authority of the rector magnificus,
prof.dr. H. Brinksma,
on account of the decision of the graduation committee,
to be publicly defended
on Friday the 20th March 2015 at 12:45
by
DLOVAN HOSHIAR MAHROF
born on the 26th of December 1973
in Al-Sulaimaniya, Iraq
This dissertation has been approved by:
Promotor: Prof. Dr. ir. Bram Nauta
Co-promotor: Dr. ing. Eric A.M. Klumperink
To Almas,
Varto and Zhareen,
Abstract
The exponential increase of wireless communication increasingly leads to spectrum congestion.
Attempts are being made to increase RF spectrum utilization efficiency by introducing Cognitive Radio
(CR) concept. A CR tries to intelligently solve the congestion problem via Dynamic Spectrum Access
(DSA), i.e. determine which frequencies are temporarily and locally free, and exploit this free spectrum.
Especially in the TV broadcasting bands below 1 GHz, such CR possibilities are being explored. Ideally, a
CR receiver should be able to operate directly adjacent to the primary service users, e.g. Digital TV
channels, which use high power levels and often leave the adjacent channels unused. Under such
conditions no or very low up-front filtering of the interferer is possible. Consequently, a CR receiver
must tolerate the existence of strong interferers, i.e. have a very high linearity front-end.
This thesis examines CR receiver linearity requirements and explores techniques that mitigate distortion.
The thesis starts by analyzing the linearity requirements for DSA. As the level and the spectral location of
the interferers can change instantaneously per location, it is relevant to monitor the spectrum and find
suitable opportunities for communication. The analysis is applied to a channelized spectrum in which a
number of interferers exist, and a CR tries to exploit any free channel. It is derived how the CR linearity
requirement depends not just on the power levels of the interferers but also on their spectral locations
around the desired CR frequency/channel. It is shown that the linearity requirement can be relaxed by
tens of dBs levels of 3rd order InterModulation product (IM3). The analysis also exploits the prediction of
the distortions in different channels for DSA. This prediction algorithm is denoted here as DPrA (i.e.
Distortion Prediction Algorithm). It processes the spectrum sensing information about the power level
and the spectral locations of the interferers to derive the linearity requirements for each potential CR
channel. Based on this information, a CR can choose the most suitable channel compatible with its
linearity capability.
A receiver with better linearity can work under worse interference conditions, and hence maximizing
linearity of a CR receiver is important. To increase the linearity of a CR receiver, CMOS receiver frontends with high linearity are explored. Receivers that exploit linear V-I conversion at RF, followed by
passive down-mixing and an OpAmp-based Transimpedance Amplifier at baseband, show high linearity
potential. However, it is shown that due to nonlinearity and finite gain in the OpAmp, the virtual ground
I
is imperfect, resulting in distortion currents. The concept of a negative conductance is proposed to
cancel such distortion currents. Through a simple intuitive analysis, the basic operation of the technique
is explained. By mathematical analysis the optimum negative conductance value is derived and related
to feedback theory. It is shown that a finite value of the negative conductance is needed to make the
feedback loopgain theoretically approach infinity, which is practically not easily possible by increasing
the gain of the OpAmp block. The technique is applied to linearize an RF receiver and a prototype is
implemented in 65nm technology. Measurement results show an increase of the in-band IIP3 from 9dBm
to >20dBm, and IIP2 from 51 to 61dBm, at the cost of an increase of the noise figure from 6 to 7.5dB and
<10% power penalty. The chip achieves a Spurious-Free Dynamic Range of 85dB in 1MHz.
II
Samenvatting
De exponentiële groei van draadloze communicatie leidt steeds meer tot congestie van het spectrum.
Pogingen zijn ondernomen om het gebruik van Radio Frequentie (RF) spectrum efficiënter te maken
door de invoering van Cognitieve Radio (CR) concept. Een CR probeert de congestie-probleem via
Dynamic Spectrum Access (DSA) op te lossen. DSA bepaalt welke frequenties tijdelijk en lokaal vrij zijn
om die toe te wijzen aan CR. De CR operatie mogelijkheden wordt vooral onderzocht in de TV uitzending
banden onder 1 GHz. In ideale geval moet een CR ontvanger kunnen ontvangen direct in de kanalen
naast de primaire servicegebruikers, zoals digitale TV zenders, die hoog vermogen sturen en vaak
verlaten de aangrenzende kanalen ongebruikt. Onder dergelijke omstandigheden zal er geen of zeer
lage pre-filteren van digitale TV signalen plaatsvinden. Bijgevolg moet een CR ontvanger het bestaan van
sterke interfereren tolereren. Dat wil zeggen dat de CR ontvanger een zeer hoge lineariteit moet
hebben.
Deze thesis onderzoekt de benodigde eisen aan de CR ontvanger lineariteit en verkent de technieken,
die de gevolge vervorming/distorsie verzachten.
Het proefschrift begint met het analyseren van de lineariteit voor DSA. Het vermogen niveau en de
spectrale locatie van de interferentie signalen verandert voortdurend per elke locatie, daarom is het
relevant om het spectrum voortdurend te meten en de geschikte vrij frequenties te bepalen voor CR
communicatie. De analyse wordt toegepast op een gekanaliseerd spectrum waarin een aantal kanalen
zijn bezet met interferentie signalen. Een CR probeert om van die vrij kanalen te benutten. Het is
afgeleid hoe afhankelijk de CR lineariteit is van niet alleen de vermogen van de interferentie signalen
maar ook van hun spectrale locaties rond de gewenste CR frequentie/kanaal. Het is aangetoond dat de
lineariteit met tientallen dBs niveaus van 3e orde intermodulatie product (IM3) kan worden versoepeld.
De analyse exploiteert het gebruik van de voorspelling van de verstoringen in verschillende kanalen voor
DSA. Deze voorspelling algoritme wordt ontwikkelt en aangeduid als DPrA (d.w.z. Distortion Prediction
Algorithm) hier. Het verwerkt de spectrum informatie over het vermogen en de spectrale locatie van de
interferentie signalen voor het afleiden van de lineariteit eisen voor elke potentiële CR kanaal. Op basis
van deze informatie, kan een CR het meest geschikt kanaal voor zijn lineariteit kiezen.
Een ontvanger met betere lineariteit kan werken onder slechtere omstandigheden van de interferentie
signalen, en daarom het maximaliseren van CR ontvanger lineariteit is belangrijk. Om de lineariteit van
III
een CR ontvanger te vergroten worden CMOS ontvanger met hoge lineariteit onderzocht. Ontvangers
die gebruikmaken van lineaire spanning naar stroom conversie bij RF, gevolgd door het passieve
frequentie translatie en een OpAmp gebaseerde transimpedantie versterker op lage frequentie, toont
hoge potentiële lineariteit. Het is aangetoond dat als gevolg van niet lineariteit en beperkte versterking
factor in de OpAmp, de virtueel grond onvolmaakt is waarmee distorsie stromingen resulteert. Het
concept van een negatieve weerstand wordt voorgesteld om die distorsie stromingen te annuleren.
Door middel van een eenvoudige intuïtieve analyse wordt de basiswerking van het techniek uitgelegd.
Door wiskundige analyse is de optimale waarde van de negatieve weerstand afgeleid en gerelateerd aan
de terugkoppeling theorie (Regel Techniek). Het is hier bewezen dat een eindige waarde van het
negatieve weerstand is nodig om de versterking loop van de terugkoppeling oneindig te maken
(theoretisch gezien), die praktisch door het verhogen van de OpAmp versterking niet gemakkelijk is. De
techniek wordt toegepast om de lineariteit van een RF IC chip ontvanger te verhogen. Een prototype is
geïmplementeerd in 65nm technologie. Meetresultaten tonen een toename van de IIP3 in-band van
9dBm naar > 20dBm, en IIP2 van 51 naar 61dBm, ten koste van een ruis toename van 6 naar 7.5dB en
een extra 10% vermogen gebruik. De chip bereikt een dynamic range (d.w.z. Spurious-Free Dynamic
Range) van 85dB in 1MHz.
IV
List of Main Abbreviations
RF: Radio Frequency
FCC: Federal Communications Commission
DTV and DVB-T: Digital TV broadcasting and Digital Video Broadcasting Terrestrial
DSA: Dynamic Spectrum Access
SR/SDR/CR: Software Radio/Software Defined Radio/Cognitive Radio
ADC/DAC: Analog-to-Digital Convertor/Digital-to-Analog Convertor
OFDM: Orthogonal Frequency Division Multiplexing
QPSK: Quadrature Phase Shift Keyed
SAW: Surface Acoustic Wave
NF: Noise Figure of the receiver
IIP3: 3rd order Input Intercept Point
IIP2: 2nd order Input Intercept Point
IM3: 3rd order InterModulation product
IM2: 2nd order InterModulation product
XM3: cross-modulation product
DPrA: Distortion Prediction Algorithm
LPF/ BPF: Low Pass Filter/ Band Pass Filter
X/ ⊗ : mathematical operation of Multiplication operation/ Convolution operation
OpAmp: Operation Amplifier
VGND: Virtual Ground of OpAmp
V
Contents
Abstract ................................................................................................................................................... I
Samenvatting ......................................................................................................................................... III
List of Main Abbreviations ....................................................................................................................... V
Chapter 1. Introduction ........................................................................................................................... 1
1.1 Cognitive Radio Motivation ............................................................................................................ 2
1.2 CR receiver hardware imperfections .............................................................................................. 5
1.3 Research Scope summary and questions ........................................................................................ 6
1.4 Outline of the Thesis ...................................................................................................................... 6
Chapter 2. Cognitive Radio Receiver Linearity Requirements [18] ............................................................ 9
2.1 Problem Definition....................................................................................................................... 10
2.2 Behavior Model for Nonlinearity .................................................................................................. 13
2.3 Analysis of the Spectral Locations of Distortion Products ............................................................. 13
2.4 Estimation of Linearity Requirements .......................................................................................... 20
2.5 Measurement Results .................................................................................................................. 24
2.6 Conclusion ................................................................................................................................... 26
Chapter 3. Distortion Prediction Algorithm and Frequency Selection ..................................................... 27
3.1 Distortion Prediction Algorithm (DPrA) ........................................................................................ 28
3.2 DPrA Application Examples .......................................................................................................... 43
3.3 Conclusions.................................................................................................................................. 48
Chapter 4. Analysis of a Very Linear Front-End [41] ............................................................................... 49
4.1 Motivation and Introduction ........................................................................................................ 50
4.2 Linearization Concept Analysis ..................................................................................................... 52
4.3 Mathematical Analysis ................................................................................................................. 56
4.4 Feedback Control Analysis ........................................................................................................... 58
VI
4.5 Stability Analysis .......................................................................................................................... 59
4.6 Conclusion ................................................................................................................................... 61
Chapter 5. Chip Design: UTCRxVLi [41]................................................................................................... 63
5.1 Receiver Implementation ............................................................................................................. 64
5.2 Noise Figure................................................................................................................................. 68
5.3 Measurement Results .................................................................................................................. 69
5.4 Benchmarking .............................................................................................................................. 74
5.5 Conclusions.................................................................................................................................. 74
Chapter 6. Conclusions and Recommendations ..................................................................................... 75
6.1 Summary and Conclusions ........................................................................................................... 76
6.2 Original Contributions .................................................................................................................. 80
6.3 Recommendations for Future Work ............................................................................................. 80
Appendix A.
Digital TV broadcasting (DTV) ......................................................................................... 83
Appendix B.
Wideband Correction Factor (∆Wideband) Effect on CR Linearity Requirement .............. 84
Appendix C.
DPrA Maple Program Implementation ............................................................................ 85
Appendix D.
Nonlinear Transimpedance Amplifier Analysis ................................................................ 87
Appendix E.
Latch-Up Analysis ........................................................................................................... 90
References ............................................................................................................................................ 93
List of Publications................................................................................................................................. 99
Acknowledgments ............................................................................................................................... 101
Biography ............................................................................................................................................ 103
VII
VIII
Chapter 1. Introduction
This chapter introduces the motivations and the main research questions regarding the importance of
distortion mitigation in Cognitive Radio. Section 1.1 begins with Cognitive Radio motivation to solve the
Frequency spectral utilization efficiency via Dynamic Spectrum Access. Afterwards in section 1.2, the
Cognitive Radio receiver hardware imperfections are discussed. Then the research scope summary is
presented in section 1.3 with the main research question. The chapter ends with the outline of the
thesis in section 1.4.
1
1.1 Cognitive Radio Motivation
The wireless communication revolution has led to a tremendous amount of applications and services in
our everyday life. Examples are the early success of GSM cellular telephony, DECT telephones at home,
Bluetooth technology for direct data exchange between devices, Wi-Fi internet access for local area high
data rate radio operation, GPS navigation, and currently the rapid expansion of wireless video and cloud
service access. To each application, government bodies allocate a specific radio frequency range in the
spectrum, called frequency band. Each band is derived by specific standards. Figure 1.1 shows the
frequency allocation made by the National Telecommunications and Information Administration (NTIA
[1]) in the USA. The Radio Frequency (RF) spectrum between 3kHz – 300GHz is divided in band(s) per
application, assigned through administrative licensing.
Figure 1.1: Spectrum allocation between 3kHz and 300GHz in the USA (NTIA [1])
Given the crowdedness of the spectrum plot of Figure 1.1 alongside with the observation that the
demand for wireless communication is growing exponentially, shortage of spectrum is foreseen, and in
this regard the chairman of the Federal Communications Commission (FCC) remarked in 2010 [2]: “Our
data shows there is a looming crisis. We may not run out of spectrum tomorrow or next month, but it’s
coming and we need to do something now”. In IEEE Spectrum [3], this problem is named “The great
spectrum famine”.
Different independent measurement campaigns (e.g. [4], [5]) found that most frequency bands were not
occupied continuously in time, i.e. spectral utilization efficiency is often poor. Although cellular network
bands are used intensively in most parts of the world, this is not true for many other frequency bands.
Measurement shows that less than 20% of the RF spectrum is actively used at any given time and place
[6]. Figure 1.2 presents an example of a spectrum measurement [4] for a part of the Digital TV (DTV)
2
broadcasting (Appendix A): channels 52 – 69, where each channel has 6MHz bandwidth, at the
Republican National Convention, New York City, USA.
Figure 1.2: Spectrum occupancy measurements [4], Location: Republican National Convention, New York City, USA
In an effort to improve the spectral utilization efficiency, FCC allows since 2008 [7] unlicensed (i.e.
secondary) users to opportunistically use TV broadcast channels that are licensed for TV broadcasters
(i.e. primary users), but are temporally locally unused.
Such free channels or bands are referred to as “white
spaces” [7] or “spectrum holes” [8]. Free channel can
for instance be utilized as shown in Figure 1.3,
referred to as “Dynamic Spectrum Access (DSA)” [9],
given the dynamic nature of this spectrum use. More
efficient use of such DTV frequency bands will be a
Figure 1.3: Opportunistic spectrum access [9]
key target of this thesis.
The DSA concept of operation poses several requirements on the radio hardware:
1. Flexibility and reconfigurability of the radio hardware to allow for dynamic switching between
different white spots across the frequency spectrum.
2. Supporting different standards, specified for different unoccupied primary users spots.
3. Sensing spectrum to detect the white spot instantaneously at any location.
Software (Defined) Radio towards Cognitive Radio:
Software Radio (SR) may achieve the ultimate level of flexibility, reconfigurability and can support all
different standards. A general schematic of a SR transceiver is shown in Figure 1.4. The SR involves
implementing all of the radio functionality in the software of the digital back-end (i.e. Digital Signal
3
Processing DSP) as described by Mitola [10]. The propagating Radio Frequency (RF) signal, with
frequency fC, is analog. This means that both the transmitted and received RF signals, via the antenna,
are also analog. Therefore a Digital-to-Analog Convertor
(DAC) in the transmitter and an Analog-to-Digital Convertor
(ADC) in the receiver are required. The focus of this thesis is
on the hardware requirements of the receiver side. The
transmitter part was the scope of another partner Ph D
project [11] inside the same research program at the
University of Twente. A true SR receiver is hard to
implement, because of the tough requirements on the ADC
resolution vs power consumption for mobile wireless
Figure 1.4: Software Radio receiver front-end
applications [12].
A solution that is more feasible is a radio receiver where part of the flexibility and configurability is
achieved by flexible analogue hardware instead of by software as shown in Figure 1.5, which is called
the Software Defined Radio (SDR) receiver.
The RF band filter, the channel filter and the
clock frequency to the mixer, which provide
the frequency down shift (or conversion)
functionality,
are
all
flexible
and
reconfigurable. The bandwidth of the RF
Amplifier can be wide to cover all the
Figure 1.5: Software Defined Radio receiver front-end
required bands, on condition that the RF filter
has enough out of band interferer rejection, so that the interferer will not distort the desired signal.
Extending the SDR and combining it with the Spectrum Sensing provides a radio that is aware of its
frequency environment and autonomously adjusts its communication parameters to fully realize DSA
(see Figure 1.3). This concept is called a Cognitive Radio (CR) [13]. The concept of CR was first proposed
by Joseph Mitola in a seminar at the Royal Institute of Technology in Stockholm (KTH) in 1998 and
published in an article by Mitola and Gerald Q. Maguire, Jr. in 1999 [14] .
In summary, the CR concept promises to increase the spectrum utilization efficiency via DSA. The
hardware physical implementation of the CR is based on SDR receiver plus Spectrum Sensing device. In
the next section, the SDR/CR receiver hardware imperfections especially the heavy linearity
4
requirements will be explained. This thesis aims to mitigate the linearity requirements challenges by
benefiting from the presence of spectrum sensing device, which is assumed to be on board.
1.2 CR receiver hardware imperfections
Imperfections of practical receivers decrease the quality of the received desired signal, via distortion and
noise [15].
The DTV interferers will often lead to distortion in practical receivers with a limited degree of up-front
filtering and linearity, which will be explained in Chapter 2. In traditional narrowband RF receivers, out
of band strong interferers can greatly suppressed by a Surface Acoustic Wave (SAW) RF band filter (a
fixed center frequency version of the RF band filter shown in Figure 1.5) after the antenna. This will
greatly reduce the distortion level of the received signal at the ADC input, i.e. the required out of band
linearity of the receiver will be also reduced. The SAW RF filter with a fixed center frequency does not
help to immune the CR receiver from the DTV interferers that actually exists in-band, hence the in-band
linearity becomes a critical specification for CR receiver. The ultimate solution is a flexible and
reconfigurable RF channel filter with high rejection (i.e. very high order filtering) of the interferers from
the adjacent channel(s). Note that guard channels are not desired to maximize the spectral utilization
efficiency. Such RF channel filters are very difficult to be implemented, especially on-chip. Different
implementations of flexible and reconfigurable RF filters are presented as example [16] and [17].
However their application as flexible and reconfigurable RF channel filter in the DTV band is bounded by
their limited adjacent channel(s) interference rejection ratio. As a consequence of the poor rejection
performance of RF channel filter, the in-band linearity of the receiver must be increased to tolerate the
received DTV interferers that actually exists in-band.
Any receiver contributes noise. The noise contribution, which is quantified by the Noise Figure (NF),
increases the noise floor. Hence the sensitivity level of the receiver that must be above the noise floor
by the minimum SNR requirement will decrease. Reducing the radio range (i.e. cell size) and/or
increasing the transmitted signal power helps always in reducing the NF requirement of the receiver,
note that this is not the case with linearity requirement, hence distortion becomes more important and
noise less, especially for the near future map of communication, which develops towards small cells.
5
The following section summarizes the research scope and presents the main research questions of the
thesis.
1.3 Research Scope summary and questions
In summary, a CR requires flexibility in receive frequency and such flexibility comes at the cost of less
up-front filtering, hence distortion products will be increased, especially because the in-band linearity is
normally limited. The high distortion products generated across the unoccupied DTV channels will finally
limit the spectral utilization efficiency. Hence distortion mitigation for CR is important regarding the
main idea of increasing the spectrum usage via DSA in the DTV spectrum band. It will be assumed that a
spectrum sensing device is available on-board, and options will be explored to benefit from the
presence of such a device. The main research questions are as follows:
1. How to analyze the distortion level (i.e. linearity requirement) across the unoccupied DTV band
for Dynamic Spectrum Access CR radio receiver?
2. How to predict the distortion level in Dynamic Spectrum Access, given Spectrum Sensing data?
3. How to increase the linearity of CR receiver hardware, given less up-front filtering?
Finally, the CR concept of operation demands both, (RF) analog and digital signal processing that
continuously interacts with each other. This makes CMOS technology to be the chosen candidate in this
thesis for possible monolithic integration between those two domains. In the following section, the
outline of the thesis will be discussed.
1.4 Outline of the Thesis
In this section, the outline of the thesis is presented in addressing the main research questions:
Chapter 2 investigates the first question:
Due to the existence of in-band strong DTV interferers and the nonlinearity of a radio receiver, different
types of distortion products will be generated inside a CR-receiver, namely intermodulation products,
cross-modulation products and self-interference products as analyzed in chapter 2. Using analysis based
on a memory-less nonlinearity model, it will be shown that CR receiver is always limited by crossmodulation and self-interference products in any white spots. While the level and the spectral location
6
of the intermodulation products across the white spots depends on the level and the spectral location of
the DTV signals. The cross-modulation and self-interference products are typically much weaker than
the intermodulation products. Thus it makes sense to monitor the level and spectral location of
interferes via spectrum sensing device, and classify the white spots into two types, namely
“intermodulation spots” and “intermodulation-free spots”. For the latter, the linearity requirement of a
CR receiver is more relaxed compared to the intermodulation spots. The analysis will be verified by
measurements.
Chapter 3 investigates the second question:
Based on the analysis in chapter 2, chapter 3 describes the development of a Distortion Prediction
Algorithm (DPrA) to quantify the level and the spectral location of the distortion products across the
white spots for Dynamic Spectrum Access. Then, according to the DPrA output, the CR receiver linearity
requirement can be quantified for different white spots as shown in chapter 3. Hence, the CR receiver
autonomously can select the most suitable white spots (i.e. unoccupied channel), taking into account
knowledge of linearity performance of its own CR receiver. Note, CR receiver with better linearity
performance can exploit more of the available white spots, hence higher spectral utilization efficiency
(i.e. the original motivation behind DSA). Therefore, increasing the CR receiver linearity is an important
target in this research.
Chapter 4 and 5 investigate the third question:
Chapter 4 focuses on increasing the linearity of CR receiver hardware. High linearity CMOS radio
receivers often exploit linear V-I conversion at RF, followed by passive down-mixing and an OpAmpbased Transimpedance Amplifier at baseband. Due to nonlinearity and finite gain in the OpAmp, virtual
ground is imperfect, inducing distortion currents. A negative conductance concept will be introduced
that allows for cancelling such distortion currents. Through a simple intuitive analysis, the basic
operation of the technique will be explained. By mathematical analysis the optimum negative
conductance value is derived and related to feedback theory. In- and out-of-band linearity, stability are
also analyzed.
The technique is applied to linearize the RF receiver in chapter 5, and a prototype is implemented in
65nm technology. Measurements show an increase of in-band linearity, quantified by IIP3 and IIP2, with
IIP3 from 9dBm to >20dBm, and IIP2 from 51 to 61dBm, at the cost of increasing the noise figure from 6
7
to 7.5dB and <10% power penalty. In 1MHz bandwidth, a Spurious-Free Dynamic Range of 85dB is
achieved at <27mA up to 2GHz for 1.2V supply voltage.
Chapter 6 summarizes the main research work:
Finally, Chapter 6 summarizes the main conclusion, makes a list of the main contributions of this work,
and provides recommendations for future work.
8
Chapter 2. Cognitive Radio Receiver Linearity Requirements [18]
This chapter investigates the first research questions “How to analyze the distortion level (i.e. linearity
requirement) across the unoccupied DTV band for Dynamic Spectrum Access CR radio receiver?”
The DSA operation inside the DTV band means that the power level and spectral location of the DTV
signals around the CR signal may instantaneously change; hence the traditional linearity analysis [15]
cannot be directly applied. The analysis of this chapter decomposes the complex view of the distortion
products into basic roots/types. Based on that, the linearity requirements for CR receiver are derived.
The content of this chapter is structured as follows. Section 2.1 introduces the problem. Then section
2.2 describes the receiver model and nonlinearity model. The spectral location analysis of the 3rd order
distortion products is done in Section 2.3. The effect of this spectral location of the distortion on the
linearity requirement is analyzed in Section 2.4. Section 2.5 verifies our theoretical analysis and presents
results from practical measurements. Finally, conclusions will be drawn in Section 2.6.
This chapter is a literal copy of the paper published in [18] with corrections related to Table 2.2 .
9
2.1 Problem Definition
Cognitive Radio is a new emerging radio communication paradigm [14] aiming at improving the
utilization efficiency of the scarce spectral resources. It senses unused “white spots” in the radio
spectrum that is licensed to a primary user and adapts its communication strategy to use these parts
while minimizing interference to the primary service.
This chapter studies requirements on the 3rd order linearity of a CR receiver for wireless applications
operating in the DTV bands [7]. Cognitive Radio requires high programmability for radio transmission
and reception because the position of the white spots changes dynamically with time (i.e. dynamic
spectrum). Traditional radio receivers are narrowband and are typically highly dedicated to a specific RFband, especially due to the fixed RF-filter (see Figure 2.1).
Figure 2.1: Traditional narrow-band RF receiver with one RF “Front-End”
The high out-of-band rejection of the RF-filter, usually a high-linearity highly selective Surface Acoustic
Wave (SAW) filter, suppresses the interference of out-of-band interferers. Traditional radio standards
define in detail how the radio-band is used, e.g. by specifying a multiple access method (TDMA, FDMA,
CDMA) and blocker profiles. Consequently in-band signals are “under control”, while RF-filtering reduces
the out-of-band interference. In such narrowband systems, typically third order intermodulation
products (IM3) produced by nonlinearities in the receiver dominate as is shown in Figure 2.2. Both the
signal and the IM3 product will be converted to the baseband and their ratio must be higher than the
minimum Signal to Distortion Ratio that is required to demodulate the transmitted information with
acceptable bit error rate.
10
Figure 2.2: Corruption of the desired signal due to intermodulation products caused by two interference signals
(Conventional narrow-band Radio)
For CR, the distinction between “out-of-band” and “in-band” signals more or less vanishes, as bands are
no longer reserved for one or a few radio standards. Also, the power of radio signals is not restricted to
a low level, as in ISM bands, in which more freedom is allowed provided low power levels are used
(typically 10-100mW). If we want to maximize spectral efficiency in the TV-bands, we like to use white
spots between DTV-signals and preferably even in the proximity of DTV signals. In such cases, very steep
high-order RF-filters would be needed, which are difficult to implement even with high-Q SAW filters. If
the frequency-distance between DTV signals is small, narrowband RF-filters would be needed. To cover
a significant part of the TV bands, many filters would be needed. From these observations we conclude
that a broadband RF receiver with relaxed RF-filter requirements is highly desired. In this chapter we
look for ways to benefit from spectral sensing which is available in a CR anyway. We will look at a
broadband receiver, but still limit the bandwidth to below an octave so that second order distortion
products are largely suppressed by the RF-filter and the 3rd order distortion is the main remaining
problem.
A broadband RF receiver implies the reception of undesired interference as shown in Figure 2.3. The
example of a DTV spectrum in Figure 2.3 consists of 20 numbered frequency spots: 5 spots contain
interference (i.e. DTV signals at spots 1, 4, 11, 16 and 19) and one spot contains the desired signal (i.e.
CR signal at spot 8).
11
Figure 2.3: An DTV instantaneous spectrum scenario at a wideband RF bandpass filter output with 20 frequency spots
In [19], the use of spectral sensing to relax linearity requirements of a receiver is addressed. The paper
assumes a dense spectrum with a large number of interferers. According to the law of large numbers,
the distribution of the intermodulation products due to the many interferers becomes even across the
spectrum and can be seen as a distortion induced (noise) floor. However, a different picture arises when
the spectrum is dominated by a few high power interference signals in the band of the RF bandpass
filter. According to our analysis and measurements, different spectral distributions of the interference
produce quite different distributions of the distortion products across the spots of the DTV spectrum.
Consequently, the linearity requirements of the CR receiver will be different for each white spot. A
prediction of the spectral location of the distortions provides the CR with the ability to choose an
appropriate white spot. The required information about the level and the spectral location of the
interference signals can be obtained from spectrum sensing, which is normally available anyhow in a CR.
Our analysis is based on a CR receiver with direct conversion architecture. The theory can be extended
to other (non-zero) IF architectures, where the image problem must be included as an extra contribution
of distortion to the desired signal, but this is outside of the scope of this chapter.
12
2.2 Behavior Model for Nonlinearity
It is common to model the nonlinearity of an RF receiver assuming a memory-less weakly nonlinear
model (e.g. [15] and [20]) with a truncated 3rd order Taylor series around the DC operating point:
s out = k 1s in + k 2 s in2 + k 3s 3in
Equation 2.1
where k1 specifies the gain, while k2 and k3 characterize the second and third order nonlinearity of the
circuit with input signal sin and output sout (s can be both a voltage or current). The sin contains all the
input signals at the output of the RF bandpass filter.
Equation 2.1 contains three terms. The first term with k1 is the amplified version of sin, the linear term.
The second and the third term will be called the 2nd order and 3rd order nonlinear terms, respectively.
Those nonlinear terms generate different distortion products. Some of those distortion products fall into
the band of interest. By using an octave RF bandpass filter [19] and RF components with differential
structure, the effect of 2nd order nonlinear term can often be handled. However, the effect of the 3rd
order nonlinear terms cannot be ignored because their distortion products always fall inside the desired
DTV spectrum.
2.3 Analysis of the Spectral Locations of Distortion Products
A CR scans the spectrum for white spots, which have a bandwidth in the order of 6-8 MHz in the DTV
spectrum. Although the DTV signals and the CR signal are wideband (i.e. the CR occupies the whole spot)
signals, The analysis starts representing them as tones with a power equal to the integral of the power
of the wideband signal. Afterwards, the analysis will be extended to deal with the spectral shape of the
wideband signals.
Referring to Figure 2.4, sin in Equation 2.1 contains three DTV signals around ω1, ω6 and ω19. To not lose
the general view, CR signal will be introduced later after specifying the spectral location of the distortion
products of the DTV signals.
13
Figure 2.4: An instantaneous scenario of the DTV spectrum dominated by three interference signals in the RF passband
The sin can be described by the following equation:


s in = Re 2 ∑ A TVn e jωn t 
 n =1,6,19

Equation 2.2
where ATV is the corresponding RMS value of the DTV (single tone) signals. Substituting sin in the 3rd
order nonlinear term of Equation 2.1 gives the following distortion products:
 3

3
3
2
2
k 3sin = Re 2  k 3A TV1 + 3k 3A TV1 A TV6 + 3k 3A TV1 A TV19 e jω1 t 

 2

 3

3
2
2
+ Re 2  k 3A TV6 + 3k 3A TV6 A TV1 + 3k 3A TV6 A TV19 e jω6 t 

 2

 3

2
+ Re 2  k 3A TV1 A TV6 e jω11 t 

 2

{ (
)
+ Re 2 3k 3A TV1 A TV6 A TV19 e jω14 t
Equation 2.3
}
 3

3
2
2
+ Re 2  k 3A TV19 + 3k 3A TV19 A TV1 + 3k 3A TV19 A TV6 e jω19 t 
2




Figure 2.5 provides a visual way to understand the spectral location of the distortion products that are
double underlined in Equation 2.3. These products are important because they fill the white spots,
where a CR may operate. They represent two types of intermodulation products:
1. The intermodulation products of two interferers (observe spot 11), which is the traditional IM3
that is already mentioned in literature [15].
2. The intermodulation products of three interferences (spot 14), which is 6 dB higher than the
traditional 2-tone IM3 for interferes with equal power. This type of distortion will also be called
IM3 in this paper.
14
Figure 2.5: Spectral location of the intermodulation products for the case of Figure 2.4
For simplicity, we will keep the power of the DTV signals equal in this paper. Of course, using Equation
2.3 case with different power can be analyzed easily.
Repeating the same analysis for another DTV spectrum scenario with three large interference signals at
different locations, gives the distortion distribution that is depicted in Figure 2.6.
Figure 2.6: Spectral location of the intermodulation products for another case
Comparing Figure 2.5 with Figure 2.6, we recognize that the first figure presents 15 white spots without
intermodulation distortion (i.e. IM3-free spots) and 2 white spots with IM3 (i.e. IM3-spots), while the
second figure presents 13 IM3-free spots and 4 IM3-spots. For all the possible spectral locations of the
three interference signals, the number of the IM3-free spots can be counted and a histogram of it can be
plotted as shown in Figure 2.7. The expected value is 13 white spots here, with a spread from 8 to 17.
15
Figure 2.7: Probability density of IM3-free spots for all possible scenarios with 3 interferers (Figure 2.6 depict one scenario)
Note that the fact that a spot is IM3-free does not mean that there is no 3rd order nonlinearity
requirement anymore for the receiver. Actually, the interferers will cause cross-modulation on top of
the desired signal as shown in Figure 2.8.
Figure 2.8: Cross-modulation products (XM3) due to interferers which cross-modulate the CR signal
To analyze the effect of cross-modulation, the mathematical expression for sin including a CR at spot 17
is written as follows:


s in = Re  2A CR e jω17 t + 2 ∑ A TVn e jω n t 
n =1,6,19


Equation 2.4
where ACR is the corresponding RMS value of the CR signal. Substituting sin in Equation 2.1 and retaining
just the terms that exist in the desired band gives:
16






 3

3
2
2
2 
Sout Desired Band = Re
2k1ACR + 2k3  ACR + 3ACR ATV + ATV + ATV  e jω
424
3
14444
4244444
3 
2 23
Desired1
 1
amplifiedCR signal
Cross-modulation
Self
interferen
ce


14444444442444444444
3


3 order distortion products
(
1
6
19
)
17
t
Equation 2.5
rd
where the first term on the right hand is the amplified version of CR signal, the second term is the selfinterference product [21] and the last three terms are the mentioned 3rd order cross-modulation [22]
products (XM3) of the DTV signals. The self-interference product can usually be neglected in comparison
to the XM3 products because the DTV signals are usually much stronger than the desired signal. The
same analysis is done to show the spectral location of the distortion products of 4 interference signals
with high power and the results can be seen in Figure 2.9 and Figure 2.10 (Expected value = 7).
Figure 2.9: Spectral location of the intermodulation products for a scenario with 4 interferers
Figure 2.10: Probability density of the existence of given number of free spots without intermodulation distortions for
scenarios with 4 interferers
17
As mention previously, both the DTV signals and the CR signal are wideband signals with about the same
bandwidth. Therefore their shape can be approximated by square blocks in the frequency domain. The
mathematical representation in the time domain of those signals and their distortion products is written
in the same way as mentioned previously with the exception that ATV and ACR now represent the
complex envelope of the DTV signal(s) and CR signal, respectively. In the time domain, the
intermodulation and the cross-modulation products are nothing else than a multiplication of three
signals, where the involved signals are indicated with arrows. E.g. three arrows constitute the inputs to
the distortion circles in Figure 2.5, Figure 2.6 and Figure 2.8, in some cases from two frequencies, in
other cases from three frequencies. In the frequency domain, this corresponds to two times convolution
of the signals. The result of this convolution is shown in Figure 2.11 for the interference scenario of
Figure 2.5, but now with more realistic block-shaped spectra instead of single tones.
Figure 2.11: Bell shapes for the distortion products of three wideband interferers
18
A Bell shape results, occupying three spots as shown in Figure 2.11. Analysis shows that more than 66%
of the distortion power is concentrated in the frequency spot in the center of the Bell, while the power
spilled over to the adjacent frequency spots is less than 17% of the distortion power each. Referring to
Equation 2.3, the bell shapes around spots 1, 6 and 19, each contain a self-interference product and two
cross-modulation products (e.g. the Bell shape around spot 6 contains its self-interference product and
the cross-modulation products of the other two interferers of spots 1 and 19 on top of the interferer of
spot 6). As a consequence of spreading, the distortion to the adjacent spots of 1, 6 and 19, the spots 2,
5, 7, 18 and 20 will be called adjacent-distortion spots (i.e. the distortion that is adjacent to the
interferers). The linearity requirements in those adjacent-distortion spots of Figure 2.11 will be higher
than that of Figure 2.5. Additionally, the bell shape of the IM3 products (i.e. around spot 11 and 14) will
reduce the number of IM3-free spots by 4 spots in comparison to Figure 2.5, as spots 10, 12, 13 and 15
will contain 17% of the total IM3 power of the Bell shape, hence those spots will be also called IM3 spots.
Paper [23] presents an analysis about the interference effects in Multi-Band - Orthogonal Frequency
Division Multiplexing (MB-OFDM) systems. It proves that the power of the IM3 resulting from two OFDM
signals (Quadrature Phase Shift Keyed (QPSK) modulation) each with a large number of sub-carriers is
higher than that of two tones that have the same power as the OFDM signals:
+
PIM = PIM + ∆Wideband [dBm]
3
Equation 2.6
3
where PIM3+ and PIM3 represent the intermodulation distortion of two wideband signals and two tones,
respectively. PIM3+ is distributed over three spots (e.g. see spots 10, 11, 12 of Figure 2.11). ∆Wideband
represents a correction term. Instead of dealing with wideband complex signals, Equation 2.6 provides
the possibility to analyze the nonlinearity with the traditional two-tone test method and simply add a
correction term.
As an example that can be applied to our case, a MatLab simulation setup has been built to simulate the
nonlinearity with two real OFDM signals at RF. QPSK modulation was used and the frequency difference
between the sub-channels is 4.46 kHz satisfying the Digital Video Broadcasting Terrestrial (DVB-T)
standard. The resulting IM3 was simulated. The simulation result is shown in Figure 2.12, where the
number of the sub-carriers per OFDM signal has gradually been increased from 1 to 900. Thus we can
compare the IM3 generated for two (narrowband) single tones with that for a truly wideband OFDM
signal with many sub-carriers, where the total signal power in all cases is kept constant.
19
Figure 2.12: Comparison of the IM3 power caused by two (single) tones and two multi-tone OFDM signals with a number
of sub-carriers from 1 to 900
Figure 2.12 shows a ∆Wideband of about 3 dB. Changing the modulation of the two OFDM signals to
16QAM, we find 3.5 dB. By further increasing the number of the QAM modulation to higher orders, the
signal characteristic of the two OFDM signals resembles the case of having two band limited noise
signals. In this case the factor is increased to 4.5 dB. Table 2.1 summarizes the simulation results:
Table 2.1: CORRECTION FACTOR ∆WIDEBAND FOR TWO OFDM SIGNALS WITH DIFFERENT MODULATION CHARACTERISTICS
Two Signals
Two OFDM: QPSK
Two OFDM: QAM16
Two Band limited Noise
Max. ∆Wideband [dB]
3
3.5
4.5
As the purpose of this paper is to compute the linearity requirements for CR, the highest value of the
maximum ∆Wideband will be taken, which is 4.5 dB.
2.4 Estimation of Linearity Requirements
The linearity of a receiver must be adequate to preserve a minimum Signal to Distortion Ratio needed at
the demodulator. As previously depicted in Figure 2.5, we distinguish two types of white spots: IM3-free
spots and IM3-spots. We will show that the CR requires higher linearity if it operates at IM3-spots than
for IM3-free spots with only self-interference and the XM3. This section begins with introducing an
estimation of the linearity requirement for the case that the CR is operating at an IM3-free spot and the
interferers are modeled by tones. Afterwards the linearity equation will be extended to cover the case
of wideband interference signals. Finally, this linearity requirement will be compared to that of a CR
operating at an IM3-spot and at an adjacent-distortion spot.
20
Referring to Figure 2.8 and Equation 2.5, the Signal to Distortion Ratio can be written as follows:
S
(k 1 A CR )
=
2
D 


 3k 3 A CR  ∑ A TV 2  
n



 n =1,6,19


2
Equation 2.7
where the self-interference has been neglected. The linearity requirement can be presented as the ratio
between k1 and k3:
k1
k3
= 3×
spot 17
S

D 
∑A
n =1,6,19
2
TV n



Equation 2.8
where S/D is the required Signal to Distortion Ratio for the CR receiver output. It is proportional to the
sum of the power of the DTV signals, which will cross-modulate the receiver CR-signal.
Equation 2.6 presents the correction factor ∆Wideband for the intermodulation power. The same ∆Wideband is
valid for the XM3 power (the ∆Wideband is just the relative difference between the modulation products of
the two tones in relation to that of the two wideband signals). Therefore Equation 2.6 provides a useful
tool to extend the derivation of Equation 2.8 to deal with wideband interference signals as explained in
Appendix B:
k1
k3
= 3×
spot 17
∆
S
× 10
D
Wideband
× 0.66
10
∑A
n =1,6,19
2
Equation 2.9
TVn
Using the mentioned maximum ∆Wideband of 4.5dB gives:
k1
k3
= 3×
spot 17
S
2
× 1.4 ∑ A TV
D
n =1,6,19
Equation 2.10
n
It is instructive to relate Equation 2.10 to the traditional IIP3 specification. According to the definition of
IIP3, the RMS value of IIP3 is related to k1/k3 as follows [15]:
AIIP =
3
4 k1
3 k3
2
Equation 2.11
4 k1
=
6 k3
[V]
21
Substituting Equation 2.10 in Equation 2.11 gives the following equation:
PIIP
3
spot 17
= 2×
S
× 1.4 ∑ PTV
D
n =1,6,19
n
Equation 2.12
[W]
We recognize that dealing with wideband signals instead of tones, the IIP3 requirement will be increased
by around 1.5 dB (i.e. 10*log(1.4)). To get a sense of what Equation 2.12 presents, let’s assume that the
interference signals of Figure 2.11 have a power of -10 dBm and the required Signal to Distortion Ratio is
10 dB. Then the required linearity to keep XM3 low enough expressed in terms of IIP3 would be 4 dBm.
Increasing the power of the interferences by 10 dB increases the requirement also by 10 dB. Equation
2.12 can be generalized as follows:
PIIP = 2 ×
3
S
× 1.4
D
∑P
TV n
[W]
Equation 2.13
n
where n refers to all the interference signals that exist in the RF bandpass filter of the CR receiver.
As a final step, let us compare IIP3 of Equation 2.12 (i.e. IIP3XM3) to that IIP3 requirement when the CR
operates in IM3-spot (IIP3IM3) like for example spot 11 in Figure 2.11. In this case the distortion products
will contain the IM3 plus the XM3 products:













3

2
2 
s out Desired Band = Re
2k1ACR
+ 2k 3  3ACR ∑ A TVn + ATV1 ATV6  e jω11 t 
1424
3


2 4243 

n =1,6,19
 1442443 1Intermodul

Desired amplified CR signal

ation
- modulation
 4Cross
144
44
4
424444444
3



3rd order distortion products


Equation 2.14
Writing down the Signal to Distortion Ratio gives:
(k1A CR )
S
=
2
D 




 3k 3A CR  ∑ A TV 2  +  3 k 3A TV A TV 2   
n
1
6

 2


n =1,6,19
2
4443 1442443  
 1444
Intermodul
ation

Cross- modulation

2
Equation 2.15
The resulting linearity requirement in terms of k1/k3 becomes:
k1
k3
= 3×
spot 11
S 
D 
∑ A TVn +
2
n =1,6,19
1 A TV1 A TV6
2
A CR
2




22
Equation 2.16
Expressing the linearity requirements in IIP3 and extending the derivation to wideband signals gives the
following two equations for spot 11 and 10, 12 (see Figure 2.11):


∆ Wdeband
∆ Wdeband
PTV1
S 
1

10
10
PIIP3
= 2×
10 424×4
0.66
0.66
4
3 ∑ PTVn + 2 110
44
424×4
4
3 P PTV6  [W]
spot 11
D  144
n =1,6,19
CR
1.4
1.4


PIIP
3
spot 10,12
= 2×
S
D
∆
∆


PTV
1
10
10
×
0.66
P
+
10
×
0.17
P
 110
TV
442443 n =∑
443 P TV  [W]
2 1442
1,6,19
CR

1.4
0.7

Wideband
Wideband
Equation 2.17
Equation 2.18
1
n
6
By comparing between Equation 2.17 and Equation 2.18, the IIP3 requirement of spots 10 or 12 (i.e. the
spots adjacent to the Bell center spot that contains 17% of the total IM3 power) is 3 dB lower than the
IIP3 requirement of spot 11 (i.e. the center spot of the Bell shape that contains 66% of the total IM3
0.17 / 0.66 = 1 / 2 .
power), hence
As mentioned previously, the CR requires also linearity requirement in the adjacent-distortion spots (see
Figure 2.11). Repeating the same analysis as previously done and using Equation 2.3, Equation 2.5 and
Equation 2.11 results:
PIIP
3
spot 2
= 2×
S
D
∆
∆

PTV 
1
10
10
×
0.66
P
+
10
×4
0.17
110
∑
442443 n=1,6,19TV 14424
3 ( 2 PTV + PTV + PTV ) P  [W]
CR 
1.4
0.7


Wideband
Wideband
1
n
1
6
19
Equation 2.19
To get a sense about the linearity requirement of Equation 2.12, Equation 2.17, Equation 2.18 and
Equation 2.19 consider the same numbers as for the previous example, while assuming that the CR
signal is equal to -60 dBm. Then the different IIP3 requirements are summarized in Table 2.2.
Table 2.2: LINEARITY REQUIREMENT OF EQUATIONS (12), (17), (18) AND (19) FOR THE SCENARIO OF Figure 2.11
Equation
Equation 2.12
Spot no.
17
Spot Description
IM3-free spot
IIP3 [dBm]
4
Equation 2.17
11
IM3-spot
21
Equation 2.18
10, 12
IM3-spot
18
Equation 2.19
2
Adjacent-distortion spot
25
Clearly, there is a very significant benefit in looking for IM3-free spots. Such spots like spot 17 can well
make a key difference in the feasibility (e.g. [28] and [31]) of CR.
23
2.5 Measurement Results
The spectral location of the distortion products is the consequence of modeling a memory-less weakly
nonlinear device with a Taylor series as presented in Equation 2.1. The model has been verified by
building a setup where a Low Noise Amplifier (LNA) from the Mini-Circuits (i.e. ZFL-1000LN) is tested
with three interference signals. The power and the spectral location of the distortion products are
measured. The LNA has gain of 18 dB, IIP3 of -6 dBm, Output 1 dB compression point of 3 dBm and its
operating region is from 0.1 to 1000 MHz (i.e. VHF/UHF band). The interference signals are three carriers
with QPSK modulation, which are generated by vector signal generators from Agilent technology. In the
first experiment, the power of each interferer is around -26 dBm and their frequency location is around
the following values: 548, 563 and 600 MHz. This case looks like the case shown in Figure 2.5 and the
measurement result is shown in Figure 2.13.
Figure 2.13: Spectral location of the distortion products in case of three interferers at 548, 563 and 600 MHz
Comparing to Figure 2.5, Figure 2.13 indeed contains two distortion products:
1. The first interferer at 548 MHz and the second interferer at 563 MHz generates the traditional
IM3 at 578 MHz (i.e. 2*563-548)
2. The combination of all the three interferers generates the previously mentioned new IM3 at
frequency 585 MHz (i.e. 600-(563-548) and (600-563)+548). Shown in Figure 2.13, this type of
IM3 is higher than the first IM3 by 6 dB as our theory has predicted (see Equation 2.3).
24
The power of those IM3 products are measured and compared to the results of our equations as shown
in Table 2.3.
Table 2.3: Comparison between the measurement and the theory results of the IM3 distortion products
IM3 frequency [MHz]
Theory [dBm]
578
585
-39.4
-33.4
Measurement
[dBm]
-38.7
-32.5
Another experiment has been done with a scenario that looks like the case shown in Figure 2.6. The
measurement result is shown in Figure 2.14.
Figure 2.14: Spectral location of the distortion products in case of three interferers at 554, 560 and 590 MHz
Consequently, the measurement results verify our theory about the effect of interference locations on
the spectral location of the distortions. The IM3 spots and the IM3-free spots are clearly shown in Figure
2.13 and Figure 2.14.
25
2.6 Conclusion
This chapter studied the 3rd order nonlinearity requirements for a CR receiver with a wideband RF
bandpass filter that operates in the DTV spectrum, where several high powers DTV signals fall in the RF
filter-band. Due to the nonlinearity of the RF receiver and the existence of strong interference signals,
different types of 3rd order distortion products will be produced. The spectral location of these distortion
products depends on the spectral locations of the interference signals. Analysis and measurements
show that white spots can be classified into two types:
1. IM3-spots, for which the distortion is dominated by IM3 products. The IM3 products are much
stronger than XM3 and self-interference if the interferers are much stronger than the desired
signal.
2. IM3-free spots where the CR signal will only be distorted by XM3 and self-interference.
If an IM3-free spot is selected for CR operation, its third order linearity is relaxed. In a scenario with
three interferers at -10dBm and a CR-signal at -60dBm, the resulting IIP3XM3=4dBm, while the IIP3IM3 is
18-25 dBm. Since the linearity of any radio design is limited, typically to not much more than 0dBm in
CMOS, spectral sensing information about the level and the spectral location of the strong interferers
can be used to predict the location of the IM3-free spots. Such a prediction mechanism seems to be
almost indispensable for a CR that can work in a wide RF-band. Next chapter is pursuing in this direction.
26
Chapter 3. Distortion Prediction Algorithm and Frequency Selection
This chapter investigates the second research question: “How to predict the distortion level in Dynamic
Spectrum Access, given Spectrum Sensing data?”
The coexistence of a Cognitive Radio signal among the primary users of the DTV spectrum increases the
linearity requirements of a wideband CR receiver considerably to very high numbers (see Table 2.2) as
derived in the previous chapter. The analysis in chapter 2 has classified the DTV white spots into IM3spots and IM3-free spots, depending on the existence of IM3 distortion products at a particular white
spot. It was concluded that the IIP3 requirements on the CR receiver will be different across the white
spots, and since the linearity of any radio design is limited, this means that not all the white spots are
equally appropriate for CR operation. This chapter aims at developing a Distortion Prediction Algorithm
(DPrA) that calculates the distortion level across the white spots. Based on the DPrA results in
combination with the theory in chapter 2, the linearity requirement per white spot can be quantified.
Section 3.1 presents the DPrA concept. Then, section 3.2 presents the verification of the DPrA concept
by applying it to the DSA1 scenarios of the previous chapter and some other application examples test its
ability to recognize the construction pattern of complex distortion products. Finally, the chapter ends
with conclusions in section 3.3.
1
Where the signals level across the bands/channels varies with respect to time for a given location
27
3.1 Distortion Prediction Algorithm (DPrA)
The analysis starts in representing the wideband1 DTV signals and the wideband CR signal (i.e. the CR
occupies the whole channel) as single frequency with a power equal to the integral of the wideband
signal power. Afterwards, the analysis will be extended to deal with the spectral shape of the wideband
signals.
The target of the DPrA is to derive the instantaneous level and spectral location of the 3rd order
distortion products across the white spots by using spectral sensing information. An example of the
instantaneous level and the spectral location of some DTV signals is shown in Figure 3.1. The calculation
of the output spectrum in this figure is already explained in chapter 2 (see Figure 2.5 and Equation 2.3).
rd
Figure 3.1: Example of the operation of the 3 order Distortion Prediction Algorithm (DPrA)
As indicated in Figure 3.1, the DPrA boils down to evaluate the following mathematical expression:
k 3s3in (t ) = k 3[sin (t )× sin (t )× sin (t )]
Equation 3.1
where k3 characterizes the third order nonlinearity term of the circuit. Note that sin contains all the input
signals passing through the RF bandpass filter. Equation 3.1 involves two times multiplication in the time
domain of sin. In this case, it consists of three signals at channel numbers: 1, 6 and 19, i.e.:


sin (t ) = Re 2 ∑ ATVn e jωn t 
 n =1,6,19

Equation 3.2
where n represents the corresponding channel number and ATV is the corresponding RMS value of the
DTV (single tone) signals.
1
Each wideband DTV signal occupies a channel bandwidth of 6-8 MHz depending on the different standards
28
Repeating the procedure of the previous chapter in substituting sin in Equation 3.1 produces the
following distortion products:
[
]

k 3 sin (t )× sin (t )× sin (t ) = Re


+ Re


+ Re


3

2  k 3ATV1 3 + 3k3ATV1 ATV6 2 + 3k3ATV1 ATV19 2 e jω1 t 

2


3

2  k 3ATV6 3 + 3k3ATV6 ATV1 2 + 3k3ATV6 ATV19 2 e jω6 t 
2



3

2  k 3ATV1 ATV6 2 e jω11 t 
2


{ (
)
+ Re 2 3k3ATV1 ATV6 ATV19 e
jω14 t
}
Equation 3.3
 3


+ Re 2  k 3ATV19 3 + 3k3ATV19 ATV1 2 + 3k3ATV19 ATV6 2 e jω19 t 

 2

Expanding the total number of the channels, and the number and spectral locations of the interferers
will increase the complexity of Equation 3.3. Thus it is not practical to implement this time domain
derivation, especially in case of a dynamic spectrum scenario that changes continuously. However, it will
be shown below that the analysis can also be done in the frequency domain in a systematic way using
matrix operations. In the frequency domain, the multiplications in Equation 3.1 correspond to
convolutions:
DPrA ⇒ Third Order Distortion Products in the Frequency Domain
Equation 3.4
⇒ [Sin (f ) ⊗ Sin (f ) ⊗ Sin (f )]
where Sin(f) is the frequency domain representations of sin(t).
To build an intuitive understanding of the matrix implementation of the DPrA, let’s start with just two
tones, as shown in Figure 3.2 and expressed as follows:


sin (t ) = Re 2 ∑ ATVn e jωn t  = ∑ Ame- jωm t + ∑ Ame+ jωm t
 n=2,3
 m=−2,-3
m=+2,+3
Equation 3.5
where m represents the channel number for double side spectrum (i.e. positive and negative
frequencies) and Am is the MAX value of the DTV (single tone) signals at channel m. For simplicity, let’s
assume that all the occupied channels contain equal signal amplitude, equal to A TV / 2 as follows:
A -3 = A - 2 = A + 2 = A + 3 = A TV / 2
Equation 3.6
29
Figure 3.2: Frequency spectral content of the of two tones (two single frequencies)
The frequency spectrum span of Sin(f) is equal to 7 channels (N=7 channels: m=-3,-2,-1,0,+1,+2,+3;)
around the zero-frequency (see Figure 3.2), each channel has a bandwidth equal to the DTV channel
bandwidth, namely fCH (for the clarity of later figures, the label fCh on x-axis will be removed). Assuming
pure tones, Sin(fm) can be written in the discrete form:
Sin (f m ) = [A + 2 δ (f m - 2 f ch ) + A − 2 δ (f m + 2 f ch )] + [A + 3δ (f m - 3 f ch ) + A − 3δ (f m + 3 f ch )]
=
2
2
A TV [δ (f m - 2 f ch ) + δ (f m + 2 f ch )] +
A TV [δ (f m - 3 f ch ) + δ (f m + 3 f ch )]
2
2
Equation 3.7
SCONV(fm) in Equation 3.8 presents the mathematical expression of the first convolution process between
the square brackets in Equation 3.4:
SCONV (f m ) = Sin (f m ) ⊗ Sin (f m )
=
=
∑ (S (ρ ) S (f
in
ρ m = − ∞ .. + ∞
m
in
ρ m = − ∞ .. + ∞
m
in
m
− ρ m ))
∑ (S (ρ ) S (m f
in
ch
Equation 3.8
− ρ m ))
Where ρm is a dummy variable required to perform the convolution operation [25]. This convolution
operation involves a multiplication between the Sin(ρm) spectrum and its flipped1 version, shifted to the
right by |m|fCH, written as Sin(m fCH - ρm). Figure 3.3 visualizes this convolution operation that calculates
the frequency content of SCONV(fm) at m=0..+6. For the negative frequency side of SCONV(fm) (i.e. at m=-6..1), a similar plot can be created, by multiplying the spectrum of Sin(ρm) with its flipped version, now
shifted to the left by |m|fCH. Figure 3.3 shows that seven shifting operations are required to calculate
the frequency content of SCONV(fm) at m=0..+6: one shifting operation for the frequency content at the
origin (i.e. at m=0) and another six shifting operations for the positive frequency content (i.e. at
m=+1..+6). To complete the spectrum content of SCONV(fm) with the negative frequency content (i.e. at
m=-6..-1), still extra 6 shifting operations are needed.
1
flipped version of the Sin(ρm) around the y-axis gives Sin( - ρm)
30
Figure 3.3: Visualizing the convolution operation of Equation 3.8
Hence for the total spectrum view, 13 shifting operation (i.e. in general form 2N-1, where N=7) from the
left to the right are required. The DPrA implements this convolution operation via Matrix multiplication
as shown in Figure 3.4, where the Qm elements of the SCONV (m f ch ) is derived. First, we form a vector,
called S in . This vector corresponds to Sin(fm) (see the 7 channels in Figure 3.2) and contains 7 elements.
The index and the value of those 7 elements correspond to the spectral location and the amplitude of
the signals that composite the Sin(fm) spectrum.
31
Figure 3.4: Matrix implementation of the convolution operation of Figure 3.3
The Sin(m fCH - ρm) is constructed in a matrix form as follows:
•
Its middle column (i.e. 7th column) is nothing else than the flipped version of S in shifted by zero
(i.e. Sin(- ρm)). Then multiplying S in elements by the elements of this column calculates the
signal SCONV (m f ch ) quantity at m=0.
•
The columns at the right of the 7th column (i.e. 8th - 13th columns) represent the flipped version
of S in , right shifted by m=+1 to +6, respectively (i.e. Sin(m fCH - ρm)). Multiplying S in with those
columns provides the signal SCONV (m f ch ) quantity at m=+1 to m=+6.
•
The columns at the left of the 7th column (i.e. 1st - 6th columns) represent the flipped version of
S in , left shifted by m=-6 to -1, respectively (i.e. Sin(m fCH - ρm)). Multiplying S in with those
columns provides the signal SCONV (m f ch ) quantity at m=-6 to m=-1.
32
The content of the Qm values of the signal SCONV (m f ch ) , which are calculated according to Figure 3.4 are
listed in the following table:
Table 3.1: Frequency content of
SCONV (m f ch ) at m=-6 to m=+6
Qm elements
Qm construction
Qm amplitude level
Q-6
Q-5
Q-4
Q-3
Q-2
Q-1
Q0
Q+1
Q+2
Q+3
Q+4
Q+5
Q+6
( A-3 )2
2 ( A-3 A-2 )
( A-2 )2
0
0
2 ( A-3 A+2 )
2 ( A-3 A+3 ) + 2 ( A-2 A+2 )
2 ( A-2 A+3 )
0
0
( A+2 )2
2( A+2 A+3 )
( A+3 )2
½ ( ATV )2
( ATV )2
½ ( ATV )2
0
0
( ATV )2
2 ( ATV )2
( ATV )2
0
0
½ ( ATV )2
( ATV )2
½ ( ATV )2
The second column of Table 3.1 specifies how the delta functions of the two tones will contribute to the
Qm elements of the signal SCONV (m f ch ) . Substituting the amplitude of the two tones, defined in Equation
3.6, the value of the distortion component is evaluated (see third column of Table 3.1). In general, the
vector Sin has a dimension 1x7 (i.e. 1xN) and the dimension of the resulting matrix is 7x13 (i.e. N x (2
N-1).
The second convolution operation in Equation 3.4 can be explained and plotted in the same way as we
did for the first convolution. The mathematical expression of this convolution is written as follows:
SCONV (f m ) ⊗ Sin (f m ) =
=
∑ (S
CONV
ρ m = − ∞ .. + ∞
(ρm ) Sin (f m − ρ m ))
∑ (S
CONV (ρ m ) Sin (m f ch − ρ m ))
Equation 3.9
ρ m = − ∞ .. + ∞
This convolution process is implemented by multiplying the result of the previous convolution
SCONV(mfCH) with the flipped and shifted version of S in . Figure 3.5 visualizes this convolution operation,
which requires in total 19 (i.e. 3N-2) shifting operations to produce the total spectrum view.
33
Figure 3.5: Visualizing the convolution operation of Equation 3.9
In this figure, one can recognize the conventional IM3 products [15] at m=±1 and m=±4 around the
spectral location of the two tones.
34
In the same way as in Figure 3.4, the convolution operation of Figure 3.5 can be mapped to a simple
matrix multiplication as shown in in Figure 3.6, where the Dm elements of the [S CONV (m f ch ) ⊗ S in (m f ch )] is
derived. Firstly, the vector SCONV is formed, which corresponds to SCONV (m f ch ) . Then the flipped
version of Sin(fm), shifted by m fCH , namely Sin(m fCH - ρm) is formed as a matrix as follows:
•
Its middle column (see Figure 3.6), the 10th column, is the flipped version of S in shifted by
zero and extrapolated with six zero’s, which is necessary to match the dimension of this
column to the dimension of SCONV (see Figure 3.5). Then multiplying SCONV by this
column provides the signal [S CONV (m f ch ) ⊗ S in (m f ch )] quantity for m=0.
•
The columns at the right of the 10th column (i.e. 11th - 19th columns) represent the flipped
version of S in , right shifted by m=+1 to +9, respectively (i.e. Sin(m fCH - ρm)). Multiplying
SCONV with those columns provides the signal [S CONV (m f ch ) ⊗ S in (m f ch )] quantity at m=+1 to
m=+9.
•
The columns at the left of the 10th column (i.e. 1st - 9th columns) represent the flipped version
of S in , left shifted by m=-9 to -1, respectively (i.e. Sin(m fCH - ρm)). Multiplying SCONV with
those columns provides the signal [S CONV (m f ch ) ⊗ S in (m f ch )] quantity at m=-9 to m=-1.
35
Figure 3.6: Matrix implementation of the convolution operation of Figure 3.5
36
The content of the Dm element values of [S CONV (m f ch ) ⊗ S in (m f ch )], which are calculated according to
Figure 3.6 are listed in the following table:
[
]
Table 3.2: Frequency content of S CONV (m f ch ) ⊗ S in (m f ch ) at m=-9 to m=+9
Dm elements
D-9
Dm construction
( A-3 )3
Dm amplitude level
( ATV )3 / (2 2 )
D-8
3 A-2 ( A-3 )2
3 ( ATV )3 / (2
D-7
3 A-3 ( A-2 )2
3 ( ATV )3 / (2
D-6
( A-2 )3
D-5
D-4
0
3 A+2 ( A-3 )2
)
2)
3
( ATV ) / (2 2 )
0
3 ( ATV )3 / (2
2
D-2
6 A+3 A-3 A-2 + 3 A+2 ( A-2 )
9 ( ATV )3 / (2
D-1
3 A+3 ( A-2 )2
3 ( ATV )3 / (2
)
2)
2)
2)
D0
D+1
0
3 A-3 ( A+2 )2
0
3 ( ATV )3 / (2
2
D-3
2
9 ( ATV ) / (2
2
6 A+2 A-2 A-3 + 3 A+3 ( A-3 )
3
6 A-3 A+3 A+2 + 3 A-2 ( A+2 )
2
9 ( ATV ) / (2
D+3
6 A-2 A+2 A+3 + 3 A-3 ( A+3 )
2
9 ( ATV )3 / (2
D+4
3 A-2 ( A+3 )2
3 ( ATV )3 / (2
D+5
D+6
0
( A+2 )3
0
( ATV )3 / (2
D+2
3 A+3 ( A+2 )
D+8
3 A+2 ( A+3 )2
D+9
( A+3 )3
)
2)
2)
2)
)
3 ( ATV ) / (2 2 )
3 ( ATV )3 / (2 2 )
( ATV )3 / (2 2 )
2
D+7
3
2
2
3
An interesting property of the DPrA matrix calculation process is its capability to track how a spectral
tones contributes to various distortion products as shown in column 2 of Table 3.2. Substituting the
amplitude of the two tones, defined in Equation 3.6, the value of the distortion component is evaluated
(see third column of Table 3.2). In summary, Table 3.2 givs insight in both the absolute and relative
contribution to the total distortion level. The content of the Dm elements in Table 3.2 is in agreement
with the conventional 3rd order distortion products derived in literature [15]) with using two tones in
time domain (i.e. two cos(ωt) signals).
37
Figure 3.7 visualizes the total 2-step matrix multiplication view of the DPrA process, which is built in the
Maple program of Appendix C. Observing the matrix dimensions of [A: 1 x N], [B: N x (2*N-1)] and [C:
(2*N-1) x (3*N-2)]. One can argue about the dimensions of the shown matrixes, which grow with the
number of the channels (i.e. N). However the intrinsic strength of the DPrA is in its matrix multiplication
form. Firstly, when the inner multiplications are between two elements where one or both of those
elements are “zeroes1”, then there is simply no need to apply a multiplication. Therefore the total
required number of multiplications may considerably be decreased. Besides that, the DPrA has another
interesting property in case the distortion in only one specific channel is of interest, e.g. when a
particular channel is proposed for use by a cognitive radio. In that case, the DPrA just needs to multiply
the Qm elements of SCONV with that associated column of the [C] matrix, defined in Figure 3.7, to that
channel number . For example, to calculate the distortion product at channel m=+4, then the DPrA just
needs to multiply the Qm elements of SCONV with the 14th column of [C] matrix.
1
Practically, zeros do not exist, as noise floor will always be there. A threshold may be specified to define this zero
content. This subject is out of our scope.
38
rd
Figure 3.7: The DPrA process to derive/predict the 3 order distortion products
Now that the distortion products across the white channels are calculated via DPrA, the equations in
chapter 2 can be directly adjusted to calculate the required IIP3 for any white Spot. The analysis of
chapter 2 derives the signal at the output of a nonlinear system when the CR signal operates at any
39
white spot among the occupied channels by the DTV primary service signals. Equation 3.10 reveals a
general form for such construction. The form consists of the amplified CR signal and the 3rd order
distortion products: Self-interference, XM3 and potential IM3 products.
Sout WhiteSpot


 jω

= Re Amplified CR signal + Self - interference + XM3 + IM 3 WhiteSpot  e
1444444424444444
3

3 order distortion products

(
)
rd
WhiteSpot t




Equation 3.10
As already concluded in Chapter 2, whether the CR operates in the IM3 spots or the IM3-free spots, the
self-interference and XM3 products will always exist. The self-interference product can be usually
neglected in comparison to the XM3 and the IM3 products because the DTV signals are usually much
stronger1 than the CR signal. The IM3 products of the DTV signals are calculated by multiplying the 3rd
order nonlinear term k3 with the DPrA results (e.g. see Figure 3.7) as follows:
Sout
WhiteSpot


 jω

= Re Amplified CR signal + XM 3 + k 3 DPrA WhiteSpot  e
14444244443 

3 order distortion products

(
(
rd
))
WhiteSpot t




Equation 3.11
Repeating the same procedure in chapter 2 by firstly writing the Signal to Distortion ratio of Equation
3.11 as follows:
S
(Amplified CR signal )
=
D
XM 3 + k 3 DPrA WhiteSpot
2
(
(
))
Equation 3.12
2
Then the amplified CR signal and the XM3 products of Equation 2.5 are substituted in Equation 3.12:


k 2A 
CR
 114243

 Amplified CR signal 
2
S
=
D 

 3k 3 2 A CR  ∑ A TV 2  + k 3 DPrA
WhiteSpot
 1444
 4n 444
42
3

XM

n
3
(
Equation 3.13






2
)
where n refers to all the channel numbers occupied by the DTV signal. ATV and ACR are the RMS values of
the DTV signal and CR signal, respectively. Then the linearity requirement can be presented as the ratio
between k1 and k3:
1
In case that the CR receiver is close to the CR transmitter, then the received CR signal is now larger than the TV
signals. An Automatic Gain Control (AGC) can be used at the CR receiver to attenuate the total received signals.
Now the attenuated TV signals will not affect the CR receiver nonlinearity anymore.
40
k1
k3
S
D
=
WhiteSpot

DPrA WhiteSpot
 3 ∑ A TV 2 +
 n
2 A CR

n




Equation 3.14
where S/D is the required Signal to Distortion Ratio for the CR receiver output. Then according to the
definition of IIP3, referred to 50Ω, the power value of IIP3 is related to k1/k3 as follows [15]:
PIIP =
3
2 k1
/ 50 [W]
3 k3
Equation 3.15
Substituting Equation 3.14 in Equation 3.15 gives the linearity requirement for any white spot:




PDPrA
S 
1
WhiteSpot
 [W]
PIIP3
= 2×
+
∑ PTV n
WhiteSpot

D 
150
P
n 23
CR44
1
14 4
424
3 

 CR - power independen t term CR - power dependent term 
Equation 3.16
2
Where:
PDPrA
WhiteSpot
 DPrA WhiteSpot 
 /50 [W]
= 


2


Equation 3.17
According to Equation 3.16, the linearity requirement depends on the following two terms:
•
A CR-power independent term: it is proportional to the sum of the power of the DTV signals,
which will cross-modulate the receiver CR-signal. This term exist in all the white spots.
•
A CR-power dependent term: it is proportional to the ratio between the IM3 distortion products
predicted by DPrA and the power value of the CR signal. This term can be minimized by
increasing the CR power signal that operates at the IM3-spots, as long as the third order
nonlinear model is still valid and no contribution yet from the 5th order nonlinear term.
The derivation of the linearity requirement can be further simplified by including the CR signal in the
vector S in , in case that its amplitude and potential spectral location is specified in advance. Then the
whole 3rd distortion products of Equation 3.10 can be directly derived by applying the DPrA to the whole
spectrum inclusive the CR signal. Hence the linearity requirements will be given as follows:
PIIP
3
Specific- WhiteSpot
=
2
S
×
150
D
PDPrA
Equation 3.18
Specific -WhiteSpot
[W]
PCR
Where PCR is now added to the construction of PDPrA
.
Specific - WhiteSpot
41
Application example As an example, let’s apply our analysis in predicting the linearity requirement to
channel 4 and 8 in Figure 3.7. From Table 3.2, the DPrA has predicted the following distortion levels:
Table 3.3: DPrA frequency content at m=±4 and m=±6
Dm elements
D-4 + D+4
Dm construction
3 A+2 ( A-3 )2 + 3 A-2 ( A+3 )2
3
D-6 + D+6
( A-2 ) + ( A+2 )
3
Dm amplitude level
( )
/ (2 2 )
2 x 3 ( ATV )3 / 2 2
2 x ( ATV )3
Then the linearity requirements at channels 4 and 6 are given as follows:


P


DPrA
S
1
Channel 4
 ∑ PTV +
 [W]
PIIP3
= 2×
n
Channel 4
D n = 2 and 3
150
PCR

4
4244
3 144
42444
3
1Fixed
term
Variable term


Equation 3.19
2
where : PDPrA
PIIP
3
Channel 4
  3 (A )3  
TV  
2
2
  2 2 
 3 (A )3 


TV  /50 [W]
 /50 = 
=


2
2













S 
1 PDPrA
= 2×
 ∑ PTV +
 [W]
D n1
150
P
= 2 and 3
CR
424
3 1442443 
 Fixed term

Variable term
Equation 3.20
Channel 6
Channel 6
n
  (A TV )3  
 2

2
 (A TV )3 
  2 2  
 /50 [W]
=
 /50 = 

2
2








2
where : PDPrA
Channel 6
Finally the analysis can be expanded to deal with wideband DTV signals instead of tones in the same
manner as in chapter 2 by introducing ∆Wideband (see Equation 2.6, maximum ∆Wideband=4.5dB) as a
correction factor to Equation 3.16 as follows:
PIIP
3
WhiteSpot
= 2×
S
D
∆
∆

PDPrA
 10 10 × 0.66 ∑ PTV + 1 10 10 × (0.66 or 0.17 )
1
4
4
2
4
4
3
244443
150 14444
PCR

n
1.4
1.4 or 0.7

Wideband
Wideband
WhiteSpot
n

 [W]


Equation 3.21
The choice between 0.66 or 0.17 depends on whether the white spot lies in the center spot or on one of
the two side spots of the Bell shape (see Figure 2.11).
42
3.2 DPrA Application Examples
To verify the DPrA concept, this section begins with applying DPrA on the chapter 2’s examples of Figure
2.5 and Figure 2.6 (i.e. with 3 interferers), which are verified by measurements shown in Figure 2.13 and
Figure 2.14, respectively. Further as the number of interferers increases, then the construction pattern
of 3rd order distortion products becomes more complex. This complexity is explored at the last example.
First spectrum scenario: There are three interferers at the channels/spots at 1, 6 and 19 (see Figure 2.5).
The 3rd order distortion products view is presented in Table 3.4 and visualized in Figure 3.8. The third
column (i.e. Signal amplitude level) is in exact consistent with Equation 3.3.
Figure 3.8: DPrA prediction of the distortion products for Interferers at Channels 1, 6 and 19
rd
Table 3.4: 3 order distortion products view
Ch.
No.
1
Signal amplitude level
Signal construction
+1 :=6 k A A A + 6 k A A A + 3 k A 2 A
3 -19 1 19
3 -6 1 6
3 1 -1
3
2
2
3
:=3 k3 2 ATV19 ATV1 + 3 k3 2 ATV6 ATV1 + k3 ATV1 2
2
-1 :=3 k A 2 A + 6 k A A A + 6 k A A A
3 -1 1
3 -19 -1 19
3 -6 -1 6
6
+6 :=6 k A A A + 3 k A 2 A + 6 k A A A
3 -19 6 19
3 6 -6
3 -1 6 1
3
2
3
2
:=3 k3 2 ATV19 ATV6 + k3 ATV6 2 + 3 k3 2 ATV1 ATV6
2
-6 := 3 k A 2 A + 6 k A A A + 6 k A A A
3 -6 6
3 -19 -6 19
3 -6 -1 1
11
14
19
2
3
2
:= k3 2 ATV6 ATV1
2
+11
:=3 k3 A-1 A6
-11
:=3 k3 A-6 A1
+14
:=6 k3 A-6 A1 A19
-14
:=6 k3 A-19 A-1 A6
+19
:=3 k3 A19 A-19 + 6 k3 A-6 A19 A6 + 6 k3 A-1 A19 A1
2
:=3 k3 2 ATV6 ATV1 ATV19
2
-19 :=3 k A 2 A + 6 k A A A + 6 k A A A
3 -19 19
3 -19 -6 6
3 -19 -1 1
43
3
3
2
2
:= k3 ATV19 2 + 3 k3 2 ATV6 ATV19 + 3 k3 2 ATV1 ATV19
2
Second spectrum scenario: There are three interferers at the channels/spots at 3, 5 and 16 (see Figure
2.6). The 3rd order distortion products view is presented in Table 3.5 and visualized in Figure 3.9. The
third column is in exact consistent with Equation 3.3.
Figure 3.9: DPrA prediction of the distortion products for Interferers at Channels 3, 5 and 16
rd
Table 3.5: 3 order distortion products view
Ch.
No.
1
3
Signal amplitude level
Signal construction
3
2
:= k3 2 ATV5 ATV3
2
2
+1
:=3 k3 A-5 A3
-1
:=3 k3 A-3 A5
2
+3 :=6 k A A A + 6 k A A A + 3 k A 2 A
3 -16 3 16
3 -5 3 5
3 3 -3
3
2
2
3
:=3 k3 2 ATV16 ATV3 + 3 k3 2 ATV5 ATV3 + k3 ATV3 2
2
-3 :=6 k A A A + 6 k A A A + 3 k A 2 A
3 -16 -3 16
3 -5 -3 5
3 -3 3
5
+5 :=6 k A A A + 3 k A 2 A + 6 k A A A
3 -16 5 16
3 5 -5
3 -3 5 3
3
2
3
2
:=3 k3 2 ATV16 ATV5 + k3 ATV5 2 + 3 k3 2 ATV5 ATV3
2
-5 :=6 k A A A + 6 k A A A + 3 k A 2 A
3 -16 -5 16
3 -5 -3 3
3 -5 5
7
14
16
:=3 k3 A-3 A5
-7
:=3 k3 A-5 A3
+14
:=6 k3 A-5 A3 A16
-14
:=6 k3 A-16 A-3 A5
2
:=3 k3 2 ATV5 ATV3 ATV16
+16 :=3 k A 2 A + 6 k A A A + 6 k A A A :=3 k ATV 3 2 + 3 k 2 ATV2 ATV + 3 k 2 ATV2 ATV
16
3
5
16
3
3
16
2 3
3 16 -16
3 -5 16 5
3 -3 16 3
-16 :=6 k A A A + 6 k A A A + 3 k A 2 A
3
18
3
2
:= k3 2 ATV5 ATV3
2
2
+7
-16 -5 5
3 -16 -3 3
+18
:=6 k3 A-3 A5 A16
-18
:=6 k3 A-16 A-5 A3
3
-16
16
:=3 k3 2 ATV5 ATV3 ATV16
44
Referring to the theory of chapter 2 and observing Table 3.5, the construction pattern of the 3rd order
distortion products across the channels are as follows:
1.
Channel 3 contains the cross-modulation (i.e XM3) products of the interferers of channel 5 and
channel 16 on top of the interferer of channel 3 plus its self-interference product:
3
2
2
3
:=3 k3 2 ATV16 ATV3 + 3 k3 2 ATV5 ATV3 + k3 ATV3 2 .
2
2. Channel 5 contains the cross-modulation (i.e XM3) products of the interferers of channel 3 and
channel 16 on top of the interferer of channel 5 plus its self-interference product:
3
2
3
2
:=3 k3 2 ATV16 ATV5 + k3 ATV5 2 + 3 k3 2 ATV5 ATV3 .
2
3. Channel 16 contains the cross-modulation (i.e XM3) products of the interferers of channel 3 and
channel 5 on top of the interferer of channel 16 plus its self-interference product:
3
3
2
2
:= k3 ATV16 2 + 3 k3 2 ATV5 ATV16 + 3 k3 2 ATV3 ATV16 .
2
4. Both channel 1 and channel 7 contain the conventional intermodulation products between
3
2
3
2
2
2
channel 3 and channel 5::= k3 2 ATV5 ATV3 and:= k3 2 ATV5 ATV3 , respectively.
5. Channel 14 contains the intermodulation product among channel 3, channel 5 and channel 16.
The distortion level in channel 14 is 2 times higher (i.e 6dB) than the conventional
intermodulation products of point 4:
:=3 k3 2 ATV5 ATV3 ATV16 , as presented in chapter 2.
6. Channel 18 contains the intermodulation product among channel 3, channel 5 and channel 16.
The distortion level in channel 18 is 2 times higher (i.e 6dB) than the conventional
intermodulation products of point 4:
:=3 k3 2 ATV5 ATV3 ATV16 , as presented in chapter 2.
45
Third spectrum scenario: There are four interferers at the channels/spots at 2, 6, 13 and 20. The 3rd
order distortion products view is quantified in Table 3.6 and visualized in Figure 3.10.
Figure 3.10: DPrA prediction of the distortion products for Interferers at Channels 2, 6, 13 and 20
rd
Table 3.6: 3 order distortion products view
Ch.
Signal construction
No.
2 + :=6 k3 A-20 A2 A20 + 6 k3 A-13 A2 A13 + 6 k3 A-6 A2 A6 + 3 k3 A22 A-2
Signal amplitude level
3
2
2
2
3
:=3 k3 2 ATV20 ATV2 + 3 k3 2 ATV13 ATV2 + 3 k3 2 ATV6 ATV2 + k3 ATV2 2
2
- :=6 k3 A-20 A-2 A20 + 6 k3 A-13 A-2 A13 + 6 k3 A-6 A-2 A6 + 3 k3 A-22 A2
6
9
10
13
16
17
2
:=6 k3 A-20 A6 A20 + 6 k3 A-2 A6 A2 + 6 k3 A6 A13 A-13 + 3 k3 A-20 A13 + 3 k3 A6 A-6
-
:= 6 k3 A-13 A-6 A13 + 6 k3 A-6 A-2 A2 + 6 k3 A-6 A20 A-20 + 3 k3 A20 A-13 + 3k3 A-6 A6
+
:= 6 k3 A-13 A2 A20 + 6 k3 A-6 A2 A13
-
:=6 k3 A-13 A-2 A6 + 6 k3 A-20 A-2 A13
+
:=3 k3 A-2 A6
-
:=3 k3 A-6 A2
+
-
:=6 k3 A-2 A13 A2 + 6 k3 A6 A13 A-6 + 6k3 A13 A20 A-20 + 6 k3 A20 A-13 A6 + 3 k3 A-13 A13
:= 6 k3 A-20 A-13 A20 + 6 k3 A-13 A-6 A6 + 6 k3 A-13 A-2 A2 + 6 k3 A13 A-20 A-6 + 3 k3 A13 A-13
+
:= 6 k3 A-6 A2 A20
-
:= 6 k3 A-20 A-2 A6
+
:= 6 k3 A-2 A6 A13
2
+
-
2
2
2
2 3
2
3 k3 2 ATV20 ATV6 + 3 k3 2 ATV2 ATV6 + 3 k3 2 ATV6 ATV13 + k3 2 ATV20 ATV13
2
3
3
+ k3 ATV6 2
2
:=3 k3 2 ATV13 ATV2 ATV20 + 3 k3 2 ATV6 ATV2 ATV13
2
3
2
:= k3 2 ATV6 ATV2
2
2
2
2
2
2
2
3k3 2 ATV2 ATV13 +3k3 2 ATV6 ATV13 +3k3 2 ATV13 ATV20 +3k3 2 ATV20 ATV13 ATV6
3
3
+ k3 2 ATV13
2
:=3 k3 2 ATV6 ATV2 ATV20
:=3 k3 2 ATV6 ATV2 ATV13
:= 6 k3 A-13 A-6 A2
20
2
+
2
2
:=3 k3 A20 A-20 + 6 k3 A-6 A20 A6 + 6 k3 A-2 A20 A2 + 6 k3 A13 A20 A-13 + 3 k3 A-6 A13
2
2
:=6 k3 A-20 A-13 A13 + 6 k3 A-20 A-2 A2 + 6 k3 A-20 A6 A-6 + 3 k3 A-20 A20 + 3 k3 A6 A-13
46
3
3
2
2
2
k ATV20 2 + 3 k3 2 ATV6 ATV20 + 3 k3 2 ATV2 ATV20 + 3 k3 2 ATV20 ATV13
2 3
3
2
+ k3 2 ATV6 ATV13
2
Observing Table 3.6, the construction pattern of the 3rd order distortion products across the channels
are as follows:
1.
Channel 2 contains the cross-modulation (i.e XM3) products of the interferers of channel 6,
channel 13 and channel 20 on top of the interferer of channel 2 plus its self-interference
2
2
2
3
2
3
:=3 k3 2 ATV20 ATV2 + 3 k3 2 ATV13 ATV2 + 3 k3 2 ATV6 ATV2 + k3 ATV2
product:
2
2. Channel 6 contains the cross-modulation (i.e XM3) products of the interferers of channel 2,
channel 13 and channel 20 on top of the interferer of channel 6 plus its self-interference
product plus the conventional intermodulation products between channel 13 and channel 20:
3. Channel 13 contains the cross-modulation (i.e XM3) products of the interferers of channel 2,
channel 6 and channel 20 on top of the interferer of channel 13 plus its self-interference
product plus the intermodulation products among channel 6, channel 13 and channel 20:
4. Channel 20 contains the cross-modulation (i.e XM3) products of the interferers of channel 2,
channel 6 and channel 13 on top of the interferer of channel 20 plus its self-interference
product plus the conventional intermodulation products between channel 6 and channel 13:
5. Channel 9 contains the intermodulation products among channel 2, channel 13 and channel 20
plus the intermodulation products among channel 2, channel 6 and channel 13:
:=3 k3 2 ATV13 ATV2 ATV20 + 3 k3 2 ATV6 ATV2 ATV13
6. Channel 10 contains the conventional intermodulation products between channel 2 and channel
3
2
2
:= k3 2 ATV6 ATV2
6:
7. Channel 16 contains the intermodulation products among channel 2, channel 6 and channel 20:
:=3 k3 2 ATV6 ATV2 ATV20
8. Channel 17 contains the intermodulation products among channel 2, channel 6 and channel 16:
:=3 k3 2 ATV6 ATV2 ATV13
47
3.3 Conclusions
The amplitude and the spectral location of the DTV signals are place and time dependent, and hence the
required linearity for a wideband CR receiver varies across the unoccupied DTV channels and varies over
place and time. The DPrA aims at predicting the instantaneous distortion levels in a dynamic way by
matrix multiplications on spectrum analysis measurements for each frequency channel. It is possible to
implement this DPrA in the digital domain of the receiver. The dimension of the required DPrA matrices
grows with the number of the covered channels, whereas the number of the inner multiplications grows
with the number of the occupied DTV channels.
The matrix algorithm used in the DPrA can be further extended to calculate the distortion products
generated by higher nonlinear order terms (e.g. 4th, 5th ... etc.). For example for the 4th order nonlinear
term, an extra matrix multiplication (i.e. due to an extra convolution) to the outcome of Figure 3.7 is
required. The outcome of this multiplication must be multiplied with k4 that characterize the 4th third
order nonlinearity of the circuit. Note that the 2nd distortion products is already calculated in Figure 3.4
by just one multiplication (i.e. due to one convolution operation) between vector S in and the
convolution matrix [A]. All the results of this chapter are verified by MatLab simulation.
48
Chapter 4. Analysis of a Very Linear Front-End [41]
Chapter 4 and 5 investigate the third research question: “How to increase the linearity of CR receiver
hardware, given less up-front filtering?”
This chapter conceptually presents the linearization technique via the application of negative
conductance on the receiver topology that is introduced in section 4.1. Then, section 4.2 gives an
intuitive model to understand the basic distortion cancellation concept. The optimum negative
conductance value is derived by mathematical analysis in section 4.3 and related to negative feedback
theory in section 4.4. Section 4.5 analyses stability issues related to this negative conductance
technique. Finally, some conclusions are given in section 4.6.
This chapter is a literal copy of the first part of the paper published in [41].
49
4.1 Motivation and Introduction
As discussed in the previous chapters, wideband receivers with high IIP3 are very important for
opportunistic DSA via a cognitive
radio.
Strong
interferers
(e.g.
incumbent TV signals) may present in
near or directly adjacent channels
inside the down converted band of
the receiver, making on-chip RF
filtering ineffective, as exemplified in
Figure 4.1 for a Digital TV band.
Figure 4.1: CR operates in an adjacent channel of Digital TV spectrum [25]
High linearity is required also to prevent cross-modulation effects [18] from desensitizing the receiver. A
part from the RF receivers, the spectrum sensing front-end also requires high in-band IIP3 in order to
minimize the errors in detecting the empty channels in the spectrum [26].
In general, linearity requirements on radio receivers become increasingly challenging, as the radio
spectrum becomes more and more crowded. Moreover, there is a trend towards more wideband and
more flexible radio hardware with less dedicated RF filtering (“Software Defined Radio”). As an example,
Figure 4.2 plots IIP3 requirements calculated
for E-UTRA for a wideband base station
receiver in three scenarios: wide area, local
area and home [27]. Apart from the high
100MHz bandwidth, note the sudden step in
IIP3 requirements at the band-edge. Also note
that less coverage area (home versus wide
area), corresponds to higher in-band IIP3 but a
smaller step to out-of-band IIP3 (i.e. around
Figure 4.2: Example IIP3 requirement for E-UTRA [29]
16dB for home area versus 40dB for wide
area). As a consequence of the lack of a reasonable transition band, on-chip analog filtering is ineffective
to relax the IIP3 requirement, and off-chip filters are expensive. Depending on the blocker scenario,
compression point requirements may or may not be affected. This chapter proposes a circuit technique
that can increase IIP3 simultaneously for in- and out-of-band, at roughly constant compression point.
50
Strong RF interference can easily clip baseband amplifiers, while higher required bandwidths limit the
amount of available loop-gain for negative feedback. When pushing linearity, avoiding voltage gain at RF
(see Figure 4.3) is instrumental [[28]-[34]]. Exploiting RF V-I conversion followed by passive down-mixing
and then simultaneous I-V conversion and filtering at IF/baseband with OpAmps, an out-of-band IIP3 of
up to +18dBm has been shown [[28],[29]]. Passive mixer-first architectures can even achieve up to
+25dBm out-of-band IIP3 [32]. However in-band IIP3 is much worse, certainly at high gain. The best inband IIP3 results that we found for receivers were +3.5dBm for [28] at 34dB gain and +11dBm for [31] at
19dB gain. Analysis shows that finite OpAmp gain can be a bottleneck, as a non-zero virtual ground node
voltage can result in distortion currents. In [35], we proposed to exploit a negative conductance
technique to cancel distortion currents. In this way, the design of the OpAmp is relaxed and its
performance no longer needs to be a bottleneck. The use of a negative conductance has been proposed
in [36] to realize TIA flicker noise shaping. Paper [36] also briefly mentions linearity improvement, but
linearity benefits were not the focus there.
Figure 4.3: High blocker tolerant linear receiver
51
4.2 Linearization Concept Analysis
To understand the OpAmp linearity limitation and the distortion cancellation technique intuitively, it is
instructive to follow a 4-step approach to analyze what happens at the virtual ground node “VGND”, as
illustrated in Figure 4.4 to Figure 4.8:
Step 1: Assume the RF V-I conversion and mixing are perfectly ideal (i.e. linear and infinite current
source resistance for GM), we can use the equivalent baseband model in Figure 4.4 (omitting the
downconversion for simplicity). Assuming a 2-tone input signal VS(f), the injected current IS(f) to the
VGND node is linear, so without IM3 tones. Now, if the OpAmp handles large signals at a high but finite
gain, its output stage will produce IM3 products at the OUT node, i.e. VOUT(f). However, as IS(f) has no IM3
and the feedback resistor RF is linear, the voltage over RF does not contain IM3 (assuming negligible
OPAMP input current). Consequently, the IM3 products of VVGND(f) are in absolute sense equal to those
of VOUT(f) both in magnitude and phase. Let’s denote this “IM3 copy” effect in Figure 4.4 as “problem A”.
Note that the two main tones of VVGND(f) are much smaller than that of VOUT(f), as the ratio VOUT(f)/VVGND
(f) for linear terms is equal to the loop gain. As a consequence the ratio between the linear terms and
the IM3 products at VGND node is much worse than at the OUT node, causing a more serious problem
discussed next.
Figure 4.4: OpAmp nonlinearity problem A: IM3 is copied from the OUT node to the VGND node
52
Step 2: Assume we add a finite output resistance RO as shown in Figure 4.5. The nonlinear voltage
VVGND(f) over RO now generates a nonlinear current IO(f), and hence IF (f) becomes nonlinear. This current
is absorbed by the OpAmp output stage and increases IM3 at both VOUT(f) and VVGND(f). We will denote
this “RO loading” effect on the VGND node in Figure 4.5 as “problem B”.
Figure 4.5: OpAmp nonlinearity problem B: RO loads the VGND node
Step 3: Once one realizes the main cause for distortion current is VVGND(f)/RO, it is easy to verify that
adding a negative conductance with value GO=1/RO between VGND and ground can be a solution (see
Figure 4.6). The negative conductance senses VVGND and generates a copy of the distorted current IO(f),
which now flows in a “local circle” via the ground. Consequently, the current injected to the VGND node
becomes linear again and we are back at the circuit of problem A, having solved problem B.
Figure 4.6: Solving problem B via negative conductance with GO=1/RO
53
Step 4: Still, the OpAmp output voltage contains some IM3, equal to that on the VGND node. By slight
overcompensation this IM3 contribution can also be cancelled. To show this, it is useful to model the
floating resistor RF with an equivalent network consisting of four single-ended linear transconductor
blocks GF (GF=1/RF), all referred to ground as shown in Figure 4.7(a). The two shorted GF blocks,
indicated with a dashed ellipse, can be replaced by a simple RF resistor to the ground (see Figure 4.7(b)).
Thus Figure 4.7(c) results with RF-VGND and RF-OUT, (loading resistances at the VGND node and the OUT
node, respectively), GF-VGND (the transconductance sensing VOUT and injecting current to the VGND node),
and GF-OUT (the transconductance sensing VVGND and injecting current to the OUT node). We assigned
different names to GF and RF blocks in order to distinguish between their effects on nonlinearity at the
VGND node and the OUT node separately. Figure 4.7(c) clearly shows the loading effect of RF (i.e. RF-VGND)
at the VGND node.
Figure 4.7: Equivalent model of the effect that RF has on the OUT node and the VGND node
54
Now, when the negative conductance cancels this loaded effect (see Figure 4.8), the injecting current of
GF-VGND becomes equal to the linear current IS. As VOUT=IS/GF-VGND=-IS.RF, the OpAmp output voltage VOUT
becomes linear. In this way, problem A is solved as well.
Figure 4.8: Solving problem A via negative conductance with GF = 1/RF
Overall, combining the solutions for problem A and B, the optimal total negative conductance is:
GTOTAL=1/RO+1/RF.
55
4.3 Mathematical Analysis
To mathematically prove this optimum cancellation condition, the OpAmp is modeled as an OTA with
nonlinear transconductance and also a nonlinear output resistance because we aim for high output
swing:
I F = gm1VIN + gm 3 VIN + go1VO + go 3 VO
3
3
Equation 4.1
In the model, we assume that the third order nonlinearities are more pronounced than the second order
nonlinear terms, which is reasonable considering the OpAmp will be implemented in fully differential
form.
In Appendix D, the nonlinear relation between VOUT and signal current IS is derived using the model in
Figure 4.9.
Figure 4.9: Baseband model with RO and the extended RF for nonlinearity derivations
It can be expressed in terms of a linear (Ω1) and third-order nonlinear (Ω3) coefficient:
VOUT = Ω 1 I S + Ω 3 I S
3
Equation 4.2
The linear coefficient Ω1 is the I/V conversion gain:
Ω1 =
1
1  1
1
+
 
 a  R O R F − VGND
Equation 4.3


 + G F − VGND 


56
Where (a) is a function of the linear terms of the OpAmp model (i.e. gm1, go1) and the RF effects at the
OUT node (i.e. RF-OUT and GF-OUT). For very high gm1, (a) reaches -∞. Consequently, the I/V conversion
gain of Equation 4.3 becomes 1/GF-VGND= -RF.
The third-order distortion coefficient (Ω3) is:
Ω3 =
 1

1

NL3 
+
 R O R F− VGND 
1  1


1
 + G F − VGND 
+
 
 a  R O R F− VGND 

Equation 4.4
4
where (NL3: see Appendix D) is related to the nonlinear terms of the OpAmp model and is a function of
(i.e. gm1, gm3, go1 and go3) and the effect of RF on the OUT node (i.e. RF-OUT and GF-OUT). Now, if the
negative conductance technique cancels 1/RO+1/RF-VGND from Equation 4.3 and Equation 4.4, we see that
Ω1 reaches 1/GF-VGND=-RF and Ω3 becomes zero (i.e. distortion is cancelled). Note that since the voltage
swing at the VGND node is small, the effect of negative conductance nonlinearity can be very small.
To verify the OpAmp model, we fitted the model derived above to simulations done for the OpAmp that
will be introduced in the next chapter. Figure 4.10 shows a close agreement.
Figure 4.10: OpAmp model Equation 4.1 verification
57
4.4 Feedback Control Analysis
The linearity benefit can also be verified by applying feedback theory to Figure 4.9 as shown in Figure
4.11, excluding GM. The feedback topology of the circuit is Voltage-Current Feedback [33]. The output
voltage (i.e. VOUT) is sensed and converted to a proportional feedback current βVOUT, where β=GF-VGND (in
Siemens). This feedback current is subtracted from the input current IS resulting in an error current
Ierror=IS-βVOUT to be amplified by the block A. Here, A=VOUT/Ierror, where A has the dimension of a
transimpedance [Ω]. It consists of all the blocks of Figure 4.9, excluding GM and GF-VGND. Actually for
finite A, there will be a non-zero Ierror due to the loading effect of RO and RF-VGND on the VGND node. Now
the negative conductance increases the input impedance of the A block to infinity by cancelling RO and
RF-VGND, so that Ierror becomes zero and A=VOUT/Ierror=infinity. Consequently, loopgain Aβ goes to infinity
and VOUT/IS achieves its ideal value 1/β=RF, i.e. perfect linearity. We conclude that the negative
conductance technique increases the loop gain by increasing the value of A. Also note that only a finite
value for GO is needed to make the loopgain theoretically approach infinity, which is not possible by
increasing gm1 in the gain block. Although the feedback theory puts the application of a negative
conductance technique in the right context, however the problem with control theory is that it assumes
blocks
with
operation,
unilateral
which
are
sometimes not easy to
identify (e.g. see Figure
4.11: feedback resistor RF
which
is
supposed
to
realize the β block also
becomes part of the A
block). In compare to the
feedback
analysis
analysis,
explains
our
in
a
simple way how IM3 is
Figure 4.11: Applying feedback theory to Figure 4.9, excluding GM
affected by RO and RF.
Now, before we finalize this chapter with conclusions, we will first deal with a potential caveat of
negative conductance: the risk of instability
58
4.5 Stability Analysis
We will consider two stability aspects: 1) the risk of oscillation, based on a small signal model, and 2) the
risk of latch-up. Let us first look at the small signal behavior, referring to Figure 4.12. As the low-pass
filtering is desired, CF is added as feedback capacitor. Capacitor CT models the total input capacitance to
ground of the OpAmp CIN-OpAmp and other capacitance CO at the VGND node (see Figure 4.3).
Figure 4.12: Circuit diagram for small signal stability analysis
For simplicity, the OTA is modeled as a frequency dependent transconductance with a dominant pole at
ωO and infinite output impedance:
gm(s) =
gm O
s
1+
ωO
Equation 4.5
Assuming no further loading at the OUT node, looking into the VGND node (see Figure 4.12), the
impedance (ZIN) consists of the reactance of CT in parallel to 1/gm(s):




1
1
1
1
s

Z IN =
//
=
// 
+
s C T gm(s) s C T  gm O
gm O ω O 
1
424
3 
 {
Resistance Inductance (L)
Equation 4.6
Therefore, a parallel RLC tank is seen looking into the VGND node. If the negative conductance would
both cancel 1/RO and gmO, then oscillation would happen at a resonance frequency that depends on the
value of CT and L (i.e. fres=1/ 2
)). However, note that the typical virtual ground impedance 1/gmO
will normally be much lower than RO and RF. Thus, as the negative conductance GTotal is designed to
cancel 1/RO and 1/RF, the point of small signal instability can be designed to be safely far away.
59
Let’s now look at the potential of latch-up of the OpAmp for a case that the negative conductance is too
strong, i.e. it produces more current than needed after compensating the current in RO. As shown in
Figure 4.13, the negative conductance injects current via RF (i.e. VVGNDGLatch-up-Risk) that needs to be
handled by the OpAmp output stage in addition to the main current coming from GM (i.e. IS):
IOpAmp-Latch-up-Risk = IS + VVGNDG Latch−up−Risk
= IS +
1



1
− G Latch −up−Risk  + a G F−VGND 


 R F−VGND

ISG Latch −up−Risk
Equation 4.7
Where the relation between VVGND and IS is derived in Appendix E.
Figure 4.13: Latch-up problem at the OUT node
Referring to Figure 4.13 and substituting GLatch-up-Risk=(1/RF)+∆G in Equation 4.7 gives the following
relation:
I OpAmp-Latch -up - Risk

1
∆G +

RF
= I S 1 −
 
a 

  ∆G +
R F 
 






Equation 4.8
The OpAmp output stage current flows throw RF and make a voltage drop. The peak of this voltage drop
is around VDD/2-VOpAmpOutputStage-OV, where VOpAmpOutputStage-OV is the over drive voltages of the OpAmp
output stage transistors. Hence, if very strong negative conductance has been used (i.e. high ∆G), then
the current of Equation 4.8 becomes higher than the OpAmp output stage current capability and the
latch-up occur.
60
4.6 Conclusion
Front-End topologies with RF V-I conversion followed by passive down-mixing and then simultaneous I-V
conversion and filtering at IF/baseband with OpAmps are quite linear. However their linearity is mainly
limited by the OpAmp where a very high swing appears at its output stage transistors. Analysis shows
that finite OpAmp gain can be a bottleneck, as a non-zero virtual ground node voltage can result in
distortion currents. Our concept proposes to exploit a negative conductance technique to cancel those
distortion currents. A mathematical derivation proves is the optimum/required negative conductance
value, which exactly agrees with our intuitive analysis. Additionally, from the feedback theory context,
this optimum negative conductance simply cancels the error current so that the loop gain theoretically
approaches infinity, which is not possible by increasing the OpAmp gain to infinity. In this way, the
design of the OpAmp is relaxed and its performance no longer needs to be a bottleneck. The risk of
stability is also analyzed, where the system is well stable around the optimum negative conductance.
61
62
Chapter 5. Chip Design: UTCRxVLi [41]
Chapter 5 follows chapter 4 in investigating the third research question: “How to increase the linearity
of CR receiver hardware, given less up-front filtering?”
A receiver prototype in 65nm STMicroelectronics is implemented to verify the concept of using a
negative conductance technique to linearize the whole receiver. This chapter discusses the receiver
design details in section 5.1. The receiver noise figure analysis including the negative conductance
contribution is discussed in section 5.2. This noise analysis and the analysis of the previous chapter are
all verified by measurements in section 5.3. The results are benchmarked to other highly linear receivers
in section 5.4. Finally, the chapter is ended with conclusions in section 5.5.
This chapter is a literal copy of the second part of the paper published in [41].
63
5.1 Receiver Implementation
We will now apply the negative conductance idea to highly linear zero-IF radio receiver architecture of
Figure 4.3 in the previous chapter, which is redrawn in Figure 5.1.
Figure 5.1: High blocker tolerant linear receiver
To demonstrate the linearity potential of this technique, we will replace the active V-I conversion by a
more linear fully passive mixer with resistors in series [29], as shown in Figure 5.2.
Figure 5.2: Replacing the LNTA (GM) of by a linear resistance RRF
64
Figure 5.3: Complete Receiver with distortion compensation by –GO
Figure 5.3 shows the complete front-end IC schematic including the negative conductance. Using the
equivalent model in Figure 4.5, we can model the RF part of each branch in I and Q as a grounded
resistor RO and a transconductor GM referred to ground as denoted in Figure 5.3. However, as resistor
RRF is in series with the mixer on-resistance RON-MIXER and the virtual ground impedance RVGND of the
OpAmp, the equivalent GM now equals 1/(RRF+RON-MIXER+RVGND). This is chosen to be 20mS to realize RF
input impedance matching of 50Ω, assuming perfect non overlapping 25% duty-cycle clocks, so the RFinput continuously sees a conduction path to ground. The equivalent output impedance of the mixer at
baseband now is RO=2(RBalUn+RRF+ RON-MIXER), where the factor 2 is due to the quadrature mixer with 25%
duty cycle, connecting each I and Q baseband part to RF two times per LO cycle. To understand this
point, let’s derive RO from the power that is delivered by a test voltage source (i.e. Vtest=Va cos(ωLOt))
“looking back” in RO as shown in Figure 5.4.
65
Figure 5.4: Derivation of RO
This source is connected to the first branch of the I-path. The current Itest will flow through
RON-MIXER+RRF+RBalUn two times LO-cycle, hence we get:
3TLO
 TLO

2
4
4
1 
Va

P=
V
I
dt
+
V
I
dt
=
test test
∫ test test  4 (R ON-MIXER + R BalUn + R RF
TLO  ∫0
TLO


2
)
Equation 5.1
This power must be equal to the power dissipation in RO:
P=
1
TLO
TLO
TLO
∫
0
2
2
Vtest
V
dt = a
RO
2R O
Equation 5.2
By equating Equation 5.1 and Equation 5.2, the following RO is derived:
RO = 2 (RON-MIXER+ RBalUn + RRF )
Equation 5.3
In the RO derivation, the power is only balanced with the fundamental, while the effect of the 3rd and
higher harmonics are neglected due to the existence of CO (see Figure 5.3). Now, the 50Ω input
impedance matching is implemented as a combination of series resistances RRF≈12Ω, the up-converted
impedances of the passive mixer switches RON-MIXER≈28Ω plus the VGND impedance RVGND≈7Ω. The
passive mixer consists of simple NMOS switches. CO=8pF effectively shorts the LO leakage and high IF
frequency components to ground. The TIA consists of a class-A input stage and a class-AB output stage,
to maximize output swing (see Figure 5.5, [37]). Common mode feedback ensures biasing at VDD/2.
66
Figure 5.5: Circuit Diagram of the fully differential OpAmp design [37]
The feedback impedance is RF=1.5kΩ and CF=8pF, to obtain 26dB voltage gain and a -3dB-bandwidth of
12MHz. The differential topology allows for a simple differential implementation of the negative
conductance (right part of Figure 5.3) and high IIP2. To be able to measure what is the effect of different
negative conductance values, -GO is implemented as a parallel array of identical “unit-transconductors”,
digitally controllable via multiplier M, with transconductance steps of 0.2mS. Thus M=28 renders
GO=5.6mS to compensate the nominal value of RO=180Ω (RO=2(RBalUn+RRF+RON-MIXER)=2(50+12+28)=180Ω).
We will now consider the noise degradation resulting from the introduction of the negative
conductance. Actually this noise can be cancelled by a noise cancellation path [[38],[29]], however this is
expected to result in a linearity bottleneck in the auxiliary noise cancellation path. Hence we will analyze
the noise figure degradation and aim for minimizing the noise penalty.
67
5.2 Noise Figure
Receiver topologies with a passive mixer and transimpedance amplifier (TIA), can suffer from
amplification of OpAmp noise [39]. The output referred OpAmp noise contribution can be written as:
2
2
n−OUT
V
 R 
= 1+ F  Vn2−OpAmp
 RO 
Equation 5.4
Where Vn-OpAmp refers to the (equivalent) input noise voltages of the OpAmp, RO and RF are as used in
Figure 4.5. For our design RF=1.5kΩ and RO=180Ω, then the amplification factor is equal to
(1+RF/RO)2=87.
Often a high RF V/I conversion (GM-value) is used to achieve an overall noise figure around or below
3dB. Here we will use 20mS, the value desired for input impedance matching.
Figure 5.6 shows a baseband model of Figure 5.2 with noise sources added. The noise of GM is
represented by the current noise source (In-Ro) of RO. The noise of RF is modeled via voltage noise source
Vn-RF, while In-GTotal represents the current noise source of the negative conductance.
Figure 5.6: Equivalent baseband model for Noise Figure analysis
For simplicity, the OpAmp is modeled as a simple Transconductance (gm). To analyze the noise
contributions of In-Ro and In-GTotal to the output voltage, Ω1 (i.e. the I/V conversion of the TIA (3)) is useful.
The straightforward NF analysis shows:


2
2

 Vn2− OpAmp 1 
 1

 1
 
2 1
 Ω1 

1 + R F 

NF = 1 +
2
 R + γ G Total  + 2
 R − G Total   + R F  gm R − 1 

R O 
I
1

O
O

F






n
−
R
O
3 144
 Ω1GM  R S  14442444
444424444443 1442443 
First Term
Third Term
2

Second Term


1
68
Equation 5.5
The first term between the square brackets in Equation 5.5 shows that the negative conductance GTotal
has a direct noise contribution to the output. Its noise contribution is scaled by /
. The
“noise excess factor” γ can be minimized to around 2/3 (i.e. theoretically) by choosing a non-minimum
channel length for the negative conductance transistors. Long-channel transistors are preferred for 1/f
noise. We used 1µm channel length in this design. The second term is the mentioned amplification
factor Equation 5.4 of OpAmp noise including the negative conductance effect (GTotal). It is interesting to
observe that this term reaches zero when the negative conductance reaches GTotal. However, the direct
noise contribution of the negative conductance is much higher than the canceled OpAmp noise
contribution. Hence the total noise figure of the circuit increases. We verified Equation 5.5 by noise
simulations using the OpAmp circuit of Figure 5.5.
The NF is increased from 6 to 7.5 dB given that GM is equal to 20mS. Note that it is also possible to apply
the negative conductance in combination with an LNTA with higher GM and hence lower NF. In that
case, the negative conductance can be lower, as RO>1/GM. However, then IIP3 of the LNTA becomes a
bottleneck.
5.3 Measurement Results
Figure 5.7 shows a photo of the implemented 65nm IC. The active area is < 0.2 mm2 including the clock
circuit. Thick metal was used for RRF for high linearity and low spread.
Figure 5.7: Die Photograph (65nm CMOS, 1.45mm x 1.45mm)
69
The front-end achieves 26 dB gain (BalUn losses are de-embedded) at 1 GHz LO, over 24MHz bandwidth
(BW), 12MHz on either side of LO. To demonstrate distortion cancelling, Figure 5.8(a) shows the
measured in-band IIP3 at 150kHz tone spacing (f1=1004.1MHz and f2=1004.25MHz) vs. M. IIP3 clearly
improves from around +9 dBm to +21 dBm!
Figure 5.8: Measurements: (a) In-band IIP3 vs. the number of parallel Negative Conductance Unit-Cells M (b) IM3 versus
input power for three M settings, with LO=1GHz
The optimum IIP3 of
+21 dBm is located at
M = 32,
which fits
to our
theory
GTotal=1/RO+1/RF=1/1500+1/180=6.22mS so M=6.22mS/0.2mS=31 very well. Figure 5.8(b) shows the IM3
curves versus power for three cases: M=0 (off), M=28 (cancelling of IO, Figure 4.6) and M=32 (overall
optimum IIP3). Up to -22dBm input power (note: this power is high for an in-band signal), IM3 improves.
The rise of distortion for high input powers > -23 dBm is due to the clipping of the OpAmp output stage
to its 1.2V supply. The negative conductance was pushed to instability (i.e. latch-up of OpAmp output
stage). This occurs at M=45 (see Equation 4.8 ∆G=∆Mx0.2mS), safely away from the optimum point by
∆M=45-32=13. This shows a close agreement with our explanation in section 4.4 and with the
simulations in Figure 5.9, which is done for the circuit of Figure 4.13.
Figure 5.9: Latch-up simulation of VOUT, input power of -16 dBm
70
One tone input signal with power of -16 dBm is used. Around this input power, the OpAmp output stage
begins to clip. According to our simulation, the latch-up occurs for ∆M ≥ 14. The same mechanism,
discussed in section 4.1, of this technique also improves IIP2 by more than 10 dB as shown in Figure 5.10.
Figure 5.10: Measurements: IM2 versus input power for three M settings, with LO=1GHz
Table 5.1 compares/summarizes the IIP2 and IIP3 improvement for three M settings 0, 28 en 32. Note
that the optimum linearity point will vary somewhat with Process, Voltage and Temperature (i.e. PVT).
The analysis in this paper gives the relation between the required negative conductance and the
resistance values RO and RF, which can be a basis for designing an automatic PVT correction circuit.
Table 5.1: IIP2 and IIP3 improvement
71
Figure 5.11 provides IIP3 curves versus the frequency offset Δf, with fixed 3.95MHz in-band IM3 position.
The negative conductance clearly increases the IIP3 both in- and out-of-band (all-Band) with a worst case
IIP3 >+10 dBm.
Figure 5.11: 2-tone IIP3 measured at IM3=3.95MHz versus tone spacing Δf, with LO=1GHz
The reason behind less linearity improvement in the transition band can be understood considering the
equivalent circuit earlier derived for stability analysis in Figure 4.12. The negative conductance cancels
only the loading of RO and RF. However, gm(s), CF and CT introduce frequency dependences.
Consequently, the “loading effect” on the VGND node (see Figure 4.5) becomes frequency dependent
and will introduce a phase shift compared with the (frequency independent) current generated by the
negative conductance. This results in imperfect cancellation, i.e. less linearity improvement at high
frequencies. This may be improved in the future by designing the negative conductance to be frequency
dependent as well. Up to 10MHz, in-band IIP3 is >+20dBm, i.e. >10dB improvement thanks to the
negative conductance. Then the IIP3 declines from 12MHz to 135MHz, on the one hand because the OTA
gain and hence its linearity degrades, but on the other hand also because the benefit from cancellation
drops (the top line in Figure 5.11 drops faster, versus Δf, than the bottom line). Note that the out-ofband IIP3 at Δf > 450 MHz is again high, +18 dBm. This is because at high Δf (i.e. spacing between the
carriers) the carriers are filtered due to the low pass filtering by CF, RF and CO, hence less IM3 products. In
this region the negative conductance doesn’t result in any benefit anymore.
72
Figure 5.12: Compression point
The compression point (CP) is around -13 dBm (hardly affected by M as shown in Figure 5.12). Due to
the virtual ground, S11 is hardly affected by the negative conductance and Figure 5.13(a) shows that
S11 < -25dB. Noise is more worrisome, but depending on the application some degradation may be
acceptable, provided that the overall SFDR still improves (i.e. IIP3 in dBm should improve more than NF
in dB degrades). Figure 5.13(b) shows that NF increases from 6.2 dB at M=0 to 7.5 dB at M=32. This
result is close to the NF prediction in the previous section. The 1/f corner was around 2MHz.
Figure 5.13: Measurements (a) S11 (b) Noise Figure, with LO=1GHz
The current consumption without the negative conductance at 1 GHz LO is 18 mA (including 8mA of
clock circuitry (i.e. on-chip drivers and divider)), and 1.6 mA more for M=32. The clock divider frequency
range (i.e. also the receiving RF frequency) is 0.2-2.6 GHz, where it consumes 2.8-19 mA. The maximum
Gate-Source voltage of the mixer switches is equal to the 1.2V supply. The LO leakage to the RF port is
less than -75 dBm. The optimum IIP3 has been measured for 5 samples. The optimum in-band IIP3 varies
±1 dB around +21 dBm and the corresponding M varies ±2 around M=32.
73
5.4 Benchmarking
Equation 5.2 benchmarks this work to other state-of-the-art receivers with high linearity and/or SFDR.
Our front-end is more linear than [[28],[30]] where active RF blocks are present. Even compared to the
mixer-first designs [[31],[32]] we achieve better in-band IIP3 while our SFDR in 1MHz of 85dB is the
highest.
Table 5.2: Summary of measurement results and comparison to other state-of-the-art receivers
Linearization
Technique
Matching
Mixer type
Baseband-stage
CMOS Techn.
Active Area
RF Frequency
Gain
In-band BW[1]
NF
In-band IIP3
SFDR @ 1MHz
bandwidth
Wide-Band IIP3
@2-tone Δf
Supply Voltage
Power
Consumption
This work
Negative GO
Ru [28]
Partial cancel
Noise/Distortion
Murphy [29]
Cancel Noise
Youssef [30]
Freq. Translated
Active feedback
Soer [31]
Feedback +
N-path filter
Andrews [32]
Feedback +
N-path filter
Switch-R
Switch-R
TIA + RC
65nm
< 0.2
0.2-2.6
26.5
24
7.5
Common-gate
Switch-I
TIA+RC
65nm
<1
0.4-0.9
34
24
4
+3.5
Switch-R
Switch-R&I
TIA + RC
40nm
1.2
0.08-2.7
70
4
2
-22
R
Gm + Switched-I
Inverter-RC
65nm
< 0.06
1.0-2.5
30
5
7.25-8.9
-20
Switch-RC
Voltage Amp
65nm
< 0.13
0.2-2.0
19
50
6.5
+11
via TIA
Switch-RC
TIA+RC
65nm
0.75
0.1-2.4
40-70
1.6
4
-67
mm2
GHz
dB
MHz
dB
dBm
75
60
57
79
29
dB
+18 @ Δf>800
+13.5
@Δf>40
1.3
15.6
> +12
@ Δf>60
1.2
62
Not
measured
1.2
60
+25
@ Δf>50
1.2 / 2.5
< 70[2]
dBm
@ MHz
V
mW
> +20
85
≥+18 @ >450
>+10 @ All Δf
1.2
13.9
1.2
39.6
[1] In-band BW is twice the zero-IF bandwidth around the LO frequency
units
[2] Includes the clock circuitry
5.5 Conclusions
Due to the strong relationship between linearity and voltage swing, it is challenging to improve linearity
in advanced CMOS technologies with low supply voltages. Architectures with RF V-I conversion followed
by a passive mixers and an OTA-RC Transimpedance Amplifier perform relatively well. In such
architectures, the OpAmp can become the bottleneck, especially for wide channel bandwidth, where the
amount of loop gain available for negative feedback is limited. Still high linearity is wanted, not only outof-band but also in-band, as RF-filtering often is ineffective for close-in interferers. The measurements in
this chapter of our receiver proves that virtual ground imperfections due to OTA nonlinearity lead to
distortion currents, which can be cancelled exploiting a negative conductance in parallel to the virtual
ground node. Although the technique results in slightly degraded noise figure from 6 to 7.5dB the inband IIP3 (and IIP2) is improved by much more (>10dB), resulting in-band SFDR=85dB in 1MHz
bandwidth.
74
Chapter 6. Conclusions and Recommendations
In this chapter, the contents and key conclusions of this thesis are summarized. Also, original
contributions are mentioned and recommendations for future work are given.
75
6.1 Summary and Conclusions
Wireless communication experiences an enormous growth, while there are hardly any new frequency
bands left for dedicated use by new services and applications. Moreover, the traditional static frequency
planning which assigns each application to a specific frequency band is inefficient, as it leaves Radio
Frequency (RF) spectrum locally and temporarily unused, as discussed in chapter 1. Although cellular
network bands are used intensively in most parts of the world, this is not true for many other frequency
bands including the Digital TV broadcasting (DTV) spectrum band. To improve the spectral utilization
efficiency, Dynamic Spectrum Access (DSA) can help. New unlicensed services can be defined as
secondary users that dynamically and opportunistically exploit bands/channels that are locally or
temporarily not used by the licensed primary users. A Software Defined Radio (SDR) that is aware of its
frequency spectrum, i.e. a Cognitive Radio (CR), can be a good candidate to implement the DSA concept.
The DTV spectrum is a well-organized channelized RF system and the chosen frequency spectrum
environment of the thesis.
The DTV interferers will often lead to distortion in practical receivers with a limited degree of up-front
filtering and linearity. Those distortion levels may limit the frequency spectral utilization efficiency that
the CR concept requires to solve via DSA. In traditional narrowband RF receivers, out of band strong
interferers are greatly suppressed by a Surface Acoustic Wave (SAW) RF band filter after the antenna.
This will greatly reduce the distortion level of the received signal at the Analog-to-Digital Convertor
(ADC) input, i.e. the required out of band linearity of the receiver will be also reduced. The SAW RF filter
with a fixed center frequency does not help to immune the CR receiver from the DTV interferers that
actually exists in-band, hence the in-band linearity becomes a critical specification for CR receiver. The
ultimate solution is a flexible and reconfigurable RF channel filter with high rejection (i.e. very high order
filtering) of the interferers from the adjacent channel(s), note that guard channel(s) are not desired to
maximize the spectral utilization efficiency. Such RF channel filters are very difficult to be implemented,
especially on-chip. As a consequence of the poor rejection performance of RF channel filter, the in-band
linearity of the receiver must be increased to tolerate the received DTV interferers that actually exists inband.
This thesis aims to mitigate the linearity requirements challenges by benefiting from the presence of
spectrum sensing device, which is assumed to be on board. The main research questions are as follows:
76
How to analyze the distortion level (i.e. linearity requirement) across the unoccupied DTV
band for Dynamic Spectrum Access CR radio receiver?
Due to the existence of in-band strong DTV interferers and the nonlinearity of a radio receiver that is
modelled by a Taylor memory-less model (focusing on the dominant 3rd order nonlinear term), different
types of distortion products are generated, namely intermodulation (IM3), cross-modulation (XM3) and
self-interference products. This point is analyzed in chapter 2, where the following two important
conclusions are drawn:
•
The level and spectral location of the intermodulation distortion products depends on the level
and spectral location of DTV signals. Given statistics of DTV signal scenarios lead to a certain
probability of existence of a “white spot” with no intermodulation products.
•
Although intermodulation products are (by definition) absent in a white spot, the CR receiver is
any always still limited by cross-modulation and self-interference products.
Therefore, true distortion free white spots do not exist if DTV signals are present after the wideband
Band Pass RF Filter. However, cross-modulation and self-interference distortion products are typically
much weaker than intermodulation products. Thus it makes sense to monitor the level and spectral
location of interferers by spectrum sensing and classifying the white spots into two types, assuming only
third order distortion products:
•
“IM3-spots”
•
“IM3-free spots”
The derived equations of chapter 2 quantify how much the linearity requirements of 3rd order Input
Intercept Point (IIP3) are relaxed when the CR operates at an IM3-free spot. For example: a scenario with
three interferers, each has -10 dBm power and a CR signal that has -60dBm power. The calculated
linearity requirements at IM3-free spots is IIP3XM3=4dBm. While the linearity requirements at IM3-spots
where the receiver is majorly distorted by intermodulation, is IIP3IM3 =18-25 dBm. The analysis is verified
by measurements. The analysis of chapter 2 is extended to not only take narrowband interferers (e.g.
narrowband complex modulated carriers) into account but also wideband Orthogonal Frequency
Division Multiplexing (OFDM) interferers by adding a correction factor (i.e. ∆Wideband).
Reviewing the literature before this research started, the in-band linearity of a Complementary Metal
Oxide Semiconductor (CMOS) radio receiver is typically not much more than 0dBm. As this is by far not
77
enough to keep distortion below the noise floor, relaxing IIP3 requirements is very useful, e.g. by
predicting where IM3-free spots will occur.
How to predict the distortion level in Dynamic Spectrum Access, given Spectrum Sensing
data?
Chapter 3 targets a Distortion Prediction Algorithm (DPrA) based on Spectrum Sensing data. The DPrA
calculates the level and the spectral locations of the distortion products per each white spot.
Theoretically this requires a long and complex multiplications in time domain with complex envelop
functions of the wideband OFDM signals. The following three steps are done to develop the DPrA in its
simple processing form:
1. By using the correction factor (i.e ∆Wideband), the wideband signals are replaced by tones, where
only two information are required about the signals, namely frequency and amplitude.
2. By replacing the multiplications in time domain with convolutions in the frequency domain.
3. By implementing the convolutions via matrix multiplication, where the position and the value of
each element of the matrix corresponds to the spectral location and the amplitude of the tones
that composite the input signals to the nonlinear receiver.
The DPrA output is substituted in the equations of chapter 2 to derive the linearity requirements across
the white spots. Accordingly, the CR receiver is now able to select the appropriate white spot(s), which
have linearity requirements below the linearity capability of the CR receiver hardware. Due to the simple
matrix multiplication of the DPrA, it can be implemented in the Digital Signal Processing (DSP) section of
a receiver, so that instantaneous prediction can probably easily be provided after every spectrum
sensing operation. Moreover, DPrA can be easily extended to be applied for higher order nonlinear
terms (4th, 5th ... etc.).
Although, the DPrA allows the CR receiver to select the spots where a not so high linearity capability is
required, however this will limit the total utilization of the white spots. By increasing the CR receiver
linearity performance, more white spots can be accessed and still achieving sufficient signal to distortion
level, even the near/adjacent channels (e.g. IIP3IM3=25dBm is required in the adjacent channels of three
interferers, each has -10dBm) to the interferers.
78
How to increase the linearity of CR receiver hardware, given less up-front filtering?
In chapter 4, it is shown that a CMOS radio receivers that exploit linear Voltage-to-Current (V-I)
conversion at RF, followed by passive down-mixing and an OpAmp-based Transimpedance Amplifier at
baseband shows high linearity potential. Due to nonlinearity and finite gain in the OpAmp, virtual
ground is imperfect, inducing distortion currents. The concept of a negative conductance is proposed in
chapter 4 to cancel such distortion currents. Through a simple intuitive analysis, the basic operation of
the technique is explained. By mathematical analysis the optimum negative conductance value is
derived and related to feedback theory. It is shown that a finite value of negative conductance is needed
to make the feedback loopgain theoretically approach infinity, which is not possible by increasing the
gain of the OpAmp block. Furthermore, stability concerns are analyzed, considering both potential
(small-signal) oscillatory behavior and (large-signal) latch-up. From the small signal behavior perspective,
the system is stable. However, for strong negative conductance value the OpAmp output stage cannot
sink the negative conductance current and latch-up can occur. Fortunately, this latch-up condition
happens at far away from the optimum negative conductance value, as quantified in chapter 4. This
point can be improved by carefully designing the output stage of the OpAmp. Another relevant
important point is that the optimum linearity point will vary somewhat with Process, Voltage and
Temperature. Hence an automatic PVT correction circuit is important to circumvent the latch-up state.
Our analysis about the optimum negative conductance value gives a basis for such circuit design.
The technique is applied to linearize an RF receiver. Chapter 5 presents a prototype that is implemented
in 65 nm technology. Measurement results show an increase of in-band IIP3 from 9dBm to >20dBm, and
IIP2 from 51 to 61dBm, at the cost of increasing the Noise Figure (NF) from 6 to 7.5dB and <10% power
penalty. The NF analysis and simulation shows that the OpAmp thermal noise contribution is totally
cancelled at the optimum negative conductance value, where the OpAmp linearity limitation is also
totally cancelled. However the negative conductance contributes now noise. In- and out-of-band (i.e. allband) linearity is also analyzed and measured, showed best performance in-band and far out-of-band. In
the transition band, linearity improvement is degraded due to phase shifts between the frequency
dependent distortion currents generated by the OpAmp versus the frequency-independent current
generated by the negative conductance. In summary, the chip achieves for in-band, in 1MHz bandwidth,
a Spurious-Free Dynamic Range (SFDR) of 85dB at <27mA up to 2GHz for 1.2V supply voltage.
79
6.2 Original Contributions
The research in this thesis contains the following original contributions:
•
The analysis of the in-band linearity requirements (IIP3) for a wideband Cognitive Radio,
considering the wideband multi-carrier property of OFDM signal; (Chapter 2 and [18])
•
The classification of white spots in a channelized DTV band into IM3 spots and IM3-free spots, for
which the linearity requirement for a CR receiver is relaxed; (Chapter 2 and [18])
•
The development and the application of Distortion Prediction Algorithm (DPrA) to calculate the
3rd order nonlinear distortion products across the white spots, by using the spectrum sensing
information. Then the translation of DPrA outcome to evaluate the linearity requirement across
the white spots; (Chapter 3)
•
The design of a highly linear receiver, with record in-band IIP3 > +21dBm, by canceling the
induced distortion current via a negative conductance at the virtual ground node of the
baseband Trans Impedance Amplifier; (Chapter 4 and 5 and [35]and [41]).
6.3 Recommendations for Future Work
The ultimate hardware implementation for CR is Software Radio, where a fast high-resolution ADC with
low power consumption and high dynamic range is required. Tunable RF channel filters with a high
quality factor help to lower the dynamic range of the ADC. Till the time that those solutions will be
reached, it is reasonable to focus on SDR receiver imperfections and mitigating them via the data given
by the spectrum sensing device that is assumed to be on board. While the spectrum sensing provides
information about the level and frequency spectral location, the cross modulation effect of a blocker
inside the SDR receiver that is presented in chapter 2 may
also provide information about the instantaneous amplitude
level of the blockers. The analyses of Chapter 2 (i.e. paper
published in [18]) did not address the cross modulation
effect of a blocker on the CR signal constellations.
Traditionally it is known that as the noise power increases,
the “clouds” around the constellations points extend
Figure 6.1: Blocker cross modulation inside the
beyond the decision boundary, thereby causing errors in the
CR received channel
received CR signal. Referring to the equations in chapter 2, the intermodulation products have the same
80
effect on the constellation points as the noise. However, that is not true for the cross modulation
products. Let’s assume a blocker with less up-front filtering is received in addition to the desired CR
signal as shown in Figure 6.1. Then as mathematically is represented in chapter 2, the RF band filter
output signal, which is the input signal to the nonlinear receiver front-end, can be written as follows:
{
sin = Re 2 sCR (t) e jωCR t + 2 sBlocker(t) e jωBlockert
}
Equation 6.1
Whereas the output signal of the nonlinear receiver at the CR channel frequency is written as follows:
sout (t) CR Channel = k1 sin (t) + k 3 sin (t)3
Equation 6.2




2  jωCR t 
= Re
2k1 sCR (t) + 3 2 k 3 sCR (t) s Blocker(t)  e

142
4 43
4
444
4244444
3
Desired amplified CR 14

Cross modulation product 


While Equation 6.2 is already represented in chapter 2 (i.e. Equation 2.5), Equation 6.2 is now written in
its instantaneous form for one blocker. Observing the cross modulation product, it can be seen that the
instantaneous CR signal (i.e. sCR(t)) is distorted with the
instantaneous square amplitude of the blocker signal. This reveals
that for example if the CR signal uses QPSK digital modulation, then
the cross modulation will just affect the amplitude of CR signal by
moving the CR constellation points towards the original on a
diagonal path as shown in Figure 6.2. Measurement verifies this
observation. Therefore the CR receiver may instantaneously track
and subtract the blocker(s) amplitude variations from its received
Figure 6.2: QPSK CR signal
signal by the mean of time domain filtering.
Other recommendation points are related to the linearization technique presented in chapter 4 and 5:
•
The receiver linearity is degraded in the transition band (i.e. the band between in and out of
band in Figure 5.11) due to phase shifts between the frequency dependent distortion currents
generated by the OpAmp versus the frequency-independent current generated by the negative
conductance. This may be improved by designing the negative conductance to be frequency
dependent as well by applying negative capacitance.
•
The receiver noise is high. This may be improved by investigating the possibility of applying the
noise cancelling technique.
81
82
Appendix A.
Digital TV broadcasting (DTV)
Most of the countries in the world has already shifted towards the Digital TV and leaving the classical
analog TV due to the efficient use of spectrum and provision of more capacity than analog, better
quality images, and lower operating costs for broadcast and transmission.
Frequency bandwidth: The DTV is implemented in different ways around the world, as example:
•
The EU has 7-8MHz bandwidth with Orthogonal Frequency Division Multiplexing (OFDM)
modulation. It follows the Digital Video Broadcasting Terrestrial (DVB_T) open standard. DVB_T
offers three different modulation schemes (QPSK, 16QAM, and 64QAM), using 1705 or 6817
carriers (2k or 8k mode, respectively). The difference between the sub-channels is 4.46kHz.
•
The USA has 6MHz bandwidth with 8-level vestigial sideband (8-VSB) modulation. This
modulation is outside the scope of this book.
Frequency range: In USA, the FCC allocated three bands of frequencies in the radio spectrum, chopped
into 6-MHz slices, to accommodate the following TV channels:
•
VHF band: 54-88 MHz for Channels 2-6 and 174-216 MHz for Channels 7-13
•
UHF band: 470-890 MHz for Channels 14-83
Each country in Europe has its own allocation of the channels across the DTV frequency spectrum. A
typical frequency range for west European countries is listed as follows:
•
VHF band: 41-82 MHz and 175-224 MHz
•
UHF band: 471-951 MHz
Statistical Distribution reported in [42]: Major cities have many occupied TV-channels, including some
with high power levels. As example: in New York, simulated TV-signals reach levels around -15 dBm,
while the strongest measured signal is at -20 dBm. In Chicago, measurements and simulations show
several channels above -10 dBm, with the highest measured power at 0 dBm. At the other extreme,
measurements in the West-Virginia National Radio Astronomy Observatory (NRAO) radio-quiet zone
show a very low occupancy, and only a single channel with a power above -80 dBm.
83
Appendix B.
Wideband Correction Factor (∆Wideband) Effect on CR
Linearity Requirement
Equation 2.6 can be rewritten for the cross-modulation products as follows:
+
PXM3 = PXM3 + ∆ Wideband [dBm]
Converting it to the linear range gives:
+
p XM3 = p XM3 ×10
∆ Wideband
10
[W]
The shape of this distortion looks like a Bell and covers three spots. However we are just interested in
the amount of it in the middle spot, which contains 66% of the total distortion power:
+
XM3
p
∆Wideband
10
spot17
= pXM3×10
×0.66 [W]
Rewriting it according to its RMS values and substituting the cross-modulation product of Equation 2.5 in
it gives:
AXM3+ = AXM3×
∆Wideband
10 10
∆
Wideband


2
× 0.66 = 3k3ACR ∑ ATVn  × 10 10 × 0.66
 n=1,6,19



where AXM3+ and AXM3 represent the RMS value of the cross-modulation products of two wideband
signals and two tones, respectively. The next step is substituting it in the Signal to Distortion Ratio,
which gives:
S
=
D 
 3k A 
 3 CR 

(k 1A CR )2
∆ Wideband

2

10

A
×
10
×
0.66
∑
TV n 

n =1,6,19


2
Then the linearity requirements can be rewritten as follows:
k1
k3
= 3 × 10
spot 17
∆ Wideband
10
× 0.66 ×
S
2
A TV n
∑
D n =1,6,19
84
Appendix C.
DPrA Maple Program Implementation
Begin
> restart;
> with(linalg): with(ListTools): with(VectorCalculus): with(plots):
> alpha:=[k[1],k[2],k[3]]:
Forming Vector Sin
SCRn:=sqrt(2)*ACR/2: SCRp:=sqrt(2)*ACR/2: # Cognitive Radio signal
> STV1n:=S1*A[-1]: STV1p:=S1*A[+1]: S1:=0: # Channel 1
> STV2n:=S2*A[-2]: STV2p:=S2*A[+2]: S2:=1: # Channel 2
> STV3n:=S3*A[-3]: STV3p:=S3*A[+3]: S3:=0: # Channel 3
> STV4n:=S4*A[-4]: STV4p:=S4*A[+4]: S4:=0: # Channel 4
> STV5n:=S5*A[-5]: STV5p:=S5*A[+5]: S5:=0: # Channel 5
> STV6n:=S6*A[-6]: STV6p:=S6*A[+6]: S6:=1: # Channel 6
> STV7n:=S7*A[-7]: STV7p:=S7*A[+7]: S7:=0: # Channel 7
> STV8n:=S8*A[-8]: STV8p:=S8*A[+8]: S8:=0: # Channel 8
> STV9n:=S9*A[-9]: STV9p:=S9*A[+9]: S9:=0: # Channel 9
> STV10n:=S10*A[-10]: STV10p:=S10*A[+10]: S10:=0: # Channel 10
> STV11n:=S11*A[-11]: STV11p:=S11*A[+11]: S11:=0: # Channel 11
> STV12n:=S12*A[-12]: STV12p:=S12*A[+12]: S12:=0: # Channel 12
> STV13n:=S13*A[-13]: STV13p:=S13*A[+13]: S13:=1: # Channel 13
> STV14n:=S14*A[-14]: STV14p:=S14*A[+14]: S14:=0: # Channel 14
> STV15n:=S15*A[-15]: STV15p:=S15*A[+15]: S15:=0: # Channel 15
> STV16n:=S16*A[-16]: STV16p:=S16*A[+16]: S16:=0: # Channel 16
> STV17n:=S17*A[-17]: STV17p:=S17*A[+17]: S17:=0: # Channel 17
> STV18n:=S18*A[-18]: STV18p:=S18*A[+18]: S18:=0: # Channel 18
> STV20n:=S20*A[-20]: STV20p:=S20*A[+20]: S20:=1: # Channel 20
> NZbegin:=15: # Number of zeroes added at the begin of the vector
> NZend:=1: # Number of zeroes added at the end of the vector
> input:=vector(1,[0]):
> for i from 1 to NZend-1 do input:=augment(input,[0]): od:
> input:=augment(input,[STV20n]): # Adding Channel -20
> input:=augment(input,[STV19n]): # Adding Channel -19
> input:=augment(input,[STV18n]): # Adding Channel -18
> input:=augment(input,[STV17n]): # Adding Channel -17
> input:=augment(input,[STV16n]): # Adding Channel -16
> input:=augment(input,[STV15n]): # Adding Channel -15
> input:=augment(input,[STV14n]): # Adding Channel -14
> input:=augment(input,[STV13n]): # Adding Channel -13
> input:=augment(input,[STV12n]): # Adding Channel -12
> input:=augment(input,[STV11n]): # Adding Channel -11
> input:=augment(input,[STV10n]): # Adding Channel -10
> input:=augment(input,[STV9n]): # Adding Channel -9
> input:=augment(input,[STV8n]): # Adding Channel -8
> input:=augment(input,[STV7n]): # Adding Channel -7
> input:=augment(input,[STV6n]): # Adding Channel -6
> input:=augment(input,[STV5n]): # Adding Channel -5
> input:=augment(input,[STV4n]): # Adding Channel -4
> input:=augment(input,[STV3n]): # Adding Channel -3
> input:=augment(input,[STV2n]): # Adding Channel -2
> input:=augment(input,[STV1n]): # Adding Channel -1
> for i from 1 to NZbegin do input:=augment(input,[0]): od:
> input:=augment(input,[0]):
> for i from 1 to NZbegin do input:=augment(input,[0]): od:
> input:=augment(input,[STV1p]): # Adding Channel +1
> input:=augment(input,[STV2p]): # Adding Channel +2
85
> input:=augment(input,[STV3p]): # Adding Channel +3
> input:=augment(input,[STV4p]): # Adding Channel +4
> input:=augment(input,[STV5p]): # Adding Channel +5
> input:=augment(input,[STV6p]): # Adding Channel +6
> input:=augment(input,[STV7p]): # Adding Channel +7
> input:=augment(input,[STV8p]): # Adding Channel +8
> input:=augment(input,[STV9p]): # Adding Channel +9
> input:=augment(input,[STV10p]): # Adding Channel +10
> input:=augment(input,[STV11p]): # Adding Channel +11
> input:=augment(input,[STV12p]): # Adding Channel +12
> input:=augment(input,[STV13p]): # Adding Channel +13
> input:=augment(input,[STV14p]): # Adding Channel +14
> input:=augment(input,[STV15p]): # Adding Channel +15
> input:=augment(input,[STV16p]): # Adding Channel +16
> input:=augment(input,[STV17p]): # Adding Channel +17
> input:=augment(input,[STV18p]): # Adding Channel +18
> input:=augment(input,[STV19p]): # Adding Channel +19
> input:=augment(input,[STV20p]): # Adding Channel +20
> for i from 1 to NZend do input:=augment(input,[0]): od:
> input:=convert(input,vector): # Sin vector or A vector
> N:=vectdim(input): # Sin vedctor dimension is [ 1 x N ]
First convolution implementation
> C1:=2*N-1: # SQ vector dimension is [ 1 x (2*N-1) ]
> M1:=transpose(convert(input,matrix)):
> for i from 1 to (2*N-1)-N do M1:=augment(M1,[0]); od:
> MM:=transpose(M1):
> v:=convert(M1,vector):
> v:=convert(v,list):
> for m from 1 to N-1 do vv:=Rotate(v,-1*m); vv:=convert(vv,vector): MM:=augment(MM,vv): od:
> M1:=transpose(MM):
> firstconv:=evalm(input&*M1): # SQ vector
Second convolution implementation
> C2:=3*N-2: # The distortion vector dimension is [ 1 x (3*N-2) ]
> M2:=transpose(convert(input,matrix)):
> for j from 1 to (3*N-2)-N do M2:=augment(M2,[0]); od:
> MM:=transpose(M2):
> v:=convert(M2,vector):
> v:=convert(v,list):
> for m from 1 to (2*N-1)-1 do vv:=Rotate(v,-1*m): vv:=convert(vv,vector): MM:=augment(MM,vv): od:
> M2:=transpose(MM):
> Outputt:=evalm(alpha[3]*firstconv&*M2):
> Output:=vector(vectdim(Outputt)):
> for n from 1 to vectdim(Outputt)do Output[n]:=expand(Outputt[n]): od:
> for m from 1 to vectdim(Output) do C[m-round(vectdim(Output)/2)]:=evalm(Output[m]): od:
Viewing the Distortion Products
> for Cn from -(NZbegin+20) to -(NZbegin+1) do Channel[Cn+NZbegin]:=evalm(C[Cn]): od:
> for Cp from NZbegin+1 to NZbegin+20 do Channel[Cp-NZbegin]:=evalm(C[Cp]): od:
> for CH from NZbegin+1 to NZbegin+20 do Channel[CH-NZbegin]:=evalm(C[CH]): Channel[-H+NZbegin]:=evalm(C[-CH]): od:
> A[-2]:=sqrt(2)/2*ATV[2]: A[+2]:=sqrt(2)/2*ATV[2]:
> A[-6]:=sqrt(2)/2*ATV[6]: A[+6]:=sqrt(2)/2*ATV[6]:
> A[-13]:=sqrt(2)/2*ATV[13]: A[+13]:=sqrt(2)/2*ATV[13]:
> A[-20]:=sqrt(2)/2*ATV[20]: A[+20]:=sqrt(2)/2*ATV[20]:
> for CH from NZbegin+1 to NZbegin+20 do Channel[CH-NZbegin]:=evalm(2*C[CH]): od:
> ATV[2]:=ATV: ATV[6]:=ATV: ATV[13]:=ATV: ATV[20]:=ATV:
> for CH from NZbegin+1 to NZbegin+20 do Channel[CH-NZbegin]:=evalm(2*C[CH]): od:
86
Appendix D.
Nonlinear Transimpedance Amplifier Analysis
In this section, a 3rd order Taylor approximation of VOUT versus IS (i.e. VOUT=VOUT(IS,IS3)) of the
transimpedance amplifier shown in Figure C will be derived. The following procedure will be applied:
j.
VOUT is derived as a function of VVGND, VVGND3 and VOUT3
VOUT=VOUT (VVGND,VVGND3,VOUT3).
k. The resulting relationship is rewritten as a function of VVGND and VVGND3, by using the definition of
the 3rd order Taylor coefficients
VOUT=VOUT(VVGND,VVGND3).
l. The inverse function, VVGND as a function of VOUT and VOUT3, is written as a 3rd order Taylor
function by using the procedure explained in [40]
m. IS is rewritten as a function of VVGND and VOUT
VVGND=VVGND (VOUT,VOUT3).
IS=IS(VVGND,VOUT).
n. Substituting VVGND of step 3 in IS of step 4 makes IS to be a function of VOUT and VOUT3
IS=IS(VOUT,VOUT3).
o. Finally, by repeating the procedure explained in [40], the function of step 5 is inversed to obtain
VO as a function of IS and IS3
VOUT=VOUT (IS, IS3).
Figure D: Baseband model with RO and the extended RF for nonlinearity derivations (redrawn Figure 4.9)
87
VOUT=VOUT (VVGND,VVGND3,VOUT3): We begin the derivation by expressing the feedback current IF at
Step 1
the VGND node and the OUT node (see Figure D) as follows:
At VGND node: IF =
VVGND
+ GF−VGNDVOUT
RF−VGND
At OUT node: IF = −
VOUT
− GF−OUTVVGND
RF−OUT
Equation D.0
Equation D.1
Referring to the OpAmp nonlinear model, we equate IF in Equation 4.1 to IF in Equation D.1 as follows:
gm1VVGND + gm3 VVGND + go1VOUT + go3 VOUT = −
3
3
VOUT
− G F−OUTVOUT
R F−OUT
VOUT = −
(gm1 + G F−OUT ) V
Step 2
VOUT=VOUT(VVGND,VVGND3): VOUT is defined as: VOUT=β1VVGND +β2VVGND2 +β3VVGND3, which is a 3rd

1 
 go1 +

R
F
−
OUT
144
42444
3
a
VGND
gm3
−
VVGND −
3

1 
 go1 +

R
F
−
OUT
144
42444
3
b
go3
3

1 
 go1 +

R
F
OUT
−
144
42444
3
c
VOUT
order Taylor approximation around VVGND=0, where β1, β2 and β3 are the Taylor coefficients:
β n =1,2,3 =
1  ∂ n VOUT 
n!  ∂ VVGND n 
VVGND =0
To derive β1, we differentiate Equation D.2 with respect to VVGND as follows:
∂ VOUT
∂ VVGND
= a + 3bVVGND + 3cVOUT
 ∂ VOUT
∴β1 = 
 ∂ VVGND
2
2
∂ VOUT
∂ VVGND
∂ VOUT
a + 3bVVGND
⇒
=
2
∂ VVGND
1 − 3cVOUT
2

(gm1 + G F−OUT )

=
a
=
−


1 
 VVGND=0
 go1 +

R F−OUT 

The same procedure is used to derive β2 and β3:
1  ∂ 2 VOUT 

β 2 = 
=0
2  ∂ VVGND 2 
VVGND = 0
and
1  ∂ 3 VOUT 

β 3 = 
= b + a3 c
6  ∂ VVGND 3 
VVGND = 0
88
Equation D.2
(
)
VOUT = {
a VVGND + b + a 3 c VVGND
1
424
3
β
1
3
Equation D.3
β3
VVGND=VVGND (VOUT, VOUT3): We write the inverse of Equation D.3 in the Taylor series form: VVGND
Step 3
=α1VOUT+ α2VOUT2 +α3VOUT3. Deriving α1, α2 and α3 can be done by the procedure below.
First, let’s substitute Equation D.3 into its abovementioned inversed form as follows:
(
VVGND = α 1 β 1 VVGND + β 3 VVGND
3
)+ α (β V
2
1
VGND
+ β 3 VVGND
)
3 2
(
+ α 3 β 1 VVGND + β 3 VVGND
)
3 3
By equating the right to the left side of the equation above [40], the coefficients α1, α2 and α3 are
derived:
(
)
1
b + a3 c
3
VVGND = VOUT −
VOUT
4
a
a 43
{
142
α1
Step 4
Equation D.4
α3
IS=IS(VVGND,VOUT): Referring to IS in Figure D, we substitute the IF Equation D.0 at the VGND node
in the following equation:
 1

1
VVGND + G F− VGND VOUT
IS = I O + I F = 
+
 R O R F − VGND 
Equation D.5
IS=IS(VOUT,VOUT3): By substituting Equation D.4 into Equation D.5, the following equation is
Step 5
obtained:
(
1  1


1
b + a3 c


IS =  
+
 + G F− VGND  VOUT − a 4
 a  R O R F−VGND 

Step 6
VOUT =
) 

1
1
 VOUT 3
R + R
F − VGND 
 O
Equation D.6
VOUT=VOUT (IS, IS3): Finally, by inversing Equation D.6, the following expression is obtained:
 1
1
NL 3 
+
R
R
F − VGND
 O



1
3
IS +
IS
4
1  1


1
1  1


1
 + G F− VGND 
+

 + G F− VGND 
 
+

R O R F− VGND 
R O R F− VGND 
 a4 4

 a4 4
3
1
444
42 4 4 4 4 44
3
1
4 4 4424 4 4 4 4 4
Ω1
Where: NL3 =
Ω3
(b + a c) is related to the nonlinear terms of the OpAmp model.
3
a4
89
Equation D.7
Appendix E.
Latch-Up Analysis
As shown in Figure D, the negative conductance injects current via RF (i.e. VVGNDGLatch-up-Risk) that needs to
be handled by the OpAmp output stage in addition to the main current coming from GM (i.e. IS):
I OpAmp- Latch- up - Risk = IS + VVGNDG Latch − up − Risk
Equation E.0
Hence, the relation between VVGND and IS is the next step in this derivation.
Figure E: Latch-up problem at the OUT node (redrawn Figure 4.13)
In order to simplify the latch-up analysis, let’s a linear OpAmp (i.e gm3=go3=0). Consequently, Equation
D.2 and Equation D.7 can be simplified as follows:
1
VVGND = VOUT
a
Equation E.1
VOUT = Ω1IS
Equation E.2
By combining the previous two equations, the following relation between VVGND and IS is derived:
VVGND =
Ω1
1
IS =
IS
a
 1


1
 + a G F−VGND 
+

R
R
O
F
−
VGND




Equation E.3
After that the negative conductance cancels the loading effect of RO on the VGND node, it injects current
via RF that needs to be handled by the OpAmp output stage (see Figure D and Figure 5.5). Now if the
negative conductance becomes too strong then the potential latch-up becomes a real risk. For the case
of latch-up, Equation E.3 can be further elaborated to obtain the following equation:
90
VVGND =
1



1
− G Latch −up  + a G F−VGND 


 R F−VGND

Equation E.4
IS
Finally, Equation E.4 is substituted in Equation E.0 to obtain the latch-up equation:
IOpAmp-Latch-up-Risk = IS + VVGND G Latch−up−Risk
= IS +
1



1
− G Latch −up−Risk  + a G F−VGND 


 R F−VGND

91
ISG Latch −up−Risk
Equation E.5
92
References
[j]
National Telecommunications and Information Administration (NTIA), available online:
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96
[mj] Dlovan Mahrof, Eric Klumperink, Zhiyu Ru, Mark Oude Alink, Bram Nauta,"Cancellation of
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97
98
List of Publications
Dlovan Mahrof, Eric Klumperink, Zhiyu Ru, Mark Oude Alink, Bram Nauta, "Cancellation of OpAmp
Virtual Ground Imperfections by a Negative Conductance applied to improve RF Receiver Linearity"
IEEE Journal of Solid-State Circuits, May 2014. (Invited paper)
Dlovan Mahrof, Eric Klumperink, Mark Oude Alink, Bram Nauta, "A Receiver with in-band IIP3>20dBm,
exploiting Cancelling of OpAmp Finite-Gain-induced Distortion via Negative Conductance" IEEE Radio
Frequency Integrated Circuits Symposium (RFIC), Seattle, June 2013. (Best Student Paper Award – 1st)
Dlovan Mahrof, Eric Klumperink, Jaap Haartsen, Bram Nauta, "On the Effect of Spectral Location of
Interferers on Linearity Requirements for Wideband Cognitive Radio Receivers" 4th IEEE Symposium of
New Frontiers in Dynamic Spectrum Access Networks (DySPAN), Singapore, April 2010.
99
100
Acknowledgments
In my opinion, the Doctor of Philosophy (Ph D) is not just a work that needs to be done. It
affects/changes your life, your way of thinking to extend that you can never imagine till the point of
writing the thesis. Finding a gap in applied techniques by other researchers is trivial as nothing is perfect.
Being creative and viewing that gap in different ways than the standard way, which is written in books
and papers, is difficult and simple. It is difficult because we are actually biased around the known
knowledge. However it is simple if you just dare to take the first step towards how you think about the
problem in your own way and compare it to the rest. I could never go through this process without the
devoted guidance, patient and kindness from my daily supervisor Eric Klumperink and my promotor
Bram Nauta. Their continue encouragements and support to me and other colleges is really amazing.
Thanks for the technical support from Gerard Wienk and Henk de Vries . They helped me in solving a lot
of issues while I was designing my first chip. They treated me with a lot of patience knowing the
stress/mood around Tap Out and measurements. Thanks to our Management assistant Madam Gerdien
Lammers for all her kind support and notes. Thanks go to my Project partners, Mark Oude Alink, Amir
Ghaffari and Saqib Subhan.
I will never forget the nice talks and discussions with Mustafa, Milad, Shadi, Kasra, Ramen, Michiel,
Harish, Jasper, Erik, Harish, Haifeng, Remko and Johan.
Thanks Zu Ru, you really gave me the chance to learn from your experience in IC design. I really miss our
nice discussions about IC design at the late nights in EL/TN building.
Thanks to the Dutch Technology Foundation STW (i.e. the applied science division of the NWO, and the
Ministry of Economic Affairs Technology Program) for funding this research.
I thank STMicroelectronics for silicon donation and CMP, and of course a special thanks goes to Andreia
Cathelin for her kind advices through the receiver chip design in 65nm ST technology.
Dr. Anna-Johan Annema, Rien van Leeuwen and Dr. Ronan van der Zee brought my first steps into this
wonderful world of electronics at my bachelor study phase. Thanks a lot!!!
Prof. Dr. Frank van Vliet and Mr. Joe Tauritz opened my eyes to see the world in Electric and magnetic
waves and how to control/feel those waves with very basic and principle way. Thanks a lot!!!
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I would like to take this chance to thank Prof. Dr. Miko Elwenspoek for teaching me to go beyond the
equations and inter the real understanding of electrodynamics. His way of teaching inspired all of his
students to love physics and material science.
My special thank goes to Mr. Reint Brink the study advisor of our faculty EWI and Mr. Said ben Ayad the
studentendecaan. They believed in me and guided me throw the whole study/life inside the University
of Twente. Their doors were always open. I can never pay them back for all their kindness and support.
Thanks, Thanks a lot to the University of Twente for giving me the chance in getting the knowledge, the
nice memories inside the classrooms and at the campus with my great ex-roommates in OchtendRust
building (Calslaan 38 – UT Campus), Gerard (& his girlfriend Aank), Pieter, Peter, Paul, Mark, Elco,
Wijnand (& his wife Nicolet), Jeroen, Marikka, Emile, Evo, Bas, Arnne, Johan, Marco, Pietra, Soublex, and
others. Thanks a lot!!!
From Bruco IC Company, I would like to thank Mr. Harry Diepenmaat, Mr. Edwin Veldman, Mr. David
Bradford, Madam Sharon Grunder and Mr. Charles Klaasen for their kind encouragements and support.
My special thank goes to Johan Koopman and Paul Bauis for their kind support in finishing my Ph D in
combination with my current work as RF IC design engineer in a flexible way. Of course, I would like to
thank all my colleges at Bruco IC, Frank, Marco H., Harry, Robert, Alexander, Eisse, Paul K., Paul V.,
Jurjen, Rinus, Hans B., Bram, Ellen, Erwin, Hans H., Jeroen, Jelle, Gerard, Rob, Marco W., Marc, Sander,
Tim, Tanya, Mirthe, Lizan, Wendy, Frans, Mariska, Michel, Marga, Caroline, Faust, Arie and Mathijs.
I would like to express my appreciation to Prof. Dr. Osama Shanaa from MediaTek USA. I learned a lot
from his comments on my RFIC 2013 paper, which have guided me through other aspects to be explored
in my JSSC2014 paper. Thanks a lot!!!
Finally, but foremost, I would like to thank my dear wife Almas for her support throughout the long
working hours and the associated ups and downs. She kept holding my hand in each step through all the
obstacles and made me to feel what is HOME and as you know West or East, HOME is the best. My real
apologies go to my dear son Varto to not be there in the first three years of his life. I can never bring the
days, months, and years back as I cannot bring one minute of the clock back. I hoop that I can teach you
from what I learned but foremost to leave you to enjoy the life as well. Last year, we completed our
family with our daughter flower Zhareen.
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Biography
From left, Eric Klumperink, Bram Nauta and me at the IEEE Radio Frequency Integrated Circuits
Symposium (RFIC), Seattle, June 2013
Dlovan Hoshiar Mahrof was born on December 26, 1973, in Al-Sulaimaniya, Iraq. He received the B.Sc.
degree in power engineering from Baghdad University, Iraq, in 1995. He received the B.Sc. degree and
the M.Sc. degree in electrical engineering from Twente University, The Netherlands, in 2005 and 2008.
From 2008 to 2012, he did his Ph.D. research on “Distortion Mitigation in Cognitive Radio Receivers”
with the IC-Design group of Twente University, headed by Bram Nauta. During the RFIC 2013
Symposium, Seattle, WA, USA, he won the Best Student Paper Award—1st place.
From 2012 until the present, he has been working at Bruco IC Company, The Netherlands, as RFIC
system and circuit design engineer. His research interests include circuit design, and advanced
techniques applied to RF Front-Ends.
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