A DIGITALLY-ASSISTED BLOCKER RESILIENT RF RECEIVER FOR

WIDEBAND SAW-LESS APPLICATIONS

by

Esmail Babakrpur Nalousi

APPROVED BY SUPERVISORY COMMITTEE:

Dr. Won Namgoong, Chair

Dr. Randall E. Lehmann

Dr. Rashaunda M. Henderson

Dr. Murat Torlak

Copyright c© 2018

Esmail Babakrpur Nalousi

All rights reserved

Dedicated to my family

A DIGITALLY-ASSISTED BLOCKER RESILIENT RF RECEIVER FOR

WIDEBAND SAW-LESS APPLICATIONS

by

ESMAIL BABAKRPUR NALOUSI, BS, MS

DISSERTATION

Presented to the Faculty of

The University of Texas at Dallas

in Partial Fulfillment

of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY IN

ELECTRICAL ENGINEERING

THE UNIVERSITY OF TEXAS AT DALLAS

August 2018

ACKNOWLEDGMENTS

During my PhD years, I had the blessing of having great supporters who helped me in

various ways to walk through this challenging journey, particularly as an international student

who came from a different academic and cultural background. First and foremost, I would

like to express my special appreciation to my advisor, Dr. Won Namgoong, for giving me

the opportunity to work with him, sharing his IC design and communication knowledge,

providing me with invaluable insights, and being approachable throughout these years. I

received encouragement and motivation from collaborating with him in the integrated system

design lab and much more in non-academic realms. Also, I would like to thank Dr. Randall

Lehmann, Dr. Rashaunda Henderson and Dr. Murat Torlak for accepting to be committee

members of this work and their helpful suggestions and comments.

My sincere thanks to Dr. Lehmann and Dr. Henderson for giving me access to RF laboratory

facilities. Thanks to my fellow labmates, Muhammad Ahmadi, Pratheep Bondalapati and

Jinkyu Park and also my friends Ali Ahmadi, Reza Lotfian, Mehrdad Heydarzadeh, Navid

Shokouhi, Mohammad Ghaderi, and Javad Birjandtalab for making these years memorable.

I also would like to thank Steve Martindell for his help in CAD setup.

Last but not least, without spiritual support of my parents, Rahim Babakrpur and Hajar

Alizadeh, and also my siblings I could not accomplish this degree. Their continuous love and

support along the way helped me stay focused and motivated.

June 2018

v

A DIGITALLY-ASSISTED BLOCKER RESILIENT RF RECEIVER FOR

WIDEBAND SAW-LESS APPLICATIONS

Esmail Babakrpur Nalousi, PhDThe University of Texas at Dallas, 2018

Supervising Professor: Dr. Won Namgoong, Chair

The demand for integrated wideband surface acoustic wave (SAW)-less receivers that support

various wireless communication bands stipulate stringent linearity requirements. Local oscilla-

tor (LO) harmonic interferers and out-of-band interferers are two significant sources of signal

distortion in wideband SAW-less receivers. Harmonic mixing products and intermodulation

products of these interferers, which can be orders of magnitude stronger than the desired

signal, fold on the desired signal band, resulting in significant distortion. To improve resilience

of such receivers to LO harmonic interferers, a digitally-assisted dual-path receiver with

nonuniform LO phases is proposed which employs an adaptive digital equalizer to suppress

distortion products. An adaptive minimum mean-squared error (MMSE) harmonic rejection

equalizer is developed that minimizes the desired signal distortion in the mean-squared error

sense in the presence of harmonic interferers and the correlated noise between the two paths.

The proposed receiver performs robust harmonic rejection of any LO harmonic including 7th

and 9th using only four uniformly spaced clocks with 25% duty cycle. Although intermodula-

tion products are inherently different in nature from harmonic mixing products, it has been

shown that concurrent suppression of both distortions using one MMSE equalizer is feasible

in the presence of distinct nonlinear receive chains. A mathematical framework is derived

for analyzing signal distortion in the presence of harmonic and out-of-band interferers. This

vi

framework models a K-path SAW-less M-phase receiver, which provides sufficient front-end

observations to cancel the distortion products. The proposed receiver jointly accounts for

distortion products as well as correlated noise of the two paths.

Furthermore, the use of passive mixer-first receiver topology to sense signals at higher LO

harmonics is proposed. The advantages of such a receiver include sensing of multiple bands

concurrently and reduced tuning range requirements in the frequency synthesizer. The

single and joint harmonic matching performance of a zero-IF M-phase mixer-first receiver

is analyzed. It is shown that minimum possible return loss for joint matching occurs when

the geometric mean of input impedances at the highest and lowest sensing bands equals the

antenna impedance. The noise figure when sensing higher order LO harmonics is shown to

result in only modest degradation, with the loss becoming even less with increasing number

of LO phases.

vii

TABLE OF CONTENTS

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Overview of Main Existing Techniques . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Analog Harmonic Rejection Mixer . . . . . . . . . . . . . . . . . . . . 3

1.2.2 Noise Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.3 M-phase Passive Mixer Filtering . . . . . . . . . . . . . . . . . . . . . 5

1.3 Overview of Proposed Techniques . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

CHAPTER 2 A DUAL-PATH 4-PHASE NONUNIFORM WIDEBAND RECEIVERWITH DIGITAL MMSE HARMONIC REJECTION EQUALIZER . . . . . . . . 9

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Proposed Receiver Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 Harmonic Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.2 Frequency Synthesizer Complexity . . . . . . . . . . . . . . . . . . . 16

2.2.3 Noise Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Digital MMSE Equalizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.2 Multiuser Detection Perspective . . . . . . . . . . . . . . . . . . . . . 19

2.3.3 MMSE Equalizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.4 Circuit Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

CHAPTER 3 DIGITAL CANCELLATION OF HARMONIC AND INTERMODULA-TION DISTORTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

viii

3.2 System Model and MMSE digital equalizer . . . . . . . . . . . . . . . . . . . 36

3.2.1 Dual-path 4-phase receiver . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2.2 K-path M-phase receiver . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

CHAPTER 4 MATCHING FOR CONCURRENT HARMONIC SENSING IN ANM-PHASE MIXER-FIRST RECEIVER . . . . . . . . . . . . . . . . . . . . . . . 49

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2 System Model and Perfect Matching . . . . . . . . . . . . . . . . . . . . . . 50

4.2.1 Perfectly Matchable Harmonics . . . . . . . . . . . . . . . . . . . . . 52

4.2.2 Single Harmonic Matching . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3 Approximate Harmonic Matching . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3.1 Input Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.3.2 Minimize Maximum |Γ | of Desired Harmonics . . . . . . . . . . . . . 55

4.3.3 Maximize Suppression of Undesired Harmonics . . . . . . . . . . . . . 58

4.4 Noise Figure of Harmonic Sensing Receiver . . . . . . . . . . . . . . . . . . . 61

CHAPTER 5 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

CURRICULUM VITAE

ix

LIST OF FIGURES

1.1 Global mobile traffic (ExaBytes per month) . . . . . . . . . . . . . . . . . . . . 1

1.2 Mobile subscriptions by technology (billions) . . . . . . . . . . . . . . . . . . . 2

1.3 Principle of analog harmonic rejection mixers; (a) Time domain equivalent ofHRM, (b) Frequency domain equivalent of HRM . . . . . . . . . . . . . . . . . . 4

1.4 Principle of noise cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 M-phase filtering using passive mixers . . . . . . . . . . . . . . . . . . . . . . . 6

2.1 Harmonic mixing in wideband SAW-less receivers . . . . . . . . . . . . . . . . . 10

2.2 a) Conventional 8-phase receiver; b) Proposed dual-path 4-phase nonuniform receiver 13

2.3 a) 8-phase 12.5% clocks b) Two sets of 4-phase 25% nonuniform clocks . . . . . 14

2.4 HRR3 vs phase mismatch for 8-phase and dual-path 4-phase receivers, δa = 0.2%and φ = 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5 ∆CG(m) vs harmonic order for 8-phase and dual-path 4-phase receivers . . . . 15

2.6 Signature vectors of 8-phase analog HRM for a) 3rd and 5th harmonics; b) 7thand 9th harmonics; c) Sensitivity of analog HRM to gain and phase mismatches;d) Proposed MMSE harmonic rejection equalizer in presence of an arbitraryLO harmonic; e) Sensitivity of the proposed MMSE equalizer to mismatches; f)Proposed MMSE harmonic rejection equalizer in presence of two arbitrary LOharmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.7 Proposed receiver topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.8 4-phase LO generation circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.9 Passive mixer receiver front-end, baseband amplifier and low-pass filter (RFswitches are triple well transistors) . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.10 Die photograph; The active area is 1 mm2 . . . . . . . . . . . . . . . . . . . . . 28

2.11 Measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.12 Detailed test bench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.13 Harmonic rejection ratio for different LO phase offsets between primary andsecondary paths (φ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.14 Noise figure versus RF frequency . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.15 Measured (solid lines) and simulation (dashed lines) results a) OBIIP3 versusblocker power at 1 GHz RF frequency; b) Blocker NF at 1 GHz RF Frequency,blocker is 80 MHz away from desired signal; c) Normalized voltage gain at 1 GHzRF frequency versus blocker power at 80 MHz offset away; d) Input return lossversus RF frequency as LO frequency varies from 200MHz to 2.9GHz in finite steps 33

x

3.1 Baseband distortion in SAW-less receivers; a) Intermodulation distortion, b)Harmonic distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 System model of a dual-path SAW-less 4-phase receiver with same LO drives butdifferent RF nonlinearities (NLpl and NLsl) . . . . . . . . . . . . . . . . . . . . 38

3.3 Die micrograph (Active Area is 1mm2) . . . . . . . . . . . . . . . . . . . . . . 46

3.4 Measured out-of-band IIP2 and IIP3 versus frequency offset . . . . . . . . . . . 48

3.5 Measured out-of-band IIP5 improvement versus interferer power . . . . . . . . . 48

4.1 M-phase passive mixer downconversion path . . . . . . . . . . . . . . . . . . . . 51

4.2 LTI model for an M-phase passive mixer at the mth LO harmonic . . . . . . . . 51

4.3 Folding shunt impedance Rsh[m] as a function of LO harmonic order for M =4, 8, 12 and 16 phases when Rsw = 10Ω . . . . . . . . . . . . . . . . . . . . . . . 52

4.4 Input impedance of an 12-phase mixer first receiver at first, third and fifth harmonics 56

4.5 Optimum baseband impedance for minimizing maximum |Γ| when matching firstand third simultaneously . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.6 Geometric impedance mean for minimizing maximum |Γ| when a) 1st is perfectlymatched; RBBopt = 498.7Ω, b) 1st and 3rd are matched; RBBopt = 583Ω, c) 1st, 3rd

and 5th are matched; RBBopt = 797.9Ω, d) 3rd and 5th are matched; RBBopt = 1037.7Ω 59

4.7 NF increment as a function of harmonic order . . . . . . . . . . . . . . . . . . . 62

4.8 Simulated harmonic NF of a 12-phase receiver . . . . . . . . . . . . . . . . . . . 62

xi

LIST OF TABLES

2.1 Comparison table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2 Comparison table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1 Approximate matching using (4.7) for concurrent harmonic sensing. Spectre RFsimulation results are in parentheses. . . . . . . . . . . . . . . . . . . . . . . . . 61

xii

CHAPTER 1

INTRODUCTION

1.1 Motivation

Wireless data has been increasing rapidly in recent years as a result of emerging new

technologies and applications with growing number of customers. The cell phones for

instance, provide live stream HD videos as opposed to their original application where only

voice data was subject to communication. Fig. 1.1 reports the global mobile traffic during a

span of 5 years from 2018 (Ericsson, 2018). As evident, the traffic generated by wireless data

is increased about 10 times in the last 5 years and expected to be much more in the future.

Figure 1.1: Global mobile traffic (ExaBytes per month)

Despite massive growth in wireless data, spectrum remains scarce and expensive which

necessitated the evolution of wireless communication standards and subsequently wireless

transceiver designs. A distinct example is FCC standardization for smart phones, where LTE

1

and 5G were introduced to enhance network capacity and provide higher data rate for mobile

subscribers as shown in Fig. 1.2 (Ericsson, 2018).

Figure 1.2: Mobile subscriptions by technology (billions)

To accommodate wireless data growth, modern radios adopt multi-band multi-mode

features into a single chip, allowing them to operate over different frequency bands and

different operation modes while remaining highly integrated. The multi-band multi-mode

receivers require multiple local oscillator (LO) generation and receive chains along with

multiple filters and multiplexers at the RF front-end. The operating bandwidth of such radios

can be further enhanced by employing carrier aggregation, where the radio simultaneously

operates over multiple frequency channels with the cost of additional complexity. Although

being dominant solution in current industry radios, their implementation is fairly complex

and inflexible. As an alternative solution, cognitive radios has been introduced as a promising

solution for a universal radio which tend to operate in a flexible fashion subject to available

spectrum for secondary users and required operating bandwidth. The aim is reducing

complexity of modern radios in terms of off-chip (e.g., filters and multiplexers) and on-chip

2

(e.g., number of LO generation and receive chains) elements while being blocker resilient. This

dissertation is mainly focused on developing solutions that can be incorporated in practical

implementation of cognitive radios.

1.2 Overview of Main Existing Techniques

1.2.1 Analog Harmonic Rejection Mixer

Harmonic rejection mixers (HRMs) are commonly used to improve LO harmonic interferer

resilient of surface acoustic wave (SAW)-less receivers (Choke et al., 2013; Lerstaveesinand

et al., 2008; Mak and Martins, 2011; Ru et al., 2008, 2009; Weldon et al., 2001). Fig. 1.3

represents the principle of HRM operation for an 8-phase realization. In this scheme, RF

downconversion realized by time domain multiplication of RF signal with an effective square

wave LO signal (due to on/off operation of the RF switch). Because of the convolution of RF

and LO spectrums in frequency domain, interferers located at LO harmonics downconvert

to baseband along with desired signal. The aim of HRM is to approximate the sine-wave

multiplication by summing and weighting of multi-phase square-wave multiplications. As

shown in Fig. 1.3, in an 8-phase realization, weighting coefficients of 1,√

2, 1 , results

in suppression of 3rd and 5th harmonics. Therefore, the effective LO spectrum will be

a sample and hold version of sine-wave RF signal with less harmonic content in compare

with square-wave LO signal. Non-overlapping LO phases and accurate weights are essential

conditions for proper operation of HRMs. In presence of these conditions, the 8-phase HRM

cancels third and fifth and leaves seventh and ninth unaffected as shown in Fig. 1.3b. The

root cause of this property is investigated and further discussed in chapter 2.

1.2.2 Noise Cancellation

A common approach for reducing noise figure of low noise amplifiers (LNAs) is noise cancel-

lation where the goal is reducing noise contribution of main device by adding an auxiliary

3

BBRF

LO

Effective LO

Spectrum

3LO 5LO 7LO 9LOLO

BBRF

C0

C1

C7

45

1

1

45

1

1

1st, 7

th and 9

th 3rd

and 5th

LO0

LO1

LO7

Unaffected

Harmonics

Suppressed

Harmonics

(a)

(b)

Figure 1.3: Principle of analog harmonic rejection mixers; (a) Time domain equivalent ofHRM, (b) Frequency domain equivalent of HRM

path in feedforward (Bruccoleri et al., 2004) (see Fig. 1.4). By controlling gain of the

auxiliary path (CS device M2), it can be shown that noise of the main device (CG device

M1) appears as common mode while signal appears as differential. Therefore, main device

noise cntribution will be minimal in differential output. Same noise cancellation principle

can be applied to wideband receivers. For example, (Murphy et al., 2012) added a Gm-first

path to alleviate poor noise figure of mixer-first receivers.

4

M1

M2

R1 R2

Vout

Vb1

Vn1

VDD

Vin

Rs

Figure 1.4: Principle of noise cancellation

1.2.3 M-phase Passive Mixer Filtering

The bidirectionality feather of passive mixers along with M-phase nonoverlapping downcon-

version has the interesting attribute of impedance transformation when seen from shared

RF node (Andrews and Molnar, 2010b) (see Fig. 1.5). Assuming baseband time constant

is significantly larger than LO period, it can be shown that the effective impedance seen at

RF node is equivalent to upconverted and scaled version of baseband impedance in series

with switch ON resistor. Therefore, by having a lowpass shaped baseband impedance, a

virtual bandpass filter can be realized without the need for physical SAW filters. The center

frequency of the RF bandpass filter will be adjustable with LO frequency and it’s bandwidth

can be tuned by baseband time constant. Also, the up-converted impedance can be employed

towards matching of the receiver to the antenna.

1.3 Overview of Proposed Techniques

There are four major limits in realizing a wideband SAW-less receiver using previously

mentioned existing techniques. 1) Analog HRMs suffer from trade-off between number of LO

phases and highest rejectable LO harmonic. Suppressing higher order LO harmonics require

5

Zs

VBB0

VBB1

VBB(M-1)

...

VRF

LO0

LO1

LO(M-1)

ZBB

ZBB

ZBB

DCLO

ZBB(w)ZRF (w)

...

Figure 1.5: M-phase filtering using passive mixers

increasing number number of LO phases which adds to the implementation complexity (e.g.,

synthesizer tuning rang, LO generation power consumption). 2) The achievable harmonic

rejection ratio (HRR) for rejectable LO harmonics is highly sensitive to gain and phase

mismatches. The existence of mismatch (random and systematic) in weighting coefficients,

LO generation circuitry, downconversion mixers and eventually layout routings is inevitable

particularly at lower technology nodes and higher frequencies. 3) Out-of-band interferers

experience limited attenuation when only M-phase filtering were to be employed. Mixer

ON resistor sets the minimum value of input impedance profile and eventually limits the

out-of-band attenuation. The intermodulation product of these out-of-band interferers will be

downconverted by LO signal or it’s harmonics and distort baseband signal even if the receiver

is linear enough to avoid desensitization. 4) Noise cancellation and interferer distortion

suppression happens independently and typically requires two calibration schemes to provide

optimum baseband signal to noise ratio.

6

To alleviate limitations of analog HRMs, an adaptive digitally-assisted harmonic rejection

receiver is proposed in this dissertation to overcome the trade-off between number of LO

phases and highest rejectable LO harmonic and also reduce sensitivity of achievable harmonic

rejection ratio to gain and phase mismatches. The primary goal is utilizing a digital-assisted

harmonic rejection equalizer while reducing complexity of RF front-end. It will be shown

that by creating non-overlapping LO phase at RF front-end and adaptive weights at digital

back-end, rejection of higher order LO harmonics is feasible using only 4 non-overalapping

uniform 25% LO phases. Since equalizer inherently tracks and counteracts the preceding

stages properly, which the gain and phase mismatch can be counted towards, the receiver

is able to null any LO harmonic. In addition to harmonic mixing products, same approach

is employed to suppress intermodulation products regardless of their order in presence of

distinct nonlinear downconversion paths, which allows complexity reduction. Therefore, one

calibration scheme is required for reconstructing desired signal in presence of correlated

noise and interferer distortion products. Moreover, a harmonic sensing mixer-first receiver

is introduced to simultaneously detect signals located at LO harmonics in order to reduce

spectrum sensing time of cognitive radios.

1.4 Thesis Contributions

The main contributions of this dissertation can be described as follows: 1) A dual-path

nonuniform 4-phase receiver with an adaptive MMSE digital equalizer is proposed which

is capable of rejecting higher order LO harmonics in a mismatch insensitive fashion; the

proposed receiver performs robust harmonic rejection of any LO harmonic including 7th

and 9th, 2) Intermodulation and harmonic distortions are suppressed using one digital

equalizer regardless of their order, 3) The required complexity of a K-path M-phase receiver

is evaluated in order to concurrently suppress multiple distortion sources when employing a

digital equalizer, 4) The use of mixer-first receiver is proposed to sense simultaneously several

7

LO harmonics instead of rejecting all of them and keeping the fundamental; It has been

shown that a satisfactory level of matching is reachable keeping a geometric mean relation

between the input impedances at the different LO harmonics, while as the number of phases

increases more harmonics can be received with better return loss. The proposed approaches

have the potential to be adopted in multi-band RF receivers with cognitive abilities.

1.5 Outline

This dissertation, which is based on the papers presented in (Babakrpur and Namgoong,

2016, 2017a,b,c) by the author, is organized as follows: Chapter 2 presents proposed digitally-

assisted harmonic rejection receiver, its implementation and measurement results. Chapter

3 explains a mathematical framework for modeling harmonic mixing and intermodulation

products followed by measurement results. In chapter 4, the harmonic sensing mixer-first

receiver is introduced and optimum matching condition for different spectrum usage scenarios

are derived. Finally, the dissertation is concluded in chapter 5.

8

CHAPTER 2

A DUAL-PATH 4-PHASE NONUNIFORM WIDEBAND RECEIVER WITH

DIGITAL MMSE HARMONIC REJECTION EQUALIZER1

2.1 Introduction

Modern wideband wireless radios need to support multiple communication standards that

operate in different frequency bands while being highly integrated. The surface acoustic wave

(SAW)-less wideband receiver is a promising candidate for such a radio and has been the

source of significant recent research. A potential drawback of the SAW-less wideband receiver

is that the absence of a narrowband filter at the receiver input causes interferers located

at the LO harmonics to also downconvert to the baseband along with the desired signal.

Although these “LO interferers” experience smaller conversion gains than the desired signal,

the resulting interference distortion can be significant as they can be orders of magnitude

stronger. An example of harmonic mixing in a wideband receiver is illustrated in Fig. 2.1,

where a strong interferer is located in the fifth LO harmonic. As the LO spectrum contains

all odd LO harmonics, any interferer located near the LO harmonics folds on top of the

desired signal at the baseband.

A common approach for improving the LO interferer resilience is the use of harmonic

rejection mixers (HRMs) (Choke et al., 2013; Lerstaveesinand et al., 2008; Mak and Martins,

2011; Ru et al., 2008, 2009; Weldon et al., 2001). In this approach, sine-wave multiplication

is approximated using multiple paths driven by different LO phases. Their outputs are

appropriately scaled then summed at the baseband to cancel the LO interferers. Not all LO

harmonics, however, can be suppressed by the analog HRM. For example, when eight phases

are employed, seventh and ninth harmonics cannot be rejected. Furthermore, the achievable

1 c©2017 IEEE. Reprinted, with permission, from E. Babakrpur and W. Namgoong, “A Dual-Path 4-PhaseNonuniform Wideband Receiver With Digital MMSE Harmonic Rejection Equalizer”, IEEE Transactions onMicrowave Theory and Techniques, Feb 2017.

9

Figure 2.1: Harmonic mixing in wideband SAW-less receivers

harmonic rejection ratio (HRR) is very sensitive to gain and phase mismatches, limiting the

achievable harmonic rejection ratio to less than 45 dB in practice (Ru et al., 2009)(Murphy

et al., 2012).

Techniques reported in the literature to improve HRR in analog HRMs include the use

of two-stage harmonic weighting (Ru et al., 2009) and mismatch calibration (Cha et al.,

2010)(Rafi et al., 2011). Two-stage analog HRM reduces sensitivity to gain errors but not

phase mismatches, which are often the dominant source of HRR degradation. Although

mismatch calibration techniques can be effective, maintaining high levels of HRR across

all operating conditions could be challenging, especially if the receiver needs to operate in

different frequency bands as required in many modern receivers.

Robust harmonic rejection can be achieved by employing digital compensation tech-

niques at the cost of increased number of analog-to-digital converters (ADCs) (Ru et al.,

2009)(Namgoong, 2013a)(Forbes and Gharpurey, 2014). A general mathematical framework

for the LO interferer distortion in polyphase mixers is presented in (Namgoong, 2013a), where

a minimum mean-squared error (MMSE) equalizer for harmonic distortion is derived. In

10

(Namgoong, 2015), the limitations of employing equally spaced LO phases is discussed and the

use of nonuniformly spaced multiphase mixers is proposed. As noted in (Namgoong, 2015),

eight multiphase mixers has sufficient degrees of freedom to completely null one harmonic

interferer regardless of its location. The uniformly-spaced 8-phase mixers represent a special

case where two harmonic interferers can be concurrently suppressed (i.e., third and fifth)

at the expense of not being able to attenuate the seventh or ninth harmonic. The MMSE

equalizer in (Namgoong, 2013a) and (Namgoong, 2015) minimizes the signal distortion in the

MMSE sense regardless of the number of harmonic interferers and LO phase mismatches.

This chapter presents a dual-path 4-phase receiver that effectively behaves as a nonuni-

formly spaced 8-phase receiver. As such, the proposed receiver can suppress any of the higher

LO interferer including seventh and ninth. Unlike the conventional 8-phase receiver, the

noise among the paths are correlated, which can be exploited to improve the receiver noise

figure. A digital MMSE equalizer seamlessly accounts for the correlated noise as well as the

harmonic interferers to achieve both high HRR and low noise figure. As the proposed receiver

consists of two 4-phase receive chains, it has sufficient degrees of freedom to suppress one

LO harmonic interferer. If multiple LO harmonics need to be suppressed concurrently, more

receive chains is required to provide additional degrees of freedom (Namgoong, 2015).

This chapter is an expanded version of (Babakrpur and Namgoong, 2016), which was

presented at RFIC 2016. The primary difference from (Babakrpur and Namgoong, 2016) is

the inclusion of a thorough comparison with conventional 8-phase receiver, none of which

is discussed in (Babakrpur and Namgoong, 2016). A detailed motivation for employing

digital equalizers and its limitations are also included. Finally, additional circuit details and

measurement results are presented in this chapter.

The organization of this chapter is as follows. In Sec. 2.2, the proposed 4-phase dual-path

nonuniform topology is introduced and its performance compared with conventional 8-phase

topology. The motivation for employing the digital equalizer and the framework for estimating

11

the MMSE equalizer is discussed in Sec. 2.3. Section 2.4 describes design of the proposed

receiver. Measurement results are presented in Sec. 2.5.

2.2 Proposed Receiver Topology

A block diagram of the popular 8-phase mixer-first receiver is shown in Fig. 2.2(a). It uses

eight passive mixers each driven by non-overlapping multiphase clocks that are separated

by 45 (see Fig. 2.3(a)). The frequency translation property of the baseband impedance to

the RF node is used to perform input matching as well as filtering at the RF node with a

tunable center frequency set by the LO.

The proposed receiver is similar to the conventional 8-phase mixer-first receiver except

that the eight polyphase paths are split into two groups using a buffer as shown in Fig. 2.2(b).

The resulting architecture consists of a primary 4-phase mixer-first path and a secondary

4-phase path isolated from the primary path by a buffer. The primary path enables matching

and filtering at the RF node, while the secondary path can be used to improve the noise

figure and to provide the additional degrees of freedom necessary for harmonic rejection.

A similar dual-path receiver architecture was presented in (Murphy et al., 2012). The

primary difference is that in the proposed receiver, each path employs a 4-phase 25% duty-

cycle LOs for downconversion instead of the eight 12.5% duty-cycle LOs as in (Murphy

et al., 2012). This difference provides greater robustness to mismatches while reducing

the operating frequency requirements of the frequency synthesizer. Furthermore, if digital

harmonic rejection were to be performed, only four ADCs would be required instead of eight.

By exploiting the noise correlation between the two paths, both architectures can achieve

low noise figure, unlike the conventional 8-phase mixer-first receiver. In (Murphy et al.,

2012), each path performs harmonic rejection independently then combines the two outputs

to cancel the correlated noise. In the proposed approach, noise cancellation and harmonic

rejection occur concurrently using the MMSE equalizer in the digital domain. Denote the

12

0

90

180

270

0

90

180

270

Buffer 0

45

90

315

8-Phase

Dual 4-Phase

(a) (b)

V0

V1

V2

V7

W0

W1

W2

W3

W4

W5

W6

W7

Figure 2.2: a) Conventional 8-phase receiver; b) Proposed dual-path 4-phase nonuniformreceiver

phase offset between the primary and secondary paths in the proposed receiver as φ as shown

in Fig. 2.3(b). Assume for ease of explanation that the buffer is ideal with no delay. Then,

when φ = 0, the two paths are identical, and as such, the receiver behaves effectively as

a 4-phase receiver without the ability to suppress any of the LO harmonic interferers. By

contrast, if φ = 45, the proposed receiver is effectively a uniformly-spaced 8-phase receiver

but with twice as wide LO duty cycle and with attendant benefits as noted earlier. For other

phase offsets, the proposed receiver is a nonuniformly spaced receiver. In practice, the phase

delay of the buffer causes the proposed receiver to behave as a nonuniformly spaced receiver

13

ϕ

V0

V1

V2

V7

W0

W1

W2

W3

W4

W5

W6

W7

V3

V4

V5

V6

(a) (b)

Figure 2.3: a) 8-phase 12.5% clocks b) Two sets of 4-phase 25% nonuniform clocks

regardless of φ as discussed in subsequent sections. In this section, we list the advantages

of the proposed topology when compared to the conventional 8-phase topology in terms of

harmonic rejection sensitivity, LO generation complexity, and noise figure.

2.2.1 Harmonic Rejection

HRMs are sensitive to gain and phase mismatches among the polyphase paths. To make a

fair comparison between the proposed receiver and the conventional 8-phase receiver, assume

φ = 45, ideal buffer with no delay, and baseband weighting coefficients of 1,√

2, 1. Then,

the only difference between the two receivers is that the duty cycle of the proposed receiver

is twice as wide as that of the conventional 8-phase receiver. In Fig. 2.4, the HRR of the

third harmonic is plotted as a function of phase mismatch when the gain mismatch is 0.2%.

For the both receivers, only one polyphase path among eight is assumed to suffer from gain

and phase mismatches. Although not evident from Fig. 2.4, the dual-path 4-phase topology

outperforms the conventional 8-phase topology by exactly 7.65 dB for all phase offsets.

14

Figure 2.4: HRR3 vs phase mismatch for 8-phase and dual-path 4-phase receivers, δa = 0.2%and φ = 45

Figure 2.5: ∆CG(m) vs harmonic order for 8-phase and dual-path 4-phase receivers

15

This improvement of 7.65 dB using the proposed receiver can be attributed to the reduced

conversion gain of the third LO harmonic relative to the first in each polyphase path when the

duty cycle is doubled to 25%. As the third harmonic power is reduced in the proposed receiver,

the amount of folding to the baseband due to mismatches is also correspondingly reduced,

resulting in improved HRR values. To quantify this improvement, denote the conversion

gain in a single polyphase path of the mth LO harmonic (CG[m]) relative to the first of an

M -phase receiver as ∆CG(m), which can be shown to be

∆CG(m) =CG[m]

CG[1]=

sinc(mπM

)

sinc( πM

)(2.1)

where M = 8 for the conventional 8-phase receiver, and M = 4 for the proposed 4-phase

dual-path receiver. ∆CG(m) in (2.1) is plotted in Fig. 2.5 as a function of different harmonic

orders for both receivers. As shown in Fig. 2.5, the proposed 4-phase dual-path receiver

enjoys 7.65 dB additional harmonic attenuation compared to the 8-phase receiver at rejectable

LO harmonics of third, fifth, eleventh, etc. This improvement in ∆CG(m) of 7.65 dB is

exactly the HRR improvement in Fig. 2.4, suggesting that the improved harmonic rejection

sensitivity in the proposed 4-phase dual-path receiver is due to the widened duty-cycle of

each polyphase path.

2.2.2 Frequency Synthesizer Complexity

One of the challenges of designing an M -phase mixer-first receiver is the need to generate

accurate multiphase clocks. A common approach to multiphase clock generation is to

appropriately divide the frequency synthesizer output. For an M -phase receiver, which

requires generation of M non-overlapping LOs each with a duty-cycle of 1/M , the frequency

synthesizer needs to operate at M/2 times the LO mixer frequency. As the proposed

receiver requires four phases, the frequency synthesizer operates at only half the frequency

of the conventional 8-phase receivers. As a result, the power consumption of the frequency

16

synthesizer and the dividers of the proposed receiver is correspondingly reduced. The phase

offset φ between the two paths in the proposed receiver does not introduce any additional

complexity as it can be set arbitrarily as shown in Sec. 2.5.

2.2.3 Noise Figure

An important drawback of the mixer-first architecture is its high noise figure. The noise

figure (NF) of an 8-phase mixer-first receiver including baseband amplifiers can be derived

based on the linear time invariant (LTI) model given in (Murphy et al., 2012)(Andrews and

Molnar, 2010b) and shown to be

NF =1 + Rsw

Rs+

V 2nop

8V 2nRs

+ 8Rs

(1+A)RBB(1 + Rsw

Rs)2

sinc2(π8)

(2.2)

where V 2nop

and V 2nRs

represent the equivalent baseband operational amplifier and source

resistance noise, respectively, Rs is the source resistance, Rsw is the mixer switch resistance,

RBB is the baseband amplifier feedback resistance, and A is baseband amplifier open loop

gain. As shown in (Murphy et al., 2012), the noise performance of the mixer-first receiver

can be improved by adding a low-noise Gm-first secondary path to cancel the noise in the

primary mixer-first path. The secondary path provides in theory complete cancellation of

baseband amplifier noise and partial cancellation of switch noise with the residual switch

noise made sufficiently negligible as shown in (Murphy et al., 2014). Therefore, the 4-phase

dual-path noise figure approximately becomes

NF = (1 +V 2nGM

V 2nRs

)1

sinc2(π4)

(2.3)

where V 2nGM

is the Gm noise. As a numerical example of the noise figure improvement using

the proposed receiver compared to the conventional mixer-first 8-phase receiver, assume

typical conditions of Rsw = 10 Ω, A = 40 dB, Vnop = 3 nv/√

Hz, RBB = 350 Ω, GM = 100

mS and RS = 50 Ω. Then, the NF of the 8-phase receiver is 4.33 dB while NF of the 4-phase

dual-path receiver is 2.38 dB.

17

2.3 Digital MMSE Equalizer

Digital compensation of harmonic distortion is employed to achieve robust and high-performance

harmonic rejection. As shown in Fig. 2.4, HRR is extremely sensitive to gain and phase

mismatches. HRR3 of an 8-phase receiver drops to less than 40 dB when one of the polyphase

paths suffers from a phase mismatch of only 1.3. As maintaining such high levels of polyphase

matching across all operating conditions is difficult, the use of digital equalizers becomes

attractive as they can adaptively account for these mismatches to achieve high HRR.

The use of digital equalizer for harmonic distortion is even more critical in the proposed

receiver for several reasons. First, because the LO phases are not uniformly spaced, the

optimal combining weights of each polyphase paths become interferer dependent. For example,

the combining weights that suppress the third harmonic is different than when attenuating

the fifth harmonic. Second, the buffer driving the secondary path suffers from group delays

that differ depending on the harmonic frequency, resulting in equivalent phase offsets in the

secondary path that is interferer dependent. Finally, when suppressing the interferers, the

effects of the correlated noise between the primary and secondary paths must be accounted

for to ensure low noise figure. These requirements necessitate the use of digital equalizers as

designing such adaptive analog combiners would be difficult.

In this section, we provide a brief background of the geometric framework used to derive

the MMSE harmonic equalizer (Namgoong, 2013a) (Namgoong, 2015) for the proposed

4-phase dual-path receiver.

2.3.1 System Model

In the proposed receiver, the received RF signal is mixed by eight LO phases (or four

equivalent differential phases) to produce four ADC outputs. Denote the differential LO

phases as θ1, θ2, θ3, θ4 and gain values as γ1, γ2, γ3, γ4. These coefficients include the

18

effects of phase and gain mismatches, respectively. The baseband signal in the mth sample

of the lth differential polyphase path, where l = 1, 2, 3, or 4, is given by

yl[m] = γl

∞∑k=1

αk(ejkθlxk[m] + e−jkθlx∗k[m]) + nl[m] (2.4)

where xk[m] is the baseband equivalent complex signal centered at the kth LO harmonic,

nl[m] is the circuit noise in the lth differential polyphase path, and αk is the gain of the kth

LO harmonic. We assume that the dc noise due to self-mixing is negligible and/or removed

using standard techniques (e.g., highpass filters). The sample index m is subsequently omitted

for notational simplicity (except when necessary for clarity). The sampled output of the

proposed receiver can be represented in vector form as

y = [y1 y2 y3 y4]T

= s1a1 + s∗1a∗1 +

K∑k=2

(skak + s∗ka∗k) + n

(2.5)

where ak = αkxk, n = [n1, n2, n3, n4]T , and sk = [γ1e

jkθ1 , γ2ejkθ2 , γ3e

jkθ3 , γ4ejkθ4 ]T . Only the

first K LO harmonics is considered as higher order harmonics are assumed to have been

removed by the inherent bandwidth limitations of the circuits and/or a broadband filter

preceding the receiver.

2.3.2 Multiuser Detection Perspective

The harmonic interferer can be viewed as interference in a multiuser detection (MUD) problem

(Verdu, 1998) or in array processing (Trees, 2002). When viewed in the MUD framework,

a1, a∗1, a2, . . . , a

∗K in (2.5) represent the transmit signals of 2K multi-access users and s1,

s∗1, s2, . . . , s∗K are the corresponding signature vectors. The objective is to estimate a1 with

signature vector s1 based on y in the presence of interference signals with signature vectors

s2, s3, . . . , sK and the image signals with signatures s∗1, s∗2, . . . , s

∗K .

19

(a) (b) (c)

(d) (e) (f)

Figure 2.6: Signature vectors of 8-phase analog HRM for a) 3rd and 5th harmonics; b) 7thand 9th harmonics; c) Sensitivity of analog HRM to gain and phase mismatches; d)

Proposed MMSE harmonic rejection equalizer in presence of an arbitrary LO harmonic; e)Sensitivity of the proposed MMSE equalizer to mismatches; f) Proposed MMSE harmonic

rejection equalizer in presence of two arbitrary LO harmonics

To gain better insight of the MUD framework and the requirements of the equalizer,

we provide a simplified geometric perspective assuming a two-dimensional system with real

signature vectors and signals. In Fig. 2.6(a), the fundamental frequency signature vector

s1 is scaled by the desired signal a1, and signature vectors for third and fifth harmonics s3

and s5 are scaled by third and fifth harmonic interferers a3 and a5, respectively. For the

conventional 8-phase HRM where LO phases are separated by 45 and gains scaled by 1,√

2,

1, the equivalent equalizer vector, denoted as hana, can be viewed in this simplified geometric

model as being aligned to s1 and orthogonal to s3 and s5. Since the equalizer output is the

20

dot product of hana with all the signature vectors, a3s3 and a5s5 are nulled, which correspond

to suppressing the third and fifth harmonics. For the seventh and ninth harmonics (see

Fig. 2.6(b)), however, the corresponding signature vectors are completely aligned with s1. As

a result, hana fails to suppress the seventh and ninth harmonics.

In the presence of mismatches, the third signature vector, for example, is not s3 but s′3

as shown in Fig. 2.6(c). Since hana is no longer orthogonal to s′3, the conventional HRM

fails to suppress the third harmonic. To attenuate s′3, hana must also readjust to maintain

orthogonality. An important observation from this geometric perspective is that to suppress

the interferer in the presence of gain and phase mismatches, hana is dependent on the specific

harmonic interferer to suppress and is not a fixed value as in the conventional HRM. Unlike

existing analog HRM, the proposed MMSE equalizer, derived in the following subsection,

adaptively finds an equalizer vector hMMSE that is (approximately) orthogonal to an arbitrary

interferer while being mindful of the desired signature vector so that the overall MMSE is

minimized. The MMSE equalizer is illustrated in Fig. 2.6(d), where sb corresponds to one

of the harmonic interferer signature vector. Denoting the signature vector of the bth LO

interferer in the presence of gain and phase mismatches as s′b, the adaptive MMSE equalizer

h′MMSE remains (approximately) orthogonal to s′b as shown in Fig. 2.6(e).

When two strong harmonic interferers with signature vectors sb1 and sb2 are present as

shown in Fig. 2.6(f), the equalizer doesn’t have sufficient degrees of freedom to be orthogonal

to both interferers. As the equalizer employs effectively 8 LO phases (i.e. two sets of 4 LO

phases), it has two degrees of freedom, one to recover the desired signal and the other to

suppress one harmonic interferer. To suppress two LO harmonics would require one additional

degree of freedom, which can be obtained by employing 12 LO phases (i.e. two sets of 6 LO

phases) instead of the current 8. In general, a digital equalizer with M effective LO phases

can suppress (M4− 1) harmonic interferers.

21

2.3.3 MMSE Equalizer

The objective of the digital equalizer is to estimate the desired signal a1 in the presence

of harmonic interferers and correlated circuit noise. As the signature vector length (or

equivalently, the number of ADCs) is less than the number of interferers 2K, the interferers

in general cannot be completely suppressed. In fact, given that the signature vector is of

length four, only one interferer (and its corresponding image signal) can be completely nulled.

The MMSE equalizer, however, attempts to estimate a1 in the MMSE sense regardless of the

number of interferers.

The MMSE estimate of a1, which is given by a1 = hHMMSEy, where superscript H denotes

the conjugate-transpose operation, and hMMSE is the MMSE equalizer, can be shown to be

(Namgoong, 2013a)

hMMSE = R−1y s1 (2.6)

where Ry = E[yyT ]. The covariance matrix Ry in (2.6) captures the second-order statistics

of the harmonic interferers and the noise correlation among the differential polyphase paths,

enabling the equalizer weights to vary according to the operating environment. By contrast,

the polyphase weights in a conventional analog HRM are fixed. The signature vector of the

desired signal s1 in (2.6) can be readily estimated a priori via calibration. As the covariance

matrix Ry is unknown in practice, it can be estimated by averaging L recently received

samples, i.e.,

Ry[m] =1

L

m∑k=m−L+1

y[k]yT [k] (2.7)

2.4 Circuit Implementation

A dual-path 4-phase receiver is realized as shown in Fig. 2.7. The primary path employs

mixer-first topology while the secondary path is a Gm-first topology. The RF front-end and

baseband blocks are implemented on-chip while the adaptive digital equalizer is realized

22

Q-path

Div.2

+

RFin

Gm

+

-

2FLO

+

-

ADC

MMSE

Equalizer

Signal +

LO Interferer +

Correlated Noise

Signal +

LO Interferer +

Noise

I-path

Q-path

I-path

LO0 LO1804

Div.2

+2FLO4

ADC

LO0 LO180

XI

XQ

Off-Chip EqulizationReceiver Front-end and BB Blocks

Figure 2.7: Proposed receiver topology

off-chip. Each path has separate frequency divider to generate four non-overlapping multi-

phase clocks from a master clock operating at 2fLO. The LO generation circuit is shown in

Fig. 2.8. The divider employs 2 current mode logic (CML) D-flip flops in parallel feedback

to generate four phases with 90 phase shift and 50% duty cycle. The output of the divider

is buffered and ANDed with LO signal to generate four phases with 25% duty cycle. The

non-overlapping clocks are DC level-shifted before feeding to the passive mixers. The LO

generation circuit is designed to provide low phase noise in order to prevent reciprocal mixing

due to out-of-band interferers. The simulated phase noise is -165 dBc/Hz at 10 MHz offset

from a 0.5 GHz master clock, which is sufficiently low.

The primary path is a mixer-first topology including two parallel identical I and Q paths.

The mixer first receiver provides a highly linear downconversion path along with wideband

input matching tunable with LO frequency. The out-of-band interferers will be attenuated at

the input of the receiver as a result of the virtual upconverted bandpass filter.

23

CLK

D

QDFF DFF

LO

Q1

Q2

Q3

Q4

Qi

LO/LO

Vbb

Vsi

DFFVDD

15/0.12 15/0.12

1KΩ

15/0.12 15/0.12

30/0.12

Figure 2.8: 4-phase LO generation circuits

Vbcm

Vb

Vo

CMFBVd Vbcm

VRF

Vs0

Vs180

Ib

Vd

500/0.4

80/2.5

5 pF

2-126 pF

2-16 kΩ 60/0.12

Fig. 2.9: Passive mixer receiver front-end, baseband amplifier and low-pass filter (RFswitches are triple well transistors)

24

One differential polyphase path of the mixer-first receiver including the RF front-end,

baseband amplifier and first order RC lowpass filter is shown in Fig. 2.9. In this circuit,

passive mixers are followed by a one stage differential amplifier in series with a lowpass filter.

Since harmonic cancellation happens after digitization, the baseband stage must handle

strong harmonic interferers. The baseband circuits are designed with thick oxide transistors

biasing with 2.5 V supply to provide high output voltage swing. The input impedance of the

receiver is tuned by a 5 bit programmable feedback resistor ranging from 2 KΩ to 16 KΩ. As

the resistor noise is divided by the open loop gain of the baseband amplifiers, the resistor

noise contribution is correspondingly reduced. The input bandwidth at the RF node is tuned

by a 6-bit shunt capacitor ranging from 2 pF up to 126 pF. A voltage buffer at the amplifier

output drives the feedback parallel RC. In order to reduce the flicker noise of the baseband

amplifiers, pMOS transistors with long channels are used for the input pair.

The secondary path which employs a Gm-first topology provides a unilateral feedforward

path for nonuniform phase spacing as well as noise cancellation. A separate frequency divider

is designated to the secondary path. The phase difference between LO sources is controlled by

an external phase shifter, which can be implemented on-chip as a tunable delay line (Andrews

et al., 2012). The Gm cell at the receiver input minimizes coupling from the secondary path

to the primary path. The virtual bandpass filter generated by the mixer-first primary path

attenuates the out-of-band interferers at the input of the secondary path by about 15 dB. The

Gm cell is a CMOS inverter with the passive downconversion paths serving as the resistor

load. The output impedance of the transconductance is designed to be less than 10 Ω in

order to reduce the voltage swing at the Gm cell output, resulting in improved linearity of

the secondary path. The I and Q downversion paths of the secondary path are the same as

Fig. 2.9 with modest differences in biasing and RC values.

The output of both paths are buffered then sent off-chip for digitization using differential

ADCs (digital sampling oscilloscope). The sampled signals are adaptively weighted and

25

combined using the MMSE equalizer to estimate the desired signal in the presence of LO

interferer(s). The estimate of Ry is obtained based on (2.7) and requires 10 real multiplications

per baseband sampling period. Matrix inversion of Ry in (2.6) is performed at the cost of

O(43) real multiplications. As hMMSE needs to be updated only intermittently when the

harmonic interferer statistics change, the matrix inversion is performed only when necessary.

Consequently, the digital complexity is dominated by the 10 real multiplications in updating

Ry, which is quite modest (Namgoong, 2013b).

If the harmonic interferer statistics remains approximately constant, which can be readily

measured by monitoring changes in the covariance matrix elements that is constantly updated

based on each digitized samples, the equalizer coefficients need not be changed and one-time

calibration would be sufficient. However, if a significant change in the harmonic interferer

statistics is detected based on the covariance matrix, the MMSE harmonic equalizer coefficients

need to be updated in the foreground.

To avoid self-mixing issue at the baseband, we used simple high pass filters prior to digital

sampling. If the dc noise is not sufficiently suppressed, the MMSE equalizer would attenuate

the residual dc noise. The drawback, however, is that the receiver would be wasting one of its

available degrees of freedom for dc noise suppression. As our chip consists of effectively eight

LO phases, it has enough degrees of freedom to recover the desired signal and attenuate one

harmonic interferer. To suppress both the dc noise and a harmonic interferer would require

additional degrees of freedom, which can be attained by employing more LO phases. As

such, the cutoff frequency of the high-pass filter was selected so that the dc noise becomes

negligible during testing of our prototype chip.

2.5 Measurement Results

The dual-path 4-phase receiver prototype is fabricated in 130 nm CMOS process. The chip

photograph is shown in Fig. 2.10 which occupies 1.3 mm by 1.3 mm including bondpads and

26

has an active area of 1 mm2. The dual metal-insulator-metal (MIM) capacitors with capacitor

density of 4.1 fF/µm2 is employed to reduce area. The manufactured die is wirebonded to a

48 lead 6×6 mm quad-flat no-leads (QFN) package. The packaged IC is then assembled into a

4-layer FR4 PCB. The wirebond and package parasitics are electromagnetic (EM) simulated

and considered in the design. Fig. 2.11 shows measurement set-up and also open-molded

photograph of the IC wirebonded to the package. Two LO sources with tunable phase

difference are applied to the primary and secondary paths. The switch caps and resistors

are controlled by an NI board (NI PXIe-1037). The output of both paths are sampled using

digital real time oscilloscope (MSO8140A) and the collected data is processed in MATLAB

on a PC. The impact of off-chip components including baluns (Picosecond-5310A), splitters

(Mini-Circuits ZFRSC-42-S+) and amplifiers (Mini-Circuits ZHL-32A+) are de-embedded

during the measurement process. The complete test bench with further details is shown in

Fig. 2.12. Prior to digital calibration, an RF tone at the desired signal frequency is applied

to measure the relative phase and gain mismatches among the digitized baseband samples.

The LO generation circuits and Gm cell are supplied by 1.2 V while baseband amplifiers are

supplied by 2.5 V. The Gm cell consumes 5 mA and the four Op-Amps consume 13 mA. The

measured current consumption of dividers varies between 4 mA to 14 mA depending on the

operation frequency.

In Fig. 2.13, HRR for harmonics up to eleventh as a function of phase offset between

two paths is plotted. In this measurement, the LO frequency is set to 150 MHz, the lowest

measured operational frequency of the receiver. The desired signal tone is at 151 MHz and

the mth LO harmonic interferer tone is situated at (150m+1) MHz. The power of desired

signal is -70 dBm while the power of interferer is set to be -30 dBm. Using the estimated

hMMSE, the conversion gains of the desired signal and harmonic interferer tones are separately

measured by themselves to compute the HRR. As shown in Fig. 2.13, varying the phase

offset between the primary and secondary paths cause the HRR performance to vary with

27

1.3mm

Pri.

Divider

Pri.

TIAs

Sec.

TIAs

1.3

mm

Sec.

Divider

Gm BB

Caps

Mx

Mx

Bias and Ctrl Pins

Bias and Ctrl Pins

Base

ban

d O

utp

ut P

ins

Inpu

t R

F P

ins

Figure 2.10: Die photograph; The active area is 1 mm2

28

Figure 2.11: Measurement setup

GM,Dividers

(1.2V) and Mixer

CM (1.5V) Biases

BB Dual Path

Biases (2.5V)

Mixer Gate and

Mixer Bulk Biases

(1.8V, 1.2V)

Main Path LO

with Balun

Aux Path LO with

Balun

Input RF

signal

Network

Analyzer (one

port S11 Meas.)

Digital Ctrl

Signals from NI

BoardDUT

2nd

IB or OOB

Interferer (Not

captured in this pic)

1st IB or OOB

Interferer

Spectrum

Analyzer

Digital

Oscilloscope

LO Bias

Tees

High Pass DC offset Filter+

Off-chip Diff. to Single-

ended Baluns

Additional Amplifier Stage

Before Sampling (Not captured in this pic)

Figure 2.12: Detailed test bench

29

the optimum occurring when the phase offset is 67.5, which results in HRR that is >75 dB

for all measured harmonics. As evident from Fig. 2.13, the proposed receiver HRR is not

sensitive to the phase offset between the two paths, achieving HRR that exceeds 60 dB for

all LO harmonics regardless of the phase offset value. This insensitivity results because the

signature vector of all the harmonics are sufficiently different (i.e., the signature vector of the

desired signal and the LO interferers are not aligned) due to the delay in the Gm cell and

LO gain/phase mismatches.

The optimum phase difference depends on the signature vectors of he harmonic interferers

with respect to the desired signal (i.e., first harmonic). As all the signature vectors depend on

LO path gain/phase mismatches and Gm-cell delay, the optimum phase is process dependent.

The φ = 67.5 provides the best performance for the particular realization. Another realization,

e.g., different LO frequency, would yield a different optimal point as mismatches would be

different. Nonetheless, the receiver performance appears insensitive to the phase difference as

explained in section 2.3.

The noise figure is measured using the ”Y-factor” method. The ”hot temperature” noise

source is employed to estimate hMMSE, which was then used to compute Y-factor and NF.

The use of MMSE equalizer improves the NF of the primary path by 2-3 dB depending on

the operation frequency of the receiver as shown in Fig. 2.14.

Fig. 2.15(a) shows the measured out-of-band third-order intermodulation intercept point

(OBIIP3) as a function of blocker offset when fRF = 1 GHz. In this measurement, two tones

are applied at fRF + ∆f and fRF + 2∆f − 1 MHz, where ∆f is varied from 10 MHz to 100

MHz. As shown in Fig. 2.15(a), OBIIP3 saturates at around 14 dBm when the frequency

offset exceeds 30 MHz, which is set by the baseband lowpass filter bandwidth. The OBIIP3

of the primary mixer-first path by itself is measured to be 5 dB higher than Fig. 2.15(a). The

overall dual-path OBIIP3 performance is limited by the secondary path nonlinearity arising

from the Gm cell.

30

Figure 2.13: Harmonic rejection ratio for different LO phase offsets between primary andsecondary paths (φ)

Figure 2.14: Noise figure versus RF frequency

The blocker noise figure (BNF) plot is presented in Fig. 2.15(b). In this measurement,

the blocker is located 80 MHz away from the desired signal at 1 GHz. The BNF increases

31

Table 2.1: Comparison table

Specifications (Murphy et al.,2012)

(Forbes et al.,2013)

(Ru et al., 2009) This Work

Technology 40 nm 130 nm 65 nm 130 nm

RX Freq. (MHz) 80-2700 50-830 400-900 100-1450

NF@1GHz (dB) 1.7 11 4 3.1

0dBm BNF† (dB) 4.1 N/A N/A 8

LO Phases 8 16 8 4

HRR3/HRR5‡ (dB) 42/45 72/71 >80/>80 >75/>75

HRR7/HRR9‡ (dB) N/A∗/N/A 67/N/A N/A∗/N/A >75/>75

OBIIP3† (dBm) 13.5 N/A 16 14

OBIIP2† (dBm) 56 N/A 56 60

BP1dB† (dBm) -1 N/A N/A -2.5

Supply (V) 1.3 1.2 1.2 1.2/2.5

Power (mW) 35-78 67 <60 35-56§

Area (mm2) 1.2 2.25 1 1

∗ Maximum rejectable harmonic order is fifth† At 80 MHz offset from 1 GHz RF frequency‡ Single interferer is applied in (Ru et al., 2009) and This Work§ Does not include power consumption of the digital section

from 3.1 dB to 8 dB when the blocker power is swept from -50 dBm to 0 dBm. The BNF

degrades with blocker power because of receiver desensitization. The small signal in-band

gain reduction as a function of blocker power is shown in Fig. 2.15(c). Similar to previous

measurements, the blocker is located at 1.08 GHz. As presented in Fig. 2.15(c), the small

signal gain drops with increasing blocker power. The 3 dB gain reduction occurs when the

blocker power reaches -2 dBm. The input return loss of the receiver is shown in Fig. 2.15(c)

as a function of RF frequency. The magnitude of S11 is less than -10 dB for operational

frequency range of 0.1-1.45 GHz (Fig. 2.15(d)).

32

(a) (b)

(c) (d)

Figure 2.15: Measured (solid lines) and simulation (dashed lines) results a) OBIIP3 versusblocker power at 1 GHz RF frequency; b) Blocker NF at 1 GHz RF Frequency, blocker is 80MHz away from desired signal; c) Normalized voltage gain at 1 GHz RF frequency versus

blocker power at 80 MHz offset away; d) Input return loss versus RF frequency as LOfrequency varies from 200MHz to 2.9GHz in finite steps

33

As seen from Fig. 2.15(d), the maximum measured operation frequency of the chip is

1.45GHz. When the receiver operates at frequencies higher than 1.45GHz, input matching,

conversion gain and noise figure performance degrade. This degradation is due to the presence

of parasitic capacitance at the RF node caused by the mixers, Gm-cell, RF pad, wirebond,

ESD protection and package.

Finally, the receiver performance is summarized in Table 2.1 and compared with recently

relevant published wideband receivers. This work, which achieves >75 dB HRR up to the

eleventh harmonic, is the first to demonstrate that seventh and ninth harmonics can be

suppressed using eight or fewer LO phases. The measured NF, area and power consumption

can be further reduced by employing more advanced CMOS processes.

The MMSE equalizer assumes that the gain/phase errors are fixed across the passband of

the desired signal. If the desired signal is wideband and mismatch is signal dependent, the

digitized signal can be decomposed to narrower subbands, each of which suffers from constant

gain/phase errors. Each of the subbands can then be separately processed and combined

if necessary. Many of the existing modulation schemes naturally lend to such frequency

decomposition (e.g., OFDM).

As it can be seen in Table 2.1, the proposed work improved harmonic rejection and also

number of rejectable LO harmonics while only employing two sets of 25% duty cycle clocks.

The out-of-band nonlinearity which is dominated by RF switch and Gm cell in primary and

secondary paths respectively, can also distort the baseband signal in wideband SAW-less

receivers. Therefore, further effort has been made to address signal distortion in presence of

out-of-band interferers which is subject of the next chapter.

34

CHAPTER 3

DIGITAL CANCELLATION OF HARMONIC AND INTERMODULATION

DISTORTION1

3.1 Introduction

Linearity requirements are stringent in wideband surface acoustic wave (SAW)-less receivers

that support various wireless communication bands. Out-of-band interferers and harmonic

interferers are the two main sources of signal distortion in wideband SAW-less receivers. The

intermodulation products of adjacent out-of-band interferers can readily fold on the desired

signal band. On the other hand, interferers located at LO harmonics mix with non-sinusoidal

LO spectrum and downconvert to baseband along with the desired signal. The location of

these interferers varies depending on the spectrum usage. Therefore, in addition to low order

distortion components, high-order intermodulation (IM) products (e.g., fourth, fifth, etc.)

as well as high-order harmonic mixing (HM) products (e.g., seventh, ninth, etc.) become

significant in these receivers. To maintain robustness to interferers, the SAW-less mixer-first

receiver with harmonic rejection mixer has been employed, but it achieves limited suppression

of harmonic and intermodulation distortions while suffering from poor noise figure(NF) and

complex LO generation circuitry (Andrews and Molnar, 2010a)(Murphy et al., 2012).

The interferer distortion in SAW-less receivers can be reduced by employing digital

compensation techniques (Babakrpur and Namgoong, 2017b; Grimm et al., 2014; Keehr and

Hajimiri, 2011; Li et al., 2015; Liu, 2017; Ma et al., 2013; Moseley et al., 2008; Namgoong,

2013a, 2015; Sundstrom et al., 2013; van Liempd et al., 2014). These works suppress either

the harmonic or the intermodulation distortion products but not both. The only exception

is (van Liempd et al., 2014), which suppresses the second-order intermodulation product

1 c©2017 IEEE. Reprinted, with permission, from E. Babakrpur and W. Namgoong, “Digital Cancellation ofHarmonic and Intermodulation Distortion in Wideband SAW-less Receivers”, IEEE Transactions on Circuitsand Systems II: Express Briefs, 2017.

35

IM2 and harmonic interferers HM3 and HM5. The receiver in (van Liempd et al., 2014),

however, does not suppress higher order interferer distortions such as IM3 and HM7. The

aim of this chapter is to suppress both interferer distortions regardless of their order using

only one adaptive digital equalizer. This approach avoids the need for multiple equalizers

to cancel different distortion products (Keehr and Hajimiri, 2011)(van Liempd et al., 2014),

thereby allowing complexity reduction in wideband receiver front-ends and digital back-ends.

In this chapter, a system-level framework is presented to model the distorted baseband

signal in the presence of out-of-band and harmonic interferer distortions. The system model

is first derived for a dual-path 4-phase receiver then extended to a K-path M-phase receiver,

which provides sufficient observations for concurrent suppression of distortion products. By

formulating the distortions in the multiuser detection (MUD) framework as described in

(Namgoong, 2013a,b, 2015), a minimum mean-squared error (MMSE) equalizer is derived

to compensate for the effects of both HM and IM products. This chapter is an extension of

(Babakrpur and Namgoong, 2017b), which focuses solely on harmonic distortion and does

not consider intermodulation products. The available equalizer degrees of freedom and the

required analog front-end complexity to cancel distortion products are then discussed for a

general K-path M-phase receiver. Finally, as a proof of concept, experimental results of a

dual-path 4-phase receiver fabricated in 130 nm CMOS process is presented.

3.2 System Model and MMSE digital equalizer

A typical SAW-less low-IF wideband receiver with two interferer distortion scenarios are

demonstrated in Fig. 3.1. The receiver is modeled by a nonlinear buffer at the input followed

by an ideal passive mixer and a baseband lowpass filter. The nonlinear buffer can be the

low-noise amplifier (LNA), low-noise transconductance amplifier (LNTA), or a virtual buffer

that models the mixer nonlinearity. LO spectrum contains fundamental and LO harmonics

as the LO waveform is pulse-shaped in hard-switching commutating mixers. In one operating

36

Signal

wRF wOB1 wOB2

LO

IFRF

wIFkfLO fLO

IMq

Out-of-band Interferers

Signal

wRF wHMk

Harmonic Interferer

wIF

HMk

(a)

(b)

Figure 3.1: Baseband distortion in SAW-less receivers; a) Intermodulation distortion, b)Harmonic distortion

scenario shown in Fig. 3.1a), the baseband distortion source is the IM product produced

by out-of-band interferers, while in another scenario shown in Fig. 3.1b), the baseband

distortion source is the HM product downconverted by a harmonic interferer. Furthermore,

any order of the distortion product (IMq, HMk) can fold on the desired signal, because

the interferer(s) can be anywhere in the input spectrum. The receiver performs the same

operation to mitigate the effects of distortion regardless of whether the interfering signal is

a HM or IM product or its order. In this section, we first derive a system framework for

a dual-path 4-phase receiver, and then develop an adaptive MMSE equalizer to suppress

baseband distortion product regardless of its nature or order. The dual-path 4-phase receiver

has enough degrees of freedom to cancel one distortion product. To simultaneously suppress

multiple distortion products, a receiver with additional paths and/or LO phases need to be

employed.

37

x(t)

ComplexAdaptive

Weighting/Summing

I

Q

y5(t)LO5

ADC

NLp

NLsLO6

LO7

ADC

LO8

y6(t)

y7(t)

y8(t)

y1(t)LO1

ADC

LO2

LO3

ADC

LO4

y2(t)

y3(t)

y4(t)

MM

SE E

qulaizer

u1[n]

u2[n]

u3[n]

u4[n]

Figure 3.2: System model of a dual-path SAW-less 4-phase receiver with same LO drives butdifferent RF nonlinearities (NLpl and NLsl)

3.2.1 Dual-path 4-phase receiver

Consider a digitized dual-path 4-phase receiver which passes the RF input signal to two

4-phase receive chains tuned to the same LO frequency but different RF nonlinearities as

shown in Fig. 3.2. In this topology, the input signal is dowconverted by two sets of 4 non-

overlapping LO phases with 25% duty cycles. Denote the four receive chains in the primary

path as receive chains one to four, and the other four in the secondary path as five to eight.

Then, the time-domain baseband output of the lth receive chain, where l ∈ 1, 2, . . . , 8, can

be written as

yl(t) = ysl(t) + ydl(t) + wl(t) (3.1)

where ysl(t) is the desired signal, ydl(t) is the distortion product, and wl(t) represents the

baseband output noise.

38

The desired signal component in the lth receive chain is

ysl(t) = α1,l

(<xBB(t)ejwRF t

×<

g1,le

jwLOt )∗ hl(t)

∼=α1,l

2<g∗1,lxBB(t)ej(wRF−wLO)t

(3.2)

where α1,l is the linear gain coefficient of the buffer corresponding to the lth receive chain,

xBB(t) is complex desired baseband equivalent signal, wRF is the carrier frequency in radians

of the desired signal, g1,l is the first Fourier coefficient of the lth LO waveform, and hl(t) is

the impulse response of the baseband lowpass filter. The harmonic residuals that fall outside

the lowpass filter bandwidth are considered to be negligible.

The distortion product can be either a kth order HM product or the qth order IM product,

i.e.,

ydl(t) =

yHMl,k

(t) HMk product

yIMl,q(t) IMq product

(3.3)

The harmonic distortion occurs due to the harmonic mixing between the input and LO

spectrum, whereas the intermodulation distortion happens due to the nonlinearity in the

buffer. The harmonic distortion product can be shown to be

yHMl,k(t) =

α1,l

(<xHMk

(t)ejwHMkt×<

gk,le

jkwLOt )∗ hl(t)

∼=α1,l

2<g∗k,lxHMk

(t)ej(wHMk−kwLO)t

(3.4)

where xHMk(t) is complex baseband signal downconverted by the kth LO harmonic, wHMk

is

the kth harmonic interferer frequency in radians, and gk,l is the kth Fourier coefficient of the

lth LO waveform.

The input-output characteristics of the nonlinear buffer can be approximated by a

memoryless polynomial. Let the qth power coefficient generate the dominant IM product at

IF. Then, the intermodulation distortion product becomes

yIMl,q(t) = αq,l

(rq(t)×<

gk,le

jkwLOt)∗ hl(t) (3.5)

39

where αq,l is the qth coefficient of the lth path corresponding to the qth power and rq(t) is

rq(t) =(<xOB1(t)ejwOB1

t + xOB2(t)ejwOB2t)q

(3.6)

where xOB1(t) and xOB2(t) correspond to complex baseband equivalent of interferers located

at wOB1 and wOB2 frequencies in radians. (3.6) can be expanded as shown in (3.7)

rq(t) =1

2q

∑m1+m2+m3+m4=q

q!

m1! m2! m3! m4!

((xOB1(t)ejwOB1

t)m1(x∗OB1

(t)e−jwOB1t)m2

×(xOB2(t)ejwOB2

t)m3(x∗OB2

(t)e−jwOB2t)m4

) (3.7)

where m1,m2,m3,m4 are non-negative integers such that (m1 +m2 +m3 +m4) = q. Among

all IM terms in (3.7), only terms that fall between frequencies (( q2)wOB1 − ( q

2)wOB2) for even

q and (( q+12

)wOB1 − ( q−12

)wOB2) for odd q are downconverted to IF. These conditions occur

when

m1,m2,m3,m4 =

q2, 0, 0, q

2

even q

0, q2, q2, 0

even qq+12, 0, 0, q−1

2

odd q

0, q+12, q−1

2, 0

odd q

(3.8)

Substituting (3.6) and (3.8) in (3.5) results in (3.9).

yIMl,q(t) =

αq,l

2q−1q!

q2! q

2!<g∗k,lx

q2OB1

(t) x∗q2

OB2(t)ej(

q2wOB1

− q2wOB2

−kwLO)t

even IMq

αq,l

2q−1q!

q+12

! q−12

!<g∗k,lx

q+12

OB1(t) x∗

q−12

OB2(t)ej(

q+12wOB1

− q−12wOB2

−kwLO)t

odd IMq

(3.9)

Sampling the baseband output of the lth receive chain,

yl[n] =

cslxBB[n] + c∗slx∗BB[n] + cdlxd[n] + c∗dlx

∗d[n] + wl[n]

(3.10)

where

csl =α1,l

4g∗1,l (3.11)

40

cdl =

α1,l

4g∗k,l HMk

αq,l

2qq!

q2! q

2!g∗k,l even IMq

αq,l

2qq!

q+12

! q−12

!g∗k,l odd IMq

(3.12)

xd[n] =

xHMk

[n] HMk

xq2OB1

[n] x∗q2

OB2[n] even IMq

xq+1

2OB1

[n] x∗q−1

2

OB2[n] odd IMq

(3.13)

The sampled signals in each chain are then digitized differentially as shown in Fig. 3.2 to

reduce the number of ADCs required to a total of four. Concatenating the differential sampled

baseband outputs of all receive chains in a vector,

u = CsxBB + C∗sx∗BB + Cdxd + C∗dxd + w (3.14)

where u = [u1, u2, u3, u4]T = [y1 − y3, y2 − y4, y5 − y7, y6 − y8]T ∈ R4, Cs = [cs1 − cs3 , cs2 −

cs4 , cs5 − cs7 , cs6 − cs8 ]T ∈ C4, Cd = [cd1 − cd3 , cd2 − cd4 , cd5 − cd7 , cd6 − cd8 ]

T ∈ C4, and

w = [w1 − w3, w2 − w4, w5 − w7, w6 − w8]T ∈ R4. The index n was omitted for notational

simplicity. The first term on the right-hand side of (3.14) represents the desired signal scaled

by the signature vector cs, while the subsequent three terms are the image of the desired

signal vector and the distortion and its image signal vectors.

To suppress the distortion caused by the image of the desired signal and the distortion

signals, an MMSE equalizer can be obtained by minimizing the following cost function:

hmmse = arg minh∈C2

E‖xBB − hHu‖2 (3.15)

Removing all irrelevant scaling terms, the MMSE equalizer can be shown to be

hmmse = R−1u cs (3.16)

41

where Ru = E[uuT ]. As the digitized sample covariance matrix Ru is unknown in practice,

it can be estimated by averaging L recently received samples, i.e.,

Ru[m] =1

L

m∑k=m−L+1

u[k]uT [k] (3.17)

The MMSE combining weights of u samples are readily realized by simply estimating the

covariance matrix Ru ∈ R4×4, inverting it, then multiplying by cs (which is known a priori).

As the MMSE equalizer in (3.16) depends on the second-order statistics of the baseband

samples (via Ru), the weights vary according to the operating environment to minimize the

mean-squared estimate of xBB. The 4-tap equalizer hmmse attempts to minimize interferer

distortion by adaptively weighting and summing baseband outputs as shown in Fig. 3.2.

The equalizer in (3.16) can suppress xd, which can be either a harmonic or intermodulation

distortion product, as long as the desired signal signature vector cs is not in the subspace

spanned by c∗s, cd, and c∗d. This condition is equivalent to ensuring that matrix C =

[cs, c∗s, cd, c

∗d] is of rank four, which would be sufficient to extract xBB while suppressing x∗BB,

xd, and x∗d. To ensure that C is full rank, an offset is introduced between the LO phases in

the primary and secondary paths, which is equivalent in effect to having a nonuniform LO

phase spacing (Babakrpur and Namgoong, 2017b; Namgoong, 2015).

3.2.2 K-path M-phase receiver

In the presence of multiple distortion sources, (3.14) can be rewritten as

u = csxBB + c∗sx∗BB +

N∑i=1

(cdixdi + c∗dixdi) + w (3.18)

where N represents the number of distortion products that are simultaneously present. Instead

of the dual-path 4-phase receiver, consider a more general K-path M -phase receiver. Then,

the receiver can suppress N distortion products as long as the following two conditions are

satisfied: 1) rank of C = [cs, c∗s, cd1 , c

∗d1, . . . , cdN , c

∗dN

] ∈ CKM/2×(2N+2), is 2N + 2; 2) number

42

of IM products is less than or equal to (K − 1) assuming that the corresponding nonlinear

polynomial gain coefficients of the K buffers are different. For example, extending the number

of phases in our earlier dual-path 4-phase receiver in Fig. 3.2 to a dual-path 6-phase receiver

can suppress at most two HM products, or one IM and one HM products.

3.2.3 Simulation results

A dual-path 4-phase, dual-path 6-phase, and triple-path 4-phase SAW-less receivers are

simulated using MATLAB. In all three receivers, the primary and secondary buffers have,

respectively, small signal gains of 10 and 8, OBIIP2 of 50dBm and 40dBm, OBIIP3 of 10dBm

and 0 dBm, and OBIIP5 of 0dBm and -10dBm. The tertiary buffer in the triple-path 4-phase

receiver has a small signal gain of 7, OBIIP2 of 43dBm, OBIIP3 of 1dBm, and OBIIP5 of

-5dBm. While buffer group delays are assumed to be constant versus frequency, the phase

offset of the secondary and tertiary LO phases with respect to the primary LO phases are set

to be 10 and -10 degrees, respectively, both of which are sufficient to provide nonuniform LO

sets. The simulation results for different distortion scenarios are shown in Table 3.1. In each

distortion scenario, the power of corresponding interferers as well as distortion reductions

are presented. The distortion reductions are defined as ∆IMq and ∆HMk, representing the

difference between the value of distortion product prior to and after digital equalization with

respect to the primary path. As discussed earlier, the dual-path 4-phase implementation is

able to suppress one distortion product, i.e., one IM product (IM3 or IM5) or one HM product

(e.g., HM3 or HM7). When two distortion products are present, even though their power

is weak, the equalizer provides minimal improvement (e.g., IM2, IM3) or significant signal

gain reduction (e.g., HM3, IM2). The dual-path 6-phase receiver can suppress the distortion

products in the presence of one IM product (e.g., IM3), two HM products (e.g., HM3, HM5),

or one IM and one HM products (e.g., (HM3, IM2) or (HM9, IM5)). In the presence of

more than one IM product or two HM products, the MMSE equalization results in minimal

43

Table 3.1: Simulation results

Receivertype

Distortionscenario

Interferer(s)power (dBm)PHMk, (POB1, POB2)

Distortionreduction (dB)∆IMq,∆HMk

Dual4-phase

IM3IM5HM3HM7IM2, IM3HM3, IM2

(-15,-15)(-15,-15)-30-30(-35,-35)-50, (-20,-20)

63.363.374.974.90.7, 3.3∆Gs =15.5∗

Dual6-phase

IM3HM3, HM5HM3, IM2HM9, IM5IM2, IM3HM3, HM5, HM7

(-15,-15)-30,-30-30, (-15,-15)-30, (-15,-15)(-35,-35)-50, -50, -50

63.381.7, 81.764.4, 64.466.8, 66.80.7, 3.3∆Gs =32.4∗

Triple4-phase

IM2, IM3IM3, IM5IM2, IM3, IM5HM3, HM5HM3, HM5, HM7HM9, IM5HM3, HM5, IM5

(-15,-15)(-15,-15)(-35,-35)-30, -30-50, -50, -50-30, (-15,-15)-50, -50, (-35, -35)

78.9, 78.977.3, 77.374.4 74.4, -17.267.9, 67.9∆Gs =33.9∗

77.4, 77.471.6, 64, -5.5

∗ Desired signal gain reduction

reduction of distortion products (e.g., IM2, IM3) or significant reduction of desired signal

gain (e.g., HM3, HM5, HM7). The triple 4-phase receiver can suppress two IM products

(e.g., IM2, IM3), two HM products (e.g., HM3, HM5), or one HM and one IM products (e.g.,

HM9, IM5).

Another important observation to note regarding the MMSE equalizer in (3.16) is that it

requires knowledge of neither the correlation coefficient between additive noise of the two

paths nor the nonlinear distortion coefficients terms. Their effects are all accounted for in the

covariance matrix Ru when estimating the equalizer in (3.16). Therefore, noise cancellation

is concurrently performed when suppressing distortion products.

44

3.3 Experimental Results

A dual-path SAW-less 4-phase prototype is fabricated in 130 nm CMOS process. The receiver

architecture is similar to (Babakrpur and Namgoong, 2017b) presented by the authors. The

primary path is based on a 4-phase mixer-first architecture, while the secondary path is

realized using a Gm-first topology. The mixer-first primary path provides wideband matching

tunable with LO frequency and RF out-of-band interferer attenuation. The secondary path,

which employs a Gm-first topology, provides a unilateral feedforward path to minimize the

coupling from the secondary path to the primary path. Additional circuit level details of

the receiver can be found in (Babakrpur and Namgoong, 2017b). The output of both paths

are digitized by differential off-chip ADCs. The sampled signals are processed in MATLAB

on a PC, then weighted and summed using hmmse derived in (3.16) to obtain an estimate

of the desired signal in the presence of HM and IM products. The covariance matrix Ru is

continuously updated using (3.17) in the background. The MMSE equalizer hmmse can be

updated at fixed time intervals or when changes to Ru estimate become significant. The

measurement setup is shown in Fig. 3.3.

Fig. 3.4 plots the OBIIP2 and OBIIP3 versus frequency offset when LO frequency is 425

MHz. The OBIIP3 measurement is based on two -15 dBm blocker tones at fLO +4f and

fLO + 24f − fIF , where fIF = 1MHz and 4f is varied from 20 MHz to 100 MHz. When

determining hmmse, a -15 dBm desired signal tone is placed at fLO + fIF . IIP3 values are

calculated based on the measured IM3 levels before and after equalization. The measured

OBIIP3 without equalization is 19 dBm at 80 MHz frequency offset. As shown in Fig. 3.4,

OBIIP3 improves by 12.2 dB at 80 MHz and >12 dB over the entire frequency offset range.

In the OBIIP2 measurement, two interferers with the same power levels as in the previous

measurement are applied at fLO +4f and fLO +4f − fIF . After digital compensation, the

OBIIP2 of the mixer-first topology increased from 60 dBm to 84 dBm at 80 MHz, while the

overall increment exceeds 18 dB over the frequency offset range of 20 MHz to 100 MHz.

45

Figure 3.3: Die micrograph (Active Area is 1mm2)

As an example of higher order intermodulation products, OBIIP5 at 80 MHz frequency

offest is also measured when two tones at 505 MHz and 544.5 MHz are applied to the receiver.

The OBIIP5 measured to be 8.2 dBm before equalization and improved to 15 dBm after

digital compensation.

The OBIIPn improvement depends on interferers power level. When the interferers and so

as intermodulation product power increases in the linear region, the equalizer will have better

estimation of the intermodulation product resulting in improving compensated OBIIPn. As

an example, the OBIIP5 as a function of interferer power is shown in Fig. 3.5. It can be seen

that OBIIP5 improves when blocker power increases. As interferer power becomes higher

than 0 dBm, the desired signal will be desensitized in the presence of interferers and the

equalizer cannot distinguish between signal and IM products properly. Although not shown,

the receiver achieves HRR>75 dB for harmonic interferers up to measured 11th (Babakrpur

and Namgoong, 2017b). Also, the overall noise figure of the dual-path receiver after applying

the equalizer is reduced by 2-2.5 dB in compare with when only primary path is functional.

46

Table 3.2: Comparison table

Specifications This Work (Murphy et al., 2012)(van Liempd et al.,2014)

Technology 130nm 40nm 28nm

RF Freq. (GHz) 0.1-1.45 0.08-2.7 0.4-6

Number of phases 4 8 8/4

OBIIP 2,3,5 (dBm) 84,31,15 55,13.5,N/A >80.5,>5,N/A

HRR 3,5,7 (dB) >75,>75,>75 42,45,N/A >70,>75,N/A

Power (mW) 43-56∗ 35-78 <40

∗ Does not include power consumption of the digital section

The receiver NF remains between 2.4 to 3.9 dB over operational frequency range of 0.1 to

1.45 GHz. As discussed in Sec. IIA, the dual-path 4-phase implementation has one degree of

freedom, which can be exploited to suppress one HM product or one IM product regardless of

their order. This work is compared with relevant wideband receivers in Table 3.2. A 6-phase

realization of the dual-path receiver can simultaneously suppress two interferer distortion

products, which can be one IM product and one HM product or two HM products.

47

Figure 3.4: Measured out-of-band IIP2 and IIP3 versus frequency offset

Figure 3.5: Measured out-of-band IIP5 improvement versus interferer power

48

CHAPTER 4

MATCHING FOR CONCURRENT HARMONIC SENSING IN AN

M-PHASE MIXER-FIRST RECEIVER1

4.1 Introduction

The ability of a receiver to sense multiple LO harmonics is attractive in a cognitive radio

system. Such a capability enables the receiver to reduce the spectrum sensing time while

relaxing the frequency synthesizer tuning range requirements (Razavi, 2010)(Ghasemi and

Sousa, 2008). When sensing multiple harmonic bands, however, potential interferers located

at other undesired LO harmonics can downconvert along with the desired harmonic signal

bands, causing signal distortion. The harmonic sensing receiver, therefore, needs to be able

to select the desired LO harmonic bands for reconstruction while suppressing LO interferers.

The ability of a harmonic-rejection mixer (HRM)-based receivers to sense higher LO

harmonics was recognized in (Forbes and Gharpurey, 2014)(Murphy et al., 2012). In an

M -phase HRM-based receiver, the received RF signal is downconverted using M LO phases

each with a phase difference of 2π/M . The downconverted signals from the M paths are

then weighted appropriately to reconstruct the desired signal at selected LO harmonics

while rejecting other harmonics. In (Forbes and Gharpurey, 2014), for example, a 16-phase

HRM-based receiver is programmed by reordering weighting coefficients to sense signals at

LO harmonics up to the seventh. Although this receiver can sense only one harmonic signal

band at a time, multiple harmonic bands could be sensed by placing additional gain paths

with appropriate weights.

In order to sense signals at one or multiple LO harmonic bands, input matching must

occur at all the desired harmonics. One approach is to employ low-noise transconductance

1 c©2017 IEEE. Reprinted, with permission, from E. Babakrpur and W. Namgoong, “Matching forConcurrent Harmonic Sensing in an M-Phase Mixer-First Receiver”, IEEE Transactions on Circuits andSystems II: Express Briefs, Sep 2017.

49

amplifier (LNTA) with wideband input matching (Forbes and Gharpurey, 2014). If the

center frequency is high, simple input matching as in (Forbes and Gharpurey, 2014) becomes

ineffective, requiring more complicated wideband matching networks, which may be power

hungry and challenging to realize in practice. Furthermore, as interferers in undesired LO

harmonics are not attenuated before downconversion, higher harmonic rejection is subsequently

needed.

4.2 System Model and Perfect Matching

An M -phase passive mixer downconversion path is shown in Fig. 4.1. In this topology, input

matching is achieved by exploiting the interaction between the passive mixers and baseband

impedances. The baseband impedance upconverts to the RF port by the use of multiple

single-ended passive mixers driven by non-overlapping LO pulses so that signal translation

between baseband and RF ports happens at all segments of the LO period. As a result,

input matching at the receiver input becomes tunable with LO frequency (Mirzaei et al.,

2010)(Andrews and Molnar, 2010a). Although the mixer-first receiver is a linear time-varying

system (assuming linear passive mixers), an equivalent linear time invariant (LTI) model

can be employed (see Fig. 4.2) for analysis purposes when the time constants of baseband

impedances are much higher than the LO period (Murphy et al., 2012)(Andrews and Molnar,

2010a). Assuming a wideband antenna whose source resistance is real and constant for all

harmonics with value Rs, the derivations in (Murphy et al., 2012) simplifies to yield equivalent

folding impedance at the mth harmonic, Zsh[m], and the upconverted baseband impedance

at the mth harmonic, ZRB[m], that are given by

ZRB[m] =1

Msinc2(

mπ

M)ZBB (4.1)

Zsh[m] =sinc2(mπ

M)

1− sinc2(mπM

)(Rs +Rsw) (4.2)

50

Zs

VBB0

VBB1

VBB(M-1)

...

VRF

LO0

LO1

LO(M-1)

ZBB

ZBB

ZBB

Figure 4.1: M-phase passive mixer downconversion path

VRF [m]

Rs

Rsw

Zsh [m] ZRB [m]

Figure 4.2: LTI model for an M-phase passive mixer at the mth LO harmonic

where Rsw is the switch resistor of each path. As Zsh[m] is real from (4.2), we subsequently

use Rsh[m] instead of Zsh[m] to underscore that Zsh[m] is real. Furthermore, for a zero-IF

receiver, ZRB[m] becomes real and denoted as RRB[m].

51

Figure 4.3: Folding shunt impedance Rsh[m] as a function of LO harmonic order forM = 4, 8, 12 and 16 phases when Rsw = 10Ω

4.2.1 Perfectly Matchable Harmonics

Using the LTI model in Fig. 4.2, matching condition at the antenna interface requires

Rsh[m] ‖ RRB[m] = Rs −Rsw (4.3)

Unlike impedance RRB[m] that can be tuned by baseband impedance RBB, Rsh[m] is a

function of the number of LO phases M and the switch resistance Rsw, whose achievable

value is dependent on process technology. Therefore, assuming baseband impedance is set

sufficiently high, matching at the mth harmonic as given in (3) requires that

Rsh[m] ≥ Rs −Rsw (4.4)

To better understand the matching limitations of an M -phase mixer at higher LO

harmonics, Rsh[m] is plotted as a function of harmonic order for 4, 8, 12 and 16 LO phases

in Fig. 4.3 assuming Rsw = 10Ω and Rs = 50Ω. The gray region represents Rsh[m] values

52

that do not satisfy (4.4) and, consequently, fail to achieve matching. A 4-phase mixer can be

matched for sensing only the first harmonic. Input impedance of a 12-phase mixer, however,

can reach 50Ω at the first, third, or fifth harmonic. By assigning proper baseband impedance,

input matching can be tuned to select one, two or three LO harmonics. Similarly, a 16-phase

receiver can be perfectly matched for sensing harmonics up to the seventh.

4.2.2 Single Harmonic Matching

Consider matching to a single harmonic LO frequency that is less than MfLO. Signals in

LO harmonics greater than MfLO are assumed negligible due to the inherent bandwidth

limitations of the circuit and/or the low mixer harmonic gain coefficient. For harmonics

less than M , the receiver input impedance can be readily shown to decrease monotonically

with increasing harmonic order regardless of the baseband impedance. Consequently, perfect

matching can be achieved at one and only one harmonic frequency. The baseband resistance

required to achieve perfect matching of Rs at the mth LO harmonic (where m < M), denoted

as RBBopt , can be obtained by substituting (4.1) and (4.2) in (4.3) then solving for RBB to

obtain

RBBopt [m] =M(R2

s −R2sw)

(2sinc2(mπM

)− 1)Rs +Rsw

(4.5)

Although the mixer-first receiver can achieve perfect matching at only one LO harmonic

frequency, baseband impedance can be optimized to provide impedances “close enough” to

Rs when concurrently sensing multiple harmonics.

4.3 Approximate Harmonic Matching

As noted in the previous section, perfect matching can be achieved in only one LO harmonic.

To support signals at multiple LO harmonics, RBB can be tuned to achieve “approximate”

harmonic matching at the desired LO harmonics. To more precisely define the term “approx-

imate”, two matching approaches with different objectives are proposed. First, we minimize

53

the maximum absolute value of return loss (Γ) of the desired LO harmonics, i.e.,

minRBB

maxm∈Hd

|Γ [m]| (4.6)

where Γ [m] is the Γ of the mth harmonic, and Hd represents the set of desired LO harmonic

indices. In other words, we want to select RBB such that the worst matching among the

desired LO harmonics is as good as possible. The solution to this problem turns out to be

quite simple and intuitive as discussed later in this section.

The second “approximate” matching approach solves a constrained optimization problem,

namely, find RBB that maximizes the minimum |Γ| of the undesired LO harmonics while

ensuring that |Γ| of the desired LO harmonics is below |Γdes|, i.e.,

maxRBB

mink∈Hu

|Γ [k]|

subject to |Γ [m]| ≤ |Γdes|, for all m ∈ Hd

(4.7)

whereHu denotes the set of undesired LO harmonic indices. In other words, while constraining

the desired LO harmonics to satisfy a certain level of input matching (i.e., |Γ| ≤ |Γdes|),

the undesired harmonics are made as unmatched as possible by maximizing the lowest |Γ|

of the undesired LO harmonics. This second optimization problem can be shown to be

quasi-convex, whose optimum solution can be readily solved using well-known numerical

techniques (Gromicho, 1998). As the resulting numerical solution would provide little insight,

we instead relax the constraints in (4.7) to obtain a simple analytic solution. We then show

that under realistic operating conditions, the analytic solution satisfies the constraints in

(4.7) and, hence, is the solution to (4.7).

4.3.1 Input Resistance

To solve the two optimization problems in (4.6) and (4.7), we note a couple of characteristics

of the input resistance of the mixer-first M -phase receiver. Using the LTI model in Fig. 4.2,

54

the input resistance at the mth harmonic is

Rin[m] = Rsw +Rsh[m] ‖ RRB[m] (4.8)

where Rsh[m] and RRB[m] are given in (4.2) and (4.1), respectively. Both RRB[m] and Rsh[m]

decrease monotonically with increasing m for m < M . Therefore, assuming M is even,

Rin[1] > Rin[3] > . . . > Rin[M − 1] (4.9)

Another characteristic to note is that as RBB increases, Rin[m] monotonically increases

for m ∈ 1, 3, . . . ,M − 1, because RRB[m] is linearly proportional to RBB while being

independent of Rsw and Rsh[m] as evident from (4.1).

4.3.2 Minimize Maximum |Γ | of Desired Harmonics

The Smith chart is used to solve the first optimization problem. Rin[m] is located on the

horizontal axis of the Smith chart with Rin[1] being the furthest to the right followed by

Rin[3] then Rin[5], etc. because of (4.9). This is illustrated in Fig. 4.4 for a 12-phase (i.e.,

M = 12) mixer-first receiver with an arbitrary baseband resistor.

Assume we are interested in sensing the first and third LO harmonics. To absorb as much

of the incoming signal energy in the first and third harmonics, |Γ| at these harmonics should

be as small as possible. In the Smith chart, constant |Γ| is represented by concentric circles

centered at the origin with larger circles denoting higher |Γ| values. Hence, the objective is to

vary RBB such that the constant |Γ| circle encompassing both Rin[1] and Rin[3] is as small

as possible. The objective in (4.6) is achieved when Rin[1] and Rin[3] are equidistant from

the origin. This can be readily shown using Fig. 4.5. Consider Fig. 4.5(a) in which Rin[1]

is closer to the origin than Rin[3]. The minimum encompassing |Γ| circle passes through

Rin[3] on the left edge while encircling Rin[1]. In this case, the constant |Γ| circle can be

further reduced by increasing RBB, since both Rin[1] and Rin[3] would then move to the

55

10.5 2 50.2

Rin[1]

Rin[3]

Rin[5]

Figure 4.4: Input impedance of an 12-phase mixer first receiver at first, third and fifthharmonics

10.5 2 50.2 10.5 2 50.2

(a) (b)

10.5 2 50.2

(c)

Rin[1]

Rin[3]

Rin[5]

Rin[1]

Rin[3]

Rin[5]

Rin[1]

Rin[3]

Rin[5]

Figure 4.5: Optimum baseband impedance for minimizing maximum |Γ| when matching firstand third simultaneously

56

right, causing the larger |Γ [3]| to decrease while increasing the smaller |Γ [1]|. To obtain

the minimum encompassing |Γ| circle, RBB should be increased until Rin[1] and Rin[3] are

equidistant from the origin, i.e., |Γ [1]| = |Γ [3]|. Similarly, if Rin[1] is further away from the

origin than Rin[3] in the Smith chart as shown in Fig. 4.5(b), RBB needs to be decreased

until Rin[1] and Rin[3] are equidistant as shown in Fig. 4.5(c).

Since the solution to (4.6) occurs when the absolute value of the return loss is the same

at the first and third harmonics,

Rin[1]−Rs

Rin[1] +Rs

=Rs −Rin[3]

Rs +Rin[3](4.10)

Simplifying (4.10), the input resistances of the first and third LO harmonics in this example

satisfy

Rin[1] ·Rin[3] = R2s (4.11)

(4.11) states that the solution to the optimization problem in (4.6) occurs when the geometric

mean of the two desired harmonic input resistances is equal to the source resistance.

For the general case of more than two desired harmonics, the worst |Γ| is minimized when

the geometric mean of the lowest and highest harmonic resistances equals Rs, i.e.,

R2s = Rin[ml] ·Rin[mh]

=

[Rsw +Rsh[ml] ‖

(1

Msinc2(

mlπ

M)RBBopt

)]·[

Rsw +Rsh[mh] ‖(

1

Msinc2(

mhπ

M)RBBopt

)] (4.12)

where ml and mh denote the indices of the lowest and highest harmonics, respectively, and

RBBopt is the baseband resistance that satisfies the equality in (4.12). The second equality is

obtained by substituting (4.1) to (4.8) for Rin[ml] and Rin[mh]. When (4.12) is satisfied, the

mlth and mhth harmonics are located at the opposite edges of the |Γ| circle in the Smith

chart. The harmonics between ml and mh will have lower |Γ| values, because they are located

inside the |Γ [ml]| = |Γ [mh]| circle in the Smith chart.

57

Examples of different matching cases that satisfy (4.6) are illustrated in Fig. 4.6 for a

12-phase mixer-first receiver assuming Rsw = 10Ω and Rs = 50Ω. In Fig. 4.6(a), the desired

harmonic is the first harmonic only and |Γ [1]| = 0 when RBBopt = 498.7Ω, which corresponds

to the perfectly matched case. In Fig. 4.6(b), the desired harmonics are the first and third

harmonics. When RBBopt = 583Ω, the |Γ| = 0.06 circle represents the smallest |Γ| circle to

encompass both the first and third harmonics. Fig. 4.6(c) corresponds to when the desired

harmonics are the first, third, and fifth. The minimum |Γ| circle that encompasses all three

passes through the first and fifth harmonics while encircling the third is 0.19, which occurs

when RBBopt = 797.9Ω. Finally, Fig. 4.6(d) is similar to Fig. 4.6(b) except that the desired

harmonics is the third and fifth harmonics. The minimum |Γ| is 0.13.

4.3.3 Maximize Suppression of Undesired Harmonics

The second approach to achieving “approximate” harmonic matching is to maximize |Γ|

of the undesired harmonics while ensuring a certain |Γ| level for the desired harmonics.

This matching approach, which is formalized in (4.7), can be shown to be a quasi-convex

optimization problem, which can be solved numerically (Gromicho, 1998). To gain better

insight, the optimization problem in (4.7) is instead solved graphically using the Smith chart.

Let |Γmax| be the radius of a |Γ| circle with all the undesired harmonics outside. Then, the

objective in (4.7) is to maximize |Γmax| while ensuring that all the desired harmonics are

encompassed by a |Γ| circle with radius |Γdes|, where |Γdes| < |Γmax|.

Our approach to solving (4.7) differs depending on whether the lowest desired harmonic

ml is one or higher. If ml = 1 and assuming a solution to (4.7) exists, RBB must be selected

so that |Γ| of the highest desired harmonic must be at the left boundary of |Γdes| circle to

maximize |Γmax|, i.e.,

|Γ [mh]| = |Γdes| (4.13)

58

10.5 2 5

Γmin = 0

0.2 10.5 2 5

Γmin = 0.06

0.2

10.5 2 5

Γmin = 0.19

0.2 10.5 2 5

Γmin = 0.13

0.2

(a) (b)

(c) (d)

Rin[1]

Rin[3]

Rin[5]

Rin[1]

Rin[3]

Rin[5]

Rin[1]

Rin[3]

Rin[5]

Rin[1]

Rin[3]

Rin[5]

Figure 4.6: Geometric impedance mean for minimizing maximum |Γ| when a) 1st is perfectlymatched; RBBopt = 498.7Ω, b) 1st and 3rd are matched; RBBopt = 583Ω, c) 1st, 3rd and 5th

are matched; RBBopt = 797.9Ω, d) 3rd and 5th are matched; RBBopt = 1037.7Ω

59

If the lowest desired harmonic is the third or higher (i.e., ml ≥ 3), we relax the constraints

in (4.7) and instead solve

|Γmax| = maxRBB

mink∈Hu

|Γ [k]|

subject to |Γ [m]| ≤ |Γmax|, for all m ∈ Hd

(4.14)

Under realistic operating conditions and reasonable |Γdes| values, the solution to (4.14) also

satisfies the constraints in (4.7) (i.e., |Γ [m]| ≤ |Γdes| for all m ∈ Hd) and, hence, is the

solution to (4.7). Using similar geometric arguments as in the previous subsection, |Γmax|

is obtained when the geometric mean of the two closest undesired harmonics to the desired

harmonics is Rs, i.e.,

Rin[ml − 2] ·Rin[mh + 2] = R2s

(4.15)

When (4.15) is satisfied, |Γ| values of the desired harmonics are less than |Γmax|.

In summary, if ml = 1, the solution to (4.7), if it exists, requires that (4.13) be satisfied.

If ml ≥ 3, the condition in (4.15) must be met. As a numerical example, Table 4.1 lists the

optimum RBB values, RBBopt , for approximate matching using (4.7) with Γdes = 0.32 (or 10dB

return loss) and the corresponding Rin and |Γ| values for different desired harmonics when a

12-phase mixer-first receiver is employed. Simulation results based on Cadence Spectre RF are

also shown. Passive mixers are modeled as an ideal switch in series with Rsw = 10Ω resistor.

When 1st, (1st, 3rd) and (1st, 3rd, 5th) are desired, RBBopt satisfies (4.13). When (3rd, 5th) are

the sensing harmonics, geometric mean of the closest rejecting bands (i.e., 1st and 7th) as

given in (4.15) determine the RBBopt . Similarly, 3rd and 7th are the closest rejecting bands

when the 5th harmonic is desired.

60

Table 4.1: Approximate matching using (4.7) for concurrent harmonic sensing. Spectre RFsimulation results are in parentheses.

Desired Harmonic(s) RBBoptRin[1] Rin[3] Rin[5] Rin[7] |Γ[1]| |Γ[3]| |Γ[5]| |Γ[7]|

1st 198.226.1(26.9)

22.7(23.5)

18.1(18.75)

13.8(14.6)

0.32(0.3)

0.38(0.36)

0.47(0.45)

0.57(0.55)

1st, 3rd 253.330.5(31.4)

26.1(26.7)

19.9(20.6)

14.7(15.4)

0.24(0.23)

0.32(0.3)

0.43(0.42)

0.55(0.53)

1st, 3rd, 5th 455.346.6(47.4)

37.5(37.7)

26.1(26.3)

17.2(17.9)

0.03(0.03)

0.14(0.14)

0.32(0.31)

0.49(0.47)

3rd, 5th 1265.4109.2(109.0)

74.1(72.3)

41.9(40.3)

22.9(23.1)

0.37(0.37)

0.2(0.18)

0.09(0.11)

0.37(0.37)

5th 1997.3163.1(167.6)

98.4(96.0)

50.1(48.0)

25.4(25.4)

0.53(0.54)

0.33(0.32)

0.01(0.02)

0.33(0.33)

4.4 Noise Figure of Harmonic Sensing Receiver

The noise figure (NF) of an M -phase mixer-first receiver at the mth LO harmonic can be

analyzed based on the LTI model given in (Murphy et al., 2012) and shown to be

NF [m] =1 + Rsw

Rs+

V 2nop

MV 2nRs

+ MRs

(1+A)RBB(1 + Rsw

Rs)2

sinc2(mπM

)(4.16)

where V 2nop

and V 2nRs

represent the equivalent baseband operational amplifier and source

resistance noise power density, respectively, and A is baseband amplifier open loop gain.

Assuming sufficiently high feedback resistance (e.g., >0.2kΩ) and baseband gain (e.g., 40dB),

the noise contribution of the baseband feedback resistor is negligible compared to that of

the baseband amplifier and switch resistor as evident from (16). Thus, the approximately

matched NF is similar to the perfectly matched case. Fig. 4.7 plots the incremental noise

figure using (4.16) for different M -phase receivers. As evident from Fig. 4.7, employing more

LO phases to match to a higher harmonic reduces the NF loss.

In Fig. 4.8, NF of a 12-phase mixer-first receiver when concurrently sensing the 1st, 3rd and

5th harmonics is simulated using periodic steady-state noise analysis in SpectreRF. In this

simulation, Rsw = 10Ω, input-referred noise voltage of each baseband amplifier is 2nV/√

Hz

and A is 40dB. The first approach to approximate matching (i.e., (4.6)) is employed to yield

RBB = 797.9Ω (see Fig. 4.6). The bandwidth is set to be 1MHz while LO frequency is 1GHz.

The simulated harmonic NF matches closely with the analytically derived equation in (4.16).

61

Figure 4.7: NF increment as a function of harmonic order

Figure 4.8: Simulated harmonic NF of a 12-phase receiver

62

CHAPTER 5

CONCLUSIONS

A wideband nonuniform dual-path receiver capable of rejecting higher order LO harmonics is

implemented. Unlike the widely employed 8-phase analog HRMs, the proposed wideband

receiver suppresses any of the harmonic interferers including seventh and ninth while using

only four multiphase clocks. This work also represents the first experimental validation of the

proposed MMSE digital equalizer, which enables robust harmonic rejection in the presence of

gain and phase mismatches. In the proposed 4-phase dual-path receiver, the MMSE equalizer

minimizes the LO harmonic distortion while accounting for the noise correlation among the

polyphase paths to achieve high HRR and low NF values. The proposed receiver achieves

HRR>75 dB for LO harmonic interferers up to measured eleventh harmonic and 3.1 dB NF

at 1 GHz RF frequency.

A mathematical system framework is derived for analyzing harmonic and out-of-band

interferers. An MMSE distortion equalizer is then employed to suppress the distortion

products, which can be an intermodulation product and/or harmonic distortion product. As

a proof of concept, the equalizer performance is experimentally evaluated in a dual-path

4-phase receiver.

Finally, The use of passive mixer-first receiver to concurrently sense higher LO harmonics

is presented. The approximate matching conditions are derived for two different objectives,

namely, minimizing the maximum return loss of the desired harmonics and maximizing the

minimum return loss of the undesired harmonics while constraining the desired harmonics

return loss. Intuitive analytical solutions are derived.

63

REFERENCES

Andrews, C., C. Lee, and A. Molnar (2012, Sep). Effects of LO harmonics and overlapshunting on n-phase passive mixer based receivers. Proc.ESSCIRC , 117–120.

Andrews, C. and A. Molnar (2010a, Dec). Implications of passive mixer transparency forimpedance matching and noise figure in passive mixer-first receivers. IEEE Trans. CircuitsSyst. I , 3092–3103.

Andrews, C. and A. Molnar (2010b, Dec). A passive mixer-first receiver with digitallycontrolled and widely tunable RF interface. IEEE J. Solid-State Circuits 45 (12), 2696–2708.

Babakrpur, E. and W. Namgoong (2016, May). A 4-phase blocker tolerant wideband receiverwith MMSE harmonic rejection equalizer. IEEE Radio Freq. Integrated Circuits Symp.,242–245.

Babakrpur, E. and W. Namgoong (2017a). Digital cancellation of harmonic and intermod-ulation distortion in wideband saw-less receivers. IEEE Trans. Circuits Syst. II, Exp.Brief .

Babakrpur, E. and W. Namgoong (2017b, Feb). A dual-path 4-phase nonuniform widebandreceiver with digital MMSE harmonic rejection equalizer. IEEE Trans. Microw. TheoryTech. 65 (2), 386–395.

Babakrpur, E. and W. Namgoong (2017c, Sept). Matching for concurrent harmonic sensingin an M -phase mixer-first receiver. IEEE Trans. Circuits Syst. II, Exp. Brief 64 (9),1017–1021.

Bruccoleri, F., E. Klumperink, and B. Nauta (2004, Feb). Wide-band CMOS low noiseamplifier exploiting thermal noise canceling. IEEE J. of Solid-State Circuits 39 (2), 275–281.

Cha, H. K., K. Kwon, J. Choi, and H. T. Kim (2010, Nov). A CMOS wideband RF front-end with mismatch calibrated harmonic rejection mixer for terrestrial digital TV tunerapplications. IEEE Trans. Microw. Theory Techn., 2717–2730.

Choke, T. et al. (2013, May). A multiband mobile analog TV tuner SoC with 78-dB harmonicrejection and GSM blocker detection in 65-nm CMOS. IEEE J. Solid-State Circuits 48 (5),1174–1187.

Ericsson (2017, accessed June 2018). Ericsson mobility report. https:

//www.ericsson.com/assets/local/mobility-report/documents/2017/

ericsson-mobility-report-november-2017-central-and-eastern-europe.pdf.

64

Forbes, T. and R. Gharpurey (2014, Sep). A 2 GS/s frequency-folded ADC-based broadbandsampling receiver. IEEE J. Solid-State Circuits 49 (9), 1971–1983.

Forbes, T., W. Ho, and R. Gharpurey (2013, Oct). Design and analysis of harmonic rejectionmixers with programmable LO frequency. IEEE J. of Solid-State Circuits , 2363–2374.

Ghasemi, A. and E. Sousa (2008, Apr). Spectrum sensing in cognitive radio networks:Requirements, challenges and design trade-offs. IEEE Communication Magazine 46 (4),32–39.

Grimm, M. et al. (2014, Jan). Joint mitigation of nonlinear RF and baseband distortions inwideband directconversion receivers. IEEE Trans. Microw. Theory Tech. 62 (1), 166–182.

Gromicho, J. (1998). Quasiconvex Optimization and Location Theory. Kluwer AcademicPublishers.

Keehr, E. and A. Hajimiri (2011, May). Successive regeneration and adaptive cancellationof higher order intermodulation products in RF receivers. IEEE Trans. Microw. TheoryTech. 59 (5), 1379–1396.

Lerstaveesinand, S., M. Gupta, D. Kang, and B.-S. Song (2008, Sep). A 48-860 MHz CMOSlow-IF direct-conversion DTV tuner. IEEE J. Solid-State Circuits 43 (9), 2013–2024.

Li, C., M. Li, M. Verhelst, A. Bourdoux, L. V. der Perre, and S. Pollin (2015, Jan). On thegeneral mathematical framework, calibration/compensation method, and applications ofnon-ideal software defined harmonics rejection transceivers. IEEE Trans. Microw. TheoryTech. 62 (1), 292–301.

Liu, Y. (2017, Jan). Adaptive blind postdistortion and equalization of system impairments fora single-channel concurrent dual-band receiver. IEEE Trans. Microw. Theory Tech. 65 (1),302–314.

Ma, Y., Y. Yamao, K. Ishibashi, and Y. Akaiwa (2013, Dec). Adaptive compensation ofinter-band modulation distortion for tunable concurrent dualband receivers. IEEE Trans.Microw. Theory Tech. 61 (12), 4209–4219.

Mak, I. and R. Martins (2011, Feb). A 0.46 mm2 4 dB-NF unified receiver front-end forfullband mobile TV in 65 nm CMOS. IEEE ISSCC Dig. Tech. Papers , 172–173.

Mirzaei, A., H. Darabi, et al. (2010, Sep). Analysis and optimization of direct-conversionreceivers with 25% duty-cycle current-driven passive mixers. IEEE Trans. Circuits Syst. I ,2353–2366.

Moseley, N., E. Klumperink, and B. Nauta (2008, Oct). A two-stage approach to harmonicrejection mixing using blind interference cancellation. IEEE Trans. Circuits Syst. II,Express Briefs 55, 966–970.

65

Murphy, D., H. Darabi, A. Abidi, et al. (2012, Dec). A blocker-tolerant, noise-cancellingreceiver suitable for wideband wireless applications. IEEE J. Solid-State Circuits, 2943–2963.

Murphy, D., A. Hafez, A. Mirzaei, and et al. (2012, Feb). A blocker-tolerant widebandnoise-cancelling receiver with a 2 dB noise figure. IEEE ISSCC Dig. Tech. Papers , 74–75.

Murphy, D., A. Mirzaei, H. Darabi, M. Chang, and A. Abidi (2014, Jan). An LTV analysis ofthe frequency translational noise-cancelling receiver. IEEE Trans. Circuits Syst. I 47 (12),266–279.

Namgoong, W. (2013a, Feb). Digital equalization of polyphase harmonic mixer. IEEE Trans.Circuits Syst. II, Exp. Brief , 467–471.

Namgoong, W. (2013b, Dec). A wideband digital receiver with hard-switching mixers forcognitive radio. IEEE J. Emerging Sel. Topics Circuits Syst. 3, 576–585.

Namgoong, W. (2015, Feb). Adaptive and robust digital harmonic-reject mixer with optimizedlocal oscillator spacing. IEEE Trans. Circuits Syst. I 62 (2), 580–589.

Rafi, A., A. Piovaccari, P. Vancorenland, and T. Tuttle (2011, Feb). A harmonic rejectionmixer robust to RF device mismatches. IEEE ISSCC Dig. Tech. Papers , 66–68.

Razavi, B. (2010, Aug). Cognitive radio design challenges and techniques. IEEE J. Solid-StateCircuits 45 (8), 1542–1553.

Ru, Z., E. Klumperink, and B. Nauta (2008, Feb). A discrete-time mixing receiver architecturewith wideband harmonic rejection. IEEE ISSCC Dig. Tech. Papers , 322–323.

Ru, Z., E. A. M. Klumperink, G. J. M. Wienk, and B. Nauta (2009, Feb). A software definedradio receiver architecture robust to out-of-band interference. IEEE ISSCC Dig. Tech.Papers , 230–231.

Ru, Z., N. A. Moseley, E. Klumperink, and B. Nauta (2009, Dec). Digitally enhancedsoftware-defined radio receiver robust to out-of-band interference. IEEE J. Solid-StateCircuits 44, 3359–3375.

Sundstrom, L. et al. (2013, Jul). Complex IF harmonic rejection mixer for noncontiguousdual carrier reception in 65 nm CMOS. IEEE J. of Solid-State Circuits 48 (7), 1659–1668.

Trees, H. V. (2002). Optimum Array Processing: Part IV of Detection, Estimation andModulation Theory. New York: Wiley.

van Liempd, B. et al. (2014, Aug). A 0.9 v 0.4-6 GHz harmonic recombination sdr receiver in28 nm CMOS with HR3/HR5 and IIP2 calibration. IEEE J. of Solid-State Circuits 49 (8),1815–1826.

66

Verdu, S. (1998). Multiuser Detection. Cambridge University Press.

Weldon, J. et al. (2001, Feb). A 1.75 GHz highly integrated narrowband CMOS transmitterwith harmonic-rejection mixers. IEEE ISSCC Dig. Tech. Papers , 160–161.

67

BIOGRAPHICAL SKETCH

Esmail Babakrpur Nalousi received his B.Sc. degree in electronic engineering from Urmia

University, Urmia, Iran, in 2010, and his M.Sc. degree in microelectronic circuits from Sharif

University of Technology, Tehran, Iran, in 2013. In 2014, he joined The University of Texas at

Dallas to pursue his education towards the Ph.D. degree in RF/Microwave integrated circuit

design. Esmail was an intern with Qualcomm, San Diego, CA, from August 2017 to April

2018, where he worked on a low-power low-noise Xtal Oscillator for cellular applications and

a mm-wave IFLO as interface between VCOs and RX/TX mixers for 5G radios. Since May

2018, he has been serving as a technical staff member of AMS/RF development engineering

team at Goodix, Irvine, CA. His research interests include mixed-signal and RF circuits and

systems.

68

CURRICULUM VITAE

Esmail Babakrpur NalousiJuly, 2018

Contact Information:

Department of Electrical EngineeringThe University of Texas at Dallas800 W. Campbell Rd.Richardson, TX 75080-3021, U.S.A.Email: Esmail.BabakrpurNalousi@utdallas.edu

Educational History:

B.S., Electrical Engineering, Urmia University, Urmia, Iran, 2010M.S., Microelectronic Circuits, Sharif University of Technology, Tehran, Iran, 2013Ph.D., Electrical Engineering, University of Texas at Dallas, Richardson, USA, 2018

A Digitally-assisted Blocker Resilient RF Receiver for Wideband SAW-less ApplicationsPh.D. DissertationErik Jonsson School of Engineering, University of Texas at DallasAdvisor: Dr. Won Namgoong