NOVEL TECHNIQUES AND ARCHITECTURES FOR ADAPTIVE BEAMFORMING

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1 NOVEL TECHNIQUES AND ARCHITECTURES FOR ADAPTIVE BEAMFORMING By THUA VAN HO, B.A.Sc, M.A.Sc A Thesis Submitted to the School of Graduate Studies in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy McMaster University (C) Copyright by Thua Van Ho, April 1990

2 NOVEL TECHNIQUES AND ARCHITECTURES FOR ADAPTIVE BEAMFORMING THUA VAN HO, B.A.Sc, M.A.Sc

3 DOCTOR OF PHILOSOPHY (1990) McMASTER UNIVERSITY (Electrical Engineering) Hamilton, Ontario TITLE: Novel Techniques and Architectures for Adaptive Beamforming AUTHOR: Thua Van Ho, B.A.Sc (University of Toronto) M.A.Sc (University of Toronto) SUPERVISOR: Professor John Litva NUMBER OF PAGES: xv,

4 iii To my parents

5 ABSTRACT Recent progress in VLSI technology has created a major impact on digital signal processing, including array signal processing. Proposals have been ma.de for using high throughput processors for digital adaptive beamforming in radar a.nd communications systems applications. In this thesis, novel techniques and architectures for adaptive beamforming will be developed and presented. These are typified by the development of adaptive beamforming algorithms for planar arra.ys and by a self-calibration algorithm for antenna arrays. The emphasis however will be placed on modern adaptive beamforming techniques in which the adaptation is carried out by means of a triangular systolic array processor performing the QH decomposi tion. Adaptive beamforming algorithms for a planar array or two-dimensional (2-D) adaptive beamforming algorithms, which are typified by the 2-D least-mean-squares (LMS) algorithm and 2-D Howells-Applebaum algorithm, arc derived and presented. The concept of 2-D eigenbeams will be given to demonstrate the performance of the 2-D adaptive ~Jeamforming techniques. As well, the 2-D adaptive beamforming problem will be formulated in terms of thc I-D case with operation taking place along rows and columns of a planar array. The adaptive processor is then implemented by using a manifold of the least-squares triarray processors, which in the limit takes the form of a 3-D systolic array. It will be shown that the structure is capable of performing adaptation along the rows and columns of the 2-D array simultaneously. iv

6 One of the major challenges that face workers in array processing is overcoming the degradation in the output of the high performance algorithms due to errors in the calibration of the array. A new self~alibration technique for solving this difficult problem will be derived and presented herein. The algorithm is based on the use.if iteration - whereby the calibration coefficients are refined through repetitive imposition of the calibration procedure. Its derivation is based on the eigen-based ~ethod and the least-squares norm minimization. It will be shown that the algorithm is capable of automatical estimating the angles-of-arrival (AOA) of the received signals and calibrating the array with a minimum phase and gain errors. Results obtained by using both simulation and measurement data will be givcn. In the case of the experimer.tal results, the measurement setup is subjectcd to multipath scenarios. v

7 ACKNOWLEDGEMENT I would like to express my sincere thank to my supervisor, Dr. John Litva, for his excellent supervision and continuous support during the cours~ of this thesis. Without his guidance and encouragement several breakthroughs in this thesis would be impossible to be achieved. I would like to express my special thank to Dr. Simon Haykin for accepting me to the CRL at the first place, and from whom I have learned the most. I also would like to express my gratitude to staff and students at the Communications Research Laboratory, McMaster University, for their friendship and help by any means during my years at the university. Finally, I am deeply grateful and most indebted to my wife, Catherine, for her love, patience and support during the course of my study. vi

8 TABLE OF CONTENTS page ABSTRACT ACKNOWLEDGEMENTS LIST OF SYMBOLS LIST OF FIGURES LIST OF TABLES CHAPTER 1 INTRODUCTION 1.1. Introduction to Adaptive Beamforming Problem iii v ix xi xiv Scope of Thesis 9 CHAPTER 2 CLASSICAL ADAPTIVE BEAMFORMING TECHNIQUES Introduction Adaptive Beamforming Algorithms LMS Algorithm Howells-Applebaum Algorithm Eigenvector Beam Concept Sample Matrix Inversion Algorithm D Adaptive Beamforming Algorithms D LMS Algorithm Relationship between 1-D and 2-D Algorithms D Howells-Applebaum Algorithm D Eigenvector Beam Concluding Remarks 45 CHAPTER 3 MODERN ADAPTIVE BEAMFORMING TECHNIQUES Introduction 3.2. QRD-LS Algorithm and Adaptive Beamforming QR Decomposition and Givens Rotation vii

9 Recursive QRD-LS Algorithm Use of the QRD-LS Algorithm in Adaptive Beamforming Triangular Systolic Array Implementation 3.3. Linearly Constrained Adaptive Beamforming Pre-processing Technique Systolic Implementation Special Cases 3.4. Adaptive Beamforming with Planar Arrays QRD-LS Algorithm Systolic Array Implementation 3.5. Concluding Remarks CHAPTER Introduction PERFORMANCE EVALUATION 4.2. I-D Adaptive Beamforming Unconstrained Method Linearly Constrained Method D Adaptive Beamforming 4.4. Concluding Remarks CHAPTER 5 AN ALGORITHM FOR SELF-CALIBRATING ANTENNA ARRAYS 5.1. Introduction 5.2. Signal Model 5.3. Self-Calibration Algorithm Gain and Phase Estimation Self-Calibration Algorithm 5.4. Results Simulation Data Measurement Data, J () II J1 II J Concluding Remarks viii

10 CHAPT;::R 6 CONCLUSIONS 6.1. Discussion and Conclusions 6.2. Recommendations REFERENCES APPENDIX A BASIC TERMINOLOGY AND CONCEPTS A.l. Basic Theory of Array Antennas A.2. VLSI Array Processors APPENDIX B EXPERIMENTAL SETUP AND MULTIPATH PHENOMENON B.1. Experimental Setup B.2. Multipath Phenomenon B.3. Array Calibration Method IX

11 LIST OF SYMBOLS X x matrix: upper case, bold face letter, e.g., Q(n). column vector: lower case, bold face letter, e.g., y(n). x element of a column vector x or a complex constant: lower case, italic letter, e.g., X. function or subset of complex space: ~pper case letter, e.g., H( 0): a function of variable O. X complex scaling constant: upper case, italic letter, e.g., M: number of antenna elements. (X,J1. constant: lower case, Greek letter. And also o spatial angle (elevation direction) > spatial angle (azimuth direction) ci» Tr( ep) R Q E[.] L,M N K d covariance matrix trace of a matrix upper triangular matrix unitary matrix expected value number cf elements (dimensions) in an antenna array number of snap shots (n). number of signals inter-element spacing >. wavelength x

12 LMS SMI PE ADA SNR INR SINR least-mean-squares sample matrix inversion processing element angle-of-arrival signal-to-noise ratio interference-to-noise ratio signal-to-interference-and-noise ratio Xl

13 LIST OF FIGURES Figure page 1.1 Narrow band adaptive antenna :J 1.2 Broad band adaptive antenna :J 2.1 Closed-loop adaptive system Correlation loop of Howells-Applebaum algorithm Open-loop adaptive system Geometry of a planar array Triangular systolic implementation for adaptive beamforming Computations performed by processing elements fl{i a) Givens rotations a) square-root-free 3.3 L5 triarray processor with P linear constraints 65 3,4 Adaptive beamforming processor with a linear constraint Configuration of a 2-D array D systolic layers for 2-D adaptive beamforming D systolic architecture for 2-D adaptive beamforming Control clocks for the 3-D systolic array processor 79 a) global clock b) direction clock c) dual-eell clock 4.1 Configuration of the antenna array used in simulation studies to 4.5 Adapted patterns of a lo-element antenna array a) unconstrained b) constrained method Residual power curve of adaptive beamforming algorithms two jammers at 7 0 and 20 0 from the boresight Residual power curve of adaptive beamforming algorithms three jammers at _15 0, 7 0 and 20 0 from the boresight to 4.11 Adapted patterns of a 10-element antenna array using a clamped element as the primary signal a) unconstrained b) constrained method 95 xii

14 4.12 Adapted pattern of a 4lC4 array, one jammer at (48,-10 ) 103 from the boresight 4.13 Quiescent pattern of a 4lC4 array Eigenbeam pattern of the adapted pattern in Fig Cross section of the 2-D adapted pattern in Fig a) at 48 in elevation b) at _10 in azimuth 4.16 Adapted pattern of a 41C4 array, one jammer at (48,-10 ) 107 using the QRD-LS algorithm a) after 20 iterations b) after 50 iterations 4.17 Residual output power of a 4.4 adaptive array 108 jammer at (48,_10 ) 4.18 Adapted pattern of a 4lC4 array, two jammers at (48,-10 ) no and (-15,-50 ) from the boresight 4.19 Retrodirective pattern of the adapted pattern in Fig no 4.20 Adapted pattern of a 4.4 array, two jammers at (48,-10 ) 111 and (-15,-50 ) using the QRD-LS algorithm a) after 20 iterations b) after 50 iterations 4.21 Residual output power of a 4.4 adaptive array 112 jammers at (48,-10 ) and (-15,-50 ) 5.1 Flow chart of the self-ealibration algorithm AOAs of impinged signals under the effect of gain 129 and phase error, 0 1 := 0, 02 = Typical eigenbeam patterns of the noise subspace a) (Jg = (Jp = 0.00, b) O'g = (Jp = 0.02, 130 c) (J = (1 = 0.04 d) 0' = (1 = P, 9 P 5.4 Minimum norm vs. AOA estimates using the self-ealibration algorithm, (1g = O'p = 0.04, reference signal at 0 = Optimal AOA estimates at different set of least-squares norms, reference signal at 0 = Typical measurement of the 32-element antennas 137 a) amplitude b) phase xiii

15 5.7 AOA estimates using different spectral estimation methods l Typical eigenbeams of the noise subspace of the measurement signals) after spatial smoothing Minimum norm vs. AOA estimates using the self-calibration reference signal at 0 = ) ~O = 0.15 beamwidth Optimal AOA estimates at different set of least-squares norms) reference signal at 0 = Adapted patterns with a constraint at 0 = 0,107 0 L45 a) before calibration b) after calibration A.1 Configuration of a linear antenna array 161 A.2 Beam pattern of a 10-element antenna array 161 a) main beam at 0 0 main beam at 20 A.3 Configuration of a planar antenna array l6'1 AA Beam pattern of a 4)(4 antenna array lg4 a) main beam at 0 0 main beam at (10 )10 ) A.5 Array pro(',essor architectures 1fi7 a) parallel processor b) pipeline processor A.6 A systolic array of matrix multiplication 168 A.7 A wavefront array of matrix multiplication 170 B.1 Geometry of the experiment setup 175 B.2 Physical view of the sampled aperture array 17G B.3 Plane view of the measurement site in Dorcus Bay, Ontario 177 B.4 Geometry of direct and indirect signals on a curved surface 17n xiv

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Optimum Array Processing

Optimum Array Processing Part IV of Detection, Estimation, and Modulation Theory Harry L. Van Trees WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION Preface xix 1 Introduction 1 1.1 Array Processing