2.2 Adaptive Array Beamforming

150 Pages·2010·9.87 MB·English

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UNIVERSITY OF SOUTHAMPTON
in the
Faculty of Engineering
School of Electronics and Computer Science
Improved Broadband Adaptive
Beamformer Performance
by
Neil Tisdale
A thesis submitted in partial fulfilment for the
degree of Doctor of Engineering
January 2010
UNIVERSITY OF SOUTHAMPTON
Abstract
Faculty of Engineering
School of Electronics and Computer Science
Doctor of Engineering
by Neil Tisdale
The protection of wireless communications links against interference is a key concern
in mission critical systems. In particular low probability of interception (LPI) systems
which operate below the thermal noise floor of the receiver are particularly vulnerable.
To protect against interference it is often necessary to include some form of active
interference suppression. Broadband adaptive beamforming is one such technique which
may be used to suppress interference by spatial and spectral filtering of the signals
received by an array antenna. The hardware requirements of adaptive beamforming
systems are high in comparison to other approaches. As a result, the total number of
adaptable weights realisable in the beamformer may be limited by the size, weight and
powerconstraintsofthesystem. Thiswilllimitthedegreesoffreedominthebeamformer
and hence, the interference cancellation capability of the beamformer.
Theeffectivenessofincreasingthenumberoftime-tapsinspace-timeadaptiveprocessors
(STAP) as a method of increasing the number of interferers the beamformer can simul-
taneously cancel in an environment containing a mix of narrowband, partialband and
broadband interference is studied. An alternative scheme to free up degrees of freedom
in the beamformer is proposed based on frequency-domain excision to pre-filter narrow-
band interference before it reaches the beamformer. This approach frees up degrees of
freedom in the beamformer, which would otherwise be consumed by the narrowband
interference, for use in cancelling partialband and broadband interference. To enable
the excision filters to identify narrowband interference while allowing partialband and
broadband interference to pass through, a novel scheme is presented which produces a
frequencymaskthatvariesonaper-binbasis. Eigenanalysisofthebeamformer’scovari-
ance matrix is used to explore the ability of frequency-domain excision to desensitise the
beamformer to narrowband interference while bit error rate (BER) simulations demon-
strate the enhanced interference protection the scheme affords an LPI communications
link.
Mismatchesbetweenthegainandphaseresponsesoftheradio-frequency(RF)front-end
channels in broadband adaptive beamformers can limit their cancellation performance
against higher power partialband and broadband interference. This performance limi-
tation arises from the decorrelation experienced by the received signals across the array
due to the interchannel mismatches. In STAP systems this performance limitation may
be mitigated by increasing the number of taps per channel in the STAP. However, the
computational complexity of adding additional time-taps tends to be high in STAP
beamformers. Two new methods of interchannel mismatch compensation are proposed
based on efficient frequency-domain methods. Simulations using software models and
experiments using a hardware STAP system demonstrate the proposed techniques’ abil-
ity to improve the cancellation performance where interchannel mismatches are limiting
cancellation performance.
Contents
Abstract i
List of Figures v
Declaration of Authorship vii
Acknowledgements viii
Abbreviations ix
Symbols xi
1 Introduction 1
1.1 Research Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Structure of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Interference Suppression 6
2.1 Single Channel Interference Suppression . . . . . . . . . . . . . . . . . . . 7
2.1.1 Time-Domain Interference Suppression . . . . . . . . . . . . . . . . 7
2.1.2 Frequency-Domain Excision Filtering. . . . . . . . . . . . . . . . . 9
2.2 Adaptive Array Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Broadband Adaptive Beamforming . . . . . . . . . . . . . . . . . . 14
2.2.2 Optimum Beamforming . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 Adaptive Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.4 Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.1 Direct-Sequence Spread-Spectrum Systems . . . . . . . . . . . . . 28
2.3.2 Interference Signals. . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.3 Array Response to Signals . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.4 DSSS Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3 Increased Cancellation Capacity in Adaptive Beamformers 35
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Use of Time-Taps to Increase Cancellation Capacity . . . . . . . . . . . . 37
iii
Contents iv
3.2.1 Rank2Modelofnon-zeroBandwidthSignalsinSTAPBeamformers 44
3.2.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3 Pre-filtering of Narrowband Interference in Beamformers . . . . . . . . . . 51
3.3.1 Front-end Excision Filters . . . . . . . . . . . . . . . . . . . . . . . 52
3.3.2 Effects of Pre-excision on Degrees of Freedom . . . . . . . . . . . . 55
3.4 Performance of System in Mixed Interference Environments . . . . . . . . 64
3.4.1 System Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4 Automatic Threshold Calculation for FDE Pre-filtering in Adaptive
Beamformers 75
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2.1 Space-time Adaptive Processor . . . . . . . . . . . . . . . . . . . . 77
4.2.2 Space-Frequency Adaptive Processor . . . . . . . . . . . . . . . . . 78
4.3 Threshold Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4 Computational Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.5 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.5.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.5.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5 Channel Mismatch Compensation For Space-Time Adaptive Proces-
sors 92
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2.1 Frequency-Domain Mismatch Compensation Filters . . . . . . . . 95
5.2.2 Mismatch Equaliser Weights . . . . . . . . . . . . . . . . . . . . . 98
5.2.3 Beamformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.2.4 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.2 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.4 Hardware Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.4.1 System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4.2 Measured Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6 Conclusions and Further Work 118
6.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
References 122
List of Figures
1.1 Illustration of the near-far problem for LPI communications systems . . . 2
2.1 Dataflow diagram of a narrowband adaptive array . . . . . . . . . . . . . 14
2.2 Dataflow diagram of a space-time adaptive processor . . . . . . . . . . . . 15
2.3 Relative complexity of a 4 element STAP and sub-band beamformer with
a weight update rate relative to the sampling rate of F = 0.001 . . . . . 17
u
2.4 DSSS transmitter (top) and receiver (bottom) . . . . . . . . . . . . . . . . 28
2.5 Uniformly spaced linear antenna array . . . . . . . . . . . . . . . . . . . . 31
2.6 System model of a beamformer with multiple signals impinging upon the
array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1 Simulated and theoretical values of 2nd eigenvalue of R . . . . . . . . . 47
gg
3.2 2nd eigenvalue of R for a variable number of taps per channel, P = 30
gg g
dBW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 First 6 eigenvalues of R , P /σ2 = 30 dB and K = 5 . . . . . . . . . . . 48
u¯u¯ g v
3.4 Eigenvalues of R variable INRs and numbers of taps . . . . . . . . . . . 50
u¯u¯
3.5 Dataflow diagram of a STAP beamformer with pre-excision filters . . . . . 52
3.6 Dataflow diagram of a single frequency-domain excision filter . . . . . . . 52
3.7 First four eigenvalues of R for excised CW. . . . . . . . . . . . . . . . . 57
q˜q˜
3.8 First eigenvalue of R for excised CW using rectangular window . . . . . 58
q˜q˜
3.9 Residual power due to excision of CW signal with P = 30 dBW . . . . . 59
g
3.10 Eigenvalues of R using Blackman-Harris window and no bins excised . . 60
q˜q˜
3.11 1st eigenvalue of R using Blackman-Harris window . . . . . . . . . . . . 61
q˜q˜
3.12 Beam pattern of power inversion beamformer for an excised CW . . . . . 62
3.13 1st eigenvalue of R using Dolph-Chebyshev window . . . . . . . . . . . . 63
q˜q˜
3.14 1st eigenvalue of R using Dolph-Chebyshev window and multiple CWs . 65
q˜q˜
3.15 Excision loss due to excision of wanted signal . . . . . . . . . . . . . . . . 69
3.16 Partial excision of broadband interference signal . . . . . . . . . . . . . . 70
3.17 Improvement in coverage of the power inversion beamformer using excision 71
3.18 Performance of combined MVDR beamformer excision system in over-
stressed environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1 Dataflow diagram of a beamformer with pre-excision filters . . . . . . . . 77
4.2 Excisionvariablethresholdforaspectrumcontaining1CWinterfererand
several partial/broadband interferers . . . . . . . . . . . . . . . . . . . . . 83
4.3 BER performance of STAP beamformer with no pre-excision . . . . . . . 87
4.4 BER performance of SFAP beamformer with no pre-excision . . . . . . . 87
4.5 BER performance of STAP beamformer with pre-excision . . . . . . . . . 88
4.6 BER performance of SFAP beamformer with pre-excision . . . . . . . . . 89
v
List of Figures vi
4.7 BER performance with interferers A, B and E where the wanted signal
and interferer E are co-located . . . . . . . . . . . . . . . . . . . . . . . . 89
4.8 BER performance with interferers A, B, C and 4 CWs . . . . . . . . . . . 90
5.1 STAP beamformer with mismatched channel responses . . . . . . . . . . . 95
5.2 STAP with proposed channel mismatch compensation scheme . . . . . . . 96
5.3 Dataflow of a single mismatch compensation filter . . . . . . . . . . . . . 96
5.4 Magnitude response of beamformer’s analogue front-end . . . . . . . . . . 104
5.5 Phase response of STAP beamformer’s analogue front-end . . . . . . . . . 104
5.6 CR vs. INR with and without channel mismatch compensation . . . . . . 106
5.7 Output SINR vs. INR with and without mismatch compensation . . . . . 107
5.8 Output SINR gain vs. INR for various filter lengths . . . . . . . . . . . . 108
5.9 Output SINR gain vs. INR for various CNRs, N = 1024 . . . . . . . . . . 109
5.10 Experimental setup for TD STAP channel mismatch compensation . . . . 110
5.11 Magnitude response of ADM channels . . . . . . . . . . . . . . . . . . . . 113
5.12 Phase response of ADM channels . . . . . . . . . . . . . . . . . . . . . . . 114
5.13 Interference power vs. null depth gain for varying filter orders . . . . . . . 115
5.14 Calibration SNR vs. null depth gain . . . . . . . . . . . . . . . . . . . . . 116
Declaration of Authorship
I, Neil Tisdale, declare that this thesis titled, ‘Improved Broadband Adaptive Beam-
former Performance’ and the work presented in it are my own. I confirm that:
(cid:4) this work was done wholly or mainly while in candidature for a research degree at
this University.
(cid:4) where any part of this thesis has previously been submitted for a degree or any
other qualification at this University or any other institution, this has been clearly
stated.
(cid:4) where I have consulted the published work of others, this is always clearly at-
tributed.
(cid:4) where I have quoted from the work of others, the source is always given. With the
exception of such quotations, this thesis is entirely my own work.
(cid:4) I have acknowledged all main sources of help.
(cid:4) where the thesis is based on work done by myself jointly with others, I have made
clear exactly what was done by others and what I have contributed myself.
(cid:4) parts of this work have been published as: [1–3].
Signed:
Date:
vii
Acknowledgements
I would like to thank Dr. Tom Kazmierski for stepping in to be my primary aca-
demic supervisor midway through my studies and for his patience and support given
the circumstances. In addition to this my thanks also go to Dr. Stephen Weiss for his
contributions during the first half of my studies and for his continued advice even after
he had left Southampton University.
During the course of the Engineering Doctorate I have received funding from both the
Engineering and Physical Sciences Research Council (EPSRC) and ERA Technology
Ltd. (now trading as Cobham Technical Services) without which I would not have been
able to undertake this work. Furthermore, I would like to thanks my colleagues at ERA
Technology Ltd. for their help and advice along the way, not least, Dr. Duncan Brooks
for his support in the role of my industrial supervisor.
Finally, I would like to give heartfelt thanks to my girlfriend and my parents for their
support and understanding which have helped sustain me during my studies.
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