Phased Array Processing: Direction of Arrival Estimation on Recon

85 Pages·2009·1.19 MB·English

Phased Array Processing:
Direction of Arrival Estimation
on Reconfigurable Hardware
Master’s Thesis
by
Jasper D. Vrielink
Committee:
prof. dr. ir. Gerard J.M. Smit
dr. ir. Andr´e B.J. Kokkeler
ir. Marcel D. van de Burgwal
ir. Kenneth C. Rovers
University of Twente, Enschede, The Netherlands
January 16, 2009

Abstract
A beamforming system consists of three different parts, the beamformer, the
beamsteering, andtheparameterestimation. Inthisthesistheparameteresti-
mation is described, the Direction Of Arrival (DOA) estimation in particular.
Two popular DOA estimation algorithms are described. The first algo-
rithm is MUltiple SIgnal Classification (MUSIC), and the second algorithm
is Estimation of Signal Parameters by Rotational Invariance Techniques (ES-
PRIT). Both algorithm can be used to estimate the DOAs of multiple signals.
Covariance Matrix Differencing (CMD) is an extension to MUSIC to improve
the performance of the MUSIC algorithm. This CMD extension is also de-
scribed in this thesis.
AmodelofMUSICandamodelofESPRITaremadeinMatlabtoanalyse
the performance, and the effects of different test scenarios on the DOA esti-
mation. Both algorithms are compared by means of these test scenarios. The
performance of the CMD extension is also analyzed by means of a set of test
scenarios. Based on the superior performance of the MUSIC algorithm when
the Signal to Noise Ratio (SNR) is low, the MUSIC algorithm is chosen to be
implemented on the reconfigurable architecture.
The MUSIC algorithm is implemented on the Montium2 architecture. The
implementationisdescribedbymeansofpseudocode. Implementationaspects
such as, accuracy, computational load, and scalability are analyzed. The com-
plete implementation requires 1.5 million clock cycles on the Montium2. This
number of clock cycles results in an execution time of 7.5ms. A practical ex-
ampleofabeamformingsystemusedasasatellitetelevisionreceiver,mounted
on the roof of a car, shows that this is an acceptable execution time in this
particular situation.
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Acknowledgement
The author hereby wants to thank the members of the Computer Architecture
forEmbeddedSystemsgroupattheComputerSciencedepartmentoftheUni-
versityofTwente,thegraduationcommitteeinparticular,fortheirsupportand
advice during this master assignment. The author also wants to thank Recore
Systems for their support with the implementation part of this assignment.
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Contents
Contents v
List of Acronyms vii
1 Introduction 1
2 Phased array processing 3
2.1 System model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Data model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Processing architecture . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.5 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Methods for DOA estimation 9
3.1 MUSIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1.1 Basic algorithm . . . . . . . . . . . . . . . . . . . . . . . 9
3.1.2 CMD extension . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 ESPRIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Eigenproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3.1 Eigendecomposition . . . . . . . . . . . . . . . . . . . . 15
3.3.2 Generalized eigendecomposition . . . . . . . . . . . . . . 19
3.4 Comparison of MUSIC and ESPRIT . . . . . . . . . . . . . . . 20
4 Modeling and simulations 21
4.1 MUSIC and ESPRIT simulations . . . . . . . . . . . . . . . . . 21
4.2 CMD MUSIC simulations . . . . . . . . . . . . . . . . . . . . . 24
4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5 Algorithm implementation 29
5.1 Montium2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2 Music algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.2.1 Covariance matrix . . . . . . . . . . . . . . . . . . . . . 32
5.2.2 Eigendecomposition . . . . . . . . . . . . . . . . . . . . 37
5.2.3 MUSIC spectrum . . . . . . . . . . . . . . . . . . . . . . 53
5.2.4 Peak selection. . . . . . . . . . . . . . . . . . . . . . . . 55
5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6 Conclusion and Recommendations 61
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
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vi Contents
6.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . 61
A Simulation results 63
A.1 MUSIC and ESPRIT . . . . . . . . . . . . . . . . . . . . . . . . 63
A.2 CMD MUSIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Bibliography 73
List of Acronyms
CMD Covariance Matrix Differencing
CORDIC COordinate Rotation DIgital Computer
DOA Direction Of Arrival
dword double word
DSP Digital Signal Processing
ESPRIT Estimation of Signal Parameters by Rotational Invariance
Techniques
FPGA Field Programmable Gate Array
LSB Least Significant Bit
MSB Most Significant Bit
MUSIC MUltiple SIgnal Classification
SNR Signal to Noise Ratio
SRAM Static Random Acces Memory
ULA Uniform Linear Array
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