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Optimal and Adaptive Subband Beamforming Optimal and Adaptive Subband Beamforming Principles and Applications Nedelko Grbi´c Ronneby, June 2001 Department of Telecommunications and Signal Processing Blekinge Institute of Technology, S-372 25 Ronneby, Sweden c Nedelko Grbi´c ISBN 91-7295-002-1 ISSN 1650-2159 Published 2001 Printed by Kaserntryckeriet AB Karlskrona 2001 Sweden v Preface This doctoral thesis summarizes my work in the field of array signal processing. Frequency domain processing comprise a significant part of the material. The work is mainly aimed at speech enhancement in communication systems such as confer- ence telephony and handsfree mobile telephony. The work has been carried out at Department of Telecommunications and Signal Processing at Blekinge Institute of Technology. Some of the work has been conducted in collaboration with Ericsson Mobile Communications and Australian Telecommunications Research Institute. The thesis consists of seven stand alone parts: Part I Optimal and Adaptive Beamforming for Speech Signals Part II Structures and Performance Limits in Subband Beamforming Part III Blind Signal Separation using Overcomplete Subband Representation Part IV Neural Network based Adaptive Microphone Array System for Speech Enhancement Part V Design of Oversampled Uniform DFT Filter Banks with Delay Specifica- tion using Quadratic Optimization Part VI Design of Oversampled Uniform DFT Filter Banks with Reduced Inband Aliasing and Delay Constraints Part VII A New Pilot-Signal based Space-Time Adaptive Algorithm vii Acknowledgments I owe sincere gratitude to Professor Sven Nordholm with whom most of my work has been conducted. There have been enormous amount of inspiration and valuable discussions with him. Many thanks also goes to Professor Ingvar Claesson who has made every possible effort to make my study complete and rewarding. Since the first day I started my studies they have both helped me enormously and given me a lof of support, not only academically. I wish to thank my closest colleague and also my dear friend Dr. Xiao-Jiao Tao for supervision and intense collaboration in my research studies. I would also like to thank all colleagues at the Department of Telecommunications and Signal Processing for the nice atmosphere they all have been part of, during my studies. I am in debt to my family and to all my friends for their support. Finally, I express my gratitude to my beloved wife Marina for her understanding and comfort. Nedelko Grbi´c Ronneby, June 2001 ix Contents Publication list ........................................................... 11 Array Notations .......................................................... 15 Introduction .............................................................. 17 Part I OptimalandAdaptiveBeamformingforSpeechSignals ................ 39-102 II Structures and Performance Limits in Subband Beamforming . ...... 105-125 III Blind Signal Separation using Overcomplete Subband Representation . ......................................... 129-151 IV Neural Network based Adaptive Microphone Array System forSpeechEnhancement ..........................................155-163 V Design of Oversampled Uniform DFT Filter Banks withDelay SpecificationusingQuadraticOptimization ...........167-176 VI Design of Oversampled Uniform DFT Filter Banks withReducedInbandAliasingandDelay Constraints .............179-187 VII A NewPilot-SignalbasedSpace-TimeAdaptiveAlgorithm ........191-200 11 Publication list Part I comprise parts of the following publications, N. Grbi´c, S. Nordholm, I. Claesson, “Optimal and Adaptive Beamforming for Speech Signals in a mixture of Spatially Coherent and Incoherent Noise Fields,” submitted to IEEE transactions on Speech and Audio Processing, Apr. 2001. N. Grbi´c, S. Nordholm, I. Claesson, U. Lindgren, European patent application entitled, “Subband Adaptive Microphone Array for Speech Enhancement,” Apr. 2001. M. Dahl, I. Claesson, S. Nordholm, N. Grbi´c, “Adaptive Microphone Array Sys- tem for Speech Enhancement,” In Proc. COST 254 Second Workshop, Toulouse, France, Jul. 1997. N. Grbi´c, J. Nordberg, S. Nordholm, “Subband Acoustic Echo Cancelling using LMS and RLS,” Research Report 1999:5, ISSN: 1103-1581, University of Karl- skrona/Ronneby, May 1999. N. Grbi´c, M. Dahl, I. Claesson, “Acoustic Echo Cancelling and Noise Suppression with Microphone Arrays,” Research Report 1999:4, ISSN: 1103-1581, University of Karlskrona/Ronneby, Apr. 1999. S. Nordholm, I. Claesson, N. Grbi´c, “Optimal and Adaptive Microphone Arrays for Speech Input in Automobiles,” to be published as book chapter in Microphone Arrays: Techniques and Applications, editors Michael S. Brandstein and Darren B. Ward, by Springer Verlag, 2001. Part II is submitted as, S. Nordholm, I. Claesson, N. Grbi´c, “Structures and Performance Limits in Sub- band Beamforming,” submitted to IEEE transactions on Speech and Audio Pro- cessing, Apr. 2001. Part III comprise the following publication, N. Grbi´c, X. J. Tao, S. Nordholm, I. Claesson, “Blind Signal Separation using Overcomplete Subband Representation,” to appear as regular paper for publica- tion in IEEE Transactions on Speech and Audio Processing, Jul. 2001. 12 Publications Part IV comprise the following publication, N. Grbi´c, M. Dahl, I. Claesson, “Neural Network Based Adaptive Microphone Array System for Speech Enhancement,” 1998 IEEE World Congress on Compu- tational Intelligence, Anchorage, Alaska, USA, Vol. 3, pp. 2180-2183, May 1998. Part V will be published as, J. M. de Haan, N. Grbi´c, S. Nordholm, I. Claesson, “Design of Oversampled Uni- form DFT Filter Banks with Delay Specification using Quadratic Optimization,” accepted for presentation at ICASSP’01, USA, May 2001. Part VI is submitted as, N. Grbi´c, J.-M. de Haan, S. Nordholm, I. Claesson, “Design of Oversampled Uni- form DFT Filter Banks with Reduced Inband Aliasing and Delay Constraints,” submitted for presentation in ISSPA 2001, Malaysia, Feb. 2001. Part VII will be presented as, N. Grbi´c, S. Nordholm, J. Nordberg, I. Claesson, “A New Pilot-Signal based Space- Time Adaptive Algorithm,” accepted for presentation at ICT 2001, Romania, Jun. 2001. Other publications in conjunction with the thesis, N. Grbi´c, X-J Tao, I. Claesson, “Performance Improvement of Multiple Array 3d Sonic Digitizer System via Calibration”, In Proc. RVK 99, Karlskrona, Sweden, Jun. 1999. N. Grbi´c, ”Speech Signal Extraction - A Multichannel Approach”, Licentiate the- sis, University of Karlskrona/Ronneby, ISBN 91-630-8841-X, Nov. 1999. X. J. Tao, I. Claesson, N. Grbi´c, “Narrowband acoustic Doppler backscattering signal analysis and estimation”, accepted for publication in IEEE Transactions on Signal Processing, Apr. 2000. Publications 13 N. Grbi´c, X. J. Tao, S. Nordholm, “Performance Analysis and Bias Correction in Synchronized Acoustic 3D Measuring System”, Inter-University Postgraduate Electrical Engineering Symposium, Australia, pp. 49-52, Jul. 2000. N. Grbi´c, S. Nordholm, A. Johansson, “Optimal Beamforming for Voice Input to Personal Communication Devices”, International Forum Cum Conference on Information Technology and Communication at the Dawn of the New Millennium, Bangkok, Thailand, Aug. 2000. J. Nordberg, N. Grbi´c, S. Nordholm, “Spatial Interference Cancellation using Blind Signal Separation and Sector Antennas,” accepted for presentation at ICT 2001, Romania, Feb. 2001. Array Notations 15 a∗ complex conjugation of a A+ pseudo-inverse of A, i.e. A+ =(AH A)−1AH ,if(AH A)−1 exists convolution operator sˆ estimate of s λ wavelength τ time delay θ direction of wave propagation σs signal power σv noise power a(θ) array manifold vector for direction θ c speed of wave propagation in m/s d point source index, range d =1, 2, ···,D dij distance between sensor i and j κ wave number, i.e. κ =2π/λ f normalized frequency of operation ω normalized angular frequency of operation fs sampling frequency H Hermitian transpose operator k subband√ index, range k =0, 1, ···,K− 1 j −1 n discrete-time index i microphone/sensor index, range i =1, 2, ···,I I number of microphones/sensors in the array qp eigenvector with index p Q matrix of eigenvectors, i.e. Q =[q1, q2, ···] γp eigenvalue with index p Rss source covariance matrix r i j sisj source covariance vector between element and element Rnn noise covariance matrix r i j ninj noise covariance vector between element and element Rxx data covariance matrix r i j xixj data covariance vector between element and element I the identity matrix sd [n]thedth source signal at time n s [n] vector of source signals at time n T transpose operator vi [n] noise signal received at i-th microphone at time n n [n] noise vector received at array at time n wi [n] weight applied to the i-th microphone at time-lag n (f) wi [n] weight applied to the i-th microphone at time-lag n for frequency f (k) wi [n] weight applied to the i-th microphone at time-lag n in subband k w [n] stacked array weights applied to the array data at time n w(f) [n] stacked array weights applied to the array data at time n for frequency f w(k) [n] stacked array weights applied to the array data at time n in subband k xi [n] data received at i-th microphone at time n x [n] stacked array data received at array at time n (f) xi [n] data received at i-th microphone at time n for frequency f x(k) [n] stacked array data received at array at time n in subband k y [n] array output at time n y(f) [n] array output at time n for frequency f y(k) [n] array output at time n in subband k 17 Introduction PART I - Optimal and Adaptive Beamforming for Speech Signals The increased
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