Adaptive beamforming (GSC) : not robust against signal model errors

1. Design, implementation, and evaluation of a robust multi-microphone noise reduction algorithm Simon Doclo1), Ann Spriet1-2), Jan Wouters2) and Marc Moonen1) 1)ESAT-SCD,KULeuven, Kasteelpark Arenberg 10, 3001 Leuven, Belgium 2)Lab. Experimental ORL, KULeuven, Kapucijnenvoer 33, 3000 Leuven, Belgium Adaptive beamforming (GSC) : not robust against signal model errors Robust generalised multi-microphone noise reduction scheme Efficient implementation using stochastic gradient algorithms noise reduction speech distortion Multi-channel Wiener Filter (SDW-MWF) Spatial pre-processing speech-and-noise periods noise-only periods Speechreference Fixed beamformer S  Blocking matrix • Stochastic gradient algorithm in time-domain: LMS-based updating formula • - allows transition to classical LMS-based GSC by tuning parameters (1/, w0) • - approximation of regularisation term in time-domain using data buffers • Complexity reduction in frequency-domain: block-based implementation (FFT) • - approximation of regularisation term  replace buffers by correlation matrices • Computational complexity(N = 3(mics), M = 2 (a), M = 3 (b), L= 32, fs = 16kHz) Noise references Classical GSC regularisation term Complexity comparable to FD implementation of QIC-GSC SP-SDW-MWF achieves better noise reduction than QIC-GSC, for a given maximum speech distortion level Non-robust design Robust design 4. Robust adaptive stage: SDW-MWF 1. Multi-microphone noise reduction techniques 4.1. Cost function • reduction of noise wrt useful speech signal in different acoustic environments • exploit spatial + spectral information of speech and noise sources • small-size microphone arrays  increased sensitivity to signal model errors (e.g. microphone mismatch) • Robustness: limit effect of speech leakage wT[k]x[k] by controlling filter w[k] • - Quadratic inequality constraint (QIC-GSC):  conservative approach • -Take speech distortion into account in optimisation criterion (SDW-MWF) • o 1/ trades off noise reduction and speech distortion (1/=0  GSC) • o regularisation term ~ amount of speech leakage • Wiener solution (using ) • Generalised scheme  different algorithms, depending on 1/ and w0 • - Without w0 : Speech Distortion Regularised GSC (SDR-GSC), i.e. standard ANC criterion is supplemented with regularisation term • - With w0: Spatially pre-processed SDW-MWF (SP-SDW-MWF) 2. Spatially pre-processed SDW-MWF 4.2. Implementation: stochastic gradient algorithms • Structure of SP-SDW-MWF resembles Generalised Sidelobe Canceller (GSC): • - spatial pre-processor  speech reference and noise references • - adaptive stage : adaptive estimation of noise component in speech reference v0[k-] • Standard GSC minimises output noise power : • Fixed + adaptive stage rely on assumptions (e.g. no mismatch, no reverberation), but in practice these assumptions are not satisfied  speech distortion • - distortion of speech component in speech reference • - speech leakage into noise references • Design of robust noise reduction algorithm : • - robust fixed beamformer  limit distortion in x0[k] and limit speech leakage • - robust adaptive stage  limit effect of (remaining) speech leakage 4.3. Experimental validation 3. Robust spatial pre-processor • Set-up: 3-microphone BTE (d=1cm,1.5cm) mounted on dummy head • - speech (0o) + 5 speech-like noise sources (75o,120o,180o,240o,285o) • - microphone gain mismatch 2=4 dB at second microphone • Performance measures: Intelligibility-weighted signal to noise ratio SNRintellig and spectral distortion SDintellig • Performance of SP-SDW-MWF: • - GSC (1/ = 0, no w0): degraded performance if significant leakage • - SDR-GSC: 1/ > 0 increases robustness (speech distortion  noise reduction) • - SP-SD-MWF(w0 ) : performance not degraded by mismatch • Comparison with QIC-GSC: QIC increases robustness of GSC, but QIC  f (amount of speech leakage) • Robustness: small deviations from assumed microphone characteristics (gain, phase, position)  large deviations from desired spatial directivity pattern • - measurement or calibration procedure: expensive, not effective against drift • - incorporate random deviations into design: consider all feasible microphone characteristics and optimise average performance using probability as weight • Simulations : N=3, [-0.01 0 0.015] m, L=20, end-fire beamformer (passband: 0o-60o) • Spatial directivity patterns for non-robust and robust beamformer in case ofno position errors and small position errors: [0.002 –0.002 0.002] m