Blind MultiChannel Identification and Equalization for Dereverberation and Noise Reduction based on Convolutive Transfer Function

This paper addresses the problems of blind channel identification and multichannel equalization for speech dereverberation and noise reduction. The time-domain cross-relation method is not suitable for blind room impulse response identification, due to the near-common zeros of the long impulse responses. We extend the cross-relation method to the short-time Fourier transform (STFT) domain, in which the time-domain impulse responses are approximately represented by the convolutive transfer functions (CTFs) with much less coefficients. The CTFs suffer from the common zeros caused by the oversampled STFT. We propose to identify CTFs based on the STFT with the oversampled signals and the critical sampled CTFs, which is a good compromise between the frequency aliasing of the signals and the common zeros problem of CTFs. In addition, a normalization of the CTFs is proposed to remove the gain ambiguity across sub-bands. In the STFT domain, the identified CTFs is used for multichannel equalization, in which the sparsity of speech signals is exploited. We propose to perform inverse filtering by minimizing the $\ell_1$-norm of the source signal with the relaxed $\ell_2$-norm fitting error between the micophone signals and the convolution of the estimated source signal and the CTFs used as a constraint. This method is advantageous in that the noise can be reduced by relaxing the $\ell_2$-norm to a tolerance corresponding to the noise power, and the tolerance can be automatically set. The experiments confirm the efficiency of the proposed method even under conditions with high reverberation levels and intense noise.Comment: 13 pages, 5 figures, 5 table

Efficient Multiband Algorithms for Blind Source Separation

The problem of blind separation refers to recovering original signals, called source signals, from the mixed signals, called observation signals, in a reverberant environment. The mixture is a function of a sequence of original speech signals mixed in a reverberant room. The objective is to separate mixed signals to obtain the original signals without degradation and without prior information of the features of the sources. The strategy used to achieve this objective is to use multiple bands that work at a lower rate, have less computational cost and a quicker convergence than the conventional scheme. Our motivation is the competitive results of unequal-passbands scheme applications, in terms of the convergence speed. The objective of this research is to improve unequal-passbands schemes by improving the speed of convergence and reducing the computational cost. The first proposed work is a novel maximally decimated unequal-passbands scheme.This scheme uses multiple bands that make it work at a reduced sampling rate, and low computational cost. An adaptation approach is derived with an adaptation step that improved the convergence speed. The performance of the proposed scheme was measured in different ways. First, the mean square errors of various bands are measured and the results are compared to a maximally decimated equal-passbands scheme, which is currently the best performing method. The results show that the proposed scheme has a faster convergence rate than the maximally decimated equal-passbands scheme. Second, when the scheme is tested for white and coloured inputs using a low number of bands, it does not yield good results; but when the number of bands is increased, the speed of convergence is enhanced. Third, the scheme is tested for quick changes. It is shown that the performance of the proposed scheme is similar to that of the equal-passbands scheme. Fourth, the scheme is also tested in a stationary state. The experimental results confirm the theoretical work. For more challenging scenarios, an unequal-passbands scheme with over-sampled decimation is proposed; the greater number of bands, the more efficient the separation. The results are compared to the currently best performing method. Second, an experimental comparison is made between the proposed multiband scheme and the conventional scheme. The results show that the convergence speed and the signal-to-interference ratio of the proposed scheme are higher than that of the conventional scheme, and the computation cost is lower than that of the conventional scheme

Hybrid solutions to instantaneous MIMO blind separation and decoding: narrowband, QAM and square cases

Future wireless communication systems are desired to support high data rates and high quality transmission when considering the growing multimedia applications. Increasing the channel throughput leads to the multiple input and multiple output and blind equalization techniques in recent years. Thereby blind MIMO equalization has attracted a great interest.Both system performance and computational complexities play important roles in real time communications. Reducing the computational load and providing accurate performances are the main challenges in present systems. In this thesis, a hybrid method which can provide an affordable complexity with good performance for Blind Equalization in large constellation MIMO systems is proposed first. Saving computational cost happens both in the signal sep- aration part and in signal detection part. First, based on Quadrature amplitude modulation signal characteristics, an efficient and simple nonlinear function for the Independent Compo- nent Analysis is introduced. Second, using the idea of the sphere decoding, we choose the soft information of channels in a sphere, and overcome the so- called curse of dimensionality of the Expectation Maximization (EM) algorithm and enhance the final results simultaneously. Mathematically, we demonstrate in the digital communication cases, the EM algorithm shows Newton -like convergence.Despite the widespread use of forward -error coding (FEC), most multiple input multiple output (MIMO) blind channel estimation techniques ignore its presence, and instead make the sim- plifying assumption that the transmitted symbols are uncoded. However, FEC induces code structure in the transmitted sequence that can be exploited to improve blind MIMO channel estimates. In final part of this work, we exploit the iterative channel estimation and decoding performance for blind MIMO equalization. Experiments show the improvements achievable by exploiting the existence of coding structures and that it can access the performance of a BCJR equalizer with perfect channel information in a reasonable SNR range. All results are confirmed experimentally for the example of blind equalization in block fading MIMO systems

Blind identification of possibly under-determined convolutive MIMO systems

Blind identi¯cation of a Linear Time Invariant (LTI) Multiple-Input Multiple-Output (MIMO) system is of great importance in many applications, such as speech processing, multi-access communication, multi-sensor sonar/radar systems, and biomedical applications. The objective of blind identi¯cation for a MIMO system is to identify an unknown system, driven by Ni unobservable inputs, based on the No system outputs. We ¯rst present a novel blind approach for the identi¯cation of a over-determined (No ¸ Ni) MIMO system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on Parallel Factorization (PARAFAC) of three- or four-way tensors constructed respectively based on third- or fourth-order cross-spectra of the system outputs. We show that the information available in the higher-order spectra allows for the system response to be identi¯ed up to a constant scaling and permutation ambiguities and a linear phase ambiguity. Important features of the proposed approaches are that they do not require channel length information, need no phase unwrapping, and unlike the majority of existing methods, need no pre-whitening of the system outputs.While several methods have been proposed to blindly identify over-determined convolutive MIMO systems, very scarce results exist for under-determined (No < Ni) case, all of which refer to systems that either have some special structure, or special No, Ni values. We propose a novel approach for blind identi¯cation of under-determined convolutive MIMO systems of general dimensions. As long as min(No;Ni) ¸ 2, we can always ¯nd the appropriate order of statistics that guarantees identi¯ability of the system response within trivial ambiguities. We provide the description of the class of identi¯able MIMO systems for a certain order of statistics K, and an algorithm to reach the solution.Finally we propose a novel approach for blind identi¯cation and symbol recovery of a distributed antenna system with multiple carrier-frequency o®sets (CFO), arising due to mismatch between the oscillators of transmitters and receivers. The received base-band signal is over-sampled, and its polyphase components are used to formulate a virtual MIMO problem. By applying blind MIMO system estimation techniques, the system response is estimated and used to subsequently decouple the users and transform the multiple CFOs estimation problem into a set of independent single CFO estimation problems.Ph.D., Electrical Engineering -- Drexel University, 200

A frequency-based BSS technique for speech source separation.

Ngan Lai Yin.Thesis (M.Phil.)--Chinese University of Hong Kong, 2003.Includes bibliographical references (leaves 95-100).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Blind Signal Separation (BSS) Methods --- p.4Chapter 1.2 --- Objectives of the Thesis --- p.6Chapter 1.3 --- Thesis Outline --- p.8Chapter 2 --- Blind Adaptive Frequency-Shift (BA-FRESH) Filter --- p.9Chapter 2.1 --- Cyclostationarity Properties --- p.10Chapter 2.2 --- Frequency-Shift (FRESH) Filter --- p.11Chapter 2.3 --- Blind Adaptive FRESH Filter --- p.12Chapter 2.4 --- Reduced-Rank BA-FRESH Filter --- p.14Chapter 2.4.1 --- CSP Method --- p.14Chapter 2.4.2 --- PCA Method --- p.14Chapter 2.4.3 --- Appropriate Choice of Rank --- p.14Chapter 2.5 --- Signal Extraction of Spectrally Overlapped Signals --- p.16Chapter 2.5.1 --- Simulation 1: A Fixed Rank --- p.17Chapter 2.5.2 --- Simulation 2: A Variable Rank --- p.18Chapter 2.6 --- Signal Separation of Speech Signals --- p.20Chapter 2.7 --- Chapter Summary --- p.22Chapter 3 --- Reverberant Environment --- p.23Chapter 3.1 --- Small Room Acoustics Model --- p.23Chapter 3.2 --- Effects of Reverberation to Speech Recognition --- p.27Chapter 3.2.1 --- Short Impulse Response --- p.27Chapter 3.2.2 --- Small Room Impulse Response Modelled by Image Method --- p.32Chapter 3.3 --- Chapter Summary --- p.34Chapter 4 --- Information Theoretic Approach for Signal Separation --- p.35Chapter 4.1 --- Independent Component Analysis (ICA) --- p.35Chapter 4.1.1 --- Kullback-Leibler (K-L) Divergence --- p.37Chapter 4.2 --- Information Maximization (Infomax) --- p.39Chapter 4.2.1 --- Stochastic Gradient Descent and Stability Problem --- p.41Chapter 4.2.2 --- Infomax and ICA --- p.41Chapter 4.2.3 --- Infomax and Maximum Likelihood --- p.42Chapter 4.3 --- Signal Separation by Infomax --- p.43Chapter 4.4 --- Chapter Summary --- p.45Chapter 5 --- Blind Signal Separation (BSS) in Frequency Domain --- p.47Chapter 5.1 --- Convolutive Mixing System --- p.48Chapter 5.2 --- Infomax in Frequency Domain --- p.52Chapter 5.3 --- Adaptation Algorithms --- p.54Chapter 5.3.1 --- Standard Gradient Method --- p.54Chapter 5.3.2 --- Natural Gradient Method --- p.55Chapter 5.3.3 --- Convergence Performance --- p.56Chapter 5.4 --- Subband Adaptation --- p.57Chapter 5.5 --- Energy Weighting --- p.59Chapter 5.6 --- The Permutation Problem --- p.61Chapter 5.7 --- Performance Evaluation --- p.63Chapter 5.7.1 --- De-reverberation Performance Factor --- p.63Chapter 5.7.2 --- De-Noise Performance Factor --- p.63Chapter 5.7.3 --- Spectral Signal-to-noise Ratio (SNR) --- p.65Chapter 5.8 --- Chapter Summary --- p.65Chapter 6 --- Simulation Results and Performance Analysis --- p.67Chapter 6.1 --- Small Room Acoustics Modelled by Image Method --- p.67Chapter 6.2 --- Signal Sources --- p.68Chapter 6.2.1 --- Cantonese Speech --- p.69Chapter 6.2.2 --- Noise --- p.69Chapter 6.3 --- De-Noise and De-Reverberation Performance Analysis --- p.69Chapter 6.3.1 --- Speech and White Noise --- p.73Chapter 6.3.2 --- Speech and Voice Babble Noise --- p.76Chapter 6.3.3 --- Two Female Speeches --- p.79Chapter 6.4 --- Recognition Accuracy Performance Analysis --- p.83Chapter 6.4.1 --- Speech and White Noise --- p.83Chapter 6.4.2 --- Speech and Voice Babble Noise --- p.84Chapter 6.4.3 --- Two Cantonese Speeches --- p.85Chapter 6.5 --- Chapter Summary --- p.87Chapter 7 --- Conclusions and Suggestions for Future Research --- p.88Chapter 7.1 --- Conclusions --- p.88Chapter 7.2 --- Suggestions for Future Research --- p.91Appendices --- p.92A The Proof of Stability Conditions for Stochastic Gradient De- scent Algorithm (Ref. (4.15)) --- p.92Bibliography --- p.9