Robust equalization of multichannel acoustic systems

In most real-world acoustical scenarios, speech signals captured by distant microphones from a source are reverberated due to multipath propagation, and the reverberation may impair speech intelligibility. Speech dereverberation can be achieved by equalizing the channels from the source to microphones. Equalization systems can be computed using estimates of multichannel acoustic impulse responses. However, the estimates obtained from system identification always include errors; the fact that an equalization system is able to equalize the estimated multichannel acoustic system does not mean that it is able to equalize the true system. The objective of this thesis is to propose and investigate robust equalization methods for multichannel acoustic systems in the presence of system identification errors. Equalization systems can be computed using the multiple-input/output inverse theorem or multichannel least-squares method. However, equalization systems obtained from these methods are very sensitive to system identification errors. A study of the multichannel least-squares method with respect to two classes of characteristic channel zeros is conducted. Accordingly, a relaxed multichannel least- squares method is proposed. Channel shortening in connection with the multiple- input/output inverse theorem and the relaxed multichannel least-squares method is discussed. Two algorithms taking into account the system identification errors are developed. Firstly, an optimally-stopped weighted conjugate gradient algorithm is proposed. A conjugate gradient iterative method is employed to compute the equalization system. The iteration process is stopped optimally with respect to system identification errors. Secondly, a system-identification-error-robust equalization method exploring the use of error models is presented, which incorporates system identification error models in the weighted multichannel least-squares formulation

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

Multichannel Speech Separation and Enhancement Using the Convolutive Transfer Function

This paper addresses the problem of speech separation and enhancement from multichannel convolutive and noisy mixtures, \emph{assuming known mixing filters}. We propose to perform the speech separation and enhancement task in the short-time Fourier transform domain, using the convolutive transfer function (CTF) approximation. Compared to time-domain filters, CTF has much less taps, consequently it has less near-common zeros among channels and less computational complexity. The work proposes three speech-source recovery methods, namely: i) the multichannel inverse filtering method, i.e. the multiple input/output inverse theorem (MINT), is exploited in the CTF domain, and for the multi-source case, ii) a beamforming-like multichannel inverse filtering method applying single source MINT and using power minimization, which is suitable whenever the source CTFs are not all known, and iii) a constrained Lasso method, where the sources are recovered by minimizing the $\ell_1$-norm to impose their spectral sparsity, with the constraint that the $\ell_2$-norm fitting cost, between the microphone signals and the mixing model involving the unknown source signals, is less than a tolerance. The noise can be reduced by setting a tolerance onto the noise power. Experiments under various acoustic conditions are carried out to evaluate the three proposed methods. The comparison between them as well as with the baseline methods is presented.Comment: Submitted to IEEE/ACM Transactions on Audio, Speech and Language Processin

Diversity techniques for blind channel equalization in mobile communications

A blind algorithm for channel distortion compensation is presented which can be employed in spatial or temporal diversity receivers. The proposed technique can be used in frequency selective and frequency flat fading mobile channels, using burst transmission schemes in the first case and OFDM modulation in the second one. The algorithm is base on a deterministic criteria and is suited for estimation when short sets of data are available.Peer ReviewedPostprint (published version

System Identification with Applications in Speech Enhancement

As the increasing popularity of integrating hands-free telephony on mobile portable devices and the rapid development of voice over internet protocol, identification of acoustic systems has become desirable for compensating distortions introduced to speech signals during transmission, and hence enhancing the speech quality. The objective of this research is to develop system identification algorithms for speech enhancement applications including network echo cancellation and speech dereverberation. A supervised adaptive algorithm for sparse system identification is developed for network echo cancellation. Based on the framework of selective-tap updating scheme on the normalized least mean squares algorithm, the MMax and sparse partial update tap-selection strategies are exploited in the frequency domain to achieve fast convergence performance with low computational complexity. Through demonstrating how the sparseness of the network impulse response varies in the transformed domain, the multidelay filtering structure is incorporated to reduce the algorithmic delay. Blind identification of SIMO acoustic systems for speech dereverberation in the presence of common zeros is then investigated. First, the problem of common zeros is defined and extended to include the presence of near-common zeros. Two clustering algorithms are developed to quantify the number of these zeros so as to facilitate the study of their effect on blind system identification and speech dereverberation. To mitigate such effect, two algorithms are developed where the two-stage algorithm based on channel decomposition identifies common and non-common zeros sequentially; and the forced spectral diversity approach combines spectral shaping filters and channel undermodelling for deriving a modified system that leads to an improved dereverberation performance. Additionally, a solution to the scale factor ambiguity problem in subband-based blind system identification is developed, which motivates further research on subbandbased dereverberation techniques. Comprehensive simulations and discussions demonstrate the effectiveness of the aforementioned algorithms. A discussion on possible directions of prospective research on system identification techniques concludes this thesis

Fractional biorthogonal partners in channel equalization and signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners

Low Complexity Blind Equalization for OFDM Systems with General Constellations

This paper proposes a low-complexity algorithm for blind equalization of data in OFDM-based wireless systems with general constellations. The proposed algorithm is able to recover data even when the channel changes on a symbol-by-symbol basis, making it suitable for fast fading channels. The proposed algorithm does not require any statistical information of the channel and thus does not suffer from latency normally associated with blind methods. We also demonstrate how to reduce the complexity of the algorithm, which becomes especially low at high SNR. Specifically, we show that in the high SNR regime, the number of operations is of the order O(LN), where L is the cyclic prefix length and N is the total number of subcarriers. Simulation results confirm the favorable performance of our algorithm

Blind identification of acoustic systems and enhancement of reverberant speech

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A Generalized Algorithm for Blind Channel Identification with Linear Redundant Precoders

It is well known that redundant filter bank precoders can be used for blind identification as well as equalization of FIR channels. Several algorithms have been proposed in the literature exploiting trailing zeros in the transmitter. In this paper we propose a generalized algorithm of which the previous algorithms are special cases. By carefully choosing system parameters, we can jointly optimize the system performance and computational complexity. Both time domain and frequency domain approaches of channel identification algorithms are proposed. Simulation results show that the proposed algorithm outperforms the previous ones when the parameters are optimally chosen, especially in time-varying channel environments. A new concept of generalized signal richness for vector signals is introduced of which several properties are studied