Linearly Constrained Minimum Variance Filter Research Articles

Distributed Rate-Constrained LCMV Beamforming

In this letter, we propose a decentralized framework for rate-distributed linearly constrained minimum variance (LCMV) beamforming in wireless acoustic sensor networks. To save the energy usage within the network, we propose to minimize the transmission cost and put a constraint on the noise reduction performance. Subsequently, we decentralize the obtained LCMV filter structure by exploiting an imposed block diagonal form of the noise correlation matrix. As a result, the beamformer weights are calculated in a decentralized fashion and each node can determine its quantization rate locally. Finally, numerical results validate the proposed method.

Separable linearly constrained minimum variance beamformers

Abstract Large-scale antenna systems offer many attractive features, including large array gain and improved spatial resolution, for example. However, classical beamforming methods, such as the linearly constrained minimum variance (LCMV) filter, do not perform well on this scenario due to large computational costs involved. To deal with this issue, we propose Kronecker-separable extensions of the LCMV filter and its stochastic gradient implementation, known as Frost’s algorithm, for uniform rectangular arrays. We study the convergence of the proposed methods, investigate their computational complexity, and assess their source recovery performance with computer simulations. Our results show that our methods exhibit important computational savings while the source recovery performance losses are small.

Enhancement and Noise Statistics Estimation for Non-Stationary Voiced Speech

In this paper, single channel speech enhancement in the time domain is considered. We address the problem of modelling non-stationary speech by describing the voiced speech parts by a harmonic linear chirp model instead of using the traditional harmonic model. This means that the speech signal is not assumed stationary, instead the fundamental frequency can vary linearly within each frame. The linearly constrained minimum variance (LCMV) filter and the amplitude and phase estimation (APES) filter are derived in this framework and compared to the harmonic versions of the same filters. It is shown through simulations on synthetic and speech signals, that the chirp versions of the filters perform better than their harmonic counterparts in terms of output signal-to-noise ratio (SNR) and signal reduction factor. For synthetic signals, the output SNR for the harmonic chirp APES based filter is increased 3 dB compared to the harmonic APES based filter at an input SNR of 10 dB, and at the same time the signal reduction factor is decreased. For speech signals, the increase is 1.5 dB along with a decrease in the signal reduction factor of 0.7. As an implicit part of the APES filter, a noise covariance matrix estimate is obtained. We suggest using this estimate in combination with other filters such as the Wiener filter. The performance of the Wiener filter and LCMV filter are compared using the APES noise covariance matrix estimate and a power spectral density (PSD) based noise covariance matrix estimate. It is shown that the APES covariance matrix works well in combination with the Wiener filter, and the PSD based covariance matrix works well in combination with the LCMV filter.

Linearly-Constrained Minimum-Variance Method for Spherical Microphone Arrays Based on Plane-Wave Decomposition of the Sound Field

Speech signals recorded in real environments may be corrupted by ambient noise and reverberation. Therefore, noise reduction and dereverberation algorithms for speech enhancement are typically employed in speech communication systems. Although microphone arrays are useful in reducing the effect of noise and reverberation, existing methods have limited success in significantly removing both reverberation and noise in real environments. This paper presents a method for noise reduction and dereverberation that overcomes some of the limitations of previous methods. The method uses a spherical microphone array to achieve plane-wave decomposition (PWD) of the sound field, based on direction-of-arrival (DOA) estimation of the desired signal and its reflections. A multi-channel linearly-constrained minimum-variance (LCMV) filter is introduced to achieve further noise reduction. The PWD beamformer achieves dereverberation while the LCMV filter reduces the uncorrelated noise with a controllable dereverberation constraint. In contrast to other methods, the proposed method employs DOA estimation, rather than room impulse response identification, to achieve dereverberation, and relative transfer function (RTF) estimation between the source reflections to achieve noise reduction while avoiding signal cancellation. The paper includes a simulation investigation and an experimental study, comparing the proposed method to currently available methods.

On the Time-Domain Widely Linear LCMV Filter for Noise Reduction With a Stereo System

This paper deals with the problem of noise reduction in stereo sound systems where the objective is not only to reduce noise, but also to preserve the spatial information of both the desired speech and noise sources so that the listener can still localize the speech and noise sources by listening to the enhanced binaural outputs. To achieve this objective, we use the widely linear (WL) framework developed previously and convert the problem of binaural noise reduction into one of monaural filtering with complex signals. We then present a way to decompose both the complex speech and noise signal vectors into two orthogonal components: one correlated and the other uncorrelated with the corresponding current signal sample. With this decomposition, the problem of noise reduction with preservation of the spatial information of speech and noise sources is formulated as an optimization problem with two constraints: one on the desired speech and the other on the preservation of the noise signal. We then derive a WL linearly constrained minimum variance (LCMV) filter, which can take advantage of the statistics and noncircularity of the complex speech signal to achieve noise reduction. In contrast to the WL Wiener and minimum variance distortionless response (MVDR) filters developed previously that can only preserve the characteristics and spatial information of the desired sound source, this new WL LCMV filter has the potential to reduce noise while preserving the characteristics and spatial information of both the desired and noise sources at the same time. Experimental results are provided to justify the claimed merits of the proposed WL LCMV filter.

Notes on design of transformation-based reduced-rank generalized sidelobe canceller for matrix LCMV filter

This paper is concerned with the design of transformation-based reduced-rank generalized sidelobe canceller (RRGSC) for the linearly constrained minimum variance (LCMV) filter. Most RRGSCs introduced in the previous literature were limited to vector form, and their performances were not compared with the LCMV filter. In order to overcome these drawbacks, we present a detailed discussion about the relationship between the general matrix LCMV filter and the transformation-based RRGSC, and obtain several new results. First, we study the effect of transformation matrix on the performance of RRGSC, and find the optimal design of the transformation matrix that can minimize the performance loss of RRGSC relative to the LCMV filter. Second, we obtain a sufficient and necessary condition for the performance equivalence between RRGSC and LCMV filter. Third, we obtain the minimum loss-free reduced-rank of RRGSC, and formulate the relationship between the reduced-rank and the minimum performance loss of RRGSC relative to LCMV filter. Application cases and computer simulations are provided to demonstrate the usefulness and correctness of the above-mentioned theoretical results.

A low-complexity two-stage receiver for space–time block-coded CDMA MIMO systems

A low-complexity two-stage receiver for the space–time block-coded (STBC) code-division multiple-access (CDMA) multiple-input multiple-output (MIMO) system is proposed in this paper. The STBC CDMA MIMO system has been extensively studied for the great demand for capacity and transmission rate in future wireless communication systems. The blind Capon multiuser receivers implemented by linearly constrained minimum variance (LCMV) filters are designed to achieve this goal. However, the LCMV filter suffers from the heavy computational load and slow convergence speed. The proposed two-stage receiver contains partially adaptive linear filters in parallel followed by a channel estimator and symbol detector. Two transformation schemes are designed for the partially adaptive linear filters. The uniqueness and exactness of channel estimation are analyzed when the noise power approaches zero. To alleviate the finite sample effects, the forward–backward averaging technique is introduced to enhance system performance. Based on the weighting analysis, we also present a simplified two-stage receiver. The computational complexities of the compared receivers are calculated. Computer simulations demonstrate that the proposed two-stage receiver has better performance than the Capon receiver with much lower computational load.