Robust Beamforming Algorithm Based on Linear Constrained Minimum Variance and Diagonal Loading

In real-world environments, the signals captured by a set of microphones in a speech communication system are mixtures of the desired signal, interference, and ambient noise. A promising solution for proper speech acquisition (with reduced noise and interference) in this context consists in using the linearly constrained minimum variance (LCMV) beamformer to reject the interference, reduce the overall mixture energy, and preserve the target signal. The minimum variance distortionless response beamformer (MVDR) is also commonly known to reduce the interference-plus-noise energy without distorting the desired signal. In either case, it is of paramount importance to accurately quantify the achieved noise and interference reduction. Indeed, it is quite reasonable to ask, for instance, about the price that has to be paid in order to achieve total removal of the interference without distorting the target signal when using the LCMV. Besides, it is fundamental to understand the effect of the MVDR on both noise and interference. In this correspondence, we investigate the performance of the MVDR and LCMV beamformers when the interference and ambient noise coexist with the target source. We demonstrate a new relationship between both filters in which the MVDR is decomposed into the LCMV and a matched filter (MVDR solution in the absence of interference). Both components are properly weighted to achieve maximum interference-plus-noise reduction. We investigate the performance of the MVDR, LCMV, and matched filters and elaborate new closed-form expressions for their output signal-to-interference ratio (SIR) and output signal-to-noise ratio (SNR). We theoretically demonstrate the tradeoff that has to be made between noise reduction and interference rejection. In fact, the total removal of the interference may severely amplify the residual ambient noise. Conversely, totally focussing on noise reduction leads to increased level of residual interference. The proposed study is finally supported by several numerical examples.

In order to solve the problem of robustness of beamforming algorithm with microphone array channel mismatch, an adaptive dynamic-weighted constrained least square algorithm-based microphone array robustness frequency invariant beamforming algorithm is proposed. In the proposed algorithm, by analyzing the microphone array model, with or without channel mismatch, the disadvantages of the constrained least square frequency invariant beamforming algorithm with channel mismatch are studied. After the probability density functions of the microphones are defined as the robustness factors and added to the constraint least square frequency invariant beamforming algorithm, the robustness is improved to a certain extent, but it is still poor. In order to further improve the robustness of the algorithm, dynamic-weighted coefficients for controlling frequency invariance in the cost function are used to regulate the sidelobe spectrum energy. The fluctuation error is defined as the ratio of the maximum to minimum value of array response formed by the same angle of arrival at different frequencies, within the frequency range of frequency invariant, to compare the proposed algorithm with the constrained least square robustness frequency invariant and minmax robustness broadband beamforming algorithm. Experimental results of the algorithms show that the fluctuation errors of the proposed algorithm are the smallest and its robustness is the best; it can effectively overcome the poor robustness of the beamforming algorithm caused by microphone array channel mismatch, and can be applied to any arbitrary array structure.

In this paper, we study the performance of the minimum variance distortionless response (MVDR) and linearly constrained minimum variance (LCMV) noise reduction filters when a source of interference and ambient noise coexist with the target signal. We demonstrate that both filters are related as we decompose the MVDR filter into the LCMV and a matched filter (MVDR solution in the absence of interference). Both components are properly weighted to achieve maximum interference-plus-noise reduction at each frequency bin. Furthermore, we elaborate new closed-form expressions for the signal-to-interference ratio (SIR) and signal-to-noise ratio (SNR) at the output of the LCMV, MVDR, and matched filters. These expressions theoretically prove that a tradeoff between noise reduction and interference rejection has to be made. In fact, the total removal of the interference may severely amplify the output ambient noise. Conversely, totally focussing on noise reduction leads to increased level of residual interference. The proposed study is finally supported by numerical examples.

Speech enhancement is an important pre-processing step in a wide diversity of practical fields related to speech signals, and many signal-enhancement methods, such as fixed beamforming and adaptive beamforming, have already been proposed for speech enhancement. However, lack of comprehensive and quantitative performance evaluation of current enhancement methods when multi-speeches exist simultaneously, it is difficult to choose an appropriate enhancement method in a practical application. This work aims to study the implementation of several enhancement methods for multi-speech enhancement in indoor environment of T60 = 0 s and T60 = 0.3 s. We first propose and compare two types of enhancement approaches. The first type is the basic enhancement methods, including the delay-and-sum beamforming (DSB), minimum variance distortionless response (MVDR), linearly constrained minimum variance (LCMV), and independent component analysis (ICA); The second type is the improved enhancement methods, including the robust MVDR and LCMV, realized by eigen decomposition and diagonal loading. In addition, the online enhancement performance based on the iteration of single-frame speech signals is then researched. The experimental results show that the enhancement effect of LCMV and ICA is relatively more stable in the case of the basic enhancement methods; in the case of the improved enhancement algorithms, the methods which employed diagonal loading iterations are better. In the case of the online enhancement, the DSB with frequency masking yields the best performance on the signal-to-interferences ratio (SIR) and possesses the capacity to suppress interferences.

We propose a new joint multiple matrix diagonalization algorithm for robust blind beamforming. This new algorithm is based on the iterative eigen- decomposition of cumulant matrices. Therefore it can avoid the stability and misadjustment problems arising among the conventional steepest-descent approaches for constant- modulus or cumulant optimization. Our Monte Carlo simulations show that our proposed algorithm significantly outperforms the JADE algorithm based on the Givens rotation for PSK source signals in terms of signal-to- interference-and-noise ratio for a wide variety of signal-to- noise ratios. Keywords-blind beamforming; eigen decomposition;JADE algorithm; cumulant; constant modulus I. INTRODUCTION The traditional beamforming techniques such as the minimum variance distortionless response (MVDR) approach (1) and the linear constrained minimum variance (LCMV) method (1) are based on the a priori knowledge of the directional vector associated with the desired source signal and may be quite sensitive to the perturbation of this vector. The perturbation of the vector direction is caused by the unknown deformation of the antenna array, the drifting effect in the electronics or the multipath propagation. Consequently, those factors strictly limit the performance of MVDR and LCMV beamformers in practice.

By comparing the disadvantages and advantages of conventional algorithms of adaptive beamformer, we put forward an adaptive beamformer based on weight iterative algorithm for suppressing RFI according to the distributing properties of radio frequency interference (RFI) in different range cell. We get the initial weight vector of the adaptive beamformer by using the algorithm of minimum variance distortionless response (MVDR). The other weight vectors are computed by the algorithm of linearly constrained minimum variance (LCMV) based on the last time weight vector. The covariance matrix of the two algorithms, i.e. MVDV and LCMV, are constructed with the array snapshots in the far range cells which have not useful radar echo. Thus the free degree of antenna array is increased. The feasibility of the adaptive beamformer is proved by using it to process the actual radar data.

Most existing methods on beamformer design, such as the minimum variance distortionless response (MVDR) method and the linearly constrained minimum variance (LCMV) method, assume that the group delay is known and often heuristically preselected to be half of the filter length. However, the optimal group delay is problem-dependent in practice, and the beamformer design performance based on the optimal beamformer response can be significantly better than the one based on the preselected beamformer response in the reverberant environment. In this paper, we consider the optimal beamformer design problem, i.e., the joint beamformer response and beamformer design problem. We introduce a new variable to represent the beamformer response and formulate the joint beamformer response design and beamformer design problem as a structured constrained convex optimization (SCCO) problem. Moreover, we exploit the separable structures of the SCCO problem and propose to use the alternating direction method of multipliers (ADMM) to solve it, and give a simple proof for the analysis of convergence. Numerical simulation results show the effectiveness of the proposed method in the reverberant environment by comparing it with the LCMV method.

The classical linearly constrained minimum variance (LCMV) beamformer corresponds, in the general case, to the linear, time invariant (TI) and spatio-temporal (ST) complex filter, the output power of which is minimized under some linear constraints. Optimal for stationary signals, this beamformer becomes sub-optimal for (quasi)-cyclostationary observations for which the optimal complex filters are (poly)-periodic (PP) and, under some conditions of widely linear non-circularity. Using these results and the fact that PP filtering is equivalent to FREquency SHifted (FRESH) filtering, the purpose of this paper is to present a first extension of the classical LCMV beamformer, taking into account the potential (quasi)-cyclostationarity and non-circularity properties of the observations. This new cyclic LCMV beamformer is shown to have an equivalent cyclic generalized sidelobe canceller (GSLC) structure. The performance computation of this new cyclic beamformer shows the interest of the latter in cyclostationary contexts and opens a reflection about the optimal constraint choice.

This paper proposes a reliable and efficient blind channel estimation method and a linearly constrained minimum variance (LCMV) receiver with circular precoding for single transmitter and receiver antenna orthogonal frequency division multiplexing (OFDM) system. The proposed blind channel estimation method is based on the interesting cross-correlation property of the cyclic prefix (CP) in an OFDM symbol. Toeplitz structure induced in the cross-correlation matrix allows us to employ a simple and reliable method for extracting channel impulse response effectively. The LCMV optimization criterion is applied for symbol detection of the OFDM symbols. At the same time, a circular precoding scheme for minimizing the maximal power of the dominant interference plus noise in LCMV receiver is considered. In the simulation study, proposed method is compared with other circularly precoded scheme and it demonstrate the superior performance of the proposed method.

Irregular microphone array design for broadband beamforming

Herein, we study an underlay beamforming technique for the coexistence scenario of satellite and terrestrial networks with the satellite return link as primary and the terrestrial uplink as secondary. Since satellite terminals are unique in that they always point towards the geostationary satellite, interference received by the terrestrial Base Station (BS) is concentrated in a specific angular sector. The priori knowledge that all the geostationary satellite terminals are facing south for the European coverage can be used in designing a beamformer at the terrestrial BS. Based on this concept, we propose a receive beamformer at the BS to maximize the Signal to Interference plus Noise Ratio (SINR) towards the desired user and to mitigate the interference coming from the interfering satellite terminals. The performances of Minimum Variance Distortionless (MVDR) and Linear Constrained Minimum Variance (LCMV) beamformers are compared for our considered scenario. It is shown that LCMV beamformer is better suited in rejecting interference even in case of Direction of Arrival (DoA) uncertainty of interfering satellite terminals as long as DoA range of the interfering sector is known to the beamformer. Furthermore, it is noted that MVDR beamformer is suitable for a large number of interferers.KeywordsSpatial FilteringUnderlaySatellite-terrestrial CoexistenceInterference Mitigation

Different beamforming techniques are looking forward to playing an important role in the next generation Multiple Input and Multiple Output (MIMO) radar based system. For the enhancement in resolution and for identification of more number of targets, MIMO radar is very useful. We get more flexibility in beampattern design using the MIMO concept in the radar system. Beamforming is used in sensor arrays for signal transmission or reception in particular directions. For improving resolution of target and reducing interference of signals from undesirables,a powerful technique is used in signal processing of MIMO radar known as beamforming. Various sorts of calculations are researched utilizing conventional beamforming and Adaptive beamforming to alter the necessary weighting on radio wire components. Effects of various errors are illustrated. Also, Linearly Constrained Minimum Variance (LCMV) and Minimum Variance Distortionless Variance (MVDR) calculations introduced which are the techniques gone under versatile beamforming and their belongings are talked about. The most useful algorithms which are the versatile techniques for beamforming as mentioned above are discussed in this paper.From the comparison of LCMV and MVDR algorithms with different number of array elements concluded which is better in different situations of the MIMO radar system.

Fixed broadband beamformers for speech applications using small-sized microphone arrays are known to be highly sensitive to errors in the microphone array characteristics. This paper describes two procedures for designing broadband beamformers with an arbitrary spatial directivity pattern, which are robust against gain and phase errors. The first design procedure optimises the mean performance of the broadband beamformer and requires knowledge of the gain and phase probability density functions, whereas the second design procedure optimises the worst-case performance by using a minimax criterion. Simulations with a small-sized microphone array show the performance improvement that can be obtained by using a robust broadband beamformer design procedure.

Enhancing multi-class SSVEP classification performance using regularized covariance estimators, spatiotemporal beamforming, and short-time EEG trials

This paper describes a simple adaptive pattern control (APC) method based on linearly constrained minimum variance (LCMV) algorithm. The desired static pattern weights are imposed on constrain set which make the overall beamformer sidelobe response equal to the desired quiescent response and simultaneously form nulls in the direction of interference. The sidelobe has many ripples in condition of small training sample size and the diagonal loading (DL) technology is applied to this method, which improve the convergence speed of sidelobe. The effectiveness of this new method is illustrated by the designed simulations