Optimal beamformer design in the reverberant environment

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.

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.

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.

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.

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 improve the robustness of microphone array beamformer in existing mismatch errors, robust beamforming algorithm based on linear constrained minimum variance and diagonal loading method is proposed. The proposed algorithm incorporates the spatial response variation function into the linear constrainted minimum variance criterion to design the frequency invariant beamformer and improve the robustness against microphone array mismatch errors in the actual environment by diagonal loading method. Simulation results and analyses illustrate that the array response within passband is robust, the stopband amplitude is controlled in the appropriate range, and the proposed algorithm based closed solution is better than the proposed algorithm based on convex optimization algorithm. Introduction As one of the key technologies for microphone arrays, broadband beamforming has been used in a wide range of audio and speech processing applications[1]. In many popular methods, the traditional linear constrained minimum variance(LCMV) beamforming method is mainly used to design narrow-band antenna beamformer[2]. If it is used to design a broadband beamformer of microphone array, it isn’t fit. It is necessary for microphone array to design broadband beamformer without specific arrays[3][4]. In order to achieve broadband frequency invariant beamformer[3], it is necessary to consider frequency invariant beamformer with mismatch errors caused by the gain, phase and position of the microphone[5][6]. For this purpose, in this paper, frequency invariant beamforming algorithm based on the linear constrainted minimum variance (LCMV), the spatial response variation function(SRV) of the microphone array, and diagonal loading method are used to design frequency invariant beamformer and improve the robustness on the given frequency range and the region. Array Model Consider a M-element linear microphone array in the far-field (not general, this method can be applied to arbitrary array structure), FIR subfilter with tap length L is added to microphone. The array output signal can be expressed as ( ) ( ) H k k = y w x , where H denotes conjugate transpose.The weight vector of microphone array response is written as 11 1 1 ( ) [ ( ), , ( ), , ( ), , ( )] T M L ML k w k w k w k w k = w L L L , T denotes transpose. 11 1 1 ( ) [ ( ), , ( ), , ( ), , ( )] T M L ML k x k x k x k x k = x L L L and it denotes the received signal of microphone array, the definition of the angle between the direction of the sound source and the line array is θ , the beam-pattern at frequency f and angle θ of arrival can be expressed as ( , ) | ( , )| T H f f θ θ = w d ,where frequency f is belongs to [ , ] l h f f ,the angle θ of the received signal is in[ , ] l h θ θ , and ( , ) f θ d denotes the array response vector. 4th International Conference on Computer, Mechatronics, Control and Electronic Engineering (ICCMCEE 2015) © 2015. The authors Published by Atlantis Press 102 Frequency Invariant Beamforming Algorithm and Diagonal Loading Method The spatial response variation function(SRV) is given by

For multi-microphone speech enhancement, different microphones might have different contributions, assome are even marginal. This is more likely to happen in wireless acoustic sensor networks (WASNs), where somesensors might be distant. In this work, we therefore consider sensor selection for linearly-constrained beamformers. Theproposed sensor selection approach is formulated by minimizing the total output noise power and constraining thenumber of selected sensors. As the considered sensor selection problem requires the relative acoustic transfer function(RTF), the covariance whitening based RTF estimation or a direct-path RTF approximation is exploited. For a singletarget source, we can thus substitute the estimated RTF or the assumed RTF to the original problem formulation in orderto design a minimum variance distortionless response (MVDR) beamformer. Alternatively, we can integrate the two RTFsto design a linearly constrained minimum variance (LCMV) beamformer in order to alleviate the effects of RTFestimation/approximation errors. By leveraging the superiority of LCMV beamformers, the proposed approach can beapplied to the multi-source case. An evaluation using a simulated large-scale WASN demonstrates that the integration ofRTFs for the sensor selection based LCMV beamformer can be beneficial as opposed to relying on either of theindividual RTF steered sensor selection based MVDR beamformers. We conclude that the sensors that are close to thetarget source(s) and also some around the coherent interferers are more informative.

Consider the max-min problem for an uplink SIMO heterogeneous network, where the base stations (BS) are coordinated dynamically for joint reception under some backhaul overhead constraints. We formulate this problem in the perspective of joint power allocation, BS assignment and beamformer design, and develop an efficient algorithm based on alternating optimization. In particular, we transfer the joint BS assignment and beamformer design subproblem into a group LASSO problem by applying the alternating direction method of multipliers (ADMM). Consequently, the problem is solved in a partially distributed manner and in each iteration a simple closed-form solution is derived. Numerical simulations demonstrate the effectiveness and efficiency of the proposed algorithm.

Joint power control with optimal beamforming design and power control with minimum antenna selection under signal to inference noise ratio constraints have been considered in separate wireless communication scenarios. In power control algorithms, multiple antennas with linear beamforming are used to reduce the interference power, which also minimizes the total transmitted power in uplink/downlink channels, while the minimum antenna selection problem is solved to reduce the computational complexity at the base stations as well as to reduce the transmits power within a group of users. In this paper, we jointly consider the power control and optimal beamforming design algorithm with limited number of best antenna set selection in uplink communication. Simulation results show that the power control algorithm combined with the best number of antenna selection method can minimize power. Consequently, the proposed algorithm can reduce significantly the computational complexity while retaining the benefits that stem from solving the sum of transmitted power minimization problem.

This paper studies and discusses robust minimum variance distortionless response (MVDR) beamformer with subarray multistage processing for circular hydrophone arrays, which is an extension of the multistage MVDR beamformer with line microphone arrays for noise reduction. The basic theory is to divide the hydrophones into a certain number of groups with each group only having two hydrophones for MVDR beamforming. After the beamforming, it is equivalent that the number of hydrophones is half of that at the adjoining former stage. Then the grouping and beamfoming processing will be repeated till that there is only one hydrophone. This subarray multistage MVDR beamformer has the following properties in the isotropic noise field: first, it is much more robust than the conventional MVDR beamformer; second, its array gain is lower than that of the conventional MVDR beamformer; moreover, the larger the sensor number in each subarray is, the higher the array gain will be, but with lower white noise gain. By choosing a proper hydrophone number of each subarray, a tradeoff can be made between the array gain and robustness.

Beamforming techniques are becoming popular in a wide spectrum of applications thanks to their promising performance. We consider applying the minimum variance distortionless response (MVDR) beamformer in a dynamic scenario, where the desired speaker, the noise components or microphone array may move. The generalized sidelobe canceler (GSC) structure offers a convenient implementation of the MVDR, allowing to track the noise efficiently. Yet, noise reduction is degraded during speech tracking. We propose a QR Decomposition (QRD) based MVDR beamformer, which allows to track both speech and noise variations in dynamic scenarios without sacrificing noise reduction during speech segments. The proposed method utilizes the QRD algorithm for the implementation of a complete system required for the realization of an MVDR beamformer, which includes the identification of noisy speech or noise-only time-frequency bins, speech tracking and noise tracking. The proposed QRD based MVDR is efficiently implemented, and its overall computational complexity is O(M2), with M being the number of microphones. The advantages of the proposed method over the GSC are exemplified in a synthetically simulated scenario.

As an effective way to realize the integrated sensing and communication for 6G, the dual-functional radar-communication (DFRC) has been studied to implement dual-functional system that simultaneously perform wireless communication and radar sensing. One of the fundamental design issues in DFRC focuses on waveform design, including the selection of basic waveform (e.g., Orthogonal Time Frequency Space (OTFS) or Orthogonal Frequency Division Multiplexing (OFDM)), and the optimal beamforming design. In this paper, we investigate the transceiver beamforming design for a multi-input-multi-output (MIMO) DFRC system, where the dual functional base station (BS) simultaneously detects the multiple targets while communicating with multiple communication users. To this end, we first characterize the multi-fold tradeoffs between communication and radar sensing by defining an achievable performance region of the proposed DFRC system. The performance of communication and radar sensing are characterized by their signal-to-interference-plus-noise ratios (SINRs), and then the multi-objective optimization problem is formulated to maximize the SINRs of all communication users and radar sensing echoes (from targets) via optimizing beamforming matrix. To solve the problem, we propose a poly-complexity solution by using the quadratic transform and successive convex approximation. Simulation results are provided to verify the proposed design.

P174 ATTENUATING MULTIPLES FOR LOW SIGNAL- TO-NOISE RATIO DATA USING OPTIMAL BEAMFORMING 1 Abstract This paper presents the theory of optimal beamforming and its application in attenuating multiples for low signalto-noise (S/N) ratio data. The key point of the theory is updating the constraint in optimal beamformer design by using adaptive beamformer with the quiescent weighted vector. Real data example shows that the newly developed optimal beamformer has improved the minimum variance unbiased (MVU) beamformer significantly in attenuating multiples for low folding and/or low S/N ratio data without much extra cost. Introduction The objective of seismic data processing is to

In this paper, we address the problem of beamforming (BF) design in a cognitive relay network (CRN), where the cognitive network not only shares the spectrum with the primary one but also acts as a relay to assist the primary signal transmission. Considering that all of the wireless channels are subject to the correlated Rayleigh fading distribution, we first formulate a constrained optimization problem to minimize the total transmit power of the cognitive base station (CBS) with multiple antennas, while guaranteeing the quality-of-service (QoS) of the primary and secondary users and keeping the mutual interference below an acceptable level. Then, by adopting the available partial channel state information (CSI), and proposing an approximation method to relax the constraints, a support vector machine (SVM) based algorithm is presented to solve the optimization problem for the BF weight vectors. The benefit of the new approach is that the slow change of the partial CSI can be taken into account. Finally, computer simulation results are provided to confirm the superiority of the proposed BF design strategy.

Submarine hydrophone arrays sample the underwater acoustic pressure field in space and time to sense the presence of sources of radiated sound and to extract tactical information from the received sounds. The outputs of the hydrophones are combined by a spatial filter (or beamformer) so that signals from a chosen direction are coherently added while the effects of noise and interference from other directions are reduced by destructive interference. The spatial filter appropriately weights the hydrophone outputs prior to summation so as to enhance the output signal-to-noise ratio, thereby improving the detection, classification, localization and tracking performance of the passive sonar system onboard the submarine. By processing real acoustic data from a submarine hull-mounted array, it is shown that an optimal (adaptive) frequency-domain spatial filter (based on inversion of the observed cross spectral matrix for each frequency bin) enhances the detection of underwater acoustic signals, when compared with conventional spatial filtering (or delay-and-sum beamforming). The degree of improvement, however, depends on the method used to normalize the cross spectral matrix. Superior detection performance for a submarine hull-mounted array occurs when the observed cross spectral matrix for each frequency of interest is normalized using the average of all the single hydrophone output powers at each frequency. It is also shown that the self-noise analysis of a submarine towed array is facilitated by processing the element-level data in the frequency-wave number domain with a constrained optimal spatial filter, which is also referred to as a Minimum Variance Distortionless Response (MVDR) beamformer. This spatiotemporal filtering method is employed to separate signals (surface ship contacts) and tow vessel noise components (direct path and multipath arrivals) according to their directions of propagation. This method is also found to separate spatially-correlated self-noise components that propagate within the towed array structure at a speed that is slower than the speed of sound travel in water. A comparison of the frequency-wave number power spectra estimated using conventional and optimal spatial filtering methods shows that the MVDR spatial filter enables the various sources of acoustic energy that are sensed by the array to be more clearly delineated in frequency-wave number space. The MVDR spatial filter is a data-adaptive spatial filter that is observed to suppress spatial leakage, to enhance the spatial resolution of a towed array through narrower beamwidths, and to provide superdirective array gain at frequencies well below the design frequency of the towed array. Frequency-wave number analysis with optimal spatial filtering is a powerful diagnostic tool for studying the self-noise characteristics of a towed linear array of hydrophones.