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Zero-forcing beamforming (ZFBF) under perantenna power constraint (PAPC) is a popular research topic. A survey is carried out in this paper to show the important results in the literature in this area. Particularly, it has been found that there are two research lines for this topic. One research line is to find the optimal solutions based on the interior point method. Another line is focused on the low complexity and parallel implementations. Important results are presented for both lines.

Zero-forcing beamforming under per-antenna power constraint (PAPC) is considered in this paper, and the objective is to maximize the minimum user information rate. A parallel low complexity zero-forcing beamformer design is proposed in this paper for MU-MIMO systems by introducing a regularized dual decomposition method. The idea of this method is to solve the problem via solving its dual problem. Since the dual objective is not differentiable, a Tikhonov regularization is introduced. The regularized problem can be solved by using a gradient-based method in a parallel manner. Moreover, the optimal solution of the Lagrangian is in a closed form. The smoothness properties of the regularized dual function are investigated. We also estimate the error bound between the optimal function value of the primal problem and that of the regularized dual problem. Corresponding convergence analysis and convergence rate of the proposed algorithm are established. Computational complexity analysis is carried out to compare the complexity of the proposed method with that of state-of-the-art interior point method. Simulation results are provided to show the effectiveness of the proposed method.

© 2015 IEEE. In industrial noise environments, the use of assistive listening headsets is a means to provide adequate access to voice communication while wearing hearing protection. This paper presents a performance evaluation and comparison of two different methods to provide the binaural speech enhancement in real industrial noise scenarios. The investigated binaural methods based on differential beamforming and multichannel Wiener filter show different strengths and weaknesses. A transient noise suppression algorithm is also proposed and evaluated. Performance evaluation shows that this algorithm, together with the binaural multi-channel Wiener filter approach, can successfully reduce the hammering noise. This can be observed from the PESQ scores and the signal characteristics.

This letter proposes a new algorithm for solving the optimal zero-forcing beamforming problem that maximizes the user achievable rate with restriction on the per-antenna element power constraints. An accelerated gradient method with step size search is proposed for solving the problem. For each iteration of the gradient approach, a quick one dimensional search is employed to obtain the step size. The advantage of the step-size search is that it is relatively fast and requires only a few calculations of the objective function. Design examples show that the proposed algorithm converges faster than the gradient approach and the accelerated gradient approach with a constant step size while achieving a low computational complexity.

A first-order zero-forcing beamformer design is proposed in this letter for MU-MIMO systems under per-antenna power constraints (PAPC). By forming the regularized dual problem, first-order methods can be applied. To achieve the limit convergence rate of first-order methods, an accelerated method is introduced to solve the regularized dual problem. Simulation results are provided to show the effectiveness of the proposed method.

The paper presents results of an investigation of a MU-MIMO system suitable for providing broadband services. The base station has a circular array and each user has a single high gain antenna. Two optimum zero forcing beamformers are considered and semi-orthogonal user selection is used to schedule users in the downlink. A key point of the investigation is to determine the maximum number of users that can be scheduled for simultaneous transmission in order to achieve high spectral efficiency and still maintain acceptable performance in terms of sum rate and also all user rates.

In this paper, we investigate a zero-forcing beamformer design with signed power-of-two coe cients for rural applications. In this design, the minimum user information rate is taken as the performance measure, while a practical system design constraint, the per-antenna power constraint, is imposed. The problem is formulated as a constrained zero-one integer programming problem. Based on a transform between two different integer spaces, the problem is transformed into an equivalent constrained integer programming problem. A global optimal two-stage design is proposed for solving the problem. In the first stage, a polynomial time quantization method is applied to obtain an initial design. In the second stage, an auxiliary function method is used to find the global optimal design. For illustration, numerical examples under several different scenarios are studied and the results are compared with those obtained by an existing method. Furthermore, the impact of the mutual interference terms in the performance measure is also studied.

Broadband beamformers are known to be sensitive to errors and mismatches in their array elements. This paper proposes a robust minimax beamformer design which takes into account sensor element characteristics. The design formulation minimizes robust integral squared error subject to relaxation constraints on the peak deviation error for the beamformer. The advantage of the proposed formulation is that the design allows a trade-off between the peak deviation error and the sensitivity of the minimax error with respect to variations in sensor element characteristics. This improvement has been achieved with almost no increase in complexity compared with the original minimax problem. Design examples demonstrate that the proposed beamformer is less sensitive with respect to variations in sensor element characteristics when compared to the traditional minimax beamformer with a minor degradation in beamformer performance.

Zero-forcing beamforming (ZFBF) is a popular pre-coding scheme for MIMO systems. Most of the studies in the literature are under total power constraints. However, the perantenna power constraints (PAPC) are more realistic. The state-of-the-art method is interior point method which is expensive to realize in practice due to the high computational complexity. Hence, a low complexity zero-forcing precoding scheme under the per-antenna power constraints is proposed in this paper. This is achieved by introducing a regularized dual method. Simulations are carried out to show the effectiveness of the proposed method, which has a low computational complexity. In addition, the algorithm can be implemented in parallel to further reduce the computational complexity.

This paper proposes a new computational procedure for solving the optimal zero-forcing beamforming problem in multiple antenna channels that maximizes user achievable rate with restriction on the per-antenna element power constraints. An interior point method with optimal step size procedure is developed in which the step size for the line search in the Newton search direction is calculated exactly for each iteration. This significantly enhances the efficiency associated with the line search. Design examples show that the proposed algorithm converges rapidly to the optimal solution with low computational complexity.

In this letter, we develop an algorithm for the design of allpass variable fractional delay filter with powers-of-two coefficients as a means of achieving low complexity and efficient hardware implementation. The algorithm includes an efficient procedure to obtain the objective function in the neighborhood of a search point, which significantly reduces the complexity associated with the global optimization approach. Design examples show that significant improvement is obtained by using the proposed method over existing methods.

Broadband beamforming techniques are of importance in several applications such as microphone arrays, sonar arrays, and radio astronomy and broadband radar. The capability to obtain a good broadband response over a wide range of frequencies is important to maintain good signal integrity and spatial selectivity. Since the beamformer needs to operate over several octaves, there are a number of important considerations in the design, such as beamformer beamwidth in the low frequency range and sensor element placement. The beamformer design can be performed directly in the wave domain. However, the more common approach is to design the beamformer in the spatially sampled domain. Another way to design the beamformer weights is according to the presented data, which gives an optimal beamformer. Other important aspects of beamforming are the capability to steer the beam towards a specific input signal and also capability to focus the beamformer in the near field.

Binaural noise-reduction algorithms based on multi-channel Wiener filter (MWF) are promising techniques to be used in binaural assistive listening devices. The real-time implementation of the existing binaural MWF methods, however, involves challenges to increase the amount of noise reduction without imposing speech distortion, and at the same time preserving the binaural cues of both speech and noise components. Although significant efforts have been made in the literature, most developed methods so far have focused only on either the former or latter problem. This paper proposes an alternative binaural MWF algorithm that incorporates the non-stationarity of the signal components into the framework. The main objective is to design an algorithm that would be able to select the sources that are present in the environment. To achieve this, a modified speech presence probability (SPP) and a single-channel speech enhancement algorithm are utilized in the formulation. The resulting optimal filter also avoids the poor estimation of the second-order clean speech statistics, which is normally done by simple subtraction. Theoretical analysis and performance evaluation using realistic recorded data shows the advantage of the proposed method over the reference MWF solution in terms of the binaural cues preservation, as well as the noise reduction and speech distortion.

This brief investigates a tradeoff between the integral squared error and the peak deviation error for a variable fractional delay (VFD) filter with a coefficient relationship. The integral squared error is minimized subject to additional constraints on the peak deviation error. The problem is solved by utilizing second-order cone programming. In addition, the performance of the VFD filter with discrete coefficients is investigated, in which the filter coefficients are expressed as the sum of power-of-two terms to reduce the filter operations to shifts and adds. Design examples show that the peak deviation error can be significantly reduced from the least squares solution while maintaining approximately the same integral squared error. Similarly, the integral squared error can be significantly reduced from the minimax solution while maintaining approximately the same peak deviation error. Furthermore, the tradeoff filters are less sensitive with respect to quantization than the least squares and minimax solutions.

This paper investigates the optimal design of allpass variable fractional delay (VFD) filters with coefficients expressed as sums of signed powers-of-two terms, where the weighted integral squared error is the cost function to be minimized. The design can be classified as an integer programming problem. To solve this problem, a new procedure is proposed to generate a reduced discrete search region to decrease the computational complexity. A new exact penalty function method is developed to solve the optimal design problem for allpass VFD filter with signed powers-of-two coefficients. Design examples show that the proposed method can achieve a higher accuracy when compared with the quantization method.

This letter develops an efficient computational procedure for the design of an odd-order variable fractional delay (VFD) digital filter with minimum peak variable fractional delay error subject to restrictions on the peak variable frequency response error. An iterative algorithm is developed to solve the formulated non-linear optimization problem where a first order linear approximation is employed for the variable fractional delay error. This results in a second-order cone programming (SOCP) problem with linear constraints. Design examples show that the peak fractional delay error can be reduced significantly from the minimax solution while maintaining approximately the same peak frequency response error. In addition, for a fixed level of peak variable frequency response error, approximately 1.61-2.09 dB improvement for the peak variable delay error can be obtained over existing methods.

This paper presents an adaptive coherence-based beamforming algorithm that enhances a target speech signal from an arbitrary direction of arrival (DOA) in the azimuthal plane, while localising and suppressing the interfering speech signal and noise from other directions. In these complex noisy acoustic environments, spatially selective speech enhancement schemes provide significant advantages over single channel enhancement methods. Experimental results demonstrate that the proposed method achieves considerable improvement in Perceptual Evaluation of Speech Quality (PESQ). Moreover, the proposed algorithm is directly suited for real-time implementation.

In this paper, we consider an optimal zero-forcing beamformer design problem in multi-user multiple-input multiple-output broadcast channel. The minimum user rate is maximized subject to zero-forcing constraints and power constraint on each base station antenna array element. The natural formulation leads to a nonconvex optimization problem. This problem is shown to be equivalent to a convex optimization problem with linear objective function, linear equality and inequality constraints and quadratic inequality constraints. Here, the indirect elimination method is applied to reduce the convex optimization problem into an equivalent convex optimization problem of lower dimension with only inequality constraints. The primal-dual interior point method is utilized to develop an effective algorithm (in terms of computational efficiency) via solving the modified KKT equations with Newton method. Numerical simulations are carried out. Compared to algorithms based on a trust region interior point method and sequential quadratic programming method, it is observed that the method proposed is much superior in terms of computational efficiency.

The real-time implementation of the existing multi-channel Wiener filter (MWF) algorithms suffer from performance degradation due to the lack of robustness against estimation errors of the second-order statistics. The reasons are twofold: one, the estimation of the statistics relies on real voice activity detector (VAD), which often fails in adverse environments. Second, the MWF solutions involve estimation of the second order clean speech statistics, which also exaggerates the errors. This paper presents an MWF algorithm that requires neither VAD nor clean speech statistics. Performance evaluation under real scenarios shows that the proposed method outperforms the conventional MWF solution in terms of the trade-off between noise reduction and speech distortion.

In this paper, a nonlinear phase finite impulse response (FIR) filter is designed without imposing a desired phase response. The maximum passband group delay of the filter is minimized subject to a positivity constraint on the passband group delay response of the filter as well as a specification on the maximum absolute difference between the desired magnitude square response and the designed magnitude square response over both the passband and the stopband. This filter design problem is a quadratic NP hard functional inequality constrained optimization problem. To tackle this problem, first, the one norm functional inequality constraint of the optimization problem is approximated by a smooth function so that the quadratic NP hard functional inequality constrained optimization problem is converted to a nonconvex functional inequality constrained optimization problem. Then, a modified filled function method is applied for finding the global minimum of the nonconvex optimization problem. By using a local minimum of the corresponding unconstrained optimization problem as the initial condition of our proposed global optimization algorithm, computer numerical simulation results show that our proposed approach could efficiently and effectively design a minimax passband group delay nonlinear phase peak constrained FIR filter without imposing a desired phase response.

This paper investigates the design of low complexity, non-robust and robust broadband beamformers with least squared criterion. An iterative algorithm is proposed to reduce the number of non-zero coefficients in both the non-robust and robust beamformers to reduce the computational complexity. Design examples show that the number of nonzero coefficients for the beamformers can be significantly reduced without a significant degradation in the integral squared error. In addition, the robust beamformer is less sensitive to non-zero coefficient reduction than the non-robust beamformer. In particular, the number of non-zero coefficients for the robust beamformer can be reduced by up to 74% with only a small reduction of 1.34dB in the integral squared error.

We propose a numerically efficient technique to approximate the joint detection probability of a coherent multiple input multiple output (MIMO) receiver in the presence of inter-symbol interference (ISI) and additive white Gaussian noise (AWGN). This technique approximates the probability of detection by numerically integrating the product of the characteristic function (CF) of the received filtered signal with the Fourier transform of the multi-dimension decision region. Naturally, the accuracy of the approximation is dependent on the number of points in the numerical integration. The proposed method selects the number of points to integrate over by deriving bounds on the approximation error. As such, a reduction of up to 1/100th of the number points can be achieved when comparing with existing single input single output (SISO) techniques. Simulation results demonstrate that the proposed method is highly accurate with the calculated errors being well within the bounded approximation error. In addition, the results are closely matched with those obtained using the Monte Carlo simulations with a typical error less than 10-4 while requiring only a fraction of the computation time.

In this paper, a modified a priori SNR estimator is proposed for speech enhancement. The well-known decision-directed (DD) approach is modified by matching each gain function with the noisy speech spectrum at current frame rather than the previous one. The proposed algorithm eliminates the speech transient distortion and reduces the impact from the choice of the gain function towards the level of smoothing in the SNR estimate. An objective evaluation metric is employed to measure the trade-off between musical noise, noise reduction and speech distortion. Performance is evaluated and compared between a modified sigmoid gain function, the state-of-the-art log-spectral amplitude estimator and the Wiener filter. Simulation results show that the modified DD approach performs better in terms of the trade-off evaluation.

This correspondence investigates the least squares and minimax design problems for allpass variable fractional delay (VFD) filters. A two stage optimization approach is proposed to solve the resulting minimax optimization problem. This approach includes a combination of a one-dimensional global search method and an adaptive scheme to refine the discretization points. In addition, the paper investigates the design of allpass VFD filters which minimizes the weighted integral squared error subject to constraints on peak error deviation from the desired response. By using approximations, the design problem can be formulated as a quadratic optimization problem. Design examples show that a tradeoff between the weighted integral squared error and the peak error deviation can be achieved. In addition, the integral squared error can be reduced significantly from the minimax solution while maintaining approximately the same peak error deviation. Similarly, the peak error deviation can be significantly reduced from the least squares solution while maintaining approximately the same integral squared error.

This correspondence proposes a general design for allpass variable fractional delay (VFD) digital filters with minimum weighted integral squared error subject to constraints on maximum error deviation from the desired response. The resulting optimization problem is nonlinear and nonconvex with a nonlinear continuous inequality constraint. Stability of the designed filters are discussed. An effective procedure is proposed for solving the optimization problem. Firstly, a constraint transcription method and a smoothing technique are employed to transform the continuous inequality constraint into one equality constraint. Then, by using the concept of a penalty function, the transformed constraint is incorporated into the cost function to form a new cost function. The nonlinear optimization problem subject to continuous inequality constraints is then approximated by a sequence of unconstraint optimization problems. Finally, a global optimization method using a filled function is employed to solve the unconstraint optimization problem. Design example shows that a trade-off can be achieved between the integral squared error and the maximum error deviation for the design of allpass VFD filters.

This paper addresses the problem of extracting a desired speech source from a multispeaker environment in the presence of background noise. A new adaptive beamforming structure is proposed for this speech enhancement problem. This structure incorporates power spectral density (PSD) estimation of the speech sources together with a noise statistics update. An inactive-source detector based on minimum statistics is developed to detect the speech presence and to track the noise statistics. Performance of the proposed beamformer is investigated and compared to the minimum variance distortionless response (MVDR) beamformer with or without a postfilter in a real hands-free communication environment. Evaluations show that the proposed beamformer offers good interference and noise suppression levels while maintaining low distortion of the desired source.

This paper investigates the problem of enhancing a single desired speech source from a mixture of signals in multispeaker environments. A beamformer structure is proposed which combines a fixed beamformer with postfiltering. In the first stage, the fixed multiobjective optimal beamformer is designed to spatially extract the desired source by suppressing all other undesired sources. In the second stage, a multichannel power spectral estimator is proposed and incorporated in the postfilter, thus enabling further suppression capability. The combined scheme exploits both spatial and spectral characteristics of the signals. Two new multichannel spectral estimation methods are proposed for the postfiltering using, respectively, inner product and joint diagonalization. Evaluations using recordings from a real-room environment show that the proposed beamformer offers a good interference suppression level whilst maintaining a low-distortion level of the desired source.