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

Abstract

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