Novel Robust Adaptive Beamformer against Bias and Non-Gaussian Signals

Abstract

In this thesis, we develop a novel robust adaptive beamformer against a bias and non-Gaussian signals. Looking toward real world applications, the beamformer system encounters the situation of both the correlated input signals and the non-Gaussian signals. The convergence performance of the conventional beamformer can be deteriorated by both the correlated input signals and the non-Gaussian signals. The affine projection algorithm has been proposed to improve the convergence performance for the correlated input signals, however the affine projection algorithm suffers from a bias of the weights at the steady-state when the reference signal is absent. Much research in the adaptive filtering has been proposed to prevent the performance degradation under the presence of the non-Gaussian signals, however conventional methods can not be directly applied to the adaptive beamformer. Thus, we present robust adaptive beamformer against bias and non-Gaussian signals. For each of the beamformers, we provide either a mechanism to eliminate the bias or a constrained optimization problem considering the characteristics of the non-Gaussian signals.

We first present a bias-free adaptive beamformer. To eliminate the bias, we analyze the bias mathematically by introducing the asymptotic solution. We prove that the bias can be alleviated by using a large regularization parameter, and propose the regularization parameter control mechanism for fast convergence speed at the initial state without the bias at the steady-state. The experimental results demonstrate that the proposed beamformer achieves both fast convergence speed and high steady-state output SINR without the bias.

We also propose a robust adaptive beamformer against the non-Gaussian signals. The conventional beamformer algorithm is based on the $L_2$-norm criterion; however the non-Gaussian signals which are very attractive for modeling the impulsive signal has no second order statistics. Thus the performance of the conventional adaptive beamformer can be seriously deteriorated in the presence of the non-Gaussian signals. In order to achieve the robust adaptive beamformer algorithm, we introduce the $L_1$-norm optimization problem which is adequate for modeling of the non-Gaussian signals. The stochastic gradient can be obtained by derivative of the cost function. The experimental results show that the proposed algorithm outperforms conventional algorithms under the environments of non-Gaussian signals.