A Study On The Robust Adaptive Beamforming Algorithms Based On The Noncircular Signals

Robust adaptive beamformer is a very important branch in array signal processing field. Robust adaptive beamformer is a sonsor array which consist of some sensors to receive signals and extract information of the desired signals while suppressing the interference and noise components in the received signal. In the conventional adaptive beamforming algorithms, the circular signal that is the second-order statistical properties of the signal can be fully described by using covariance matrix is exploited. However, the signal is always noncircular in practical applications, which means the pseudo covariance matrix is not equal to zero. The widely linear(WL) beamforming algorithm has been proposed to extract the information of the desired signal which is contained in the received signal and its conjugate. Then, the optimal weight vector can be obtained. However, when the number of the snapshots is finite, the range of eigenvalue of the sample covariance matrix(SCM) has increased, which lead to the performance degradation and large computation.To circumvent this issue of lower robustness, WL MVDR and WL worst-case beamforming algorithms based on interference-plus-noise covariance matrix(INCM) are proposed in this thesis. The augmented SCM is not consistent for the actual augmented covariance for the finite number of training samples. The reconstruction of the augmented INCM can be obtained by combing MVDR spatial spectrum, the estimate of the noncircular coefficient and augmented steering vector. Then, the reconstructed INCM can be used instead of augmented SCM in these two algorithms, therefore, the effect of the desired signal can be removed. Moreover, the OAS and QCAP methods are exploited to estimate the augmented steering vector of the desired signal and the uncertainty level.In order to overcome with the problem of the slow convergence speed of the conventional least mean squares(LMS), the WL LMS algorithm based on set-membership(SM) framework for adaptive beamformer is devised, which exploits stochastic gradient(SG) and recursive least squares(RLS) to obtain the process of the joint iterative optimization of the reduced-rank matrix and weight vector. Owing to the constraint condition of the SM framework, the reduced-rank matrix and weight vector can be updated selectively, which provide a much faster convergence speed. Then, the WL reduced-rank robust adaptive beamforming algorithm based on MVDR for noncircular signals is proposed. This algorithm both utilizes the property of noncircular and the corrected former of the MVDR. In this former, the process of the joint iterative optimization of the reduced-rank matrix, weight vector and diagonal loading level can be obtained by SG method. Obviously, the diagonal loading level can be obtained adaptively. Therefore, the proposed WL beamformer algorithm has provided more robustness and lower computational complexity than the existing approaches.