Study On Robust Adaptive Widely Linear Beamforming Algorithms

Beamforming is an important research field of array signal processing. It aims at receiving the signal of interest (SOI) and suppressing interferences and noise, simultaneously. Traditional beamforming only uses the covariance matrix assumed that the received signals are second order circular signals. However, for second order noncircular signals, such as BPSK, ASK, PAM used in wireless communication, their second order statistics contain covariance matrix and complementary covariance matrix. Widely linear beamforming can fully use the second order statistics to improve the performance, which has a better output signal-to-interference-and-noise ratio (SINR) bound. But, suffering from the same problem with traditional beamforming, widely linear beamforming is vulnerable to errors. In practical applications, there exist different kinds of errors, such as signal pointing error, array amplitude and phase error, mutual coupling. Thus, it is valuable to research on robust widely linear beamforming against errors.In this thesis, after introducing the basic knowledge of robust widely linear beamforming, new robust widely linear beamforming algorithms are proposed as there exist weaknesses in the existing algorithms. The main content and contributions are summarized as follows:First, considering many priori information needed for the existing algorithms, a projection constraint based robust widely linear beamforming is proposed. The proposed algorithm fully utilizes the eigenvectors of the sample covariance matrix, and only needs the angle section of the SOI. The main idea of the method is to use the correlation of the eigenvectors and extend steering vector (ESV). At the first step, an interference-plus-noise subspace is constructed using the correlation. Then, the projection of the ESV on the subspace is used to estimate the SOI’s ESV. Finally, the weight vector can be obtained using the extended covariance matrix and estimated ESV. Simulation results show better performance of the proposed method when multiple errors exist.Second, as the existing robust widely linear beamforming are based on the minimum variance criterion, for non-Gaussian signals, the minimum variance criterion is not optimal. Thus, for sub-Gaussian noncircular signals, two algorithms are proposed. The main idea of the proposed beamformers is the combination of the widely linear and the minimum dispersion criterion. The sub-Gaussian property and noncircularity of the signals are fully used. The experiments show that the proposed methods have excellent performance even in high signal-to-noise ratio (SNR), and can process more signals than antenna numbers.At last, as the noncircularity coefficient estimation based widely linear beamforming needs precise information of the steering vector, its performance degrades in mutual coupling errors, a robust widely linear beamforming for mutual coupling is proposed. The proposed method brings in the idea of auxiliary elements. By utilizing the output of middle subarray, a method to estimate the noncircularity coefficient when mutual coupling exists is given. Then, the widely linear weight vector can be obtained using the estimated noncircularity coefficient and subarray’s steering vector. Simulation results verify the effectiveness of the proposed method when mutual coupling exists.