Adaptive Beamforming Algorithms Under Nonideal Conditions

As one of the most important issues in the array signal processing, beamforming is a spatial filtering technique. In order to enhance the signal of interest (SOI) and suppress inferences and noise, it can adjust weight vector for receiving the signal from a certain direction. It has found wide applications in varied fields of signal processing, including radar, sonar, wireless communications, seismic exploration, radio astronomy, medical diagnosis, speech signal processing, etc. The standard Capon beamformer, as one of the well-known adaptive beamformers, has remarkable resolution and interference suppression capability. However, adaptive beamformer is highly sensitive to the covariance matrix mismatch and steering vector (SV) of the SOI mismatch. Therefore, the performance of traditional adaptive beamformer will degrade seriously under nonideal conditions. During the past decades, robust adaptive beamforming (RAB) has become a research topic and a series of RAB techniques have been developed. In this dissertation, we further study on adaptive beamforming algorithms under different scenarios and propose several RAB algorithms. The main contributions and innovative points of this dissertation are listed as follows:Considering the performance of traditional projection approach degradation in the case of unknown the number of signals and low signal-to-noise ratio (SNR), we propose a new projection matrix approach for RAB. Based on the knowledge of the signal angular sector, a judgment standard is proposed. The standard can be used to search the eigenvector that belongs to signal subspace from the sample covariance matrix and estimate the corresponding projection matrix. Then, the SV error of the SOI can be eliminated by projecting the nominal SV to the estimated signal subspace, where the robustness of the RAB can be improved. The main advantage is that the proposed algorithm can estimate effectively the projection matrix of the signal subspace without the number of the signals and it can enjoy a good performance at low SNR.Under nonideal conditions, considering that the adaptive beamforming algorithms with the sample covariance matrix always result in the self-null phenomenon of the SOI, a new RAB algorithm is proposed based on interference-plus-noise covariance matrix reconstruction. Based on the characteristic of the SV error model, the SVs of the interferences can be constrained in an annulus uncertainty set corresponding to the direction range of the interferences with the imprecise information about the array structure. The annulus uncertainty set can be seen as a high-dimensional domain, where the center axis is the curve corresponding to the nominal SV function. The interference covariance matrix can be reconstructed by integrating the Capon spectrum over the surface of the annulus, where the integral can be calculated approximately by discrete sum method. The noise covariance matrix can be estimated by the minimum eigenvalue of the sample covariance matrix. With the reconstructed interference-plus-noise covariance matrix, the nominal SV can be corrected via maximizing the beamformer output power by solving a quadratically constrained quadratic programming problem. Finally, based on the principle of minimum variance distortionless response, the robust adaptive beamformer can be obtained. The main advantage is that the proposed algorithm is robust against unknown arbitrary-type mismatches.Considering that the maximization of the RAB output power results in an insufficient suppression of interferences and noise, an RAB algorithm is proposed based on minimum sensitivity. Under nonideal conditions, a general definition of beamformer sensitivity is introduced from the desired signal covariance matrix, which is an excellent criterion to measure the beamformer performance without interference. Then a novel SV estimation method is proposed based on the minimum sensitivity criterion. It leads to a non-convex optimization problem, which can be efficiently solved using semidefinite relaxation. Simultaneously, the matrix reconstruction method is utilized to estimate the desired signal covariance matrix and interference-plus-noise covariance matrix. Finally, based on the principle of minimum variance distortionless response, the robust adaptive beamformer can be obtained.Considering that the standard Capon beamformer is highly sensitive to imprecise prior information about the array structure, two RAB algorithms are proposed based on non-Gaussian noncircular signals. For non-Gaussian signals and noncircular signals, the minimum variance criterion and widely linear technique can be used to improve the beamformer performance, respectively. In the case of exactly known the SV and noncircularity coefficient of the SOI, an RAB algorithm based on widely linear minimum variance is proposed jointly using the non-Gaussian property and noncircularity. When the information about the SV and noncircularity coefficient of the SOI is imprecise, we propose an RAB algorithm based on widely linear quadratically constrained minimum variance jointly utilizing the non-Gaussian property and noncircularity. Since the proposed algorithms make full use of the characteristics of the received signals, the performance has a huge improvement compared with the traditional beamforming algorithm.