Robust Beamformor With Uncertainties Of Steering Vector And Covariance Matrix

Among those attractive research fields of array signal processing, adaptive beamforming, which has a wide application in communication, sonar, radar, seismology, medical imaging and so on, is one of the most important of them. The traditional beamforming methods are supposed to maintain the signal of interest and suppress the interferences at the same time. However, in practical scenarios, if some of the underlying assumptions on the environment, sources, or sensor array become violated, the performance of the traditional beamforming methods will degrade significantly. Therefore, it is very important to study how to improve the robustness of adaptive beamforming methods.In recent decades, many robust adaptive beamforming methods were proposed by researchers, thanks to a good performance when the available snapshots are less than the number of array sensors which will result in the fact that the sample data covariance matrix is irreversible, diagonal loading method is a popular one among them. In this dissertation, we propose a new robust adaptive beamforming method which also belongs to diagonal loading. The main research content is summarized as follows:(1) Introduce the basic knowledge of beamforming and several common adaptive beamforming methods together with their derivations, then analyze their characteristics and defects combined with their derivations.(2) Introduce several important robust adaptive beamforming methods which belonging to diagonal loading, including their research status, derivations and computational complexities. Analyze and compare their performance advantages and disadvantages.(3) Propose a new diagonal loading method of which the loading factors are variable. Robust adaptive methods which belonging to diagonal loading, such as worst-case method and RCB method,only consider the situation where only steering vector errors exist. Thus, an innovative point of the proposed method in this paper is that both the uncertainties of steering vector and covariance matrix are taken into account by corresponding constraints. Later, a min-max optimization problem is proposed in which the aim is to find a steering vector with the maximum output power under the worst-case covariance mismatch. Here, we relax this min-max optimization problem to a max-min optimization problem which can be solved by using the Karush-Kuhn-Tucker optimality conditions. In addition, diagonal loading methods reduce input signal-to-noise ratio by injecting an artificial white noise into incoming data. As a result, a higher loading level implies increased robustness at the expense of flexibility in adaptive interference cancellation and noise reduction. So the other innovative point here is that the eigenvalues magnitudes were considered, with greater loading for small eigenvalues and smaller loading for large ones.(4) Simulation results of the proposed method and other methods are presented here. By comparing the results, we find that the proposed method outperforms other methods tested in the simulations.