Study About Robust Adaptive Beamforming

As an important branch of the signal processing domain, the array signal processing is widely applied for many areas such as radar, sonar, radio astronomy, seismology, direction finding (DF) / location finding, wireless communications, and tomography. Beamforming is a ubitiquitous task in array signal processing. The adaptive beamformers can select the weight vector as a function of the received data to optimize the performance subject to various constraints. Although the adaptive beamformers can have better resolution and much better interference rejection capability than the traditional data-independent beamformers, they are much more sensitive to errors, such as the array steering vector errors. The adaptive beamformers maybe suffer severe performance degradation even if there is a slight steering vector mismatch, which is difficult when they are applied to practical applications because these mismatches are unavoidable. As a result, much efforts have been devoted over the past three decades to devise robust adaptive beamformers. Based on the existing results, this dissertation proposed several new algorithms to improve the robustness of the adaptive beamformers, which make the adaptive beamformers more robust for the complicated scenarios.In this dissertation, a Bayesian approach based on secondary sample to robust adaptive beamforming is proposed firstly. In this algorithm, the direction-of-arrival (DOA) is assumed to be a discrete random variable with a priori probability density function (pdf) defined on a set of candidate points. Whether or not the secondary sample is required is based on the a posteriori probability distribution of a set of candidate point's, which can be calculated from the array received signals. And then, the resulting beamformer is a weighted sum of the beamformers pointed at the latest set of point's, which are combined according to the value of the a posteriori probability for each pointing direction. The study shows that the proposed Bayesian approach based on secondary sample to robust adaptive beamforming can be used to track the DOA's variation of the moved object.This dissertation proposes, for the first time, the concept of Equivalent DOAs. In the robust adaptive beamforming based on equivalent DOAs method, all factors causing the steering vector uncertainties are ascribed to the DOAs uncertainty only. The equivalent DOA of each sensor can be estimated out one by one with the assumption that the elements of the steering vector are uncorrelated with each other. In this way, based on the a priori known array structure, the: desired signal steering vector and the corresponding adaptive beamformer can be obtained from these equivalent DOAs. The simulation results demonstrate that the proposed algorithm can be used to improve the robustness of the adaptive beamformers.Considering the conservativity of the worst-case robust adaptive beamforming, the probability-constrained approach is investigated, which is a more flexible one to robust adaptive beamforming. In this dissertation, a precise relationship between the two approaches is built in the case of zero-mean Gaussian steering vector mismatch, which shows that the probability-constrained beamformer design can be interpreted in terms of the worst-case beamformer design. The study shows that the precise relationship built in this dissertation is more robust to the steering vector uncertainty with a wide range.