Novel Robust Adaptive Beamforming Algorithms with Improved Estimation of Array Covariance Matrix and Signal Steering Vector

Robust adaptive beamforming has long been an attractive research topic over several decades due to wide applications in vast fields of signal processing such as, radar, sonar, wireless communications, medical imaging, microphone array speech processing and other areas. Adaptive beamforming improves the reception of desired signals in the presence of interference signals automatically by sensing the presence of interferences and suppressing them while simultaneously enhancing desired signal reception without prior knowledge of the signal and interference environment. However, under certain circumstances, adaptive beamformers suffer performance degradation due to several reasons which include small sample size, the presence of the desired signal in the training data, the presence of nonstationary interference, or imprecise knowledge of the steering vector of the desired signal. Moreover, conventional approaches are very sensitive to these types of mismatches, do not provide sufficient robustness and may suffer from severe performance degradation in such situations. In this thesis, we propose three different types of novel adaptive beamforming techniques to resolve the effects caused by some of the aforementioned difficulties. A general goal in adaptive beamforming is to adaptively steer a beam towards a desired signal, while placing nulls at interference directions. The well-known minimum variance distortionless response (MVDR) adaptive beamformer is designed to linearly combine the outputs of the sensors in order to minimize the array output power, while maintaining a fixed response towards the desired signal. However, it is well known that the MVDR beamformer is quiet sensitive to the mismatch between the actual steering vector and the assumed one, which could be caused by any array imperfection. In the first approach, a robust adaptive beamforming technique based on a modification of the robust Capon beamforming approach is introduced which estimates the steering vector using eigenspace projection-based approximation. The steering vector is estimated as a reasonable approximation for the orthogonal projection of the presumed steering vector of the desired signal onto the signal-plus-interference subspace. In this approach, the optimal diagonal loading factor corresponds to the minimum of the estimated beamformer output power. Also, estimation of the desired signal’s direction-of-arrival is utilized to update the presumed steering vector. On the other hand, during the past decade, many approaches based on the processing of the sample covariance matrix have been proposed. However, since the desired signal component is usually included in this matrix, the beamformer is sensitive to slight mismatches. Although, some techniques have been proposed to remove the signal-of-interest (SOI) component from the signal covariance matrix using the reconstruction of the interference-plus-noise covariance (IPNC) matrix, these have a number of drawbacks. In the second approach, we introduce a low complexity procedure for IPNC matrix construction. The main motivation of this algorithm is to simplify the estimation of the IPNC matrix using its theoretical expression which is based on projection processing for covariance matrix construction and desired-signal steering vector estimation. In this accordance, the optimal minimum variance distortion-less response beamformer is closely achieved through approximating the interference-plus-noise covariance matrix by utilizing the eigenvalue decomposition of the received signal’s covariance matrix. Moreover, the direction-of-arrival (DOA) of the desired signal is estimated by maximizing the beamformer output power in a certain angular sector. In particular, the proposed beamformer utilizes the aforementioned DOA in order to estimate the desired-signal’s steering vector for general steering vector mismatches. In addition, adaptive beamforming methods are sensitive to underlying assumptions on the environment, sources, or sensor array violation, especially when interferences are moving fast. In recent years, research efforts have been devoted to the development of beamforming using covariance matrix taper (CMT) or additional constraints in the optimization programming for suppression of pre-defined angular ranges. This research presents an innovative beamforming approach in which the nonstationary interference source is estimated during the period in which snapshots are taken. Then, a new interference-plus-noise covariance matrix reconstruction is introduced which is derived from a simplified power spectral density function that can be used to shape the directional response of the beamformer. Finally, the beamformer is designed to impose nulls toward the regions of the moving interference based on the reconstructed covariance matrix. The essence of the proposed method is to express the inverse of the reconstructed covariance matrix in such a way that significantly reduces computational complexity. Theoretical analysis and simulation results indicate the superior performance of the introduced proposed approaches in the presence of mismatches relative to other some existing methods.