Array processing is an area of study devoted to processing the signals received from an antenna array and extracting information of interest. It has played an important role
in widespread applications like radar, sonar, and wireless communications. Numerous adaptive array processing algorithms have been reported in the literature in the last several decades. These algorithms, in a general view, exhibit a trade-off between performance and required computational complexity.
In this thesis, we focus on the development of array processing algorithms in the application of beamforming and direction of arrival (DOA) estimation. In the beamformer design, we employ the constrained minimum variance (CMV) and the constrained constant modulus (CCM) criteria to propose full-rank and reduced-rank adaptive algorithms.
Specifically, for the full-rank algorithms, we present two low-complexity adaptive step size mechanisms with the CCM criterion for the step size adaptation of the stochastic gradient (SG) algorithms. The convergence and steady-state properties are analysed. Then, the full-rank constrained conjugate gradient (CG) adaptive filtering algorithms are proposed according to the CMV and CCM criteria. We introduce a CG based weight vector to incorporate the constraint in the design criteria for solving the system of equations that arises from each design problem. The proposed algorithms avoid the covariance matrix
inversion and provide a trade-off between the complexity and performance.
In reduced-rank array processing, we present CMV and CCM reduced-rank schemes based on joint iterative optimization (JIO) of adaptive filters. This scheme consists a bank of full-rank adaptive filters that forms the transformation matrix, and an adaptive reduced-rank filter that operates at the output of the bank of filters. The transformation
matrix and the reduced-rank weight vector are jointly optimized according to the CMV or CCM criteria. For the application of beamforming, we describe the JIO scheme for both the direct-form processor (DFP) and the generalized sidelobe canceller (GSC) structures. For each structure, we derive SG and recursive least squares (RLS) type algorithms to iteratively compute the transformation matrix and the reduced-rank weight vector for the reduced-rank scheme. An auxiliary vector filtering (AVF) algorithm based on the CCM design for robust beamforming is presented. The proposed beamformer decomposes the adaptive filter into a constrained (reference vector filter) and an unconstrained (auxiliary vector filter) component. The weight vector is iterated by subtracting the scaling auxiliary vector from the reference vector. For the DOA estimation, the reduced-rank scheme with the minimum variance (MV) power spectral evaluation is introduced. A spatial smoothing (SS) technique is employed in the proposed method to improve the resolution. The proposed DOA estimation algorithms are suitable for large arrays and to deal with direction finding for a small number of snapshots, a large number of users, and without the exact information of the number of sources.
