Transformation-based linearly constrained reduced rank adaptive beamforming

Linear constraints, such as constraints or derivative constraints, can be obtained by linearly constrained minimum variance beamformer (LCMVB) in adaptive beamforming. With a limited sample support, reduced rank processing is applied to LCMVB to reduce the adaptive degrees of freedom, improve the convergence performance, and reduce the computational complexity. In application of the adaptive radar, the desired signal is not involved in the training data used to compute the adaptive weight vector. In this paper, the T-LCMVB architecture is applied in reduced rank processing of the adaptive radar. The transformation-based versions of linearly constrained eigencanceler, and linearly orthogonal projection algorithm are proposed, named as T-LCEC, and T-LCOP respectively. T-LCEC has an excellent numerical stability even if the interference in the training data falls into the constrained s. T-LCOP can preserve constraints wherever the interferences are spaced relative to the constrained s.