Widely-linear Recursive Adaptive Matching Pursuit algorithm for adaptive beamforming

In many applications of digital signal processing, signal characteristics could change. This requires the utilization of adaptive filters. The Recursive Least Squares (RLS) algorithm has established itself as the best adaptive filtering algorithm, but practical implementations of the algorithm are often associated with high computational complexity. Recently, Recursive Adaptive Matching Pursuit (RAMP) algorithm based on Matching Pursuit principle was presented. It has a nice tradeoff between complexity and the convergence speed. In this paper, we present an extension of the RAMP algorithm for adaptive filters to widely-linear complex-valued signal and system modeling. Application of the algorithm to adaptive beamforming of mixed BPSK and QPSK signal transmissions shows that the system can extract all of the transmitted signal outputs in certain overloaded scenarios.