A Kronecker product CLMS algorithm for adaptive beamforming

In this paper, an adaptive algorithm is derived by considering that the beamforming vector can be decomposed as a Kronecker product of two smaller vectors. Such a decomposition leads to a joint optimization problem, which is then solved by using an alternating optimization strategy along with the steepest-descent method. The resulting algorithm, termed here Kronecker product constrained least-mean-square (KCLMS) algorithm, exhibits (in comparison to the well-known CLMS) improved convergence speed and reduced computational complexity; especially, for arrays with a large number of antennas. Simulation results are shown aiming to confirm the robustness of the proposed algorithm under different operating conditions.