Stochastic Modeling of the KCLMS Algorithm in the Context of Adaptive Beamforming

This paper presents a stochastic model for the Kronecker product constrained least-mean-square (KCLMS) algorithm applied in adaptive beamforming. Such an algorithm considers that the beamforming vector can be expressed as a Kronecker product of two smaller vectors, thus yielding improved convergence and less computational complexity (in comparison to the CLMS). The proposed model entails expressions describing the mean behavior of the beamforming vectors, the evolution of the output signal-to-interference-plus-noise ratio (SINR), and the correlation matrices related to the beamforming vectors. Simulation results are shown confirming the accuracy of the model.