Low-complexity adaptive step size constrained constant modulus SG algorithms for adaptive beamforming

In this paper, we propose two low-complexity adaptive step size mechanisms to enhance the performance of stochastic gradient (SG) algorithms for adaptive beamforming. The beamformer is designed according to the constrained constant modulus (CCM) criterion and the proposed mechanisms are employed in the SG algorithm for implementation. A complexity comparison is provided to show their advantages over existing methods, and a sufficient condition for the convergence of the mean weight vector is established. Theoretical expressions of the excess mean-squared error (EMSE), in both the steady-state and tracking cases, are derived based on the energy conservation approach. The effects of multiple access interference (MAI) and additive noise are considered. Simulation experiments are presented for both the stationary and non-stationary scenarios, illustrating that the proposed algorithms achieve superior performance compared with existing methods, and verifying the accuracy of the analyses.