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

This paper proposes two low-complexity adaptive step size mechanisms for adaptive beamforming that employs stochastic gradient (SG) algorithms. The algorithms employ the constrained constant modulus (CCM) criterion as the design approach. A complexity comparison is given and a convergence analysis is developed for illustrating their properties. Theoretical expressions of the excess mean squared error (EMSE), in both the steady-state and tracking phases, are derived for the proposed algorithms by employing the energy conservation approach. Simulation experiments are presented for both the stationary and nonstationary scenarios, illustrating that the new algorithms achieve superior performance compared with existing methods, and verifying the accuracy of the convergence and tracking analyses. Key words–Adaptive beamforming techniques, spatial-division multiple access (SDMA), constrained constant modulus (CCM), modified adaptive step size (MASS), time averaging adaptive step size (TAASS).