Adaptive blind SIMO identification: derivation of an optimal step size for the unconstrained multichannel LMS algorithm

Adaptive algorithms for blindly identifying SIMO systems are appealing because of their computational efficiency and capability of continuously tracking a time-varying system. Adaptive multichannel LMS (MCLMS) algorithms (with and without the unit-norm constraint) are analyzed and the optimal step size is derived. A simple yet effective variable step-size unconstrained MCLMS algorithm is proposed and its performance is evaluated with simulations.