Selecting optimal norm and step size of generalised constant modulus algorithms under non-stationary environments

A family of generalised constant modulus algorithms (GCMAs) based on the norm of complex variables was recently proposed. However, the optimal norm and step size of GCMAs have not been derived owing to the complexity of the proposed cost function. The steady-state mean square error (MSE) of a class of GCMAs under non-stationary environments is now given in a closed form. The optimal norm and step size can be derived to minimise the steady-state MSE with this closed form. Numerical simulations confirm the superior performance of the optimal norm and step size.