Convergence analysis of a mixed controlled l₂ - l_p adaptive algorithm

A newly developed adaptive scheme for system identification is proposed. The proposed algorithm is a mixture of two norms, namely, the l₂-norm and the l_p-norm (p≥1), where a controlling parameter in the range [0,1] is used to control the mixture of the two norms. Existing algorithms based on mixed norm can be considered as a special case of the proposed algorithm. Therefore, our algorithm can be seen as a generalization to these algorithms. The derivation of the algorithm and its convexity property are reported and detailed. Also, the first moment behaviour as well as the second moment behaviour of the weights is studied. Bounds for the step size on the convergence of the proposed algorithm are derived, and the steady-state analysis is carried out. Finally, simulation results are performed and are found to corroborate with the theory developed.