l(2)-norm feature least mean square algorithm

In many practical applications, systems and signals show energy concentration in a few coefficients. This prior knowledge can often be incorporated into algorithms designed for tasks such as compressive sensing and system identification. This Letter proposes a new least mean square (LMS)-based algorithm that exploits the hidden sparsity of the system that the adaptive filter intends to estimate. The algorithm minimises the $\ell _2$l2-norm of a linear transformation of the coefficient vector, using the minimum distortion principle. Simulation results demonstrate good performance of the proposed algorithm with respect to the LMS algorithm. In addition, a stochastic model of the advanced algorithm is proposed, which provides accurate mean-square deviation and mean-square error predictions.