A Tensorial LMS Algorithm for Sparse System Based on Kronecker Product Decomposition

In this paper, we propose a sparse constrained tensorial least mean square (LMS) algorithm, which is suitable for the identification of multilinear sparse systems. The greatest challenge involves a large parameter space, which can effectively form a sparse tensor. Its main idea is to exploit a method based Kronecker product decomposition (KPD), so that the global sparse impulse response can be estimated by using a combination of shorter sparse adaptive filters, which reduces the complexity of each update. In addition, these shorter sparse sub filters are estimated by adding a lp norm based sparsity promoting penalty function to the objective function. Simulation results show the proposed algorithm can be a good candidate for sparse system identification and outperforms traditional sparse LMS algorithms in performance.