Adaptive identification of sparse systems with variable sparsity

In the context of system identification, it is shown that sometimes the level of sparseness in the system impulse response can vary greatly depending on the time-varying nature of the system. When the response is strongly sparse, convergence of the conventional approach such as least mean square (LMS) is poor. The recently proposed, compressive sensing based sparsity- aware ZA-LMS algorithm performs satisfactorily in strongly sparse environments, but is shown to perform worse than the conventional LMS when sparseness of the impulse response reduces. We propose an algorithm which works well both in sparse and non-sparse circumstances and adapts dynamically to the level of sparseness, using a convex combination based approach. The proposed algorithm is supported by simulation results that show its robustness against variable sparsity.