Multi stage adaptive filter for identification of the systems with variable sparsity

Adaptive identification of sparse systems is one of the popular adaptive signal processing topics due to its application in acoustic and network echo cancellation, adaptive channel estimation and several other areas. It has been observed that sometimes the amount of sparseness in the identifiable system impulse response can vary greatly depending on the nonstationary nature of the system. The compressive sensing based sparsity-aware adaptive algorithm performs satisfactorily in strongly sparse environment, but is shown to perform worse than the conventional ones when sparseness of the impulse response decreases. We propose an algorithm which works well both in sparse and non-sparse circumstances, and adapts dynamically to the level of sparseness using a dual stage adaptive filtering approach using an affine combination of the outputs of two single stage adaptive filters using two different algorithms. The proposed algorithm is supported by simulation results that show its robustness against variable sparsity.