Adaptive Sparse System Identification in Compressed Space

In this paper, we propose a method for adaptive identification of sparse systems. The method requires low number of filter weights, significantly less than the number of taps of sparse system. The approach is based on compressed sensing (CS) technique. In fact, we adaptively estimate a compressed version of high dimensional sparse system. The aim is accomplished by using the structure of random filter and an interpolator at the transmission line. They are arranged such that the linear time invariant (LTI) property of the overall system (compressed system) is preserved. The unique features of the identification in the reduced dimensions are investigated. Stability in high convergence rates and robustness against highly correlated input signals are two important advantages of the proposed method. Furthermore, we propose a modified algorithm for optimization of the random filter and illustrate its impact by numerical results. Two appropriate reconstruction algorithms are evaluated for recovery of original sparse system. Simulation results indicate that at low levels of sparsity, the proposed approach outperforms the conventional least mean square (LMS) method and has comparable performance with the regularized LMS algorithms, only by half number of the filter weights.