A Robust Zero-point Attraction LMS Algorithm on Near Sparse System Identification

The newly proposed $l_1$ norm constraint zero-point attraction Least Mean Square algorithm (ZA-LMS) demonstrates excellent performance on exact sparse system identification. However, ZA-LMS has less advantage against standard LMS when the system is near sparse. Thus, in this paper, firstly the near sparse system modeling by Generalized Gaussian Distribution is recommended, where the sparsity is defined accordingly. Secondly, two modifications to the ZA-LMS algorithm have been made. The $l_1$ norm penalty is replaced by a partial $l_1$ norm in the cost function, enhancing robustness without increasing the computational complexity. Moreover, the zero-point attraction item is weighted by the magnitude of estimation error which adjusts the zero-point attraction force dynamically. By combining the two improvements, Dynamic Windowing ZA-LMS (DWZA-LMS) algorithm is further proposed, which shows better performance on near sparse system identification. In addition, the mean square performance of DWZA-LMS algorithm is analyzed. Finally, computer simulations demonstrate the effectiveness of the proposed algorithm and verify the result of theoretical analysis.Comment: 20 pages, 11 figure

Reweighted lp Constraint LMS-Based Adaptive Sparse Channel Estimation for Cooperative Communication System

This paper studies the issue of sparsity adaptive channel reconstruction in time-varying cooperative communication networks through the amplify-and-forward transmission scheme. A new sparsity adaptive system identification method is proposed, namely reweighted norm ( < < ) penalized least mean square（LMS）algorithm. The main idea of the algorithm is to add a norm penalty of sparsity into the cost function of the LMS algorithm. By doing so, the weight factor becomes a balance parameter of the associated norm adaptive sparse system identification. Subsequently, the steady state of the coefficient misalignment vector is derived theoretically, with a performance upper bounds provided which serve as a sufficient condition for the LMS channel estimation of the precise reweighted norm. With the upper bounds, we prove that the ( < < ) norm sparsity inducing cost function is superior to the reweighted norm. An optimal selection of for the norm problem is studied to recover various sparse channel vectors. Several experiments verify that the simulation results agree well with the theoretical analysis, and thus demonstrate that the proposed algorithm has a better convergence speed and better steady state behavior than other LMS algorithms