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 𝒍𝒑 norm (𝟎 < 𝒑 < 𝟏) penalized least mean square（LMS）algorithm. The main idea of the algorithm is to add a 𝒍𝒑 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 𝒍𝒑 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 𝒍𝒑 norm. With the upper bounds, we prove that the 𝒍𝒑 (𝟎 < 𝒑 < 𝟏 ) norm sparsity inducing cost function is superior to the reweighted 𝒍𝟏 norm. An optimal selection of 𝒑 for the 𝒍𝒑 norm problem is studied to recover various 𝒅 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.