The issue of sparsity adaptive channel reconstruction in time-varying cooperative communication networks through the amplify-and-forward transmission scheme is studied. A new sparsity adaptive system identification method is proposed, namely reweighted l p norm (0 < p < 1) penalised least mean square (LMS) algorithm. The main idea of the algorithm is to add a l p norm penalty of sparsity into the cost function of the LMS algorithm. By doing so, the weight factor becomes a balance parameter of

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... e associated l p 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 l p norm. With the upper bounds, the authors prove that the l p (0 < p < 1) norm sparsity inducing cost function is superior to the reweighted l 1 norm. An optimal selection of p for the l p 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 behaviour than other LMS algorithms.