Abstract
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 the 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.
Highlights
Cooperative communication has been widely studied recently in wireless networks because of its significant performance in enhancing the transmission capacity and exploiting spatial diversity to against the influence of path loss and channel fading [1]
In order to explore the sparse features of the cooperative relay communication system, we propose a new sparse aware LMS algorithm for relay channel reconstruction
A novel sparse adaptive channel estimation algorithm has been proposed in this paper for the time-variant cooperative communication systems
Summary
Cooperative communication has been widely studied recently in wireless networks because of its significant performance in enhancing the transmission capacity and exploiting spatial diversity to against the influence of path loss and channel fading [1]. Classic algorithms include basis pursuit (BP) algorithm, orthogonal matching pursuit (OMP) method and iterative thresholding algorithms [7,8,9] These algorithms are not applicable for sparse channel estimation in fast time-varying environments. The sparsity constraint can be l1 norm [10], reweighted l1 norm [12], l0 norm [13], and nonconvex sparsity penalty These algorithms have good performance on faster convergence rate and smaller mean square error (MSE) comparing with the traditional adaptive filtering method, such as zero-point attraction Least Mean Square algorithm (ZA-LMS) [10], reweighted zero attracting LMS (RZA-LMS) [11] and so on. We introduce the reweighted lp norm constraint LMS and derive the expectation of the misalignment vector and provide the steady-state analysis of the proposed algorithm.
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