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Both least mean square (LMS) and least mean fourth (LMF) are popular adaptive algorithms with application to adaptive channel estimation. Because the wireless channel vector is often sparse, sparse LMS-based approaches have been proposed with different sparse penalties, for example, zero-attracting LMS and Lp-norm LMS. However, these proposed methods lead to suboptimal solutions in low signal-to-noise ratio (SNR) region, and the suboptimal solutions are caused by LMS-based algorithms that are sensitive to the scaling of input signal and strong noise. Comparatively, LMF can achieve better solution in low SNR region. However, LMF cannot exploit the sparse information because the algorithm depends only on its adaptive updating error but neglects the inherent sparse channel structure. In this paper, we propose several sparse LMF algorithms with different sparse penalties to achieve better solution in low SNR region and take the advantage of channel sparsity at the same time. The contribution of this paper is briefly summarized as follows: (1) construct the cost functions of the LMF algorithm with different sparse penalties; (2) derive their lower bounds; and (3) provide experiment results to show the performance advantage of the propose method in low SNR region. [ABSTRACT FROM AUTHOR]

SUMMARY Cognitive radio network (CRN) is an emerging technology that can increase the utilization of spectrum underutilized by primary users (PUs). In the literature, most exiting investigations on CRNs have focused on how secondary users (SUs) can coexist harmlessly with the PUs. Despite the importance of such a coexistence issue, it is also crucial to investigate the coexistence of SUs because (i) the PUs usually rarely use the licensed spectrum and (ii) the advantages of CRN will significantly increase the number of SUs in the future. To address this challenging issue, we propose, in this paper, an optimal randomized spectrum access scheme, whose main ideas include the following: (i) an SU shares its sensing results with neighboring SUs and (ii) with the regional sensing results, an SU will access available channels with a non-uniform probability distribution. We first formulate a multichannel optimal randomized multiple access (MC-ORMA) problem that aims to maximize the throughput of the CRN; we then develop efficient distributed algorithms to solve the MC-ORMA problem; we derive the closed-form value of collision probability for each SU; and finally, we conduct extensive numerical experiments and compare our theoretical analysis with simulation results to demonstrate the advantages of our scheme. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]