Multiple-Input Multiple-Output (MIMO) relay communication systems are used as an efficient system in spectral\nefficiency and power allocation view point. In these systems, some of the facilities need channel state information\n(CSI). Besides, new estimation methods based on compressed sensing (CS) are well known for their spectral efficiency\nand accuracy. In this paper, we have used a Distributed CS-based channel estimation method to improve the accuracy\nand spectral efficiency of channel estimation for MIMO-Orthogonal Frequency Division Multiplexing relay network.\nSpecifically, using Least Squares (LS) estimation increases the accuracy of well-known Compressive Sampling Matching\nPursuit (CoSaMP) algorithm and proposes Block-verified CoSaMP (B-vCoSaMP). To improve the accuracy of estimation,\nwe are encountered with a combinatorial optimization which is dealt with probability-based approaches in this paper.\nMore particularly, three probability-based optimization methods have been proposed to optimize the mutual\ncoherence of measurement matrix called Sequential Cross-Entropy (SCE), Extended Estimating of Distribution\nAlgorithm (EEDA), and Parallel Cross-Entropy (PCE). All these methods are based on sampling from a Probability\nDensity Function (PDF) which is updated in each iteration using elite samples of the population. The simulation results\nrepresent the accuracy and speed of the proposed methods, and the comparison is expressed as well.
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