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# Thread Subject: how to implement MCG maximal channel gain algorithm in cooperative for MIMO communications in wireless sensor networks

 Subject: how to implement MCG maximal channel gain algorithm in cooperative for MIMO communications in wireless sensor networks From: sathish kumar Date: 17 Aug, 2012 03:45:14 Message: 1 of 1 In this case, the source node knows the instantaneous CSI between all the cooperative nodes and the destination node, i.e., the channel gain matrix H with dimension r×k, and the correlation information among all the nodes. we want the product of those channel gains to be as large as possible. Due to the fact that the eigenvalues of R are equal to Rii,we have the following properties ?Rii=1 = ? lamda(Rii) = det(Rh.R) =(Rh.Qh Q.R)                                  = det(Hh.H), where Qh means hermitian transpose of Q unitary matrix R upper triangular matrix it is clear that in order to maximize the product of the channel gains, ?R1,1?2??R2,2?2 . . . ?RN,N?2, we only need to maximize the determinant of the corresponding channel matrix (Hh.H). To accomplish this, consider the use of a maximal channel gain (MCG) algorithm as follows: at the (k+1)-th step, where k nodes have already been chosen, and the corresponding channel matrix H(k) are known, where H(k) is the channel matrix when k nodes are chosen, we want to select one additional node S? from the set S containing the remaining K-k nodes such that S?= argmax{det((H(k+1))h.(H(k+1))}.where (H(k+1))h means hermitian transpose of H(k+1) We repeat this until all the K nodes are chosen. Therefore, at each step, we obtain a selected combination of nodes, \$, with an increasing number of nodes in it. In total, the algorithm runs K steps, thus the search space for the previous optimization problem has only K combinations. Finally, we choose the optimal subset \$? which results in the largest D2 for the cooperative transmission while meeting the specified total end-to-end delay and energy constraints.