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This paper presents outage probability analysis and a practical algorithm for antenna selection in multiple-input multiple-output wireless communication systems employing space-time block codes (STBC). First, to minimize the outage probability in these systems, a satisfactory antenna selection criterion for an STBC is to maximize the channel Frobenius norm. Analysis shows that the more receive antennas are selected, the better the performance. However, the performance of transmit antenna selection heavily depends on how fast the channel changes. When the channel changes slowly, since STBC averages the channel gains of the selected transmit antennas, selecting more transmit antennas causes lower coding gain and thus higher outage probability. When the channel is fast changing, it is shown analytically that the system can no longer provide transmit selection diversity in the high SNR regime. Since the transmit diversity can be still provided by using STBC, the best STBC scheme varies with SNR. Although the outage analysis helps determine the STBC scheme, finding the optimal antenna subsets with maximum channel Frobenius norm for each fading state is still a challenging problem. This is because solving the problem optimally requires an exhaustive search with exponentially growing complexity. When the numbers of antennas are large, the problem becomes intractable. To reduce the complexity, this problem is formulated as a quadratically constrained quadratic programming (QCQP) problem. Despite the fact that the problem is nonconvex, a semidefinite relaxation of QCQP enables the problem to be solved approximately in polynomial time. Simulation results indicate that the loss of semidefinite relaxation to optimal selection is negligible.
Date of Publication: July 2008