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In this letter we solve the transmit antenna selection problem for a zero forcing spatial multiplexing system with knowledge of the channel statistics at the transmitter. We show through Wishart matrix analysis that the signal-to-noise ratio on the kth stream is a weighted Chi-squared variable with the weight equal to-the kth diagonal entry of the inverted transmit correlation matrix. We use this result to develop selection algorithms for two cases-maximizing ergodic capacity and minimizing the average probability of error. Monte Carlo simulations illustrate potential performance improvements.
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Gore et al. (2002) studied this question.
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