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The authors address an optimal power allocation problem for minimizing the outage probability for M parallel block-Nakagami-fading channels under a long-term average sum transmit power constraint with finite rate feedback of Channel State Information (CSI). A simulation-based optimization technique called Simultaneous Perturbation Stochastic Approximation algorithm (SPSA) is employed first to numerically derive a locally optimal power codebook. Due to the high computational complexity and long convergence time of SPSA, they make an ordering assumption on the power codebook entries and derive effective hyper-plane based approximations to the channel quantization regions and present a number of low-complexity suboptimal quantized power codebook design algorithms.
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