Outage minimization for parallel fading channels with limited feedback

We 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, we make an ordering assumption on the power codebook entries and derive effective hyperplane based approximations to the channel quantization regions and present a number of low-complexity suboptimal quantized power codebook design algorithms. Unlike existing work on outage minimization for multiple-input multiple-output (MIMO) channels with limited feedback, we do not assume that identical transmission power is used for all channels within each channel quantization region. We also do not resort to a Gaussian approximation for the instantaneous mutual information in general as used in many existing work. Based on our power ordering assumption and hyperplane based approximations, we show that allocating identical power to all channels within a given channel quantization region in the limited feedback scenario is asymptotically optimal only at high average power (or average signal-to-noise ratio (SNR)) for the Rayleigh fading case, whereas for the general Nakagami case, the transmit power allocation for an individual channel within each quantized region is asymptotically proportional to the corresponding Nakagami fading parameter (severity of fading). We also present a novel diversity order result for the outage probability for the Nakagami fading case. Finally, we derive a suitable Gaussian approximation based low-complexity power allocation scheme for a large number of parallel channels, which has important applications in wideband slow-fading orthogonal frequency-division multiplexing (OFDM) systems. Extensive numerical results illustrate that only a few bits of feedback close the gap substantially in outage performance between the limited feedback case and the full instantaneous CSI at the transmitter case.