Efficient algorithms for outage minimization in parallel fading channels with limited feedback

In this paper, we address the optimal power allocation problem for minimizing the notion of information theoretic outage for an M parallel block-Rayleigh-fading channels using a finite rate power codebook (limited feedback). In contrast to the existing literature on outage minimization for MIMO systems with limited feedback, we derive effective approximations to the channel quantization regions in order to design a number of low-complexity power allocation algorithms for various ranges of average power constraints. Unlike previous work, we show that it is not generally optimal to allocate same power to all channels, and that this is only asymptotically optimal at high average power (average SNR). We also derive a suitable Gaussian approximation based power allocation scheme for large number of parallel channels which has important practical applications in multi-carrier systems such as OFDM. Extensive numerical results illustrate that only a few bits of feedback (for M = 4 or M = 6) closes the gap substantially in outage performance with the full instantaneous channel information at the transmitter. For large number of channels, less than 1 bit of (broadcast) feedback per channel can achieve the same outage probability (10^-4) with approximately only a 2.5 dB average power (or average SNR) gap.