Variable-Length Limited Feedback Beamforming in Multiple-Antenna Fading Channels

We study a multiple-input single-output fading channel, where we would like to minimize the channel outage probability or symbol error rate (SER) by employing beam-forming via quantized channel state information at the transmitter (CSIT). We consider a variable-length limited feedback scheme where the quantized CSIT is acquired through feedback binary codewords of possibly different lengths. We design and analyze the performance of the associated variable-length quantizers (VLQs) and compare their performance with the previously studied fixed-length quantizers (FLQs). For the outage probability performance measure, we construct VLQs that can achieve the full-CSIT performance with finite rate. Moreover, as the signal-to-noise ratio P tends to infinity, we show that VLQs can achieve the full-CSIT outage probability performance with asymptotically zero feedback rate. For the SER performance measure, we show that while the SER with full-CSIT is not achievable at any finite feedback rate, the diversity and array gains with full-CSIT can be achieved using VLQs with asymptotically zero feedback rate as P -> infinity. Our results show that VLQs can significantly improve upon the traditional FLQs that require infinite feedback rate to achieve the outage probability or the diversity and array gains with full-CSIT.