Trellis coded beamforming vector quantization with fractional bits per antenna

We study the problem of quantizing an M dimensional beamforming vector with M relatively large. Using a conventional beamforming vector codebook to quantize beamforming vectors incurs a complexity that scales exponentially with M, making it unsuitable when M is large. In, we proposed to use a trellis-based quantization scheme to tackle the complexity problem, and we present two enhancements in this paper. First, we let each trellis stage process multiple channel dimensions, resulting in a quantization improvement at the cost of increasing the quantization complexity to O(M2^2BL). Second, we permute the trellis state transitions and outputs to map neighboring beamforming vectors to neighboring channel coded vectors. The second enhancement is beneficial when implementing feedback, as feedback information is time-sensitive and retransmission may not be worthwhile. Simulations show the improvements of our proposed techniques.