Index assignment for beamforming with limited-rate imperfect feedback

Beamforming in most multiple-antenna systems often requires channel state information (CSI) at the transmitter through feedback. In practice, CSI must be quantized into a finite set of vectors and feedback only sends the index representing the desired vector. In addition to quantization error of the channel coefficients, feedback errors, which lead to incorrect beamforming vectors to be applied at the transmitter, also degrade beamforming performance. We present an index-assignment algorithm that minimizes the impact of feedback errors. The proposed algorithm requires exhaustive search to find the best mapping. When the codebook size is large, the complexity of the algorithm becomes prohibitive. We thus propose a group-based index assignment (GIA) that has a low computational load while still performing better than random index assignments.