Minimum Codebook Size to achieve Maximal Diversity Order for RVQ based MIMO Systems

Multiple antenna systems provide both capacity and diversity gains relatively to single antenna based networks. These gains rely heavily on the availability of channel state information. In this manuscript we assume that the receiver has accurate channel information, which is quantized and fed back to the transmitter. Sufficient conditions for the feedback rate are provided that guarantee no loss of diversity due to channel quantization. Considering a K × M MIMO system, we show that to achieve a diversity of D = M – K + 1 which is the maximum allowable, a feedback channel with rate of log2(1 + D) bits per channel use is enough