Efficient Codebook Design for Co-Operative MIMO Systems With Decode-and-Forward Relay

We present an efficient codebook for co-operative multiple-input multiple-output systems that use decode-and-forward relay. To achieve full diversity gain, the channel state information (CSI) of the source-to-relay link should be quantized and forwarded with low overhead to the destination. To achieve this requirement, we investigate explicit and implicit vector quantization techniques. The explicit vector quantization technique exploits the reduced dimensionality of the channel Gram matrix, but has weak feed-forward efficiency when the number of feed-forward bits is small. To improve this efficiency, we use Jensen's inequality and eigen-decomposition to exploit the upper bound of the pairwise error probability. The proposed design criterion mitigates the eigen-spreads of the exact CSI and the quantized CSI. With the proposed quantization, the bit-error-rate (BER) approaches the lower-bound within 1.3-dB at $\text{BER} ={10^{-5}}$ by using 0-bit feed-forward.