Static and Differential Quantization Codebook Design for MIMO Precoding Systems

We treat the problem of quantization codebook design for MIMO precoding schemes. We propose a design criterion based on the capacity measure which is different from the maximum mutual-minimum-distance conventionally used to design the codebook. The latter criterion is derived from SNR maximization which is not necessarily the capacity- optimal quantization strategy. While the capacity expression does not directly define a valid distance metric for the design, a bound on the capacity expression can be used to formulate the quantization codebook design. We introduce a new distance metric on the Grassmanian manifold which is used to design the optimal precoder codebook. While the original formulation can be used for the (space) correlated channel model, we propose a differential codebook design in order to track changes in the channel statistics when the channel is correlated in time (or in frequency, e.g., across different tones in OFDM systems). Simulation results has shown considerable improvement through the proposed codebook design both for single user (SU-) and multiple user (MU-) MIMO systems.