Constrained Optimization of Universal Codebook for MIMO Precoding

In this paper we propose a new efficient algorithm for finding good codebook targeting multiple input multiple output (MIMO) precoding transmission. The proposed algorithm is constrained optimization that satisfies a set of design constraints such as unitary, constant modulus, constrained alphabet, and nested. These constraints aim at practically important properties such as low complexity and low peak-to-average-power-ratio and have been carefully taken into account in the codebook design at 3GPP. Our algorithm is based on rotations of the discrete Fourier transform (DFT) matrix and attempts to maximize the minimum chordal distance between any two precoders in the codebook in each rank. The algorithm works iteratively: at each step it identifies a bottleneck precoder in terms of minimum chordal distance and then finds a better precoder replacing the bottleneck precoder. Simulation results illustrate that the codebook found by the proposed algorithm performs better than conventional codebooks in both single user MIMO as well as in dynamic switching of single user and multi user MIMO transmission.