Precoder codebook design for linear dispersion codes in spatially and temporally correlated MIMO channels

Despite the popularity and importance of linear dispersion (LD) codes, precoding for LD codes has rarely been investigated. In this paper we propose a method for designing a precoder codebook for LD codes in spatially and temporally correlated channels. Our codebook consists of two parts: a unitary codebook and a diagonal codebook. We propose a systematic algorithm for a unitary codebook design because unitary codebooks are hard to generate using numerical optimization methods. For each column (starting with the first column), we generate a set of vectors in the null space of previous columns. These vectors are generated by skewing i.i.d. unit vector codebooks by means of channel statistics-dependent transformations. A diagonal codebook is generated using a vector quantization technique. We use mutual information as a design criterion throughout this paper. Numerical results illustrate the benefits of matching a codebook to channel statistics and employing adaptive power shaping.