On spectral efficiency of vector precoding for Gaussian MIMO broadcast channels

The spectral efficiency of practically oriented vector precoding schemes for the Gaussian multiple-input multiple-output (MIMO) broadcast channel is analyzed in the large system limit. Considering discrete complex input alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the transmit energy penalty imposed by the linear front-end. The energy penalty is minimized by relaxing the input alphabet to a larger alphabet set prior to precoding. The so-called "replica method" of statistical physics is employed to derive the limiting empirical distribution of the precoder's output, as well as the limiting energy penalty. Particularizing to a "zero-forcing" (ZFJ linear front-end, and non- cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be characterized by the Markov chain u-x-y, where u is the channel input, x is the equivalent precoder output, and y is the channel output. A comparative spectral efficiency analysis of two illustrative examples reveals significant performance gains compared to linear ZF precoding in the medium to high E _b/N_o region. In particular, we demonstrate that convex extended alphabets, amenable to efficient energy minimization algorithms, provide an attractive alternative to alphabets based on the discrete Gaussian integer lattice, for which the energy minimization problem is NP-hard.