Vector Precoding for Gaussian MIMO Broadcast Channels: Impact of Replica Symmetry Breaking
The so-called "Replica method" of statistical physics is employed for the large system analysis of vector precoding for the Gaussian Multiple-Input Multiple-Output (MIMO) broadcast channel. The transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. Focusing on discrete complex input alphabets, the energy penalty is minimized by relaxing the input alphabet to a larger alphabet set prior to precoding. For the common discrete lattice-based relaxation, the problem is found to violate the assumption of replica symmetry and a replica symmetry breaking ansatz is taken. The limiting empirical distribution of the precoder's output, as well as the limiting energy penalty, is derived for one-step replica symmetry breaking.