Lower bound on the BER of a pre- and postequalized vector communication system

This paper is concerned with communication over a multiple-input multiple-output channel. In the first reference, a lower bound on the bit-error rate of a pre- and postequalized communication system was derived for uniform bit loading. Here, we extend the lower bound to nonuniform bit loading. The lower bound applies to communication systems for which: 1) the cascade of the pre-equalizer, (noise-free) channel, and postequalizer is a diagonal matrix (a generalized zero-forcing condition satisfied by many designs in the literature); and 2) the encoding/modulation (decoding/demodulation) is done independently over the dimensions of the pre-equalizer input (postequalizer output). The lower bound is stated as a function of the bit loading, channel, and transmitter power only, and applies to uncoded, as well as coset-coded, systems. Toward deriving the lower bound, we minimize a weighted average of the noise variances at the postequalizer output.