Asymptotically minimum-BER Tx-Rx design for MIMO channel under ZF constraint

We consider a communication system, operating over a multiple-input-multiple-output (MIMO) channel, with the following general structure: 1) the input data stream is demultiplexed into parallel data streams of possibly different rates, i.e. non-uniform bit-loading; 2) the parallel data streams are encoded/modulated and the symbols are fed to a transmitter (Tx) matrix whose outputs form the MIMO channel´s inputs; 3) the MIMO channel´s outputs are fed to a receiver (Rx) matrix whose outputs are demodulated/decoded; 4) the parallel decoded data streams are multiplexed into one output data stream. The encoders/modulators and demodulators/decoders, which satisfy mild conditions, are assumed to be given. The channel is assumed to be known. We find a zero-forcing (ZF) Tx-Rx pair as a function of the Tx power, such that as the Tx power becomes large the BER (averaged over the parallel data streams) approaches the true minimum BER achievable by a ZF Tx-Rx pair for the same Tx-power