On the distribution of the SINR in precoded multicarrier systems using linear MMSE equalization

To calculate the unconditional bit error probability directly, the Signal to Interference-plus-Noise Ratio (SINR) distribution of a communications system must be known. However, for precoded systems employing Minimum Mean Square Error (MMSE) equalization, a suitable distribution has not been found yet. In this paper, we propose, as an approximation for the SINR of a precoded multicarrier system employing linear MMSE equalization, the use of the lognormal distribution with the smallest Kullback-Leibler distance to the observed SINR distribution. Simulation results show that the lognormal distribution matches accurately the SINR distribution. The Bit Error Rate (BER) performances with analytical computations using the lognormal distribution are very close to Monte Carlo simulations, even for high SNR values.