OCDMA Channel Statistic as a Mixture of Chi-Square Distributions

Optical code division multiple access (OCDMA) systems, intensively investigated these last years, are known to suffer from multiple access interference (MAI). In addition, the photodetection process leads to beatings between the desired user information and the interferer ones, strongly degrading the system performance. To simplify the performance analysis, noise statistic is generally approximated by a Gaussian distribution which is not very accurate regarding to optical considerations. In this paper, by considering beat noise along with MAI, we develop a more precise analysis of the probability density function of the decision variable as a mixture of chi-square distributions. To investigate beat noise impact, the theoretical error probability expression is then determined. The results permit obtaining the conditions required to reach the optimal performance in beat noise corrupted OCDMA systems.