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The aim of this paper is to carry out an analysis of optical network by calculating bit error rate (BER) as a function of signal to noise ratio by using Hermitian polynomial for different homodyne crosstalk levels. The results have been plotted for different crosstalk level for BER as a function of single to noise ratio (SNR) by using exact analysis and Gaussian approximation and the results are compared. Simulations have been carried out in MAT Lab Version 7.4. We present an exact analytical probability density function and a closed form bit error rate formula for optical network which performance is degraded by homodyne crosstalk. In homodyne (intrachannel) crosstalk, the interfering signal is at same wavelength as the desired signal. This effect is more severe than interchannel crosstalk (in which interfering signal operates at different wavelength), since the interference falls completely within the receiver bandwidth.