The cross-correlation between the transmitted reference signal and the received signal with additive white Gaussian noise (AWGN) requires a detailed analysis to model consistently the noise statistics at the output of the cross-correlation process. The statistic of the output noise is affected by the signal pattern, and in general, it is not Gaussian. However, we will demonstrate that increasing the period of the PRBS pattern, the statistic of the cross-correlation output noise approaches the Gaussian density. Strictly related to the statistic of the cross-correlation output noise is the probability density function of the cross-correlation gain.