When there are more than one sample per bit, the peak shape of the cross-correlation output between transmitted PRBS and received PRBS assumes a triangular profile, with one or more noise samples along triangular sidelines. This modifies the cross-correlation noise outcome and, consequently, the probability of detection. The occurrence of multiple correlated noise sources requires statistical description using multivariate Gaussian probability density. The probability that the largest noise peak overcomes the expected signal–signal peak leads to the concept of False Alarm Rate and to the generalization of the equation of the probability of detection.