Generalized Q-functions for application to noncoherent serial detection of spread-spectrum communication signals

This correspondence considers performance analysis of a particular sequential hypothesis test based on noncoherent correlation from overlapping data, which has application in acquisition for spread-spectrum communications. The main contribution of the correspondence is to define a special function (GQ-function) and to express the false alarm and detection probabilities in terms of these functions. The evaluation of these functions in terms of a truncated series is also discussed and compared with standard techniques. An upper bound of the approximation error is derived to determine the number of terms for a given accuracy. Some examples of application to serial detection of direct-sequence spread-spectrum signals are provided, evidencing the possible reduction of the mean acquisition time allowed by multidwell serial tests.