single dwell time system allowed the false alarm and detection probabilities of (1.70) and (1.71) to be replaced by the simpler expressions in (1.79) and (1.80). We recall that the basis for validating this assumption was a central limit theorem argument based on the large values of pre-detection bandwidth-post- detection integration time product BTd typical of the single dwell time system. Since in a fast-decision rate acquisition system, like the matched filter receiver, post-detection integration is not feasible, the central limit argument made previously does not apply here. Instead one must use the exact probability distributions of the decision statistic under Rapid Acquisition Using Matched Filter Techniques hypotheses H and H as determined from the solution to the problem of non-coherently detecting a Gaussian random variable (C) in additive "white" (bandlimited) Gaussian noise. Under certain circumstances, it is possible to simplify matters and obtain results similar to (1.70) and (1.71). Although these simplifications are based on Gaussian approxi- mations to the mixture of two noise processes, one of which is signal dependent [14], it is to be re-emphasized that the assumption of a Gaussian test statistic remains invalid and thus expressions analogous to (1.79) and (1.80) are inappropriate. 1.5.2.1 Exact Results Defining, analogous to (1.62), the effective signal-to-noise ratio Yi under hypothesis Hi by (1.189) where EJNo All is the chip signal-to-noise ratio and Gi(e) is the nor- malized variance of the partial correlation C as defined in (1.186), then the false alarm probability PFAo and detection probability PDo of the matched filter (correlation) detector are given by [14] (1.191) where (1.192) is a normalization of the actual detection threshold n (see Figure 1.125b), (1.193) is the signal-to-noise ratio associated with the partial correlation random variable C, and the coefficients Fk and Gk are evaluated recursively as Gk+1 = + (k + 1) Gk; Go = exp(-n*) (1.194a) Pseudonoise Code Acquisition in D