st relate the conditional false alarm probabilities {PFAili-1} defined in (1.102) to the dwell times {Tail and the detection thresholds {n}}. Since, as previously mentioned, the overlap of the integration times of the integrate-and-dump circuits causes the outputs Z1, Z,..., , ZN to be a set of fully dependent random variables, computation of P FAil i - 1 involves evalua- tion of an i-dimensional integral over the joint probability density function p(Z, Z, , Zi). Such evaluations are at best tedious if not altogether impossible. To circumvent this computational bottleneck, we consider a procedure for obtaining an upper bound on the acquisition performance of the N-dwell sys- tem. This will allow direct comparison with the comparable performance of the single dwell system to assesss how much improvement can be gained as a function of the number of dwells N. To illustrate the procedure as clearly as possible, we shall first present its details for the simple case of a two-dwell system, i.e., N = 2. Consider that we choose the decision thresholds N1 and N2 such that the unconditional detection probabilities PD1 and PD2 are equal, i.e., (1.119) This choice does not necessarily guarantee an optimum decision; however, it allows us to obtain a simple upper bound on performance that will be suf- ficient to indicate the benefit in going to an N-dwell system. Next, we note from the law of total probability that (1.120) where the overbar denotes the complement of the event. For example, (1.121) when signal is present. Since PD21 < 1 and PDI=1 - PD1, then from (1.120), P2P21D11-PD1 (1.122) or, using (1.119), (1.123) Since, from (1.103), the left-hand side of (1.123) represents the system detection probability for the double dwell system, if PD denotes the system detection probability of the single dwell system and we set 2P-1=PD (1.124) The Multiple Dwell Serial PN Acquisition System then we are guaranteed that the two-dwell systm will have an equal or higher detection probability. This in turn implies, from (1.113) and (1.1