thermore, since KPF can be written as (KTd)(PFA/Td), then for the continuous system KTd is equivalenced to the false alarm penalty time Tp and in view of the above, PFA/TA is equivalenced with the false alarm rate 1.3 THE MULTIPLE DWELL SERIAL PN ACQUISITION SYSTEM A generalization of the single dwell serial PN acquisition system is a multi- ple dwell technique which, by virtue of its additional threshold testing, does not constrain the examination interval per cell to be a constant interval of time. Nevertheless, this scheme falls into the class of fixed dwell time PN acquisition systems as discussed earlier in the introduction in the sense that the variation in integration time is achieved here by allowing the examina- tion interval to consist of a series of fixed short dwell periods (each longer than its predecessor) with a decision being made after each. Allowing the integration time in a given cell examination interval to increase toward its maximum value in discrete steps, as per the above, permits dismissal of an incorrect alignment earlier than would be possible in a single dwell system which is constrained to always integrate over the full examination interval. Since most of the cells searched indeed correspond to incorrect alignments, this ability to quickly eliminate them produces a considerable reduction in acquisition time, particularly for long codes. Consider the N-dwell serial synchronization system illustrated in Figure 1.15. The received PN code signal plus noise multiplied by the local replica of the PN code and the output of the multiplier is applied to each of N non- coherent¹9 detectors. The i-th detector, i = 1, 2, N, is characterized by a detection probability PDi, a false alarm probability PEAi and a dwell time Tdi. These three parameters are for a non-coherent detector, related to each other as per the discussion in Section 1.2.4, in particular, (1.81). On the assumption that the detector dwell times are ordered such that Td1STd2STd3S (1.100) 19 Again, as in the single dwell case, the mu