for an (N - 1)-dwell system, starting with (1.123), we may, by induction, arrive at the result II PDN-12NP-(N-1). - - Thus, we wish to set Pn=NP-(N-1 (1.141) P 1 + (1.142) Pseudonoise Code Acquisition in Direct-Sequence Receivers PD=.025 FALSE ALARM PROBABILITY,PEA Figure 1.20. Acquisition performance improvement factor for two-dwell system over single dwell system versus false alarm probability with detection probability as a parameter; y' = -10 dB. Similarly, generalizing (1.126), it is simple to show that k = 1, 2, ...,N. (1.143) Since the right-hand side of (1.113) with k = N is again the system false alarm probability of the N-dwell system, we wish to set PFAN = PEA. (1.144) Finally, using (1.143) in (1.129), we have G(N) < WI - All Gu(N). (1.145) The Multiple Dwell Serial PN Acquisition System For the non-coherent detector, the analogous relationships to (1.132) are 1,2,.. , N - 1 (1.146) Again since Td1 TdN, we have PFA = < (1.147) For PEA1 = PFA2 PEAN or PEA1 = PFA2 PFA,N-1 = 1 and PFAN = PFA < 1, (1.145) becomes (1.148) Thus, for some set of false alarm probabilities PEA < . . . < P2 < P < 1 (1.149) FALSE ALARM PROBABILITY, PFA Figure 1.21. Acquisition performance improvement factor for three-dwell system over single dwell system versus false alarm probability with detection probability as a parameter; y' = -20 dB. Pseudonoise Code Acquisition in Direct-Sequence Receivers FALSE ALARM PROBABILITY, PFA Figure 1.22. Acquisition performance improvement factor for three-dwell system over single dwell system versus false alarm probability with detection probability as a parameter; y' = -10 dB. and corresponding dwell times < Td,N-1 (1.150) there exists a minimum of the function Gu(N), namely, G(N) + + - Ta2) + PFA,N-1(TdN - Tä,N-1). (1.151) The ratio Td/G(N) is then a measure of the minimum improvement in acquisition performance of the N-dwell system over the single dwell system. Note that obtaining (1.151) requires an (N - 1)-dimensional minimization. Figures 1.21 and 1.22 illustrate the relative performance 