irect-Sequence Receivers UPPER BOUND EXACT RESULT APPROXIMATION Ec/No,dB Figure 1.30a. PFAo versus EJNo for the matched filter detector with partial corre- lation (E = 1, n* = 10) (reprinted from [14]). UPPER BOUND EXACT RESULT APPROXIMATION Figure 1.30b. PFAo versus EJNo for the matched filter detector with partial corre- lation = 1, n* = 12.5) = (reprinted from [14]). Rapid Acquisition Using Matched Filter Techniques (1.194b) Figures 1.30a and 1.30b illustrate PFAo versus EJNo for E = 1 (yo = E/No) and normalized threshold values n* = 10 and 12.5, respectively. Also shown is an upper bound on PFAo given by P11195 which over the region of EJNo illustrated is very tight. Figures 1.31a and 1.31b are the companion illustrations of P Do versus EJNo for E = 0,.5 and n* = 7.5,10, and 12.5. Also, the matched filters are assumed to integrate over 64 chips. 1.5.2.2 Approximate Results An approximate approach [14] valid for low EJN, where the partial corre- lation "noise" is small with respect to the dominant thermal noise, is to model the quadrature total noise components at the matched filter outputs as inde- pendent Gaussian random variables with variance (1.196) which reflects the additive contributions of the thermal noise and partial cor- relation "noise" under hypothesis Hi Under this assumption, the false alarm and detection probabilities of the matched filter detector simplify to (1.197) (1.198) Pseudonoise Code Acquisition in Direct-Sequence Receivers EXACT RESULT APPROXIMATION Ec/No,dB Figure 1.31a. P Do versus EJNo for the matched filter detector with partial corre- lation (E = 0,M = 64) (reprinted from [14]). EXACT RESULT APPROXIMATION Ec/No,dB Figure 1.31b. P Do versus EJNo for the matched filter detector with partial corre- lation (E = .5,M = 64) = (reprinted from [14]). Rapid Acquisition Using Matched Filter Techniques where (1.199) Equations (1.197) and (1.198), which are in the form of (1.70) and (1.71) respectively with N B = 1, are superimposed (in dotted lines) on the previ- ous exact results in Figur