e-TTu IDEAL DETECTOR ABSOLUTE VALUE DETECTOR SQUARE-LAW DETECTOR BIAS POINT, dB Figure 1.51. Variation in false alarm parameter f with bias point (reprinted from [30]). mentations, such a gain normalization was not introduced into the simula- tion runs. Further simulation results [30] performed on the same four detector types produced the following approximate relationship (valid for N > 3) characterizing the average number of samples per dismissal (average sam- ple number): (1.287) where d is a dismissal parameter whose variation with detector type and bias is illustrated in Figure 1.52 and TL denotes the lower detection thresh- old (a negative quantity). Here again TL is related to N2 and n'2 in the iden- tical way that T was previously related to N1 and n'i for the four cases under investigation. Furthermore, the results in Figure 1.52 were generated by setting the bias point to the desired value and then setting to give PFA = 10-6 in accordance with (1.286) and the value of f determined from Figure 1.51. Pseudonoise Code Acquisition in Direct-Sequence Receivers Nd 1.5-dT for No 3 3 IDEAL PFA = 10-6 ABSOLUTE VALUE ENVELOPE SQUARE BIAS POINT, dB Figure 1.52. Variation of dismissal parameter d with bias point (reprinted from [30]). In summary, the noise-only simulation results of Figures 1.51 and 1.52 indi- cate that increasing the bias is effective both in reducing the false alarm prob- ability (except for the ideal detector) and reducing the average number of samples per dismissal. Simulation results for the signal-plus-noise hypothesis are presented in Figures 1.53 and 1.54, which plot missed detection probability (1 - P) ver- sus bias for perfect code phase (operation at the precise peak of the PN code autocorrelation function) and random code phase, respectively. For both sets of plots the pre-detection signal-to-noise ratio y is chosen equal to 0 dB. Furthermore, for each value of bias point, values of f and d are determined from Figures 1.51 and 1.52, which for PEA = 10-6 and N d = 10.5 allow calculation 