of the upper and lower thresholds T and TL from (1.286) and (1.287), respectively. Figure 1.53 reveals the not too sur- prising result that for each detector implementation there exists an opti- mum value of bias in the sense of minimum miss probability. Clearly, for the ideal detector with perfect code phase, this optimum bias should the- oretically be equal to the pre-detection signal-to-noise ratio, i.e., 0 dB. The simulation results essentially bear this out. What is perhaps surprising, how- PN Synchronization Using Sequential Detection PFA = 10-6 N = 10.5 y=0dB ENVELOPE DETECTOR SQUARE ABSOLUTE VALUE IDEAL BIAS POINT, dB Figure 1.53. Bias points for the various detector types, perfect code phase (reprinted from [30]). ever, is the fact that the ideal detector appears to show no advantage over the other three implementations when all are biased at their respective optimum points. (The fact that the ideal detector minimum appears slightly larger than that for the envelope detector is due to statistical variations in calculating 1 - PD and Nd). Another interesting result which may be gleaned from those in both Figure 1.53 and 1.54 is the fact that the ideal detector is much less sensitive to variations about the optimum bias point than the other detectors. This implies more robust performance for the ideal detector in the sense of being more tolerant to parameter variations. This comes as an added bonus to its already optimum behavior in the sense of minimum dismissal time versus miss probability. A comparison of Figures 1.53 and 1.54 reveals the anticipated results that (1) the optimum bias points are all lower for random code phase, (2) the miss probability is higher for random code phase, and (3) the optimum points are all more sharply defined for random code phase. Suppose now we assume that the various configurations are designed cor- responding to their optimum bias points as determined from Figure 1.54, Pseudonoise Code Acquisition in Direct-Sequence Receivers PFA = 10-6 No==10.5 y=OdB SQUARE ABSOLUTE VA