LUE IDEAL ENVELOPE DETECTOR BIAS POINT, dB Figure 1.54. Bias points for detectors with random code phase (reprinted from [30]). namely, -2 dB for the ideal detector, 4.0 dB for the square-law envelope detector, and 2.5 dB for the absolute-value envelope detector. Corre- sponding to these optimum bias points, upper and lower thresholds can be determined for each configuration from Figures 1.51 and 1.52 and (1.286) and (1.287), assuming PFA and N are fixed. Then, as the pre-detection sig- nal-to-noise ratio varies about its design point of 0 dB, the miss probability will vary about its design point value (minimum of curves in Figure 1.54) as indicated in Figure 1.55. This portrayal of the variation of miss probability as a function of the predetection signal-to-noise ratio for a fixed design point is often referred to as the "operating characteristic" of the sequential test [11]. To a first-order approximation, the results of Figure 1.55 reveal that the operating characteristic is the same for all four implementations when they are designed with optimized bias. To wrap up our discussion of simulation results, we now return to the time- out type of sequential detection system introduced earlier in Figure 1.53. Again, this system could be configured with other types of detector imple- mentations as in our discussion of the two-threshold system. However, since the relative performance of these various detector implementations would qualitatively be the same for the acquisition system with the time-out fea- ture as for the two-threshold system, we shall concentrate only on the square-law envelope detector and focus all our attention on whatever behav- ioral differences occur due to the change in decision logic. PN Synchronization Using Sequential Detection RANDOM CODE PHASE IDEAL, BIAS = -2 dB ENV DET, BIAS = 1.4 dB SQ LAW, BIAS = 4.0 dB ABS VAL, BIAS = 2.5dB =10.5 Nd = 20 SIGNAL - TO - NOISE RATIO, dB Figure 1.55. Comparison of S/N performance of various detector types at optimum bias point for 0 dB S/N (reprinted fro