 long relative to the filter time constant. Low Probability of Intercept Communications given by (1.44) where the normalized threshold k' is related to the threshold k of Figure 1.12 (1.45) The normalization in (1.45) is chosen to make (1.33) analogous to the rela- tions derived for the previous I & D detector configurations. Letting t = t1 + TM in (1.44) (the detection probability is maximized if the RC filter output crosses the threshold at the termination of the message), then eliminating k' between PFA and PD (as before) gives a relationship for the SIN required by the interceptor, namely, (1.46) Comparing (1.46) with (1.4) together with (1.5) it is observed that, for given values of Wss, TM, PFA, and P, the interceptor pays a "synchronization penalty" of 10 log10 (1 - e-2) = 0.63 dB relative to the ideal wideband detector. Summing up the expected performance of the wideband energy detector for the condition of unknown message epoch, it is seen that the average S/N performance penalty paid for any one of the three proposed "fixes" amounts to about 0.7 dB, and the maximum penalty does not exceed 1.5 dB. Which of the three approaches should be used by the interceptor will likely be dependent on cost and other operational factors. (4) Filter Bank Combiner with Overlapping I & Ds, Each of Hop Interval Duration Analogous to the modification of the wideband detector discussed in (1) of Section 1.2.2.1 and illustrated in Figure 1.9, it is proposed that a filter bank combiner make use of quadrature overlapping I & Ds, each of hop interval duration, as shown in Figure 1.13. In the most general case, channel thresh- old decisions made on the NT in-phase I & D outputs are logically OR'd, CHANNEL I 2 ( ) dt THRESHOLD ( )dt THRESHOLD THRESHOLD CHANNEL NT-P THRESHOLD CHANNEL NT Figure 1.13. Filter bank combiner (unity output threshold) with overlapping I & D detectors. Low Probability of Intercept Communications accumulated over a message duration, and compared with an integer thresh- old, k. A similar situation takes plac