s d in dB with PEA as a parameter. For the sample typical values of PD = .9 and PFA = 10-6, we obtain d = 6 (7.8 dB), which for given values of SS bandwidth and total message time enables com- putation, from (1.4), of the minimum value of SIN above which the com- municator is detectable. Before leaving this subsection, we point out that using a continuous inte- grator (over a T-sec interval) rather than an I & D as indicated in Figure 1.1, in general, yields significantly better performance since it ensures align- ment in time with the signal. However, calculations based on I & D detec- tion and the assumption of perfect alignment of sampling times with signal occurrences will provide close estimates of the detection performance of continuous integration [5]. Thus, we have justified the ease of analysis afforded by the assumption of I & D detection with perfect message align- ment. More will be said later on regarding the degradation due to imperfect alignment. One other simplifying assumption is made in arriving at (1.4) and (1.5) from (1.81), namely that S/NoW < 1 and thus V1 + 2S/ NoW II 1. This is equivalent to assuming equal vari- ances for the integrator output under signal-plus-noise-and noise-only conditions. Low Probability of Intercept Communications PFA=10" 10-12 10-14 10-16 10-18 10-20 10-30 10-40 10-50 -6 -4 -2 O 10 12 14 16 Figure 1.2. Radiometer probability of detection PD and probability of false alarm PFA versus parameter d = [Q21(PFA) - Q-1(P)] (reprinted from [4]). (2) Optimum Multichannel FH Pulse-Matched Energy detector From (1.4), it may be seen that the wideband detector's performance in terms of S/N° is proportional to the square root of the spread-spectrum total band- width, Wss. Actually, all basic square-law detectors behave in proportion to the square root of the input bandwidth. Thus, if it is somehow possible to effectively reduce Wss, greater SIN sensitivity will be obtained. The only realistic way to effectively reduce Wss is to subdivide the total bandwidth into, say, K sub-bands 