.099519 0.091581 0.763 0.191098 0.122153 0.822 0.313252 0.139639 0.867 0.452890 0.139656 0.900 0.592547 0.124139 0.925 0.716686 0.099298 0.944 0.815985 0.072199 0.958 0.881843 0.048115 0.968 0.936299 0.029594 0.976 0.965893 0.016900 0.982 0.982793 tional probability of detection PD(N). Note that eight or more hits per mes- sage are required to raise PD(N) to the point where it equals or exceeds the desired PD = 0.9. The probability of this happening is only Pr{n 8} = 0.55. (For the full-band FBC, there is no hit conditional statistic SO that PD = 0.9 can be expected with unit probability.) the inference, then, is that, if PD is to be quite close to 0.9 in a single-message basis, a further modification of PI is in order. Say it is desired to equal or exceed PD = 0.9, with a corresponding hit-related probability of 0.9. This requires PD(N) 0.9, which, from Table 1.1 demands that N > 5. Using these values in (1.12) results in = 0.37 (rather than 0.25, as above). Suppose, now, that the PB-FBC is reduced to a single channel. The per- hop hit probability becomes Phit = 10-6 and the probability of one or more hits in the 8000-hop message sequence would be only 7.9 X 10-3. Clearly, since at least one hit is required for detection, these are very unfavorable odds, and the interceptor would not use a single-channel FBC no matter how high SIN might be. What, then, is a reasonable lower limit on the number of channels, i.e., how small can f be allowed to become? As a minimum, at least one hit per message is needed. In [3], it is suggested that f must be greater than or equal to 1/N Taking f = Phit = 1/N the probability of one or more hits per message is 1 - (1 - 1/Nh)N For very large Nh, it can be easily shown that this quantity approaches 1 e-1 = 0.632. This figure may be only marginally acceptable, as explained previously. If the probability of one or more hits per message is to be, say, 0.9, then Phi will have to be icn- reased from 10-6 to 2.87 X 10-4 and the minimum f becomes f = 2.3/Nh. Further, on the basis that a sin