,.... will contain a signal component with power propor- tional to (1.60) Thus, a more exact characterization of the FBC performance than that given in (1.8) and (1.9) is the following. The per-hop (frame) detection and false alarm probabilities PDf and P FAf (i.e., the probabilities of a one out of the OR circuit in Figure 1.6 under signal-plus-noise and noise-only conditions) are given by Pot=1-II(1-PD1) (1.61) (1.62) where the product over i in (1.61) goes over the NT FBC channels and PDI denotes the individual channel detection probabilities (no frequency error assumed at this juncture). Note that all PDI have the same mathematical form, with the signal-to-noise ratio for each channel proportional to Yi of (1.60) (i = 0 corresponds to the hop pulse channel). If, as was previously assumed, the (sin x/x)2 dependence of the effective power within the Low Probability of Intercept Communications N--channel energy detectors is ignored, (1.61) simplifies to - PDI, (1.63) where PDI and PEAI are the previously defined individual channel detection and false alarm probabilities. Now since P DIo PDI for i # 0, the following simplifying assumption can be made: (1.64) which, when substituted into (1.61), yields (1.65) Comparing (1.63) and (1.65), it is observed that the per-hop detection prob- ability is degraded approximately (in terms of SNR) by Yo relative to its value obtained by ignoring the true (sin x/x)2 spectral nature. Thus, since, for a unit threshold (l = 1 in Figure 1.6), the per-hop and overall message probabili- ties are related by PFA = NhPFAf III NhNTPFAI, (1.66) then comparing (1.66) with (1.8), (1.9) may be readily modified to include the effect of the channel filter on the required S/N namely, (1.67) where now = -1(PFA/NhNT)-Q-1(Pp/Nh). - (1.68) For the partial-band FBC, the results of (1.64) and (1.65) are even better approximations since the remaining channels are far apart from one another and, thus, there is negligible adjacent channel (sin x/x)2 spillover. When a frequency error Af exists between t