he hop frequency in a given hop inteval and the center frequency of the corresponding BPF, the SNR degradations Yi of (1.59) and (1.60) are simply replaced by (1.69) Interception Detectors -(i-1/2+AfT))/T/ Vi(AfTn) (1.70) Table 1.4 tabulates go(AfTh) versus AfTh. Clearly, the worst case degradation occurs when AfT = 0.50. For the full-band (N T channel) FBC at this value of AfT two adjacent channels in each hop interval will have identical sig- nal energy, each degraded by yo(0.5) = 0.4514 relative to the total. In this instance, the per-hop detection probability, ignoring the (sin x/x)2 spillover into the other channels, is given by (1.71) where, in general, PD1,(AfTh) denotes the individual channel detection probability in the presence of a frequency offset Af. For the partial-band FBC, in each hop interval, it may be assumed that only one channel has signal-plus-noise with the total signal energy degraded by yo(AfTn). Thus, the per-hop detection probability for the PB-FBC becomes PDF = 1 -[1-fP(AfTh)][1-PAI - (1.72) where f is the channel reduction factor (previously defined) from the PB- FBC. The result is that a frequency error of Af will require an effective increase in S/N° by a factor of yo(0)/yo(AfT), In general, as was previously discussed under (1) of Section 1.2.2.2, the Doppler effects render Af to a random variable status, which may be taken to be uniformly distributed between - 1/2Th and 1/2T. An average SIN Table 1.4 Frequency offset losses. yo(AfTh) 0.7737 -1.1143 0.7697 -1.1371 0.7576 -1.2054 0.7380 -1.3196 0.7112 -1.4799 0.6781 -1.6871 0.6395 -1.9417 0.5964 -2.2446 0.5499 -2.5968 0.5012 -2.9996 0.4517 -3.4543 Low Probability of Intercept Communications modifying factor may thus be obtained by averaging yo(DfTn) over the uniform distribution in frequency. This factor is computed to be 1.55 or 1.9 dB and comprises the two components 1/yo(0) = 1.1 dB and 1/yo(AfT = 0.8 dB. 1.2.3 Detector Implementation In this section, some of the problems of realizing the detector types discussed in Section 1.2.1