at NT = WSTIM which, when substituted in (1.6) results in the alternate expression Figure 1.5 is a plot of the ratio dB) of S/N° as determined from (1.4) to S/N° of (1.7) versus WSSTM with the total number of hops NT in the SS bandwidth as a parameter. For a given WSSTM and NT these results illustrate the increase in detectability obtained by the interceptor by using an opti- mum multichannel detector rather than a wideband radiometer. For exam- ple, if WSSTM = 8 X 10°, then for NT = 106, the optimum detector has an 11.1 dB advantage. If this could be fully realized, it would allow an almost four- fold increase in the detection range over that possible with the wideband radiometer. Clearly, the price for the optimum detector's superior perfor- mance is complexity, both in terms of functional operations and the num- 4Note that in comparing the required SINo's of the two detectors, it is not necessary to know either the SS bandwidth W ss or the hop rate Rh = 1/Th. Rather the product of W and the mes- sage time TM, and the total number of hops N in W55, are all that enter the calculation. 5This value of WST is used in [4]. CHANNEL I ( ) 2 ( )dt IO ( ) CHANNEL 2 n = l CHANNEL NT Figure 1.4. Optimum detector for frequency-hopped signals. NT=107 NT=106 NT=105 WSSTM Figure 1.5. S/No performance gain of optimum multichannel detector over wideband radiometer. Interception Detectors ber of channels required; for the example above, the detector must have one million channels! Since this seems prohibitive in terms of size, power, and cost (even in the MIC and LSI era), the optimum detector is deemed unfea- sible. A more realistic approach is that of the partial-band filter bank com- biner. First, we discuss the full-band filter bank combiner in terms of its differences with respect to the optimum multichannel detector. (3) Filter Bank Combiner (FBC) Detector Figure 1.6 shows the basic FBC. A comparison with the optimum detector of Figure 1.4 reveals that the energy detector portions are the same but that a decision in each c