or channels, each having bandwidth WK = WSI/K. Each channel then forms the basis of a separate energy detector and the outputs of the K channels are further processed to render the overall detection decision. Figure 1.3 shows the functional configuration wherein each channel has bandwidth WSIIK and is contiguous with respect to those adjacent. Internation CHANNEL I ENERGY DETECTOR CHANNEL 2 RF INPUT O ENERGY DECISION DETECTION OUTPUT DETECTOR ALGORITHM CHANNEL K ENERGY DETECTOR Figure 1.3. Topology of the multiple-channel detector. Low Probability of Intercept Communications It can be shown (see Appendix 4A) that an arbitrary choice of K with- out regard to the FH frequency cell bandwidth, Wh, and the FH hop period Th, will lead to performance inferior to that of the wideband detec- tor. The key to superior operation is that the individual channels be matched to the individual hop pulses in both bandwidth and time. Thus, WK = W and T = An optimum multichannel detector is one having NT channels (NT is the totla number of hop cells in Wss) and utilizing a likelihood ratio decision algo- rithm. Figure 1.4 indicates the essential elements. Each channel consists of an energy detector (BPF, squarer, and integrator), followed by scaling. The channel outputs are summed at the end of each hop period and the sums from all Nh hops in the message are multiplied, with the result being com- pared to a threshold, l, in order to decide if a signal is present at the detec- tor input. The generalized performance expression for the optimum multichannel detector cannot be obtained due to an inability to specify the output prob- ability distribution functions. When Nh is large (e.g., Nh > 100), however, it is possible to closely approximate the true answer by using Gaussian statis- tics, with the result that SIN is given by [4]: (1.6) where I¹ is the inverse of the zero-order modified Bessel function of the first kind, and d is given as per (1.5). Since NT = Wss/W and TM = NhTh, then letting WhT = 1 (as is typical for FH), we arrive 