 the interceptor knows the message duration (TM) and the hop time interval (Th). Epochs for the mes- sage and its constituent hops are presumed to be unknown. It is also assumed that the interceptor has no means of "learning" SO that timing information gleaned from one message transmission will aid in synchronization and detection of a subsequent message (should it occur). (1) Wideband Detector with Overlapping I & Ds, Each of Duration Equal to that of the Message Consider, first, a simple modification of the wideband (single-channel) detector wherein the square-law detector output now feeds two TM-sec inte- grate and dumps (I & Ds) which overlap TM12 (see Figure 1.9). For this inter- ceptor detector, a signal or noise-only decision will be made every TM12 seconds. Assuming with noise only present at the input, an output from either threshold device (corresponding to an I & D output that exceeds the thresh- Low Probability of Intercept Communications THRESHOLD SQUARE- DETECTOR THRESHOLD Figure 1.9. Overlapping I & D detector. old k) constitutes a false alarm. The false alarm rate (FAR) is the product of the decision rate 2/TM and the false alarm probability per decision PFA, i.e., FAR=2,PM (1.25) where, as before, for large WSTT, (1.26) Thus, to achieve the same false alarm rate as for the basic non-overlapping I & D case, the false alarm probability of (1.26) must be one-half its previ- ous value. To determine the probability of detection PD, it is assumed that, with signal-plus-noise present at the input, an output from either threshold device constitutes a true decision, i.e., message detection. When the I & Ds are over- lapped as in Figure 1.9, then, in the worst case, three-quarters of the signal energy will be covered by one I & D and three-quarters by the other (assuming that the signal energy is uniformly distributed). This situation is depicted in Figure 1.10. The above statements can be put into mathematical terms as follows: Pp=Pr{V1>korV2>k} =1-Pr{V1<kandV2<k} (1.27) where, for large W. ss T M, V1 and