er bounds on the SIN requirement for the overlapping I & D detector as found from (1.37) are then, respectively, 0.3 dB and 1.2 dB greater than the S/N° requirement for the perfectly synchronized wideband energy detector. Alternately stated, for the above performance parameters and the detector of Figure 1.9, the penalty paid by the interceptor for lack of message time synchronization is between 0.3 and 1.2 dB. (2) Wideband Detector with Single (Non-Overlapping) I & D Duration Equal to Half the Message Duration A simpler configuration than that of Figure 1.9 is to maintain the identity of the ideal wideband (single channel) detector but reduce the post-detection I & D interval by a factor of two. Thus, by consecutively integrating over only half the message duration, the interceptor is guaranteed to have one inter- val which contains signal-plus-noise over its entire duration regardless of his initial epoch. Of course, since the integration interval is now only half as long as before, then, relative to the ideal wideband detector with integration over the full message duration and perfect time synchronization, an S/N° penalty of approximately a factor of V2 (1.5 dB) will be paid. In the following, a more exact mathematical formulation of the above con- clusion will be developed. The worst case situation from the interceptor's viewpoint occurs when one integration interval (the 0-th) sees full signal and the two adjacent intervals (-1-st and 1-st) each contains signals in only half the interval, as shown in Figure 1.11. NOISE ONLY SIGNAL PLUS NOISE (18D) I (I&D), (181 D) Figure 1.11. Worst case signal condition. Low Probability of Intercept Communications For this case, the probability of detection is (1.38) where (for large WSSTM) MO = 2WssTM(1 y) (1.39) Since the false alarm probability is still given by (1.26) with, however, TM replaced by TM/2, then using the lower bound of (1.38) on PD, together with (1.39), a simple upper bound is obtained on the required interceptor S/N namely, (1.40) Comparing (1.40) with 