cies may, with equal likelihood, be transmit- ted on any given hop interval, is Phit = f. One view of the performance penalty paid for a partial-band detector is to consider what happens to the per-channel detection probabilities PDI and PEAL if the transmitted message is sufficiently long (for the moment, assume that it is infinite in duration or continuous), then, on the average, the effec- tive per-hop detection probability is P'DI = PDIPhit The per-channel false alarm probability, however, is unchanged, as it always depends on the absence of a hit. Now, since PD and PEA are the real measures of performance, using relationships akin to (1.8), the following results are obtained: P'D=NhP'DI=(NhPDI)Phit = = (1.10a) P'FA = NhNTPFAI = (NhNTPFAI)f. (1.10b) But, because Phit = f, it is readily seen that P'D = PDf and P'FA = P Af,i.e., = the original probabilities are reduced by the channel reduction factor, f. There are only two ways to restore the desired performance: (1) increase the per-channel PDI and PFAI values by 1/f, which requires a higher SIN relative to the full-band FBC, or (2) increase N by 1/f. This latter fix implies that the communicator's message must therefore be longer by a factor of 1/f (which is no problem if the message is continuous) but, since the intercep- tor has absolutely no control over the message duration, increasing N rep- resents an untenable solution. Use of the PB-FBC should be predicated on its performance being equiv- alent to the full-band FBC for all conditions except that of a larger SIN requirement. On very short messages, however, the considerations are a bit more complex. What must be factored into the performance criteria is the probability of a given number of hits, n, per message, this being determined by the binomial distribution, viz., (1.11) Defining PI and PI as the per-channel detection and false alarm prob- abilities needed to achieve the PB-FBC short message detection and false alarm probabilities, PD and PEA, the actual PD conditioned on n is given by (1.12) where