ly been defined in (3A.1b). Taking the partial derivative of (3A.10) with respect to B and evaluating at B=0 gives exp{-1f2(B,u',v')} X dv'. (3A.12) (3A.13) At = 0, sincw(i-B)=0fori1 - (3A.14) 1,0,+1 (3A.15) (3A.16) Appendix 3A This takes care of the second partial derivative in (3A.12). For the first par- tial derivative, we observe that Io(V2yf(B,u,sin B)0 = - (B)|)(V2yu') (3A.17) Substituting (3A.16) and (3A.17) into (3A.12) gives the desired result, i.e. (3A.18) This Page Intentionally Blank Chapter Part 5 SPECIAL TOPICS This Page Intentionally Blank Chapter Chapter 1 LOW PROBABILITY OF INTERCEPT COMMUNICATIONS The design of a communication link to have low probability of intercept (LPI) capability is predicated on the requirement for it to operate in a hos- tile environment wherein the enemy tries to detect the presence of the com- municator's transmission. A typical scenario might consist of an underwater or surface vehicle (the communicator) attempting to correspond with a satel- lite (the receiver) via transmission of a short message, and an enemy search aircraft (the interceptor) whose mission it is to detect the presence of RF energy corresponding to this communicated message. The key words in the last sentence are detect and energy since typically the interceptor's perfor- mance is judged by his ability to determine (detect) that the communicator has initiated a transmission (energy) and not by what might occur follow- ing this accomplishment, e.g., location of the communicator, decoding of the message, etc. To further emphasize this point, the interceptor is ordinarily acquainted only with such communicator information as his frequency band, modulation format, and those spread-spectrum (SS) modulation character- istics such as bandwidth and code (hop) rate, which are insufficient by them- selves to allow for decoding of the message. Thus, in the absence of information related to the time of message initiation and the secure codes used to generate the SS modulation, the interceptor's detection strategy