This report presents the results of a theoretical analysis of a frequency hopping, multiple frequency shift keyed, spread spectrum communication system using a nonprocessing communication satellite transponder. A large number of users are assumed to be hopping pseudo-randomly about the transponder passband in time synchronization and approximate frequency synchronization. The users are assumed to be free to hop independently with the result that they occasionally interfere with one another. Formulations are presented that permit assessment of the level of mutual interference, thereby facilitating the selection of system parameters that will maximize the communication throughput of the system. The results presented here are purely theoretical. Numerical calculations will be presented in graphical form in a future report. These will then be used to develop a satellite loading procedure. They will also be extended to apply to hard-limiting satellite transponders and to consider the effects of jamming.

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