The Effect of Pseudorandom Frequency Hopping on the Probability of Simultaneous Usage of a Communication Satellite

When the up-link frequency band repeated by a communications satellite is hopped in a periodic manner, when users are divided so that a group of them can transmit only when a particular frequency band is repeated, and when message arrivals for one user are independent of message arrivals for any other user, the users in a group are independent. When the frequency hopping is done in a pseudorandom rather than a periodic manner, the users are dependent. The effect of the dependence is, in practical cases, to increase the probability of there being a large number of simultaneous users which increases the probability of system overload. General expressions for the probability of system overload and for the fraction of the information lost due to overload are obtained. These expressions illustrate the effect of the dependence induced by the pseudorandom frequency hopping. Examples are presented. Accepted for the Air Force Stanley J. Wisniewski Lt Colonel, USAF Chief, Lincoln Laboratory Office