On the Capacity of Randomly Used Shared Channels

The channel capacity of a communication channel made available to a user on a shared basis with other users is here considered. An overall system bandwidth B is divided into segments and parceled out to subscribers in an overlapping manner. Viewing emissions by the sharing user as Gaussian noise, the channel capacity is treated as a random variable, and its probability function, mean, and variance are studied. For a fixed power to each user, it is found that the average capacity of a user is maximum when the number of multiple assignments of a frequency band is approximately the inverse of the probability of use. The increase in channel capacity over exclusive assignment is also determined. The probability function of the capacity is worked out for some specific case to show its dependence on the frequency assignment policy, and a general procedure for determining the probability function is given.