SS/TDMA satellite communications with k -permutation switching modes

The Satellite-Switched Time-Division Multiple Access (SS/TDMA) scheme has been one of the most effective techniques designed to allocate the communication bandwidth provided by communication satellites. The scheduling problem for SS/TDMA corresponds to finding a positive linear combination of a predefined set of (0,1)-matrices which covers a given traffic matrix ${\bf T}$ such that the sum of the multiplying constants used in the linear combination is minimum. In this paper, an algorithm is given to solve the optimization problem using a result which is a generalization of a theorem by Birkhoff and von Neumann. The case of k-permutation matrices is first addressed. The result is then further extended to more general sets of (0, 1)-matrices.