Abstract
In this paper we consider an SS/TDMA system with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> uplink beams, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> downlink beams, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K, 1 \leq K \leq \min (M, N)</tex> transponders. An optimal time slot assignment algorithm for any <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M, N, K,</tex> and any traffic matrix is presented, where optimality means achieving the minimal possible total duration for the given traffic matrix. The number of switching matrices generated by the algorithm is bounded above by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N^{2} - N + 1</tex> for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K = M = N</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MN + K + 1</tex> otherwise. Extensive simulation results on randomly generated matrices are carried out, showing that the average number of switching matrices generated is substantially lower than the bounds.
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