Asymptotically Optimal Scheduling Algorithm for Compute-and-Forward
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Consider a Compute and Forward (CF) relay network with L users and a single relay. The relay tries to decode a function of the transmitted signals. For such network, letting all L users transmit simultaneously, especially when L is large causes a degradation on the information the relay is able to decode which in fact goes to zero very fast with L. Therefore, a restriction on the number of simultaneously transmitting users must be made and in each transmission phase only a fixed number of users may transmit, i.e., user scheduling. Accordingly, in this work we provide an asymptotically optimal polynomial scheduling algorithm for CF. We show that scheduling under CF not only guarantee non-zero rate but provide gain to the system sum-rate and in fact this rate grows as O(L). We present analysis for the suggested algorithm and show that the optimal schedule relies on a semi-deterministic function of the scheduled signals. The performances of the suggested algorithm are compared with a universal upper bound on the performances of CF and evaluated using simulations.
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