Joint scheduling for dual-hop block-fading broadcast channels

In this paper, we propose joint user-and-hop scheduling over dual-hop block-fading broadcast channels in order to exploit multi-user diversity gains and multi-hop diversity gains all together. To achieve this objective, the first and second hops are scheduled opportunistically based on the channel state information and as a prerequisite we assume that the relay, which is half-duplex and operates using decode-and-forward, is capable of storing the received packets from the source until the channel condition of the destined user becomes good to be scheduled. We formulate the joint scheduling problem as maximizing the weighted sum of the long term achievable rates by the users under a stability constraint, which means that on the long term the rate received by the relay should equal the rate transmitted by it, in addition to constant or variable power constraints. We show that this problem is equivalent to a single-hop broadcast channel by treating the source as a virtual user with an optimal priority weight that maintains the stability constraint. We show how to obtain the source weight either off-line based on channel statistics or on real-time based on channel measurements. Furthermore, we consider special cases including the maximum sum rate scheduler and the proportional fair scheduler. We demonstrate via numerical results that our proposed joint scheduling scheme enlarges the rate region as compared with a scheme that employs multi-user scheduling alone.