Optimality of threshold policies for transmission scheduling in correlated fading channels

We consider exploiting perfect channel state information for optimal scheduling for point-to-point data transmission over correlated fading wireless channels, where retransmissions are allowed via the use of a channel-aware ARQ protocol. The objective is to achieve a trade-off between energy and packet loss rate subject to a hard delay constraint. Specifically, the aim of the transmission scheduling problem is to minimize the sum of accumulated transmission costs and a penalty cost on the number of lost packets, subject to the constraint that each batch of a finite number of link layer packets has to be transmitted within a prespecified number of transmission time slots. Using the concept of supermodularity, we prove that under some conditions on the costs, the optimal transmission scheduling policy is threshold in the residual transmission time and the buffer occupancy. These two threshold results substantially reduce the computational complexity required to implement the optimal transmission scheduling policy.