Optimal control of transmission errors with power allocation and stability in ARQ downlink

In the current work a downlink scenario is studied where packets for each user are buffered at the base station waiting for service. The service rates are considered constant and determined by QoS requirements. Errors due to outages occur and are reported to the base station via a reliable binary feedback link. Erroneous packets are held in the queues and an Automatic Retransmission Request protocol that can be powercontrolled repeats transmission until success. Having a total power budget P_tot available per slot to divide among users, the question which is the stability region of such a system is investigated and a power allocation that stabilizes the queues for all vectors within the aforementioned region is introduced. The optimal power allocation is the solution of a nonconcave maximization problem, the properties of which are analyzed. Algorithms based on the Lagrange dual problem are proposed that provide the actual or a relatively good approximation of the solution.