Generalized Channel-Aware Power Control Scheme for Random Access with Multi-Packet Reception

This paper develops a generalized channel-aware power control scheme to enhance the multi-packet reception (MPR) capability for random access. In the proposed scheme, each user randomly selects its transmit power with a probability in accordance with a distribution function based on its own channel state. For two-user systems, we show that the optimal power distribution function has a simple discrete structure, based on which the optimal random access strategy can be efficiently computed. Leveraging the relevant insights, we further propose a decentralized binary power control scheme for general K-user systems. It is established that such a simple scheme can asymptotically approach the performance of the optimal centralized scheme, as the system load grows large. Numerical results show that the proposed schemes obtain noticeable performance improvement over the existing alternatives.