Optimization of Capture in Multiple Access Radio Systems with Rayleigh Fading and Random Power Levels

Abstract

To enhance the throughput of a slotted random access protocol in a radio communication system, we describe the use of a scheme in which multiple power levels are used at the transmitters. We first consider a situation in which n transmitters are simultaneously trying to send a packet to a central receiving station using a time-slotted access protocol, like slotted ALOHA. Each of these transmitters randomly chooses one of m discrete power levels during each attempt to send a packet. One of the simultaneously sent packets can often be successfully received due to the power capture effect. In this paper, we determine the optimal transmit probabilities for the power levels as well as the optimal values of the power levels themselves, when their range is constrained and in the presence of Rayleigh fading and power capture. After determining the precise optimal power levels and probabilities for maximizing the capture probabilities (i.e., for a given n), we propose a less complex, but nearly optimal, approximate approach based on using logarithmically equi-spaced levels. After demonstrating the closeness of our suboptimal results to the optimal results, we apply our approach to the problem of optimizing the throughput of the slotted ALOHA protocol for a case in which the input traffic is generated according to a Poisson process.