On the randomization of transmitter power levels to increase throughput in multiple access radio systems

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. We consider two types of capture models: (1) one in which the transmitter with the largest received power captures the channel, and (2) one in which the transmitter captures the channel only if its signal-to-interference ratio is above some threshold when received at the central station. 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 for cases both with and without Rayleigh fading. 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. Several numerical examples are presented along with a demonstration of how the optimal choice of power levels and probabilities can enhance throughput relative to previous ad hoc methodologies.