Power levels and packet lengths in random multiple access

Multiple-power-level ALOHA has been proposed to take advantage of the capture phenomenon in order to improve the throughput of a multiple random access system. We study the effect of the use of multiple transmission power levels and of the corresponding packet lengths on the system throughput and energy efficiency. We prove that the single-power-level system in which all transmit at the maximum allowable power level achieves both optimal throughput and energy usage efficiency under a condition on the decodability threshold value.