Power levels and packet lengths in random multiple access with multiple-packet reception capability

This paper extends our earlier results. We assume that the receiver has the capability of capturing multiple packets so long as the signal-to-interference-plus-noise ratio (SINR) of each packet is above a designed threshold T throughout its transmission period. We prove that, compared with a multiple-power-level system, the single-power-level system in which all nodes transmit at the maximum allowable power level achieves optimal throughput, under a condition that T exceeds the value 3.33. Given a minimum throughput requirement, under the same condition on T, the single-power-level system also achieves the maximum average packet capture probability as well as the optimum energy usage efficiency. If the multiple-power-level systems are constrained such that higher power levels always have shorter packet lengths, then the above results hold for T greater than 2.