Analysis of a deterministic power level selection algorithm with small and large power steps for Aloha networks under saturation

Standard power control techniques are not deployable in Aloha networks due to lack of central controlling entity and/or inefficiency of such algorithms in large networks with bursty traffic. To handle this problem in practice, simple transmission power selection algorithms are used for ranging and/or combating harsh channel conditions. In such algorithms, the transmission power is steadily increased by an amount called power step, until the packet is successfully transmitted. Noting that ranging is the major concern of this approach, small power steps are ideal for its operation. However, as we will show in this paper, using small power steps with this algorithm causes a throughput collapse in large networks, when capture effect is considered in the analysis. In the asymptotic case, the throughput of this algorithm will be less than the throughput of the Binary Exponential Backoff (BEB) scheme which only uses a single power level. To show these results, we will present an asymptotic analysis of this algorithm with small power steps in an ideal communication channel where BEB is used as the retransmission scheme. In order to strengthen the results, we will prove the existence of better choices for power steps by extending the analysis for large power steps and we will show that properly chosen large power steps guarantee higher throughputs and require approximately the same average powers as small power steps. Our analysis and simulation results show that small power steps should be avoided with the mentioned power selection algorithm except probably for ranging and once the ranging process is complete, larger power steps should be used to exploit the capture effect.