Optimum Power Selection Algorithms in Aloha Networks: Random and Deterministic Approaches

Abstract

In this paper, we discuss the optimum random and deterministic power selection algorithms in Aloha networks, where nodes run Exponential Backoff (EB) for contention resolution. In random case, the transmission power of a packet is selected from the available power levels, based on a predetermined probability mass function, while with the deterministic algorithms the transmission power of a packet is a deterministic function of the number of collisions the packet has experienced. Most of the related works in the literature have not addressed the power-throughput characteristics of the power selection algorithms for use in practical system designs and, therefore, this subject has been the major motivation of this paper. For the random case, we will derive optimum random power selection algorithms for unconstrained and constrained power budget scenarios and the corresponding optimum power-throughput characteristics will be presented for the latter case based on perfect capture model. Next, we will introduce a method to extend these results to SIR-based capture model, which will result in sub- optimum power steps and the sub-optimum power-throughput characteristics for the random case. This characteristic will reveal power budget requirements for the target throughput values. In the next step, deterministic power selection algorithms will be introduced and discussed with unconstrained and constrained power budget scenarios and sub-optimum power-throughput characteristic will be derived based on the perfect model. Similar methods, introduced for the random case, may be used to adapt the results to SIR-based model. Finally, by comparing the presented power-throughput characteristics, it will be demonstrated that optimum random and sub-optimum deterministic power selection algorithms have very similar behaviors. Therefore, noting that deterministic algorithms do not require any random power generator block, they may be preferred to random algorithms in similar scenarios.