On the Optimal Transmission Range in Multi-hop Wireless Ad Hoc Networks

In wireless ad hoc networks with randomly distributed nodes, we measure the normalized optimum transmission range and the network throughput, which is inversely proportional to the minimized number of transmissions required to reach the destination over multi-hop path, of various medium access schemes. Our objective is to determine the optimum transmission range that achieves the most optimal tradeoff between the progress of packets in desired directions towards their respective destinations and the number of transmissions required to deliver the packets. We analyze the optimum average transmission range with ALOHA based scheme where simultaneous transmitters are dispatched according to a uniform Poisson distribution and compare it with the maximum transmission range with various grid pattern based schemes where simultaneous transmitters are positioned in specific regular grid patterns. It is shown that at typical values of signal-to-interference ratio threshold and attenuation coefficient, the most optimal transmission range can be obtained with triangular grid pattern based scheme. However, our results show that designing the medium access scheme which optimizes the transmission range in the network should take into account the parameters like signal-to-interference ratio threshold and attenuation coefficient. Our results also show that the most optimal transmission range and network throughput with grid pattern based medium access schemes outperform the optimum average transmission range and network throughput achievable with ALOHA based medium access scheme only by the factors of at most 2 and 3 respectively. Later on, we also discuss the asymptotic behavior of the optimal transmission range in wireless ad hoc networks with grid pattern based medium access schemes.