Analysis of macro diversity based on maximum ratio combining in long range ALOHA networks

In low power wide area networks, packets transmitted by a device are not addressed to a specific base station: any surrounding station can receive them. This opens the way to several macro diversity schemes. As opposed to independent decoding of packets received by each base station, we propose using maximum ratio combining (MRC) to improve system performance. We use stochastic geometry to analyze the packet loss probability when MRC is implemented for both pure and slotted Aloha and obtain a closed formula when the path loss exponent \(\gamma \) is 4. However, the formula is valid when all base stations on an infinite plane participate in the MRC procedure, which gives the most optimistic evaluation. We developed simulations to get the performance when a finite number of receivers in the MRC is considered and focus on the case with only 2 receivers. We use a curve-fitting approach based on the simulation results to get a closed-form formula of the packet loss probability with 2 receivers. This curve-fitting approach is also applicable to other cases in which more receivers are leveraged by MRC. The formula is easy to use and accurate when \(\gamma \in \left[ 3.3, 4.5\right] \) and the loss probability is greater than \(0.5\%\). For pure Aloha when advanced transmission techniques (e.g., interleaving, robust channel coding, etc.) are applied and when the capture ratio is 3 dB, the system capacity for a \(10\%\) packet loss probability is increased by a factor greater than 1.26 compared to a simple scheme in which each base station independently decodes packets.