Area Rate Efficiency in Multi-Link Molecular Communications

We consider a multi-link diffusion-based molecular communication (MC) system where multiple spatially distributed transmitter (TX)-receiver (RX) pairs establish point-to-point communication links employing the same type of signaling molecules. To exploit the full potential of such a system, an in-depth understanding of the interplay between the spatial link density and inter-link interference (ILI) and its impact on system performance is needed. In this paper, we consider a three-dimensional unbounded domain with multiple spatially distributed point-to-point non-cooperative transmission links, where both the TXs and RXs are positioned on a regular fixed grid. For this setup, we first derive an analytical expression for the channel impulse responses (CIRs) between the TXs and RXs in the system. Then, we derive the maximum likelihood (ML) detector for the RXs and show that it reduces to a threshold-based detector. Moreover, we derive an analytical expression for the corresponding detection threshold which depends on the statistics of the desired signal from the dedicated TX, the statistics of the MC channel, and the statistics of the ILI. We also provide a low-complexity suboptimal decision threshold. Furthermore, we derive an analytical expression for the bit error rate (BER) and the achievable rate of a single transmission link. Finally, we propose two new performance metrics, namely area rate efficiency (ARE) and area and time rate efficiency (ARTE), suitable for holistically evaluating spatially distributed multi-link MC systems. In particular, ARE and ARTE capture the tradeoff between transmission link density and achievable rate per link and the tradeoff between transmission link density, achievable rate per link, and inter-symbol interference (ISI), respectively. Hence, ARE and ARTE can be exploited to determine the optimal transmission link density for maximizing the throughput of the entire system.