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 user density and inter-user interference (IUI) and its impact on the 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 between all TXs and RXs. 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, the statistics of the MC channel, and the statistics of the IUI. Furthermore, we derive an analytical expression for the bit error rate and the achievable rate of a single transmission link. Finally, we propose a new performance metric, which we refer to as area rate efficiency (ARE), that captures the tradeoff between the transmission link density and the IUI. The ARE characterizes how efficiently the available TX and RX areas are used for information transmission and is expressed in bits per unit area. We show that there exists an optimal transmission link density for maximizing the ARE. The presented results reveal that the optimal link density depends on the number of molecules used for modulation and the value of the diffusion coefficient, while the impact of the chosen grid structure and the concentration of background noise molecules is negligible.