  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. 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.
