Symbol-by-Symbol Maximum Likelihood Detection for Cooperative Molecular Communication

In this paper, symbol-by-symbol maximum likelihood (ML) detection is proposed for a cooperative diffusion-based molecular communication (MC) system. In this system, the transmitter (TX) sends a common information symbol to multiple receivers (RXs) and a fusion center (FC) chooses the TX symbol that is more likely, given the likelihood of its observations from all RXs. The transmission of a sequence of binary symbols and the resultant intersymbol interference are considered in the cooperative MC system. Three ML detection variants are proposed according to different RX behaviors and different knowledge at the FC. The system error probabilities for two ML detector variants are derived, one of which is in closed form. The optimal molecule allocation among RXs to minimize the system error probability of one variant is determined by solving a joint optimization problem. Also for this variant, the equal distribution of molecules among two symmetric RXs is analytically shown to achieve the local minimal error probability. Numerical and simulation results show that the ML detection variants provide lower bounds on the error performance of simpler, non-ML cooperative variants and demonstrate that these simpler cooperative variants have error performance comparable to ML detectors.

I. Introduction

Molecular communication (MC) has been heralded as one of the most promising paradigms to implement communication in bio-inspired nanonetworks, due to the potential benefits of bio-compatibility and low energy consumption [2]. In MC, the information transmission between devices is realized through the exchange of molecules. Since no source of external energy is required for free diffusion, it is the simplest molecular propagation mechanism. One of the primary challenges posed by diffusion-based MC is that its reliability rapidly decreases when the transmitter (TX)-receiver (RX) distance increases. A naturally-inspired approach, which also makes use of the envisioned collaboration between nanomachines, is allowing multiple RXs to share information for cooperative detection. Often, cells or organisms share common information to achieve a specific task, e.g., calcium (Ca²⁺) signaling [3].