An Effective Constellation Design for Concentration Shift Keying in Molecular Communication Systems

In this article, we study a previously overlooked work of designing the constellation for concentration shift keying (CSK) in diffusion-based molecular communication (MC) systems, considering the adverse effects of signal-dependent noise and intersymbol interference (ISI). Against this background, the conventionally used uniform constellation strategy is no longer the optimal choice for CSK. Considering the discrete nature of messenger molecules, the constellation design of CSK is essentially a nonlinear integer programming problem. However, due to the nonconvexity of the goal function, general convex optimization methods cannot be easily employed. To solve the aforementioned problem, a novel CSK strategy with a brute-force search algorithm is proposed to obtain the optimal constellation numerically. Moreover, a low-complexity search algorithm that provides new insight into reducing the complexity of MC systems is further presented. Specifically, we theoretically derive the optimal threshold and employ a maximum likelihood detector that effectively minimizes the average symbol error rate (SER) by leveraging the knowledge of ISI at the receiver. Finally, we can obtain a fitted equation for the nearly optimal constellation points under specific channel parameters, attaining the SER performance similar to the optimal one, while the search complexity is much lowered.