Error Analysis of Molecular Communications System with Hybrid Channel Transmission Scheme

In this work, we present the performance analysis in terms of the bit error rate (BER) for an $\mathcal{M}{\text{ - ary}}$ molecular concentration-position modulation ($\mathcal{M}{\text{ - MCPM}}$) based molecular communication (MC) via a diffusion-based system. We consider the discrete-time channel models (DCMs) and their approximations for the considered MC system. We derive the expressions of the probability of error of the $\mathcal{M}{\text{ - MCPM - based}}$ MC system considering a fixed threshold detector and a fixed value of the concentration-bit-wise scaling parameter. We compare the considered channel models for the $\mathcal{M}{\text{ - MCPM}}$ and binary concentration shift keying (BCSK) schemes in the high inter-symbol interference regimes and show through the numerical results that the Poisson approximation of the MC channel model has a lower BER as compared to the other approximations of DCM. Furthermore, we also observe that the Poisson approximation of the channel model for the $\mathcal{M}{\text{ - MCPM}}$ scheme outperforms with an increase in molecular intensity, bit duration, diffusion coefficient, and a decrease in transmission distance.