Linear Receiver Design for Time-Varying Poisson Molecular Communication Channels with Memory

This work investigates a novel approach for designing the linear filter and the threshold of the memory-less detector in the receiver of a diffusion based molecular communication system. We focus on the case where the transmitted symbols propagate through a Poisson channel with memory that introduces inter-symbol interference. Inspired by the theory of matched filtering under Poisson regime and considering all the possible mean values of the interference, we propose two new design methods for computing the coefficients of the filter. While in the development of the theory under Poisson regime the interference is not considered in the design of the filter, in our proposal we take it into account in the time-variation of the mean value. Since the proposed approach gives better performance for low transmission rate, another design based on linear programming is proposed for the high-rate case. For the design of the detector's threshold we use an averaging method over the output of the receiving filter. The performance of the two proposed designs, in terms of bit error rate, is compared to that achieved by an approach which is based on the maximization of the signal-to-interference plus noise ratio (SINR). We show that our design achieves almost the same performance of the maximum SINR one with the advantage of lower complexity.