# On the Design of Matched Filters for Molecule Counting Receivers

## TL;DR

This paper develops optimal matched filters for molecular communication receivers that account for diffusion noise, ISI, and external interference, significantly improving detection performance over existing methods.

## Contribution

It introduces a novel matched filter design tailored for molecular communication systems considering multiple impairments, with derivations and performance analysis.

## Key findings

- Proposed filter maximizes SIR in molecular communication.
- Filter reduces to sum detector or correlator in special cases.
- Simulation shows significant performance improvement over benchmarks.

## Abstract

In this paper, we design matched filters for diffusive molecular communication systems taking into account the following impairments: signal-dependent diffusion noise, inter-symbol interference (ISI), and external interfering molecules. The receiver counts the number of observed molecules several times within one symbol interval and employs linear filtering to detect the transmitted data. We derive the optimal matched filter by maximizing the expected signal-to-interference-plus-noise ratio of the decision variable. Moreover, we show that for the special case of an ISI-free channel, the matched filter reduces to a simple sum detector and a correlator for the channel impulse response for the diffusion noise-limited and (external) interference-limited regimes, respectively. Our simulation results reveal that the proposed matched filter considerably outperforms the benchmark schemes available in literature, especially when ISI is severe.