Higher Order Derivatives: Improved Pre-Processing and Receivers for Molecular Communications

Significant inter-symbol interference (ISI) challenges the achievement of reliable high data-rate molecular communication (MC) links. Inspired by recent results showing the ISI mitigation capability of pre-processing received signals by differentiation, the impact of using higher order derivatives is studied herein. The trade-off between ISI mitigation and noise amplification with higher order derivatives is characterized. Optimal maximum-likelihood sequence detection (MLSD) is investigated as well as low complexity banded MLSD to exploit the pulse narrowing induced by differentiation. Furthermore, analysis suggests the existence of an optimal derivative order. The bit error ratio (BER) for a fixed threshold detector is tightly approximated and employed to find the optimal derivative order. Numerical results confirm the aforementioned trade-off and show that reliable communication can be established using symbol durations considerably smaller than the peak time.