  While molecular communication via diffusion experiences significant
inter-symbol interference (ISI), recent work suggests that ISI can be mitigated
via time differentiation pre-processing which achieves pulse narrowing. Herein,
the approach is generalized to higher order differentiation. The fundamental
trade-off between ISI mitigation and noise amplification is characterized,
showing the existence of an optimal derivative order that minimizes the bit
error rate (BER). Theoretical analyses of the BER and a
signal-to-interference-plus-noise ratio are provided, the derivative order
optimization problem is posed and solved for threshold-based detectors. For
more complex detectors which exploit a window memory, it is shown that
derivative pre-processing can strongly reduce the size of the needed window.
Extensive numerical results confirm the accuracy of theoretical derivations,
the gains in performance via derivative pre-processing over other methods and
the impact of the optimal derivative order. Derivative pre-processing offers a
low complexity/high-performance method for reducing ISI at the expense of
increased transmission power to reduce noise amplification.
