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

Abstract

While molecular communication via diffusion experiences significant inter-symbol interference (ISI), recent work suggests that ISI can be mitigated via time differentiation preprocessing 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.

Towards High Data-Rate Diffusive Molecular Communications: Performance Enhancement Strategies

“…In the section, signal-to-noise ratio (SNR) defines the ratio of the mean transmission power (M ) and the external Poisson noise rate per bit (N λ s ), as Furthermore, the m th order derivative operators are evaluated using the ADS detector to provide a very low complexity receiver design. It is worth noting that the last m samples of each symbol is discarded for the D m -ADS scheme, in order to avoid the non-causal ISI introduced by the forward derivative operator [84], [85]. Specifically, the following operation is performed for detection:…”

“…Overall, [85] show that the D m operator provides powerful ISI mitigation due to compression of the right-tail of the f hit (t) function. As a consequence of this, if the transceiver is able to transmit using large transmission powers, it can circumvent the noise amplification issue and achieve an order of magnitude higher data rates than conventional schemes while preserving reliable communication.…”

“…First proposed by [84]; therein it is observed that applying a time derivative to the received sample vector y is shown to decrease the time dispersion of the signal. These initial endeavors are generalized for an arbitrary derivative order m in [85], and it has been shown that higher order derivatives are able to outperform m = 1 or no derivatives (m = 0). However, it is also shown in [85] that increasing m arbitrarily does not lead to a monotonically improving error performance, as m governs a trade-off between ISI mitigation and noise amplification.…”

“…These initial endeavors are generalized for an arbitrary derivative order m in [85], and it has been shown that higher order derivatives are able to outperform m = 1 or no derivatives (m = 0). However, it is also shown in [85] that increasing m arbitrarily does not lead to a monotonically improving error performance, as m governs a trade-off between ISI mitigation and noise amplification. Herein, we will characterize said noise amplification phenomenon.…”

“…However, in high data rate DiMC systems, this approach heavily underestimates ISI, resulting in poor error performance. That said, due to the aggressive ISI mitigation provided by the D m operator, it is shown in [85] that such a banded MLSD yields operable error performances. Therefore, the D m operator makes MLSDlike detectors considerably more feasible for high data rate DiMC systems.…”