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ISI Mitigation Techniques in Molecular Communication

Burcu Tepekule, Ali E. Pusane, H. Birkan Yilmaz, Chan-Byoung Chae, Tuna Tugcu

arXiv:1410.8313v1cs.ETcs.IT

TL;DR

MCvD faces ISI and energy-efficiency challenges that limit high-data-rate communication, while receiver decisions also depend on threshold selection. The paper proposes analytical threshold computation, MTSK and residual-molecule power adjustment, and an energy-efficient DFF; it reports lower BER for MTSK and greater energy-efficiency advantage for DFF because of lower computational complexity.

  • Problem

    MCvD must address ISI, energy efficiency, and threshold selection to support high-data-rate communication.

  • Method

    The paper analytically determines the optimum threshold and proposes MTSK, residual-molecule power adjustment, and an energy-efficient DFF.

  • Results

    MTSK significantly decreases bit error rates, while DFF may be more advantageous than MMSE when energy efficiency is prioritized.

  • Takeaways & Limitations

    The proposed techniques target improved communication quality, shorter symbol durations, higher data rates, and energy efficiency.

Abstract

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Molecular communication is a new field of communication where molecules are used to transfer information. Among the proposed methods, molecular communication via diffusion (MCvD) is particularly effective. One of the main challenges in MCvD is the intersymbol interference (ISI), which inhibits communication at high data rates. Furthermore, at the nano scale, energy efficiency becomes an essential problem. Before addressing these problems, a pre-determined threshold for the received signal must be calculated to make a decision. In this paper, an analytical technique is proposed to determine the optimum threshold, whereas in the literature, these thresholds are generally calculated empirically. Since the main goal of this paper is to build an MCvD system suitable for operating at high data rates without sacrificing quality, new modulation and filtering techniques are proposed to decrease the effects of ISI and enhance energy efficiency. As a transmitter-based solution, a modulation technique for MCvD, molecular transition shift keying (MTSK), is proposed in order to increase the data rate via suppressing the ISI. Furthermore, for energy efficiency, a power adjustment technique that utilizes the residual molecules is proposed. Finally, as a receiver-based solution, a new energy efficient decision feedback filter (DFF) is proposed as a substitute for the decoders such as minimum mean squared error (MMSE) and decision feedback equalizer (DFE). The error performance of DFF and MMSE equalizers are compared in terms of bit error rates, and it is concluded that DFF may be more advantageous when energy efficiency is concerned, due to its lower computational complexity.

2 Yonsei Institute of Convergence Technology, Yonsei University, Seoul, Korea

MCvD offers energy-efficient molecular information transfer, but ISI, energy constraints, limited modulation diversity, and empirical threshold selection complicate high-rate communication. The paper proposes analytical thresholding and transmitter- and receiver-side techniques to improve communication quality, data rate, and energy efficiency.

  • I. INTRODUCTION: MCvD is an energy-efficient molecular communication method, but diffusion creates a trade-off among data rate, energy efficiency, and communication quality.Longer symbol durations reduce residual molecules and ISI but lower data rate.
  • I. INTRODUCTION: The paper evaluates transmitter- and receiver-based ISI mitigation techniques, including MTSK, power adjustment, DFF, and MMSE comparison.The proposed techniques are presented as contributions addressing high-rate communication and energy efficiency.
  • I. INTRODUCTION: Existing CSK and MoSK modulation techniques do not directly mitigate ISI, requiring large signal powers for low error rates.The paper identifies insufficient energy efficiency as a consequence of these approaches.
  • I. INTRODUCTION: The paper proposes MTSK to reduce ISI, power adjustment using residual channel molecules, and a lower-complexity decision feedback filter.The filter is proposed as an alternative to MMSE and decision feedback equalizers.
  • I. INTRODUCTION: An analytical technique determines the optimum receiver threshold before transmission instead of selecting it empirically through repeated error-rate evaluation.The empirical approach requires long pilot sequences and repetition when system parameters change.

II. MOLECULAR COMMUNICATION VIA DIFFUSION AND ISI

The paper models MCvD as molecule transport from a point source to an absorbing spherical receiver in a three-dimensional fluid. Molecular propagation follows Brownian motion, and the received signal is formed when molecules reach and are absorbed by the receiver.

  • II. MOLECULAR COMMUNICATION VIA DIFFUSION AND ISI: The MCvD model uses messenger molecules as information carriers between a point source and a spherical receiver with absorbing receptors.Both source and receiver are located in a three-dimensional fluid medium.
  • II. MOLECULAR COMMUNICATION VIA DIFFUSION AND ISI: Messenger molecules diffuse through the fluid according to Brownian motion before arriving at the receiver.Brownian motion is modeled as a continuous-time stochastic process associated with thermal motion.
  • II. MOLECULAR COMMUNICATION VIA DIFFUSION AND ISI: In the simulation model, displacement in each dimension follows a Gaussian distribution with variance 2D∆t.The model independently applies random movement in each dimension at small time steps.
  • II. MOLECULAR COMMUNICATION VIA DIFFUSION AND ISI: The model ignores collisions between messenger molecules for simplicity and uses Brownian-motion dynamics for Monte Carlo simulations.This is an explicit modeling assumption.

A. Absorption rate of a perfectly absorbing spherical receiver

The paper derives the absorption response of a perfectly absorbing spherical receiver from the diffusion equation and uses its time-dependent hitting behavior to guide symbol-duration selection and ISI mitigation.

  • A. Absorption rate of a perfectly absorbing spherical receiver: The diffusion model derives molecule absorption at a perfectly absorbing spherical receiver from Fick’s diffusion equation with relevant boundary and initial conditions.The perfect-absorption limit makes every collision lead to absorption.
  • A. Absorption rate of a perfectly absorbing spherical receiver: The hitting-rate function fhit(t) describes the time-dependent absorption response of the diffusion channel.The paper obtains the hitting rate from the molecule distribution and illustrates it for specified receiver radius, distance, and diffusion coefficient.
  • A. Absorption rate of a perfectly absorbing spherical receiver: 52 ms is the approximate peak time of fhit(t) for rr = 5µm, r0 = 10µm, and D = 79.4µm2/s.At this point, the fraction of absorbed molecules reaches its maximum value.
  • A. Absorption rate of a perfectly absorbing spherical receiver: The symbol duration ts should favor descending hitting probabilities, with p1 > p2 > p3 > ..., to reduce ISI.The first hitting probability should be largest relative to later-symbol contributions.

B. Modulation and demodulation techniques

The section reviews BCSK and BMoSK and explains how residual molecules produce ISI. It motivates new modulation and filtering approaches because existing schemes have energy-efficiency and high-data-rate limitations.

  • B. Modulation and demodulation techniques: BCSK represents bits through messenger-molecule number, while BMoSK represents symbols through the type and number of received molecules.BCSK uses a threshold for bit decisions, whereas BMoSK can compare the received counts of two molecule types.
  • B. Modulation and demodulation techniques: BCSK decisions require a pre-determined threshold, which the literature typically selects empirically using long sequences and error-rate comparisons.The threshold separates bit-1 decisions from bit-0 decisions according to received molecule counts.
  • B. Modulation and demodulation techniques: Residual molecules from previous symbols cause ISI in both BCSK and BMoSK systems.The paper states that BMoSK is less susceptible to ISI than BCSK.
  • B. Modulation and demodulation techniques: BMoSK requires two molecule types and nearly doubles released molecules because bit-0 symbols also use a constant molecule count.This creates an energy-efficiency limitation despite BMoSK’s lower ISI susceptibility.
  • B. Modulation and demodulation techniques: At high data rates, the reviewed modulation techniques are inefficient for both energy efficiency and ISI mitigation.The section also identifies the lack of a non-empirical threshold technique for BCSK sequences.

III. ISI THRESHOLD COMPUTATION TECHNIQUE

The paper develops an analytical method for computing ISI-dependent detection thresholds instead of relying solely on empirical search. It models candidate sequence histories, derives threshold bounds, and uses fixed-point iteration when direct analytic minimization becomes difficult.

  • Empirical threshold calculation requires large received-count samples and repeated computation when system parameters change.
  • Hitting probabilities characterize the diffusion channel, and symbol duration should produce descending probabilities p1 > p2 > p3 > ... to reduce ISI.
  • Each symbol history changes the Gaussian mean and variance, so candidate histories require distinct optimal thresholds.
  • For each candidate, MAP detection yields threshold equations; the overall threshold minimizes the summed candidate error probabilities.
  • For i > 2, the aggregate threshold equation is difficult to solve analytically, so numerical methods and fixed-point iteration are used.
  • With ts = 200ms and M = 100, the example obtains γ*_{2,0} = 4.0189, γ*_{2,1} = 15.1198, and γ*_{2} = 12.7882.

A. Least Mean Squares Regression

The paper uses least mean squares regression to approximate later optimal thresholds after molecule accumulation causes threshold values to converge. The regression output is compared with empirical thresholds and validated using simulated molecule-count distributions.

  • Computing thresholds for large symbol indices becomes increasingly costly because the number of candidate sequences grows as powers of 2.
  • Thresholds increase early in transmission and converge toward a constant as accumulated molecules approach saturation.
  • LMS regression estimates thresholds beyond the first 20 values, while empirical thresholds are also plotted for comparison.
  • For a length-105 random binary message, the LMS-derived threshold lies at the intersection of the conditional molecule-count distributions.
  • Approximately after 100 bits, threshold values converge to a constant that can be used for continuous transmission.
  • Empirical thresholds perform slightly better because they are fitted using information from the particular original message.

1. On the other hand, thresholds

Threshold convergence depends on the probability of bit-0. Lower bit-0 probabilities produce slower convergence because accumulating molecules continue increasing.

  • Lower P[bi = 0] values yield slower threshold convergence because the number of accumulating molecules keeps increasing.
  • Figure 10 presents threshold curves for different values of P[bi = 0].

IV. TRANSMITTER - BASED ISI MITIGATION

The paper proposes two transmitter-based ISI mitigation techniques: MTSK modulation and power adjustment using residual molecules. The methods target ISI reduction and energy efficiency across several modulation schemes.

  • Two transmitter-based techniques are proposed to mitigate ISI.
  • MTSK is an energy-efficient modulation technique that uses two molecule types to reduce detrimental ISI effects.
  • The power-adjustment strategy reuses residual molecules from previous symbols and applies to BCSK, BMoSK, and MTSK.

A. Molecular transition shift keying

MTSK encodes bit-1s with two molecule types selected by the following symbol, reducing ISI from accumulated molecules. Its BER is reported as significantly lower than competing modulation techniques, at the cost of greater system complexity.

  • ISI mitigation: MTSK reduces ISI by decreasing residual molecules from previous symbols, making symbols harder to detect under accumulated interference easier to distinguish.The stated motivation is to distinguish whether the number of received molecules corresponds to the intended symbol.
  • ISI behavior: Residual molecules are concentrated mainly in the immediately preceding time slot, while contributions from two or more earlier slots are less significant.The behavior is illustrated using hitting probabilities p_k for k = 1, 2, ..., 10.
  • MTSK encoding: MTSK encodes bit-0 by emitting no molecules and bit-1 using type-A or type-B molecules selected according to the following symbol.The scheme uses a constant number M of molecules for bit-1 symbols.
  • Detection: MTSK decoding uses separate thresholds for type-A and type-B molecules and decides bit-1 when either molecule count exceeds its corresponding threshold.A bit-0 decision requires both estimated molecule-type bits to be zero.
  • Performance: BER curves from Monte Carlo simulations show significantly decreased error rates with MTSK, while using two molecule types increases system complexity.The comparison used 10^4 realizations and threshold values computed by Algorithm 1.
  • Performance: MTSK is preferred over BMoSK when two molecule types are allowed because the reported communication-quality improvement is very significant.The comparison is made for the same tested sequence and error probabilities.

B. Power Adjustment

The power-adjustment approach reuses residual molecules to maintain the received signal for bit-1 while reducing molecular accumulation. Simulations report lower error rates, but longer memory improves quality at the cost of greater memory requirements and threshold-analysis limitations.

  • Power-adjusted modulation: Power adjustment modifies BCSK, BMoSK, and MTSK to utilize residual molecules from previous symbols.The modified schemes are denoted BCSK-PA, BMoSK-PA, and MTSK-PA.
  • Mechanism: Sending fewer molecules after earlier transmissions can preserve the expected received count for bit-1 while reducing molecular accumulation and subsequent ISI.The method uses residual molecules from previous time slots to maintain the intended received signal.
  • Trade-off: Increasing K improves communication quality but introduces a trade-off between memory length and communication quality.The approach uses a finite memory because continuously calculating effects from many prior symbols is impractical.
  • Threshold limitation: Maintaining a constant received count for bit-1 makes bit-0 counts fluctuate with K, preventing γ∗(i) from being calculated for large i.Simulations therefore use empirically found threshold values in that regime.
  • Performance: Power adjustment decreases error rates significantly for all three modulation techniques in Monte Carlo simulations with memory lengths K = 2 and K = 4.The comparisons used 15,000 realizations on BER curves shown in Figures 16 and 17.

V. RECEIVER – BASED ISI MITIGATION

The proposed decision-feedback filter uses previously detected bits to compute signal-dependent thresholds with lower computational complexity than MMSE equalization. It can achieve comparable BER, but requires more receiver memory and may suffer error propagation.

  • DFF design: The proposed DFF is a new decision-feedback filter for molecular communication designed as a receiver-based ISI-mitigation method.Its block diagram is given in Figure 18.
  • Complexity: DFF has computational complexity O(1), whereas the MMSE equalizer has complexity O(S^3) when distribution-parameter computation is ignored.DFF requires solving only the quadratic equation, while MMSE updates equalizer coefficients as needed.
  • Trade-off: DFF's complexity is independent of filter taps, but matching MMSE BER requires more memory elements.This creates a complexity–memory trade-off between the two equalizers.
  • Threshold computation: With the previous bit estimate available, DFF considers two candidate sequences and computes a signal-dependent threshold by solving a quadratic equation.The threshold calculation assumes previous decisions are correct.
  • Limitations: DFF performance may decrease because feedback based on an incorrect previous decision can cause error propagation.The receiver also becomes impractical if it requires infinite memory, motivating finite-memory formulations.
  • BER comparison: Around a bit error rate of 10^-3, DFF requires memory length S = 35, whereas MMSE requires S = 13.The comparison uses BER as a function of memory length.

VI. RESULTS AND DISCUSSION

The paper evaluates analytical thresholding and transmitter- and receiver-side techniques for reducing ISI and improving energy efficiency in MCvD. Results indicate that MTSK and power adjustment reduce error-related effects, while DFF trades memory for lower computational complexity.

  • Thresholding: An analytical method determines optimal decision thresholds that minimize overall error when system parameters are known.LMS regression is applied to the first 20 threshold values to calculate thresholds for later symbols regardless of sequence length.
  • Thresholding: Monte Carlo simulations verify that the analytical threshold values are optimal for minimizing the overall bit error rate.The analytical thresholds are compared with empirically found thresholds.
  • Transmitter-based techniques: MTSK uses multiple molecule types to increase data rate by suppressing ISI and significantly decreases bit error rates compared with BCSK and BMoSK.The comparison was conducted through Monte Carlo simulations.
  • Transmitter-based techniques: Power adjustment uses residual molecules in the channel and significantly decreases ISI and bit error rate for a fixed signal power across modulation techniques.CSK-PA, MoSK-PA, and MTSK-PA were compared via Monte Carlo simulations; a trade-off exists between PA memory length and communication.
  • Receiver-based techniques: DFF calculates and updates decision thresholds using previously estimated bits, requiring more memory than MMSE to reach the same error rate.Because its optimal-threshold calculation has computational complexity O(1), DFF is more advantageous when energy efficiency is a priority.
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