Feedback-Controlled Adaptive Signal Detection Scheme for Diffusion-Based Molecular Communication Systems

Abstract

This paper proposes a feedback-controlled adaptive method for detecting signals in diffusion-based molecular communication (MC) systems. Signal detection via a receiver nanomachine is a critical challenge for the exchange of information in MC systems. Incorrect estimations or small errors in signal detection can lead to high data detection errors. Existing methods for improving detection performance require high time costs or computational complexity. This paper proposes a simple and practical method that enables receiver nanomachines to automatically estimate signal detection times according to the measured molecular concentrations and weighted feedback errors. The proposed method adjusts the detection time even when the initial parameter values of the system are unknown to the receiver nanomachines. Simulations were performed to evaluate the bit error rate performance of the proposed and existing methods in terms of different data rates, transmission distances, and estimation error lengths under different initial conditions. The simulation results reveal that the implementation of the proposed method is simpler and demonstrates superior performance compared with that of existing methods.

1. Introduction

Molecular communication (MC) is a promising communication technique for use in nanoscale machine systems [1]. A transmitter nanomachine emits molecules that propagate in a fluid environment to a receiver nanomachine via diffusion. These molecules are absorbed and decoded by the receiver nanomachine. MC is anticipated to be a key innovative technology for nanoscale machines for healthcare, environmental protection, agriculture, and nanomedicine applications [2,3].

Compared with traditional electromagnetic communications, MC systems provide the following distinct features: (1) They use molecules as a communication carrier, and signal transmission occurs by changing the molecular emission time, concentration, or type. (2) The emitted molecules propagate via diffusion, and their movement is governed by Brownian motion [3]. (3) Because of the size and power-consumption limitations of nanomachines, applications are limited to slow communication systems with low energy consumption. Consequently, the design of MC systems, including signal modulation, signal detection, synchronization, and transceiver optimization, poses new fundamental challenges [4,5,6]. The two most critical challenges of system design are how to design transmitter and receiver nanomachines that can encode and modulate information into signals, and how to detect and decode information from the received diffused signals, respectively.

In terms of signal detection, much research on MC assumes that, in nanomachines, perfect time synchronization occurs for modulation and demodulation [7]. Methods based on single-spike feedback signals were proposed [8]. A transmitter estimated the distance by measuring the round-trip time (RTT) or signal attenuation of the received feedback signal. Both schemes employed the distance function of RTT and molecular concentration to calculate the distance. These methods were expensive, and the transmitter and receiver nanomachines had to be tuned for the diffusion coefficient or number of transmitted molecules. However, in real MC systems, automatic synchronization does not occur. In an MC system, in contrast to traditional radio communications, information is transmitted through the slow process of diffusion-based propagation. This process results in intersymbol interference (ISI), which impairs the accurate detection of subsequent symbols. To decode a signal, a maximal-likelihood estimator was proposed in [9] for a clock offset between two nanomachines. A transmitter recorded the sending time of the message and passed it to the receiver. The receiver then used this information to estimate the clock offset. Clock synchronization between a transmitter and receiver in a mobile MC system was investigated in [10] to estimate the clock offset using the least-squares and peak-time methods. A synchronization technique was proposed in [11] that utilized synchronization and information molecules with different diffusion coefficients. The start of the signal was estimated on the basis of the high concentration of synchronization molecules, which had a higher diffusion coefficient than that of the information molecules. A two-way time synchronization scheme was proposed in [12] that considered the use of a bidirectional flow channel for the exchange of forward-feedback messages. Additionally, several studies were conducted that used techniques such as quorum sensing [13], blind synchronization with delay [14], and signal-peak observation [15,16].

For event detection, a feedback-based method for detecting signal-peak concentration was proposed [17]. Although the time cost was reduced, estimation accuracy was low. Distance-estimation schemes based on molecular concentration were proposed to improve signal detection performance [18,19]. These studies estimated the distance by measuring either the peak concentration time or the received concentration energy. However, it had a higher requirement in terms of system complexity. Moreover, it required an initial value of the estimated distance by detecting the peak concentration time at the receiver nanomachine. Furthermore, it required several iterations for convergence, and the time cost or computational complexity was significantly high.

Although previous studies have demonstrated improved performance in their proposed synchronization schemes, the complexity of nanomachines has limited performance. In particular, the use of different molecular types or instant message-sending times could be too complex for the computational ability of the transmitter or receiver nanomachine, thereby limiting the adaptability of such schemes in real MC systems. Furthermore, many studies have assumed that the concentration detection time remains constant. This assumption means that when an initial molecular impulse is emitted, the receiver always detects the signal and decodes it after an elapse of a certain time. However, a constant detection time cannot be maintained due to propagation delays or random molecular movements. A small error at the start of detection can adversely affect the detection of signals. Moreover, in practice, when the system parameters are unknown, the initial detection time is not available to the receiver. Therefore, to correctly decode the information under various MC environments, a simple and adaptive signal detection method is needed.

This paper proposes a feedback-controlled adaptive method for signal detection in a diffusion-based MC system. The proposed method is designed to enable a receiver nanomachine to automatically adapt the detection times on the basis of the measured molecular concentrations and weighted feedback errors. The proposed method adjusts the signal detection time even when the initial parameter values of the system are unknown to the receiver. In addition, the proposed method does not require tuning of the system parameters between the transmitter and receiver. The main contributions of this work include the following: (1) The detection time is automatically adapted to minimize the ISI- and noise-related detection errors under time-varying channel conditions. (2) The proposed method can be easily realized in a real MC system; the receiver nanomachine can be simply implemented using a single type of molecules even when the system parameters are unknown to the receiver. (3) The proposed method can be easily integrated with existing modulation techniques or asynchronous modulation systems, which can assist in the implementability and scalability of MC systems.

The remainder of this paper is organized as follows. Section 2 introduces the proposed signal detection method for MC based on a diffusion model and provides analysis of the system convergence. To evaluate the proposed method, the results are presented in Section 3. Conclusion and future works are presented in Section 4.

2. Proposed Method

Section 2 contains two parts: the system model and feedback-controlled signal detection. Section 2.1 describes the diffusion-based MC model that considers the signal residuals and Brownian noise. Section 2.2 presents the proposal for a feedback-controlled adaptive detection scheme and shows a numerical example of the proposed scheme.

2.1. System Model

This paper considers a diffusion-based molecular system that comprises two nanomachines, i.e., a transmitter and a receiver, and a fluid propagation channel. To transmit information, the transmitter emits a single type of molecules. The emitted molecules propagate through a diffusion-based fluid medium under the action of Brownian motion. The receiver absorbs and decodes the molecules according to the time-varying molecular concentrations.

We assumed that M bits were available to send a symbol with equal time interval $T_e$ during symbol duration $T_s$, i.e., $T_s=M{T}_e$. Let $d_i=\{b_0,b_1,\cdots ,b_{M-1}\}$$(i=0,\cdots ,\infty )$ be the i-th symbol, which is a binary information sequence in which $b_k\in \{0,1\}$$(k=0,\cdots ,M-1)$. The transmitter emits an impulse of Q molecules to send a bit $b_k=1$. However, no molecules are released to send $b_k=0$. The transmission distance between the two nanomachines is denoted as r. According to Fick’s law of diffusion [20], the molecular concentration measured at the receiver at time t is expressed as follows:

$$\begin{array}{c}\hfill f\left(t\right)=\frac{Q}{{\left(4\pi Dt\right)}^{\frac{3}{2}}}exp(-\frac{r^2}{4Dt}),\end{array}$$

(1)

where D is the diffusion coefficient. According to (1), the concentration at a point at fixed distance r from the transmitter reaches its peak at $t_m=\frac{r^2}{6D}$, and the peak value of $f\left(t\right)$ is $f_{max}={\left(\frac{3}{2\pi e}\right)}^{1.5}\frac{Q}{r^3}$. After sending the k-th bit in $d_i$, the molecular concentration measured by the receiver at time t$(k{T}_e\le t<(k+1)T_e)$ becomes

$$\begin{array}{c}\hfill c\left(t\right)=\sum _{j=0}^k{b}_j[f(t-j{T}_e)+n_j\left(t\right)],\end{array}$$

(2)

where $n_j\left(t\right)$ represents the counting noise induced by the j-th emitted molecules, as modelled by the Brownian noise on the basis of random molecular motion. Many studies have assumed that peak time $t_m$ remains constant, which implies that when an initial molecular impulse is emitted, the receiver always detects the signal and decodes it after $t_m$ has elapsed. However, a constant detection time cannot be maintained due to propagation delays or random molecular movements under time-varying channel conditions. A small error at the start of the detection adversely affects the detection of the signals. Moreover, if the system parameters are unknown, the value of $t_m$ is not available to the receiver. Therefore, to correctly decode the information, an estimation of the detection time is necessary.

Figure 1 shows the concentration of the received molecules at various distances r and molecules Q. Figure 1a shows that the concentration inversely decays with the transmission distance. The peak time when the concentration reaches its maximum becomes slower with the distance. In addition, the concentration level at the peak time sharply decreases with the distance, which limits the signal decoding performance. Figure 1b shows that the peak time was independent of Q, but the concentration level at the peak time decreased as Q decreased. In other words, the changes in peak time and maximal concentration level were affected by the system parameters.

2.2. Feedback-Controlled Signal Detection

Let ${\widehat{T}}_d\left(k\right)$$(k=0,\cdots ,M-1)$ be the estimated detection time for the k-th information of $d_i$ in $T_s$. The receiver samples the concentration level at every $T_p$, i.e., $T_p=\frac{T_e}{N_s}$, where $N_s$ is the number of sampling during $T_e$. Among the samples, the receiver measures the peak concentration level at time $t_d\left(k\right)$, which is defined as the peak time of the sampled molecule for the k-th information. The transmitter emits an impulse of molecules according to binary information sequence $d_i$. H is assumed as the maximal length of ISI, and L (<H) is introduced as the maximal number of historical estimation errors to be reflected for adjustment in the subsequent detection time. Then, the receiver estimates the signal detection time of the $(k+1)$-th bit $(0\le k<M-1)$, ${\widehat{t}}_d(k+1)$, which is determined as follows:

$$\begin{array}{ccc}\hfill {\widehat{t}}_d(k+1)& =& {\widehat{t}}_d\left(k\right)+{\alpha }_k\sum _{j=0}^{min(k,L)}{\alpha }_j(t_d(k-j)-{\widehat{T}}_d(k-j))\hfill \\ \hfill {\widehat{T}}_d(k+1)& =& {\widehat{t}}_d(k+1)+k{T}_e,\hfill \end{array}$$

(3)

where ${\widehat{t}}_d\left(0\right)={\widehat{T}}_d\left(0\right)=t_m$ when the system parameters are known to the receiver. Otherwise, the values of ${\widehat{t}}_d\left(0\right)$ and ${\widehat{T}}_d\left(0\right)$ are set to random values. The values of ${\alpha }_k$ and ${\alpha }_j$ were set as ${\alpha }_k=\frac{2}{L^{*}+1}$ and ${\alpha }_j=\frac{L^{*}-j+1}{L^{*}}$, respectively, where $L^{*}=min(k,L)$.

In accordance with (3), the estimated detection time for the subsequent bit is adapted according to the weighted feedback errors $(t_d-{\widehat{T}}_d)$. The receiver measures the initial molecular concentration at ${\widehat{T}}_d\left(0\right)$ and decides the bit by comparing the measured concentration using decision-making threshold $c_r$. The receiver measures the initial peak time of the molecular concentration among the samples, i.e., $t_d\left(0\right)$, and uses it to estimate next detection time ${\widehat{t}}_d\left(1\right)$ using previously estimated value ${\widehat{T}}_d\left(0\right)$. Thus, the detection time for the next bit is adjusted in the direction to minimize the estimation error. Eventually, according to (3), this control process causes the detection time to converge to an accurate time for maximal molecular concentration, i.e., ${\widehat{T}}_d=t_d$. Note that only when the concentration level is higher than $c_r$, the peak time information is used for estimation of the next detection time. If it is less than $c_r$, the previous estimated detection time is used as is to reduce the effect of the detection time under a rapid change in concentration or dynamic channel condition. Algorithm 1 presents the detailed procedure of the proposed method.

Algorithm 1: Proposed detection method.

Figure 2 shows a numerical example of the proposed method using the measured molecular concentration at the receiver when $d_1=\{1,0,1,0\}$, $i=1$, and $M=4$. Both ${\widehat{t}}_d\left(0\right)$ and ${\widehat{T}}_d\left(0\right)$ are considered random values. When the molecules reach the receiver, $t_d\left(k\right)$ $(k=0,1,2,3)$ is measured by the receiver. The next detection time ${\widehat{T}}_d\left(k\right)$ $(k=1,2,3)$ is estimated using (3). Threshold $c_r$ is made proportional to peak $f_{max}$, i.e., $c_r=\gamma f_{max}$, where $0<\gamma <1$. Hence, the receiver decides for the subsequent bit by comparing the measured concentration at ${\widehat{T}}_d$ with $c_r$. Figure 2 shows that if the received molecular concentration at each ${\widehat{T}}_d\left(k\right)$ $(k=0,1,2,3)$ exceeds the threshold $c_r$, the proposed method decides for bit-1; otherwise, the decision is bit-0. Figure 2 shows that the actual maximal molecular concentration points are indicated by the filled circles, whereas those of the received molecular concentrations at the proposed signal detection times are denoted by asterisks. Figure 2 shows a gradual decrease in estimation error $|t_d\left(k\right)-{\widehat{T}}_d\left(k\right)|$, which enables accurate data decoding.

3. Simulation Results

This section presents the simulation results using MATALAB to evaluate the effectiveness and performance of the proposed method. The bit error rate (BER) performance of the proposed method was compared with that of the binary concentration shift keying (CSK) [21] and faster molecular-based CSK (FM-CSK) methods [11]. The CSK method is a conventional approach that uses fixed-time synchronization-based detection. It requires knowledge of the statistics for the quantity of molecules that arrive at the sampling time. The FM-CSK method provides a beneficial effect on BER performance by using two types of molecules with different diffusion coefficients. Bit-1 and bit-0 were transmitted by the emission of Q molecules and without molecules, respectively. The $\gamma$ value of $c_r$ was set to 0.8, and the initial detection time was set to a random value.

Table 1. Simulation parameters.

Parameter	Value
Distance between two nanomachines r	400∼1100 nm
Number of bits in a symbol M	4, 8, 12
History length L	1∼7
Diffusion coefficient D	$2.2\times {10}^{-9}$ m2/s
Number of molecule released from transmitter Q	$5\times {10}^5$
Symbol duration $T_s$	8 ms
Sampling number $N_s$	5

lists the simulation parameters, and the results were averaged over 100 iterations.

Figure 3 shows the BER performance of the proposed, CSK, and FM-CSK methods in cases where $M=4$, $M=8$, and $M=12$, respectively. The transmission distance between the transmitter and receiver was set between 400 and 1100 nm. Figure 3 clearly shows that, with the increase in transmission distance, the BER values of all three methods also increased. This result indicates that a higher M value led to a higher BER because the severity of the disturbance of the diffusion-based channel was intensified as the distance increased, which resulted in a larger detection error. Furthermore, as the number of bits of the symbol increased, BER was deteriorated by a stronger ISI. Among the three methods, CSK demonstrated the worst performance at all M values and distances, except when the distance was less than 450 nm, because CSK employed a fixed-time synchronization-based detection that is sensitive to ISI in a fluctuating environment. On the basis of the peak concentration levels of the synchronization molecules, a small initial estimation error could significantly affect the detection accuracy. Conversely, in terms of BER performance, the proposed method consistently outperformed the CSK and FM-CSK methods at all distances and M values. Moreover, no significant increase occurred in the BER performance curve of the proposed method with the increase in either M or distance compared with those in the CSK and FM-CSK methods.

Figure 4 shows the effect of L on the BER performance. The value of L was $L=1\sim 7$ at various distances between $r=600$ and 1100 nm, respectively. The value of M was set to 8. The results reveal that, for a distance of less than 800 nm, the increase in L did not significantly affect BER. However, at distances of more than 900 nm, a higher L value evidently led to a lower BER, which means that the more historical the data for the reflection are, the more helpful the proposed method is in reducing the estimation errors for longer transmission distances between transmitter and receiver.

4. Conclusions

This paper proposed a feedback-based signal detection method for MC systems that uses measured molecular concentrations and weighted feedback errors to control the detection time. The proposed method adjusts the detection time even when the initial parameter values of the system are unknown to the receiver nanomachines. The proposed method is simple and can be easily integrated with existing modulation techniques by automatically adjusting the detection time without extra functions by the receiver. The simulation results reveal that, when compared with the existing methods, the implementation of the proposed method is simpler and demonstrates superior performance. A scheme to determine the optimal value of the decision threshold in any environment needs to be investigated in future works. In addition, a distance estimation technique for the decision threshold and high-accuracy performance of MC systems will be investigated. Lastly, the actual implementation of MC systems is necessary in order to confirm the superiority of the proposed algorithm.