A Learning Automaton-Based Algorithm for Maximizing the Transfer Data Rate in a Biological Nanonetwork

Featured Application

This protocol can be used for biological nanonetworks utilizing synthetic biology in order to transfuse the biological entities with the appropriate characteristics.

Abstract

Biological nanonetworks have been envisaged to be the most appropriate alternatives to classical electromagnetic nanonetworks for applications in biological environments. Due to the diffusional method of the message exchange process, transfer data rates are not proportional to their electromagnetic counterparts. In addition, the molecular channel has memory affecting the reception of a message, as the molecules from previously transmitted messages remain in the channel, affecting the number of information molecules that are required from a node to perceive a transmitted message. As a result, the ability of a node to receive a message is directly connected to the transmission rate from the transmitter. In this work, a learning automaton approach has been followed as a way to provide the receiver nodes with an algorithm that could firstly enhance their reception capability and secondly boost the performance of the transfer data rate between the biological communication parties. To this end, a complete set of simulation scenarios has been devised, simulating different distances between nodes and various input signal distributions. Most of the operational parameters, such as the speed of convergence for different numbers of ascension and descension steps and the number of information molecules per message, have been tested pertaining to the performance characteristics of the biological nanonetwork. The applied analysis revealed that the proposed protocol manages to adapt to the communication channel changes, such as the number of remaining information molecules, and can be successfully employed at nanoscale dimensions as a tool for pursuing an increased transfer data rate, even with time-variant channel characteristics.

1. Introduction

Molecular communications have recently gained attention as noteworthy candidates in the research of nanonetworking. Referred to as biological nanonetworks (BNs), networks of this type utilize molecular mechanisms to convey information using mostly chemical signals. This is an emerging field which has great potentials to provide a pivotal alternative to traditional electromagnetic communications for use in biological environments. BNs utilize small particles and biota such as molecules or plasmid vesicles to deliver information. Owing to the peculiarities of the communication channel, this type of network in not suitable for the direct transfer of the established communication protocols, instead requiring new kinds of algorithms tailored to the unique characteristics of the biological environment and the limited capabilities of the communication nodes.

Owning unique merits such as biocompatibility, biodegradability, low energy consumption and inherent energy management, BNs have attracted attention due to their ability to be incorporated into various interdisciplinary applications (such as pharmaceutical, medical, environmental and industrial), and have become the dominant communication paradigm in biological applications. A molecular communication nanonetwork is based on the deployment of engineered biota, or other bio-inspired devices, or even artificially fabricated structures as part of a biocompatible nanomachine. According to the established field work, there are three different types of molecular communications (MCs) based on the way the information disseminates through the medium [1,2]: walkaway-based, advection-based and diffusion-based. In this work, a diffusion-based communication system is under consideration. In this type of communication system, information propagation is realized mostly through spontaneous diffusion, inside a common Newtonian medium. A well-known type of this communication is the calcium signaling among cells, through the ligand–receptor binding mechanism [3,4,5].

While the characteristics of the aforementioned models are well studied, their application in a communication system entails the problem of signal detection due to the stochastic nature of the movement of the signaling molecules. Dictated by the aforementioned need, various signal detection schemes have been proposed [6,7,8]. The noise, acting as an unwanted signal, severely limits the ability of the receiver to detect the transmitted signal. The dominant noise considered in this type of nanonetwork is counting noise, which is considered as an additive signal-dependent noise with a zero mean [9].

The authors of [10] provided all the latest contributions related to modulation, coding and detection techniques for a typical transmitter–receiver architecture. Nakano et al. [11] provided a comprehensive review on mobile MCs. In [12], the authors presented the key research directions towards high-data-rate molecular communications. The authors of [13] studied a system with modified concentration-shift-keying-based modulation, to release a larger amount of signaling molecules for bit 1 than bit 0. The received signal is reconstructed using average distance variation, and it is subtracted from the total received signal in subsequent bit duration, by applying a maximum a posteriori rule. The results showed a lower bit error rate from solutions like the one by G. Chang et al. [6], which uses a concentration-based adaptive threshold detection method. In another similar work for adaptive threshold detection in molecular communications [14], the authors proposed a simple algorithm where in each step, the number of molecules that arrived is compared to the number of received molecules during the previous bit period. If in the previous step the number of molecules is less than the one in the current step, the algorithm outputs a message reception, and in contrast to fixed threshold detectors, it exploits the intersymbol interference in the threshold determination.

Under the same rational, in this work a simple and applicable learning automaton-based algorithm is presented as a suitable tool to reach maximum transfer data rate in diffusion-based wireless BNs (the term wireless is defined as nanonodes not interacting via the established biological signaling pathways but mainly via released information molecules). The algorithm does not depend on predefined thresholds for the detection of the incoming messages, but keeps count of the times the concentration of the information molecules near the receptor increases and subsequently decreases. Via the learning automaton process, nodes rectify the required numbers of ups and downs for a message detection. Furthermore, in every successful iteration, the aforementioned criteria are amended so as to provide faster response and higher transfer data rates between transmitter and receiver. The proposed scheme, in comparison to other solutions, does not rely on prior knowledge of the diffusion coefficient of the signaling molecules or the quantity of transmitted molecules, as in [13]. Moreover, it does not need the presence of a time synchronization infrastructure, as in [14], compensating for the additional processing requirements.

The organization of this paper is as follows: Section 2 demonstrates the proposed simulated system model and its theoretical foundations. In Section 3, the learning automaton is presented, and in Section 4 the performance of the protocol is evaluated. In Section 4.1 and Section 4.2, major points from the results are discussed, along with possible future extensions. Finally, Section 5 concludes this work.

2. System Model

2.1. Theoretical Background

The most common method to set up a biological nanonetwork is to use signaling molecules in order to encode the information under an on-off keying (OOK) concentration-based modulation, and rely on the Brownian motion for the message propagation (we exclude chemotactic effect because it is out of the scope of our work). In this model, communicating entities release information molecules into the intercellular medium and through the ligand–receptor binding process; each party measures the particle concentration in its vicinity and reconstructs the transmitted message from the received pulses. Fundamental to the BN is the fact that the molecular channel has an inherent memory and the diffused substance remains in the channel, requiring either low or high concentrations for the transmitted message [1,15].

The main driving force for binding is the unbound ligand concentration, meaning that the model is based on the law of mass action, just like diffusion does. Once the diffusion process transfers the information molecules to the receiver, the latter counts the number of occupied binding sites to measure the concentration, as shown in Figure 1, and reacts accordingly by releasing signaling molecules as the response to the received message. Each one of these sites can trap only one molecule at a time for a period of time equal to the residence time (RT). These molecules are bound to only one signaling molecule [16,17]. As the concentration of the signaling molecules near the receiver’s surface periphery increases, the probability of a successful connection also increases. It should be noted here that the receptor concentration is held constant for simulation purposes, and the ligand is varied.

2.2. System Setup

With the purpose of studying the maximum practical transfer data rate of a system consisting of one base station (BS) and multiple nodes under the rules of a learning automaton-based reception algorithm, we devised a number of simulation scenarios. The simulator was developed on an agent-based paradigm, and for this purpose the ANYLOGIC commercial simulation platform [18] was utilized. Based on the principles of IEEE P1906.1/Draft 1.0 Recommended Practice for Nanoscale and Molecular Communication Framework [19], the appropriate simulation elements were considered (transmitter, receiver, message, message carrier and the medium). Moreover, the requirements for any molecular communication framework were also met, discerning five components: message carrier, motion component, field component, perturbation and specificity (for a complete analysis, the reader is referred to [20]).

The starting point of the channel modeling is Fick’s laws. We focus on the point-to-point link between the BS and one node, Figure 2, even though all communication nodes are able to retransmit without any operational outage in a broadcast scheme. Information molecules propagate from the transmitter to the receiver according to the concentration gradient. The BS initiates the communication by releasing a pulse and the nodes respond back as soon as they detect the pulse.

Figure 2 shows the simulation system used in this work. At the center of the simulation area resides the BS, and someone can discern its sensing radius, being the circle that envelops the red figure. Accordingly, all the other nodes have the same sensing radius, inside which the signaling molecules can be trapped from the receptors. Different colors stand as the different types of information molecules released from the communication parties. In a multinode environment, the BS is able to release different types of molecules for different receiver nodes. In this work, we consider a unicast type of communication in order to remove the possibility of saturation for the binding sites.

Upon reception, BS sends the next message immediately in order to minimize delay and maximize transfer data rate, in a continuous process. Every receiver has its own type of information molecules in order to mitigate the inter-link interference (ILI), which emerges when the receiver receives other transmitters’ molecules [21].

3. Learning-Automaton-Based Communication Protocol for a High Data Rate

The main objective of the proposed protocol is to provide an efficient way to enhance network performance, while retaining the ability to adapt to environmental changes. Contributing to this aim, a simple (so as to be easily adopted from the biological nodes) yet effective algorithm was developed, in order to detect an incoming pulse without the use of any predefined threshold. The algorithm supervises the number of times the moving average of the perceived concentration decreases after a significant (relevant to the total concentration) rise in the concentration. That way, the local maximum is determined for each pulse (rise phase), followed by the appropriate number of decreases in the concentration (drop phase). Specific initial values for these two parameters (numbers of ascents and descents) are not considered as a prerequisite due to the operation of the LA.

As some of the previous works in the field based their detection algorithms on predefined thresholds, we wanted a solution that could be applied with an “ad hoc”-like manner, meaning that there should be no a priori knowledge of any of the operational parameters of the system. That being the case, the proposed algorithm has two basic parameters: Firstly, the number of required ascensions after a “local maximum”. While this maximum may not be the absolute maximum, yet it may be the absolute one for the received pulse. In regard to this, in Figure 3 the number of received molecules having various velocities and the same BS–node distance were simulated to show the importance of the velocity in the perceived concentration. As shown from the red line, the highest local maximum was at around 32 s. Yet, the node was able to sense the message only after 55 s, as the algorithm tried to find a sufficient number of ascendings followed by equivalent descendings. This is the novelty of this work, along with the learning automaton procedure, as it does not rely on any knowledge from the network to discern an incoming pulse-message.

Likewise, for the blue line, the decreased speed of the information molecules resulted in a long tailed reception pattern. The highest local maximum was perceived at around 75 s, and the algorithm was not able to discern a pulse until the point of 200 s due to the slow decay. Finally, in the last case shown in the figure, the green line shows the result of an even smaller velocity (18 μm/s) with a local maximum at around 110 s. Lower velocities for the signaling molecules mean that the received pulse will have a lower local maximum and will need more time to clear the channel. Due to the operation of the proposed detection algorithm, the node is not able to discern the incoming message up to the point of 270 s that is shown in the Figure, as the number of declines related to the inclines is not sufficient for the message detection and requires more time to decrease the perceived density from the the remaining molecules. Due to the long tailed graph, in this simulation case, the operation of a learning automaton is essential in order to adapt its parameters.

Learning automata (LA) [22] are artificial intelligence tools that can be applied to learn the characteristics of a system’s environment. LA do not need any knowledge of the environment they operate in or any analytical knowledge of the task to be optimized in order to function properly. A LA is a finite state machine tool which improves its performance by providing feedback from environments with mercurial conditions, such as the BNs. As shown in Figure 4a, there is a set of possible actions $B_i\left(n\right)$, along with the corresponding probabilities $P_i\left(n\right)$. $p_1\left(n\right)$$p_2\left(n\right)$ …$p_m\left(n\right)$ constitute a vector which represents the probability distribution for m actions at each instant n. It holds that ${\sum }_{i=1}^m{p}_i\left(n\right)=1$. Initially, the LA has no prior knowledge about the environment it operates in, and as a consequence, all initial probabilities are the same. At each iteration n, the action $b_i$, $1\le i\le m$ is selected with probability $p_i\left(n\right)$. The action taken by the automaton corresponds to a stochastic reaction $A_i\left(n\right)$, which is used to update the probability vector. Upon completion of the n iteration, the LA selects the next action based on the updated probability vector $p(n+1)$. This results in different update actions for each probability, based on the feedback received from the environment. After a number of iterations, the LA in its theoretical form will select the optimal action that has the minimum penalty probability vector.

The use of LA, in the context of this study, is the detection of the optimal values for the numbers of ascensions and descensions that should be taken into consideration from the message detection algorithm. Via the operation of the LA, the response from the BS (stands as the environment for the LA) is being translated into the probabilities for each of the two parameters: to increase or to decrease. Figure 4b shows the 3 different set of actions followed by the LA. State 1 is the preferred state whenever the node misses a transmitted message (network environment $b=-1$), and the protocol must decrease the ascensions and increase the descensions. The opposite applies for state $\left(2\right)$ ($b=1$ and therefore an additional message has been sensed), and the third state $\left(3\right)$ ($b=0$) is the one where the node successfully receives the message transmitted from the BS. In the latter state, only the number of descensions is decreased, seeking the maximum transfer data rate.

The LA has to decide in each state which selection will minimize the penalty and will be the next state. Assuming that the LA is at state 1 (the orange cycle in Figure 4b) and the node running the LA receives a feedback of $a_i=1$, then the algorithm will update the probability vector, and at the next iteration, the red cycle state will be the favorable one. Whenever the feedback is $a_i=0$, the system will promote the transition to the state 3 (green cycle). Related to the specific actions, if the LA is at state 2 and the environmental response is translated to a lost message, then the favorable transition will be towards state 1. At the same time, the LA will relax the required number of ascensions, as the lost message is the result of a low density pulse. If the LA is at the state 1 and the system receives positive feedback, meaning that it sensed exactly the message that the BS sent, then the favorable direction would be towards the state 3. The system will remain at that state as long as it receives the exact number of messages that have been sent from the BS (action b = 0). It should be noted that the most visited state should be state 3, as it means that the node has received successfully the message that the BS has sent (in that case, the action b = 0 will be selected again) and just relaxes the number of descensions in order to detect the message as fast it can in order initiate the response from the node and increase the transfer data rate between the communicating nodes.

The probability update scheme is described based on the following relations. Relations (1) are applied for environmental response $b=-1$ (before normalization); relations (2) are applied for environmental response $b=1$; and finally, relations (3) are applied most of the time, as the node operates towards the maximum transfer data rate (environmental response $b=0$). Coefficient b is a multiple of a so as to promote the last probability over the other two.

$$P_1(t+1)=P_1\left(t\right)+a-a{P}_1\left(t\right),P_2(t+1)=P_2\left(t\right)-a{P}_2\left(t\right),P_3(t+1)=P_3\left(t\right)-a{P}_3\left(t\right)$$

(1)

$$P_1(t+1)=P_1\left(t\right)-a{P}_1\left(t\right),P_2(t+1)=P_2\left(t\right)+a-a{P}_2\left(t\right),P_3(t+1)=P_3\left(t\right)-a{P}_3\left(t\right)$$

(2)

$$P_1(t+1)=P_1\left(t\right)-b{P}_1\left(t\right),P_2(t+1)=P_2\left(t\right)-b{P}_2\left(t\right),P_3(t+1)=P_3\left(t\right)+b-b{P}_3\left(t\right)$$

(3)

As there are two parameters, the available combinations are four; however, we opted only for the case where the first parameter increases and the second decreases, and the exact opposite case. The reason for such a choice relies on the fact that whenever a transmitted message is lost, the algorithm should relax the number of required increases and at the same time increase the number of required decreases, in order to sense pulses with shallow curves. As shown in Figure 5, pulses with different numbers of signaling molecules result in various reception patterns. In order to demonstrate the difference, we simulated a scenario where the BS releases two pulses, one at a time, having different numbers of signaling molecules with the same velocity. In the first case (green line), the BS transmits a pulse with a high number of information molecules. As a direct result, the concentration of molecules at the receiver side increases rapidly to a high value (having a maximum value of 50 molecules around 45 s) and has a clear decline (highlighted with the red line).

On the other hand, in cases where the BS transmits a pulse of a significantly lower number of molecules, as shown in Figure 5 (purple line), the receiver node senses a decreased concentration (maximum value of 18 molecules) at a later time point (around 100 s). The proposed algorithm senses an incoming pulse only after a clear decline in the perceived concentration, and this means that pulses with steeper curves are faster and more reliably received from the receiver. In cases where the node senses inaccurately more than one pulse, even if the BS has sent only one, the algorithm increases the number of required rises and reduces the number of required decreases so as to be able to adapt to steeper curves of concentration.

The main idea behind the proposed work is to provide a way to identify any type of incoming concentration graph without prior knowledge of the channel’s characteristics or the operational ones, such as the number of transmitted molecules, their diffusion coefficient and the duration of the transmission slot. Higher concentration transmission pulses result in high incline graphs; and low concentration pulses, for the same distance, result in shallow incline graphs. In order for a node to sense an incoming pulse, this incline should be followed by an equivalent decline without a time restriction. This means that for steeper inclines, as the algorithm reaches a local maximum, it starts counting the number of declines. If in the meanwhile it reaches another local maximum, it resets the number of declines and starts over. That way, after the highest local maximum, followed by a number of declines, the node decides that it has received an incoming message. Related to Figure 5, the node that senses the red drawing line has the highest local maximum at around 45 s, and it is able to discern the pulse after almost 50 s. On the other hand, the node that senses the blue–purple drawing line has the highest local maximum at around 100 s, but it takes almost another 100 s to discern the incoming pulse.

The algorithm also decreases the number of the required declines after every cycle in pursuance of a faster response, resulting in a higher transfer data rate. Even though this continuous decrement of the parameter will eventually lead to miscounting an additional pulse, the operation of the LA will restore the system to a stable state again. We opted to push the system for maximum performance in addition to the flexibility to adapt to new network conditions, as cases with varied numbers of released molecules for increased energy efficiency and cases with mobile BS would be otherwise out of the range of this protocol, as it could not adapted to the network changes.

4. Performance Evaluation

4.1. Numerical Simulations and Results

The efficiency and applicability of the proposed algorithm were tested by means of a number of simulation scenarios to test the performance in various channel setups. Both the BS and nodes run the same algorithm, but in order to concentrate to the convergence of the automaton at the node, the BS runs a simplified version of this, and always has the best possible values without changes. The BS, in the case of no received response from node A, resends the message with a higher number of molecules. Akin to that, it ensures the reception from the node, as the node senses the increased concentration and amends the appropriate parameters accordingly.

Upon the first successful reception of a message from node A, in the next message, the BS sends the time of its transmission and starts a Berkeley-like sync sequence of messages [23]. Node receives the message and responds, including its internal time. The BS then calculates the time drift and sends back only the time margin that every node should adjust internally. Utilizing this protocol, in the forthcoming transmissions, node and BS will have the same time-out period with obvious gains in energy and performance, as lost messages will be handled by time-out interrupts. All the different values for the simulation parameters are shown in

Table 1. Simulation parameters and values.

Parameter	Value
simulation area dimensions	non confined
Dataset Size	2000 values (related to the probing rate)
step for ascensions	+100/$-100$
step for descensions	+30/$-30$
number decreases of the descensions	$-10$ every algorithm iteration
Bacterial Diffusion Coefficient	12,000–114,000 μm2/min
Informatio Pulse ( number of bacteria)	500–2200 bacteria
Bacterial speed	27 μm/s
Tumble Duration	Exponential with mean 0.15 s
Number of BS messages transmitted per scenario	100
Message input distribution	Normal distribution-various values
Move forward duration	Exponential with mean 1/4 s
volume exclusion effect shape	Spherical with 2 μm radius
Node sensing radius	70 μm

.

The performance of the network is presented in Figure 6. In this figure we can discern the minimum, the maximum and the average values of the time that a transmitted pulse “is on air” (Bs to node) for different numbers of signaling molecules. In Figure 6a, the distance between transmitter and receiver is 150 μm. In Figure 6b, the same distance is 300 μm. As demonstrated, lower intensity pulses have a higher variance but result in faster responses. Increasing the number of molecules per pulse causes the variance to decrease while the mean value increases. Consequently, the perception of the pulses becomes more consistent. The discrepancy for the pulse with the 2200 information molecules is owed to the saturated receptors in the surface periphery of the receiver (160 is the total number of receptors). Therefore, the node is not able to sense the decrease in a timely manner.

In order to shed light to the advantage of the LA approach over an established work in the literature, we amended the simulation framework in a way that the BS sends messages to the node having a statistical distribution for the number of diffused signaling molecules per message. More specifically, we feed the system through the BS, with s pulses of signaling molecules, the number of which follows the normal distribution, for various configurations. In simulations of this type, the BS does not wait for the response from the node in order to fire the next message; rather, it diffuses the next message based on predefined time intervals ranging from 100 s to 150 s. Below 100s, the system is unstable, as the stochastic nature of the diffusion does not guarantee the delivery inside this margin. We opted for the algorithm in [14], as this model has a variable threshold and can be directly compared to the logic of the LA. The specified protocol is named the adaptive threshold detector (ATD) and keeps the number of received molecules from the previous bit period and compares them to the molecules received in the current bit period. If the number of molecules received in the current bit period is larger that the one in the previous bit period, the ATD algorithm will output one as the received message; otherwise, it will output zero.

Figure 7 shows the bit error rate (BER—the number of message errors divided by the total number of transmitted messages). We recall that each transmitted biological message represents one bit of information. In the first set of simulations, the BS diffuses the message in the medium under a normal distribution $N(\mu$,${\sigma }^2$) with mean value 1000 and standard deviation equal to 50. For the first set of simulations, one can extract two pieces of information from the Figure. Firstly, the ATD algorithm seems to have a balanced error output at the level of $45\%$, and the LA approach improves its performance as the message rate decreases. Both solutions have the same performance around the 100 s area, and the LA algorithm outperforms the ATD solution mainly due to ability to detect the optimum parameters in order to improve the error rate and consequently increase the usable message rate.

The second set of simulations, shown in Figure 7, proves that the ATD approach keeps its performance level for even more fluctuated input signals (the input signal distribution has a higher deviation in relation to the previous simulation set). Meanwhile, the LA approach had an increased error rate related to the previous one, as the higher deviation resulted in increased corrective actions, resulting in degraded performance. Yet, around the point of 130 s, the proposed solution drastically decreased its error rate, as less dense messages provided ample time to find the best possible parameter configuration, achieving higher performance. After the point of 150 s, the LA minimized the error rate in the current system configuration, as the time interval was high enough to fade out the possible fluctuations and provide smoother curves.

Aiming to point out the performance of the LA algorithm for a time-variant channel in comparison to a fixed threshold way of determining the message, another set of simulations was conducted, as shown in Figure 8. In this scenario, the BS sends a message, having a variable number of signaling molecules based on a normal distribution and waits for the response from the node, in order to release the next pulse of molecules. As a consequence, the two-way communication system depends on the reception capabilities of the receiver node. In case of a missed or double-received message, we consider this transmission as an erroneous one. Having the ability to adapt to the different channel characteristics, the LA approach has significantly lower BER compared to the solution with the predefined thresholds. As expected, the latter solution, for which the threshold for each scenario was set equal to the mean value of the distribution used for each case, follows the molecule distribution, as half pulses were below the threshold and half were above it, resulting in a stable BER.

In order to derive the number of signaling molecules S that should be arrived at the node’s periphery, we used the following equation:

$$MAX[C_S\left(x\right)=\frac{M_S}{{\left(4\pi D_{S}t\right)}^{3/2})}exp(-\frac{|X_n{-X|}^2}{4D_{S}t})]$$

(4)

where:

• $D_S$ is the diffusion coefficient of the signaling molecules;
• $M_S$ is the rate of release of signaling molecules;
• $X_n-X$ is the distance between node and BS.

(While it would also be practical to measure the maximum number of bacteria that had reached the node’s periphery and accordingly set the thresholds for each case, we opted for this solution so as to give to the fixed threshold solution the ability to adapt to the channel changes. Correspondingly, this demands the establishment of a mechanism that provides guaranteed delivery of the initial messages, but this was out of the scope of this work, and we manually set the appropriate initial parameters for Equation (4)).

One should notice that the value in the forth scenario (the one having the distribution (1000, 200)) seems to have caused a slightly better performance than the other cases, but we believe this was due to the high deviation and the number of iterations (100 messages for this series of simulations). In all the cases, the LA surpassed the performance of the predefined threshold solution, whereas at the level of 250, due to the high deviation, it minimized its performance margins, as it tries to find the best possible value for the parameters based on the previous channel condition, though the next message may have a significantly different number of molecules, and the previous values become outdated.

In the final scenario, the speed of convergence of the learning-automaton was under investigation. As shown in Figure 9, starting from a high number of required ascensions demands a great amount of time to reach a stable state. Slow though it may seem, there are two reasons responsible for this behavior. Firstly, this was caused by the small number of corrective changes, as after each erroneous iteration, the LA amended the number of required ascensions by 100 and 50 for ups and downs, respectively. Secondly, the distance between receiver and transmitter was 300 μm, which is a relatively high distance, and for every iteration, almost 250 s was required. The initial number of 2200 ascensions was used to show that even in cases where the algorithm starts from a large number of ascensions, it has the ability to find the best possible value. In order to provide a possible relation between the number of ascensions and the time of convergence, the best fitting trend line was added to the Figure 9, which was based on a third-degree polynomial function. The point of convergence for this setup is around 700 ascensions, but this is relevant to the specific simulation parameters.

4.2. Discussion

Unlike existing algorithms in the literature, the proposed algorithm has an elastic perception of the pulse due to the number of highs and lows it detects. Driven by the absence of a well-defined threshold for a pulse, the algorithm keeps track of the concentration values, and by counting the decreases after a local maximum, it can therefore sense pulses with long tails and shallow slopes. In combination with the LA feedback, in case of an erroneous reading, it adapts its parameters, conforming again to the new context. We should note here that each network configuration affects the communication between two entities in various ways. High-density pulses of slow moving molecules may result in decreased performance in comparison to lower density pulses of high velocity molecules, as in cases where the BS and the node are close. This happens because the fast molecules will increase the concentration at the node side, providing ample time for the algorithm to sense the message. On the other hand, slow moving molecules would provide a more distinguishable pulse, but their low velocity will create a long tail and will demand more time from the receiver side to detect the incoming message. For that reason, the use of an adaptive algorithm would have advantages over a fixed threshold algorithm in cases of a time-variant channel.

Furthermore, while it seems a trivial task to identify a local maximum, this can only be achieved by having all the information available, and it takes place in an asynchronous way (we detect the local maximum by knowing all the other nearby maxima). Calculating such a maximum in a real-time way is not possible, and that is why the proposed solution exhibits a delay in the export of the outcome. (Nodes sense the maximum concentration at time x, but there should be plenty of time to realize if this is the pulse global-maximum concentration or it is just a fluctuation of an even higher concentration pulse. This is the reason for the apparent high time of convergence of the LA solution.

A high transfer data rate relies on the reduction of the message error rates, and in biological nanonetworks with low signal propagation speeds and high turnaround times, the notion of reliability is of significant importance. The proposed solution, as shown from the simulation scenarios, provides a way to improve reliability with a plethora of network and channel characteristics, and increase the usable transfer data rate.

Lastly, it should be noted that the proposed LA solution has a significantly better performance that the one that was shown in Section 3, but this comes with the cost of more complex logic.

Figure 6b reveals that this type of study should take into consideration a plethora of parameters, such as the number of receptors in the cells periphery, originating from the peculiarities of the biological environment. Future work should investigate the effect of chemotaxis and the way it affects the network performance. Injecting the operation of the proposed LA with the ability to respond with cumulative messages would highly assist with the minimization of interference noise and would provide valuable insights to future nanonetwork protocol designers.

5. Conclusions

The fast and simple way to sense the incoming pulses by using a LA-based protocol was introduced in this work. To this end, different scenarios have been devised in order to test the functional characteristics of the proposed solution. The algorithm supervises the concentration of the received pulse, and it determines, based on a set of parameters, if it is an incoming message transmission. Injected with the capability of a learning automaton to adapt to the network changes, the proposed algorithm outperforms in bit error rate solutions with both fixed and adaptive threshold detection. The algorithm seems to have a consistent performance for various network configurations. More specifically, lower concentration pulses seem to fit better to its operation principles, as the time-on-air for these messages is lower that for messages with higher values of concentration. On the other hand, for high concentration pulses, the algorithm may require additional time for the reception process, yet it seems to have a more consistent outcome.

In comparison with existing similar solutions, the LA has comparable performance to the established works related to high transfer data rates; however, as the time between transmissions increases, the algorithm is capable of eliminating any reception errors, as long as the channel characteristics remain the same. Then again, the algorithm can adapt to the channel changes due to the LA operation and can provide increased reliability and a higher transfer data rate.

We should take into consideration a detail that was mentioned in the previous section about the ligand–receptor binding model. The transmitted message reaching the vicinity of the node should find a free receptor protein in order to bind and transfer its DNA to the receiver. If at the time of arrival at the node’s membrane, there are no free receptors, then the signaling molecule will move away. As a result, the receiver node will not sense the increased density. As this communication model is based on the presence of free receptors in the cell’s periphery, it is obvious that there are additional parameters that should be taken into consideration when designing communication protocols for biological nanonetworks.

Take together, a multifaceted approach and a careful design is required for the development of communication protocols in biological nanonetwork, as there are different parameters that take part in the communication process. The algorithm in the present work helps to mitigate the effects of the volatile network environment of the biological nanonetworks.