6

Modulation Analysis of Molecular Communications in the Macro-Scale

6.1 Introduction

M olecular communication at the macro scale (cm to km) is a novel way of transmitting information compared to the heavily studied micro-scale (nm to $\mu m$ ). While in Chapter 5 the parameters of the macro-scale were studied experimentally and theoretically, additional analysis is needed to understand this novel communication and implement it as a communication paradigm.

In this chapter, both experimental and theoretical modulation analysis of macro-scale molecular communications are conducted. The experimental studies were made on the $M_C$ -ary $M_C$ = 2 (i.e., 0, 1), $M_C$ = 4 (i.e., 00, 01, 10, 11) and $M_C$ = 8 level transmission. A Symbol Error Rate (SER) study of molecular communications of 2-ary modulation is also tested. In addition, a theoretical analysis of an SER study was also conducted based on the simulation model given in chapter 4, which also shows the consistency with the experimental results. Molecular Inter-Symbol Interference (Mo-ISI) is discussed and an optimal transmission duration is calculated. Finally, a channel model is developed to explain the asymmetrical nature of the communications.

The major contributions of this chapter are as follows;

1.

$M_C$ -ary Transmission study: A comparison was made with experimental data of $M_C$ -ary transmission of three levels ( $M_C$ = 2, $M_C$ = 4 and $M_C$ = 8) and for three different symbol periods ( $T_s$ = 30 s , $T_s$ = 60 s and $T_s$ = 90 s) which shows that the simulation framework can be used to model molecular communications at the macro-scale.

2.

Molecular ISI (Mo-ISI): A study was made to analyse the effects of Molecular ISI (Mo-ISI) in macro-scale molecular communications. The model developed in Chapter 4 is shown to have strong agreement with the experimental results. Mathematical equations were derived from the model to analytically calculate the residual chemicals from different types of transmissions.

3.

Optimal Symbol Duration: An optimal symbol duration time is calculated by maximizing the error function (erf( $\cdot$ )) used in the solution for the advection-diffusion equation.

4.

$M_C$ -ary SER Analysis: An SER analysis was conducted both experimentally ( $M_C$ = 2) and theoretically ( $M_C$ = 2, 4, 8, 16 and 32).

5.

Message Transmission Experiment: An experimental transmission of a message encoded to chemicals was conducted. The transmitted message was compared to the theoretical model developed in Chapter 4.

6.

Molecular Channel: The type of the channel is defined as asymmetric and the capacity of the communication is described based on the asymmetric nature of the communication.

7.

Parameter effect on SER, MI and Distribution of Received Symbol Values: A theoretical study of the Mutual Information (MI), SER and distribution of received symbol values was made on the four parameters: transmission distance ( $x_d$ ), advective flow ( $u_x$ ), longitudinal diffusivity ( $D_L$ ) and symbol period ( $T_S$ ).

The structure of the Chapter is as follows. In Section 6.2 the experimental results along with theoretical comparisons are described for the $M_C$ -ary transmission. In Section 6.3 , Molecular ISI is studied. Two types of experiments were conducted ( $k$ and $o∕z$ ) and analysed with the theoretical model developed in Chapter 4 . Section 6.4 presents the experimental transmission of a message using chemicals. In Section 6.5 the channel capacity is described and MI is calculated. Section 6.6 discusses the experimental analysis of $M_C$ = 2 modulation along with theoretical comparisons to $M_C$ = 2, $M_C$ = 4, $M_C$ = 8, $M_C$ = 16 and $M_C$ = 32. In Section 6.7 the effects of various parameters on the achievable mutual information and SER are simulated based on the framework mentioned in Chapter 4 . In Section 6.8 an analysis was made on the symbol distribution of a 4-ary transmission and the variance ( ${\sigma }^2$ ) of the symbols is discussed. The chapter ends with conclusions in Section 6.8.

6.2 M-ary Transmission

$M_C$ -ary transmission is a type of modulation in which instead of relying on the transmission of one bit at a given time, multiple bits are transmitted. The experimental parameters of the M-ary transmission can be seen in Table 6.1 . In the experiment 3 bit durations were tested: 30s, 60s and 90s. The message that was chosen for transmission is “MCX” in American Standard Code for Information Interchange (ASCII).

6.2.1 2-Ary Transmission

In 2-ary transmission, two levels of concentration are used in the transmission the values and its corresponding bit values can be seen in Eq. ( 6.1 ).

The experimental results along with comparison to the theoretical model can be seen in Figures 6.0a , 6.0b and 6.0c . As it can be seen, the distinction between two states is discernible even on the shortest bit duration and the theoretical model shows strong agreement with the experimental results. Even though, the clarity between bits is high, the throughput of the communication is low since only 1 bit is transmitted during a given symbol time.

6.2.2 4-Ary Transmission

In 4-ary transmission, four levels of concentration are used in the transmission. The values and its corresponding bit values can be seen in Eq. ( 6.2 ).

The experimental results along with comparison to the theoretical model can be seen in Figures 6.0d , 6.0e and 6.0f . The $M_C$ = 4 level modulation transmission has shown some detrimental effect due to doubling the bits transmitted in a given second. However, the signals of 60s and 90s bit duration shows clear distinction between levels, however the level differences is smaller in 30s transmission.

6.2.3 8-Ary Transmission

In 8-ary transmission, eight levels of concentration are used in the transmission and the corresponding bit values can be seen in Eq. ( 6.3 ). The results show the effect on increasing the transmitted bits per second from 2 to 3 has increased the ISI in the system.

It must be noted that the initial pulse differs from the predicted signal. This can be caused by particle interaction with the membrane present in the inlet, However, as the transmission evolves, the theoretical model predicts the experimental values accurately.

6.3 Molecular Inter-Symbol Interference (Mo-ISI)

To understand the behaviour of the bit transmission and the leftover chemical it leaves in the detector, a series of experiments were conducted. In these experiments a sequence of bits were transmitted. The experimental parameters for the experiments can be seen in Table 6.2 .

The first set of experiments were done by sending a single 0 bit between increasing amount of 1s ( $o∕z$ = 1 is 10101..., $o∕z$ = 2 is 11011011... etc.).

The second set of experiments were conducted by sending equal amounts of 1’s and 0’s ( $k$ = 1 is 101010..., $k$ = 2 is 11001100..., $k$ = 3 is 111000111... etc.).

6.3.1 One-to-Zero (o/z) Experiments

The results for the $o∕z$ can be seen from Figure 6.1a to 6.1e with an additional one more zero in each following Figure. As it can be seen , the more “0” present in the transmission, less particles are left in the system. And in $o∕z$ = 5, the signal reaches the background noise of the system.

6.3.2 k Experiments

The experimental results of sending equal amounts of 1s and 0s can be seen from Figures 6.1f , 6.1g , 6.1h and 6.1i . As it can be seen when a single sequence of 101010... is transmitted, the system takes time for the absorption/removal process to reach equilibrium. This is due to the way the system absorbs and cleans out the particles inside the detector.

When the system introduces the particles into the detector, the system absorbs based on how much the bit gives in addition to the background noise and when the system clears out the particles from the detector, the flushing will be proportional to the already present particles in the system. This flushing will increase when the detector has more particles. This will continue until the particles in the system becomes high enough that add/remove function of the communication equalises. However, when the system introduces more particles before a flushing occurs the system needs less pairs to stabilise. This is due to the removal and absorption processes that are directly proportional to the mass injected and mass present in the detector respectively. More mass absorbed by the detector causes more mass to be removed in the removal process, decreasing the time it takes to reach equilibrium.

6.3.3 Residual Background Signal

One of the important aspects of molecular communications is the leftover particles that decrease the amount of information that can be transmitted in a given symbol period. This property is unique to molecular communications. In electromagnetic (EM) communications, the interference is normally constant (i.e., $N_0$ stays stable). However, in molecular communication, the residual chemicals from 1-bit symbol can gradually increase the desired level and if the symbol duration is not kept at a reasonable duration, it will cause incorrect decoding. To model the ISI the equation derived in Eq. ( 4.11 ) is used. In this model the ISI can be modelled based on the interaction of the absorption ( ${𝜃}_1$ ) and the removal ( ${𝜃}_0$ ) of the particles. To simplify the equation, the part of the function where the absorption occurs is defined as:

In the first part of the experiment ( $k$ study) equal numbers of bits ( $U_1=U_0$ ) were sent in sequence. A diagram of this kind of transmission can be seen in Figure 6.3 (A). Based on this bit transmission, the total ISI caused by the transmission can be expressed as:

where $\upsilon$ is the dimension operator (i.e., $\upsilon$ = 2 for 2D). In the second part of the experiment ( $o∕z$ study) an uneven amount of 1’s and 0’s is sent in sequence ( $U_1\ne U_0$ ).The diagram for this transmission can be seen in Figure 6.3 (B). This change in transmission can be modelled as:

If the transmission has an even amount of state changes between bits 1 and 0, which can be seen in Figure 6.3 (C), the generalised equation that gives ISI is:

and if the transmission has an odd amount of state changes, the equation can be written by including an additional absorption ( ${𝜃}_1$ ) value to Eq. ( 6.7 ):

The results of the leftover background-noise experiment compared to the theoretical model can be seen in Figures 6.3a and 6.3b for a $o∕z$ study and $k$ study, respectively.

As can be seen, the model agrees well with the experimental data when the leftover particles from the transmission create a large amount of interference. However, as the chemicals create less and less interference, the model prediction becomes less accurate. This is due to the effect of the ambient noise playing a more important role. To mitigate the effect, an optimal time for the symbol period can be calculated based on the equations derived in Chapter 4 .

The Optimal Symbol Period (OSP) can be calculated by maximising the value in the error function erf( $\cdot$ ). For the detector to retain no chemicals from transmission the error function must produce the value 1. However, due to the impracticality of this (erf($\infty$) = 1), a finite value must be chosen for the determination of the OSP. For a given value of n = 2 the error function produces the value of 0.995, which can be used for the practical cases of molecular communications.

By solving the error functions $\left(erf\left(\cdot \right)\right)$ present in the absorption/removal equations given in Eq. ( 4.18 ), the optimal sampling period can be calculated . As can be seen in both equations, there are two error functions. The main differences being the distance values; former being $x_d$ and latter being $x_{𝜖}$ . Since the distance that chemicals travel against the flow is negligible compared to the actual distance of the propagation ( $x_d\gg x_{𝜖}$ ) only the former part of the equation is used in calculation of the optimal sampling period. For a given $n$ value the optimal symbol period ( $T_{OSP}$ ) can be calculated as follows:

By solving the aforementioned equation with respect to $T_{OSP}$ two solutions ( $T_{max}$ , $T_{min}$ ) can be derived which are presented below:

To calculate the 2D solution it is assumed the diffusion is homogeneous across all cartesian dimensions ( $D_x$ = $D_y$ = $D_z$ ).

As long as the above criterion in Eq. ( 6.11b ) are not met, transmission will retain the ISI during the communication. The presence of the ISI will shift the distribution of 0 bits to a higher value as the transmission evolves, and if the receiver uses a static threshold detection ( ${\tau }_s$ ), it will increasingly decode 0 wrongly as the transmission continues and will create an uneven probability between $p(1|0)$ and $p(0|1)$ , making the communication asymmetric.

6.4 Message Transmission Experiment

One of the major problems of using molecules in transmission is the leftover from previous chemicals. Chemicals sensors, therefore need to be cleaned in order to overcome the problem of the memory effect. However, the sensor cleaning time can be long especially with a membrane present in the detector, adding a further delay to the signal. Moreover, because of the behaviour of molecular communications, the transmission time given for a single bit may not be enough for the signal to reach to the background noise level, e.g., if there is a single 0 between a string of 1’s, the 0 bit produces a higher signal current than the background noise level at the beginning of the transmission (i.e., a single 0 cannot flush all the chemicals leftover from consecutive 1’s). In addition, the next “1” bit adds additional chemicals ( ${𝜃}_1$ ) to the leftover chemicals ( ${𝜃}_{ISI}$ ) which in turn produces even higher signal current. Therefore, if there are more 1’s than 0’s present in the transmission this could lead to an increase of the overall signal amplitude, making a simple threshold detector inefficient at decoding the transmission correctly.

In the experimental transmission system, the signal current values (measured by the QMA) for the “1” bit ranges from 0.1 nA to 0.53 nA and 0 ranges from 0.37 nA to 0.006 nA. The overlaps between 0 values and 1 caused by the residual chemicals from the previous bit can cause incorrect decoding of the transmitted signal. To overcome this, instead of relying on the amplitude values of each bit, the behaviour of the bits relative to the previous bit was investigated

6.4.1 Results

The properties of chemical transmission make the simple threshold detection inefficient because of varying amplitude values based on the residue chemicals from previous transmission, therefore a detection method based on relative bit value is better suited for this type of communication system. The mechanism of the algorithm is as follows;

• The initial bit is determined by a predefined threshold in which this experiment is defined as ${\tau }_s$ = 0.1 nA.

• The second bit is then defined relative to the previous decoded bit; if it is higher it is defined as 1, lower it is defined as 0.

To avoid errors due to unpredicted signal amplitude changes (e.g., due to fluctuations in the air), the following error correction routine was implemented:

• Every retrieved signal data was compared to the previous one and if the difference is within a specified range it was defined as the previous bit. The range is calculated empirically since every chemical will react differently with the detector. For acetone, the range value coefficient assigned as $k_{\tau }$ = 0.1.

The results of the transmission can be seen in Figure 6.5 . In the experiment, a message was sent in ASCII binary code. The message chosen was the first line from the novel Moby Dick “ Call me Ishmael ” [354]. The message was converted to chemical data where bit “1” was assigned as a signal gas pulse of 8 ml/min and bit “0” was with no pulse; and both bits having a carrier flow of 750 ml/min nitrogen gas was used. Using a static threshold value of ${\tau }_s$ = 0.191 nA, 5 bits out of 120 transmitted were decoded incorrectly however, with the algorithm the decoding error value decreased to 1 bit in 120 bits. The errors occurred with the threshold detection is due to the changing amplitudes of 0’s and 1’s as the transmission evolves. The lower errors in the relative bit decoding shows that the algorithm is better at decoding a molecular message than threshold detection.

6.5 Channel Capacity

When a 1-bit symbol is introduced to the detector, unless the symbol duration is shorter than the optimal given in Eq. ( 6.11b ), the detector will absorb less mass than it was introduced into the environment. Moreover, since the flush mechanics relies on the particles that are already in the detector, the bit 0 cannot remove all the particles in the detector in the given time. Based on the ISI properties of the communication mentioned in the previous section, the communication channel can be expressed as asymmetric. The diagram of the channel can be seen in Figure 6.6 .

To define the channel capacity, the mutual information ( $I(\cdot ;\cdot )$ ) must be measured. The channel capacity with a block length of $n$ that possesses memory effects can be generalised have the following equation [82], [86]:

The mutual information is a measure of how much one random variable tells about another with the definition of it given below [82]:

where $H(Y^n)$ is the Shannon entropy of the probability vector $Y$ and $H(Y^n|X^n)$ is the conditional entropy of $Y$ given $X$ . Based on the equations given in Eq. ( 6.12 ) and ( 6.13 ), the achievable MI is calculated by simulating the probabilities based on the simulation framework given in Chapter 4.

6.6 Symbol-Error Rate (SER)

To analyse the symbol-error rate (SER) properties of Macro-scale molecular communications, an experiment was conducted, with the parameters of the experimental setup can be seen in Table 6.4 .

Bit duration of 5s, 10s, 15s and 20s are experimented. Each experiment transmitted 100 bits randomised with equal probabilities of 1s and 0s. In each experiment 300 $\mu l$ of sample is introduced into the Evaporation Chamber (EC). 5s, 10s, 15s and 20s experiments were done 3 times and the average error is taken.

The experimental along with the theoretical comparison of SER can be seen in Figure 6.7a . The theoretically calculated MI based on the experimentally obtained SER can be seen in Figure 6.7b . As it can be seen, the experimental results show agreement with the numerical results obtained from the simulation ( $\rho$ = 0.94). A static threshold ( ${\tau }_s$ ) was used in decoding of the received bits. The theoretical analysis of M-ary modulation in therms of SER and MI can be seen in Figure 6.6a and Figure 6.6b respectively. To calculate the mutual information for both experimental and theoretical results, the Shannon entropy along with conditional entropy are calculated individually and subtracted from each other as shown in Eq. 6.13 .

6.7 Theoretical Results

In this section of the study, three parameters of the transmission are studied for symbol error rate (SER) analysis and the channel capacity. These parameters are: transmission distance ($x$), longitudinal diffusivity ( $D_L$ ) and advective flow ( $u_x$ ). Two types of comparisons were made. Firstly, a comparison was made by varying the signal-to-noise ratio (SNR) for both SER and mutual information and secondly, the parameter becomes the variable for SER and mutual information to better observe the parameters effect on these communication properties. The parameters used in the theoretical study can be seen in Table 6.5 .

6.7.1 Symbol Duration

As it can be seen in Figure 6.8a and Figure 6.8b , as the symbol period is increased, the attainable mutual information experiences an increase and the amount of errors in the system decreases.

This behaviour is attributed to the amount of energy given per symbol ( $E_s$ ). As the symbol time increases, the average energy per symbol will see an increase which is the primary factor in improving the capacity and decreasing the produced SER . This effect can also be observed in Figure 6.9a and Figure 6.9b where the increase of symbol duration increases the MI.

6.7.2 Coefficient of Diffusivity

In Figures 6.10a and 6.10b , it can be seen that the increase of diffusivity has neglible effect on the SER and the MI.

This could be due to the fact that with the presence of an advective flow, the effect of diffusion is suppressed where the increase of the parameter plays a minor role. However in Figures 6.11a and 6.11b , it can be seen that with the increase of the SNR the effects of diffusion become more noticeable and based on the simulation results, the effect seems to increase the MI. However as stated the effect is negligible.

6.7.3 Transmission Distance

As it can be seen in Figures 6.12a and 6.12b , as the transmission distance is increased, the attainable mutual information experiences a decrease and the amount of errors in the system sees an increase.

This is caused by the insufficient time given for the detector to detect the particles. As distance increases, the propagation time increases as well and additionally the diffusive properties dilutes the transmission, where the chemicals start propagating in directions other than the path of the advective flow, which increases the time needed to absorb all the chemicals in the medium. The effect of increased transmission distance can be seen in Figures 6.13a and 6.13b .

6.7.4 Advective Flow

The effect of advective flow on the channel capacity can be seen in Figure 6.15b and 6.14b . As the velocity of the transmission is increased, the channel capacity sees an increase with a corresponding decrease in errors. This is caused by the effect of advection rather than the effect of diffusion.

The effect of advection has a higher increase in channel capacity than diffusion. The effect of increasing the advective flow on the increase of the MI and the reduction of the SER can be seen in Figures 6.15a and 6.14a .

6.8 Bit Distribution

To analyse the bit distribution of molecular communications, simulations were done by changing the properties of the propagation. These are: longitudinal diffusivity, advective flow and the transmission distance. The effect of these parameters will be analysed by transmitting 4-level transmission.

6.8.1 Symbol Period

The effect of symbol period on the symbol distribution can be seen in Figure 6.16a and distribution variance in Figure 6.16b . As can be seen from both figures, the increase of symbol period has a positive effect on the separation of the symbol distribution and decreases the variance of the distribution of the symbols.

6.8.2 Advective Flow

Advection is defined as the transport of a substance by the use of bulk motion. In this chapter, the advection is modelled as a 1-D vector in the $x$ -direction and the effect of the flow on bit distribution can be seen in Figure 6.17a . As can be seen, the increase in flow plays a major role in the decrease in the variance ( ${\sigma }^2$ ) of the distribution and the stability of the mean ($\mu$) of the distribution. The results show that a small increase in the flow plays a substantial role in the separation of bits.

6.8.3 Diffusivity

Diffusivity is the action the particle take by utilising internal energy to propagate in a random fashion. Some particles will move against the direction of the flow which causes delay in the saturation and the flush of the signal, i.e. when bit 1 is introduced, the action of absorption takes longer as diffusivity is increased and flush time is increased as diffusivity is increased.

Because of this, the effect of increased diffusivity does not have a profound effect on the decrease of the bit distribution variance as advective flow. The results also show that an increase in advection is a much better choice for improving the detection of bits than increasing the diffusivity.

6.8.4 Transmission Distance

One of the detrimental effects of molecular communication is the distance of transmission ( $x_d$ ). Because the advective flow ( $u_x$ ) of the system cannot compensate for the increase in distance, the detection of the chemicals gets delayed and particles that are sent get misdirected from the transmission path so that less particles arrive at the detector. Straying from the path can be caused by numerous parameters such as diffusivity of the transmitted particles, flow or collisions with particles present in the environment.

The distribution of chemicals with the transmission distance can be seen in Figure 6.19b and the variance can be seen in Figure 6.19a . As can be seen the increase of distance causes the bit distributions to merge. This in turn causes a decrease in correct decoding of the message and given enough distance makes communication impossible.

6.9 Conclusion

This chapter presents an experimental and analytical study on the M-ary transmission properties of macro-scale molecular communications. As a transmitter, an in-house-built odour generator was used and as a detector a mass spectrometer with a quadrupole mass analyser (QMA) was utilised. $M_C$ = 2, $M_C$ = 4 and $M_C$ = 8 level transmissions were made experimentally using a solution of acetone and methanol as the signal chemical. A simulation model was developed based on the advection-diffusion equation and was compared to experimentally detected signals. It was shown that the simulation agrees with the experimental results. In addition, experimental results of the SER analysis of acetone on $M_C$ = 2 level modulation, a theoretical analysis was made on the $M_C$ = 4 and $M_C$ = 8 level modulation along with a theoretical comparison of $M_C$ = 2, which produced similar results to the experiment. A binary asymmetric channel was used to model the channel capacity and determine the optimum symbol rate for this particular macro molecular communications system. It was shown that the macro-scale molecular communication can be modelled and simulated using a variation of the advection-diffusion equation. In addition, parameters such as advective flow aids in terms of reducing the SER more than increasing the diffusivity coefficient and the distance at which transmission takes place has a detrimental effect on the channel capacity of the system. An in-depth analysis into Mo-ISI was carried and by using the model developed in Chapter 4 it was shown that the model is able to replicate the experimental results. From the model equations were derived that allow calculations of the ISI in a given transmission. Based on the model discussed in Chapter 4 , the bit distribution of the transmission is studied for three parameters and their effects were discussed. The Following Chapter will focus on the multiple chemical transmission of molecular communication.