Molecular Communication Channel Modelling in FPGA Technology Electronic Communications of the EASST Volume 080 (2021) Conference on Networked Systems 2021 (NetSys 2021) Molecular Communication Channel Modelling in FPGA Technology Daniil Romanchenko, Matis Tartie, Ba Que Le, Jorge Torres Gómez and Falko Dressler 4 pages Guest Editors: Andreas Blenk, Mathias Fischer, Stefan Fischer, Horst Hellbrueck, Oliver Hohlfeld, Andreas Kassler, Koojana Kuladinithi, Winfried Lamersdorf, Olaf Landsiedel, Andreas Timm-Giel, Alexey Vinel ECEASST Home Page: http://www.easst.org/eceasst/ ISSN 1863-2122 http://www.easst.org/eceasst/ ECEASST Molecular Communication Channel Modelling in FPGA Technology Daniil Romanchenko, Matis Tartie, Ba Que Le, Jorge Torres Gómez and Falko Dressler {d.romanchenko, matis.tartie, ba.q.le}@campus.tu-berlin.de {torres-gomez, dressler}@ccs-labs.org School of Electrical Engineering and Computer Science, TU Berlin, Germany Abstract: Molecular communication (MC) is a new paradigm for communication processes with a variety of applications such as health care and industrial sectors. The rapid development of MC, with the support of testbeds and simulators, requires scalable modeling tools. In this paper, we propose a field-programmable gate ar- ray (FPGA) design-based approach for the emission, diffusion, and reception of molecules. Results exhibit a close correspondence to state of the art analytical mod- eling of MC processes. Keywords: Molecular communication, FPGA, nanotechnology, nanodevices. 1 Introduction Molecular communication (MC) systems is nowadays a focus of study due to their promising applications in health care and communication industry sectors [KDB+19, HSF+19]. Supporting them, a variety of simulators have been developed to account for the emission, diffusion, and reception processes; examples include nanoNS3, BiNS2c, AcCoRDc as discussed in [BD19]. Also, a field-programmable gate array (FPGA)-based approach for gain and delay simulation using Verilog has been proposed in [SSLP20]; yet, without exploiting all simulation capabilities. In a different direction, in this paper, we concentrate on the physical MC model suggested in [PA10]. The given transfer functions of the model can be transformed into the discrete model and, in turn, be directly implemented on FPGA hardware. The resulting implementation allows better simulation speed thanks to the parallel structure of the FPGA and the flexibility to quickly adapt the test framework. The contribution of this paper is to provide a proof of concept, showing that scalable MC modeling is possible in FPGA technology. 2 Modeling MC Channels in FPGA Following the report in [PA10], a MC system is represented by processes of molecules emis- sion, diffusion, and reception, as depicted in Figure 1. These subsystems, when characterized through their equivalent transfer functions as linear time-invariant systems (LTI) system (cf. Equations (1) to (3) [PA10]), can be then conceived in FPGA technology. To that end, departing from these equations, we follow the transformation process described in Figure 2a to devise their corresponding FPGA block diagram [OS13]. In a first step, we apply the bilinear transform on the continuous transfer function H(s) to derive the discrete counterpart H(z). In a second step, we extract the coefficients ai and bi from H(z) to devise an FPGA block diagram in a direct form II, as shown in Figure 2b. Finally, in a third step, we implement the system through a direct form II structure [OS13]. During the emission process, the particles are being released into the communication medium, depicted as space S, or taken back into the reservoir E from it. The particles emission process converts the input signal sT (t) into particles concentration rT (t) as shown in Figure 1. In the transfer function this behavior is 1 / 4 Volume 080 (2021) mailto:\{d.romanchenko, matis.tartie, ba.q.le\}@campus.tu-berlin.de mailto:\{torres-gomez, dressler\}@ccs-labs.org Molecular Communication Channel Modelling in FPGA Technology R Particle E Emission Diffusion Reception A B C 11 Particle flux Figure 1: MC channel abstraction, inspired by [PA10]. expressed trough the resistor value as Re = 1/D (cf. Equation (1)). The capacitance Ce = 1 F is a constant as consequence of balancing the net flux of emitted particles. Direct Form II (a) Methodology to derive the Direct form II block diagram. 1 1 + + + + + + + + (b) Generalized block diagram in Direct form II. Figure 2: Deriving the direct form II block diagram HA(s) = 1 1 + sReCe (1) HB(s) = K0(‖x̄‖ √ s2 + sβ ) (2) HC(s) = sCr 1 + sRrCr (3) The diffusion process al- lows for the particles to travel through the medium by con- verting the particle concentra- tion rT (t) at the emitter to the particle concentration cR(t) at the receiver (cf. Figure 1). It is modeled as an LTI sys- tem through the channel im- pulse response (CIR) function given in [PA10, Eq. 24]. The resulting transfer function is shown in Equation (2), where K0(x) is a second kind mod- ified Bessel function, ‖x̄‖ is the distance from the transmit- ter to the receiver, β = 1cd·τd , cd = ± √ D/τd is the wave- front speed, and τd is the re- laxation time. This transfer function is however not a ra- tional function, which prevents the immediate application of the methodology mentioned above. To circumvent this problem, we approximate the Bessel function in Equation (2) using curve fitting in MatLab to derive rational functions for the absolute values. Then, we depart from a standard rational function with a numerator of second-degree and a denominator of third-degree to apply the methodology depicted in Figure 2. Finally, the reception process converts the given concentration cR(t) into the output signal sR(t) (cf. Figure 1). The receiver R consists out of receptors, which can capture a particle or release the captured NetSys 2021 2 / 4 ECEASST Channel Transmitter Receiver N = 20 Receiver N = 100 Coefficients i ai bi ai bi ai bi ai bi 0 1 -0,0417 1 5e-11 1 8e7 1 9,52e7 1 3,1120 0,0410 1 5e-11 0,6 -8e7 0,9048 -9,52e7 2 -3,2228 0,0417 3 1,1108 -0,0410 Analytical solution a1 None −T−2ReCeT +2ReCe − T−2RrCr T +2RrCr b0 None T T +2ReCe 2Cr T +2RrCr b1 None T T +2ReCe − 2CrT +2RrCr Table 1: The coefficients of the nominator (bi) and denominator (ai) after the bilinear transfor- mation and analytical solutions particle back. These are modeled to capture the particle only when it is not currently occupied, and it will only release the particle back whenever it was occupied by the particle. An electrical output signal is produced by a particle (ligand) forming a receptor-ligand complex, which is represented as a particle capturing. The rate constant k controls how hard it is for a molecule to form and break a receptor-ligand complex, hence Rr = 1/k, and the number of receptors is controlled through the capacitance Cr . Based on the transfer functions in Equations (1) and (3), we obtain the analytical solutions in Table 1, based on which we evaluate the coefficients. Through these coefficients, we then directly implement the FPGA scheme depicted in Figure 2b. In the case of Equation (2), we derive the scheme’s coefficients after their approximation. 3 Results In this section, we compare the derived FPGA design to the original model in [PA10]. Selected results depicted in Figure 3 have been obtained through MatLab and Simulink. Parameters are taken from [PA10] for the emitter, the diffusion, and the reception processes. Thus, emitter and the diffusion transfer func- tions are depicted in the frequency spectrum from 0–1 kHz, while the receiver in the range 0–10 MHz. The normalized gain of the transmitter module in Figure 3(a) is depicted considering D = 10−6 m/s2, Ce = 1 F, and Re = 1/D at a sampling frequency of 10 kHz. The normalized gain of the diffusion module in Figure 3(b) is obtained for the distance ‖x̄‖ = 10 µm, relaxation time τd = 10−9 s at a sampling fre- quency of 2.5 kHz. The normalized gain of the receiver module shown in Figure 3(c) is obtained for rate constant k = 108 /M/sec, with a variable number of receptors of Cr = 20 F and Cr = 100 F, Rr = 1/k [Ω] at a sampling frequency of 10 MHz. The corresponding coefficient values and analytical solutions for them are shown in Table 1 in the re- spective columns. Results exhibit that the FPGA design repeats the original transfer function. Transmitter and emitter modules show results, which are not equal but quite identical to the results obtained through the LTI system model. In the diffusion module, due to the fact that we approximated the function’s ab- solute values, their resulting discrete representation exhibits some differences. Nevertheless, the result remains quite accurate up to about 800 Hz. 4 Conclusions The resulting FPGA design of a MC model is supposed to scale well with thanks to parallelism. Scal- able desings can be conceived as simply as connecting more direct form II blocks (cf. Figure 2 b). Besides, the complexity of the system model will be directly given by the total of adders and multipli- ers used on the same block. The communication testbed could potentially run multiple communication systems simultaneously with each system modeling a different parameters setup. The suggested design is generic, meaning it is not fixed to any concrete implementation, thus, it can be applied in any FPGA 3 / 4 Volume 080 (2021) Molecular Communication Channel Modelling in FPGA Technology Frequency [Hz] C h a n n e l A tt e n u a ti o n [d B ] 0 500 1000 (a) Transmitter -200 -150 -100 -50 0 0 500 1000 (b) Channel -60 -50 -40 -30 -20 -10 0 0 5 10 (c) Receiver 10 5 -40 -30 -20 -10 0 Figure 3: Comparison of FPGA simulations and modelled transfer functions. technology. As a future improvement, a more flexible or even analytical solution could be found. Another possible improvement is related to the design, which can be extended to multiple communication lines to model a complex multiple-input and multiple-output (MIMO) systems. Acknowledgements: Reported research was supported in part by the project MAMOKO funded by the German Federal Ministry of Education and Research (BMBF) under grant number 16KIS0917. Bibliography [BD19] F. Bronner, F. Dressler. 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A physical end-to-end model for molecular communication in nanonetworks. IEEE Journal on Selected Areas in Communications 28(4):602–611, May 2010. doi:10.1109/JSAC.2010.100509 [SSLP20] A. Singh, S. P. Singh, M. Lakshmanan, V. K. Pandey. Gain and Delay Simulation for Molecu- lar Communication Using Verilog. In ICACCCN 2020. IEEE, Virtual Conference, Dec. 2020. doi:10.1109/icacccn51052.2020.9362898 NetSys 2021 4 / 4 http://dx.doi.org/10.1145/3345312.3345490 http://dx.doi.org/10.1109/jproc.2019.2916081 http://dx.doi.org/10.1109/JSAC.2010.100509 http://dx.doi.org/10.1109/icacccn51052.2020.9362898 Introduction Modeling MC Channels in FPGA Results Conclusions