On Performance of SISO Nanonetworks-based Molecular Communications Saied M. Abd El-atty1 , Z. M. Gharsseldien2 and Konstantinos Lizos3 The Dept. of Computer Science and Information, Arts and Science College, Salman Bin Abdulaziz University 054-11991 Wadi Adwassir, Riyadh, Saudi Arabia 1 The Dept. of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, 32952, Menouf, Egypt. 2 The Dept. of Mathematics, Faculty of Science, Al-Azhar Uni., Nasr City,11884, Cairo, Egypt 3 Head of IT Department, Embassy of Greece,Nobels gate 45, 0244, Oslo, Norway
[email protected],
[email protected] and
[email protected] Abstract- Mobile ad hoc molecular nanonetwork (MAMNET) introduces a new paradigm for the realization of future nanonetworks. In MAMNET, the transmission of nanoscale information between nanomachine and infostation is based on collision and adhesion process. In this study, we develop a single input single output (SISO) molecular communication system for transmitting nanoscale information. We employ the features of MAMNET, taking into account the electronic structure of the neurotransmitter, which affects the collision and adhesion process. Consequently, we deploy a realistic adhesion process by determining the critical velocity required for two molecules to adhere. The critical velocity is a function of molecule size, hardness, density and inter-molecule near-field interaction. The metrics performance of SISO system is measured in terms of average packet delay, throughput and incurred traffic rate. The numerical results show the effectiveness of the proposed SISO system in the future nanonetworks. Keywords—Nanomachine; Collision; Adhesion; Molecular communication; Nanonetwork; SISO.
I. INTRODUCTION Nanonetworks are communication networks that typically or entirely exist at the nanoscale. Nowadays, nanotechnology is capable of fabricating devices in a scale ranging from one to one hundred nanometers [1]. Thereby, the components of those nanonetworks need to be in the nanoscale and are referenced as nanomachines (NMs). Nanomachines are able to perform specific tasks, e.g., processing, sensing and actuation [2]. Further, nanomachines can exchange nanoscale information, interconnected by means of nanomechanical, acoustic, electromagnetic and chemical or molecular communication [1]. The molecular communication is considered the most promising approach for nanonetworking. Recently, A. Guney et al [3] proposed a first step towards a state of the art framework in respect to nanoscale information transmission in mobile ad hoc molecular nanonetworks (MAMNET). Communicating among nanomachines (NMs) is accomplished on a molecular level, which is based on the collision rate and adhesion probability. Furthermore, the performance of MAMNET is evaluated by adopting the principles of neural communication [4]. Neurotransmitters are carrier signals, used to transmit nanoscale information within neuron system. Presynaptic signals are transmitted via release of neurotransmitter from the presynaptic neuron, which binds to receptors at the postsynaptic neuron [5]. Although a neuron
typically releases only one type of neurotransmitter, there are many different types of neurotransmitters [6]. From the list of neurotransmitters released by a neuron, the type of transmitter released by a neuron determines the action on the postsynaptic neuron. This can be either excitatory, e.g., glutamate and acetylcholine or inhibitory, e.g., GABA and glycine [6]. Kobayashi and Terao [7] have calculated the absolute hardness, H and absolute electronegativity, Ea parameters and applied this to neurotransmitter in order to identify or characterize different types of neurotransmitters and receptors. The electronic structure of neurotransmitters can be defined by using H and Ea parameters [7] and [8]. Moreover, they pioneered this research and showed that there is a direct relationship between H and biological activity of neurotransmitters. Although MAMNET paradigm involves precisely the neurospike molecular communication, it doesn’t take into account the electronic structure of neurotransmitters. Therefore, it is of fundamental importance to study the influence of neurotransmitter electronic structures during nanomachine communication in nanonetworks. In this work, we develop a single input single output (SISO) molecular communication system for transmitting nanoscale information by employing the features of MAMNET while taking into account the electronic structure of neurotransmitters. Accordingly, we employed a realistic adhesion process by determining the critical velocity required for two molecules to adhere. The critical velocity is a function of molecule size, hardness, density and inter-molecule near-field interaction. In addition, the error probability of neurospike detection and the channel capacity of neurospike are derived in terms of the optimal threshold at detector and signal to noise ratio (SNR). On the other hand, the metrics performance of SISO system in terms of average packet delay, throughput and incurred traffic rate are measured. The reminder of the paper is organized as follows. A brief summary of MAMNET design is provided and then we pursue with the development of molecular communications basedbiophysical at Subsections A and B. In Section III, we illustrate the theory of neurospike communication in neuron system. The performance analysis of nanonetwork-based SISO system is investigated in Sections IV. The numerical results of the proposed SISO system are presented in Section V. Finally, a brief conclusion of this paper is presented at Section VI.
978-1-4799-3223-8/14/$31.00 ©2014 IEEE
II. MOBILE AD HOC MOLECULAR NANONETWORKS MAMNET is a new nanonetwork paradigm and it is derived from the shared wireless infostation model (SWIM) [9]. MAMNET consists mainly of two nano-scale mobile nodes, namely nanomachine and infostation. Analogous to traditional wireless communication systems, nanomachines have the ability to carry specific environmental information from transmitter nanomachine (TN) to receiver nanomachine (RN) by means of molecular communication techniques. The molecular communication is able to interconnect multiple nanomachines, resulting in nanonetworks [1]. Infostation represents a central control or relay unit that performs a decision in response to the received information or a gateway that connects MAMNET to a microdevice [1]. According to the mobility of nanomachines, molecules can only connect when in physical contact i.e., intermittent connectivity [10]. Further, due to the probabilistic behavior of the molecules exhibiting Brownian motion, the molecular communication in MAMNET is performed by three successive procedures, namely, collision, adhesion and transmission respectively, as illustrated in Fig.1. A. Molecular communications based-biophysical Molecular communication is defined as the transfer of nanoscale information using molecules as message carriers [16]. Inspired by biophysical, molecular communication is performed by the chemical interaction among different molecules and it is based essentially on the collision and adhesion technique. As inspired by traditional mobile ad hoc network (MANET), in molecular communication, due to the random motion or freely diffuse of molecules in aqueous medium, the mobile molecules (nanomachines) collide with each other and the molecular adhesion occurs between the collided molecules [11]. Molecules adhesion is accomplished by the ligand-receptor binding process [12]. Therefore, after collision procedure, the adhesion should happen to allow nanoscale information transmission, thus enabling successful communication between molecules. The main goal of this study intends to illuminate on various fundamental aspects of collision and adhesion of those molecules. With an emphasis on realistic adhesion procedure, the biophysical process for molecules interaction is similar to nano-particles interactions; it should be studied under the influence of near-field interaction [13]. This study is taking into consideration the electronic structure. In particular, we isolate and focus on a single aspect of molecule adhesion, targeting the determination of the impact velocity needed for
two nanoscale molecules to adhere as a function of molecule size, hardness, density and inter-molecule near-fields interaction. Therefore, after the collision of any two molecules, the occurrence of adhesion may happen or not, depending on the coefficient of restitution, e. Notably, e =1 is perfectly elastic impact and e =0 is a perfectly plastic i.e., full adhesion impact [13]. Consider a central collision of two molecules i and j with an initial velocity vi(0)=v0=-vj(0) in opposite directions. By using the average impulse for an individual molecule, we take into account the consistency with Nesterenko's experimental observations on bonding. T. Zohdi [13] has obtained an approximation for the surface pressure, based on the contact area, Ac. Thereby, a parameter e for an individual molecule (nanomachine or infostation) may be approximated by a linear scaling with pressure-to-hardness ratio as follows [13] ⎡⎛ m | v (t ) −v k (0) | ⎞ ⎤ e = max ⎢⎜1 − k k c ⎟ , 0⎥ 2 H k t c Ac ⎠ ⎦⎥ ⎣⎢⎝
(1)
where tc=μ.rk/v0 denotes the collision time and Ac denotes the contact area between two nanomachines while μ is a parameter to measure a per cent of collision at the critical velocity, μ is dimensional less, m k = (4 / 3)ρk π rk3 is the mass of molecule with radius rk and density ρk, and Hk is the hardness coefficient. Setting e =0 (full adhesion), vk(tc)=0 and vk(0)=vk0 in Eq.(1), it is possible to further elaborate and obtain the critical velocity as follows, vk20 ≥
3H k μ Ac 2πρ k rk2
(2)
In the presence of inter-molecules near-fields interaction (such as Van Der Walls energy, electrostatic energy and others) the adhesion condition take the following form, ⎧ 3μ ⎡ 2H k AC − Eavg ⎤ ⎦ ⎪ ⎣ 2 4 πρ r ⎪ k k vk20 ≥ ⎨ ⎪ 3μ ⎣⎡ 2H k AC + Eavg ⎦⎤ ⎪ 4πρk rk2 ⎩
for attrative energy
(3)
for repulsive energy
where Eavg is the average impulse, acting between the molecules due to the inter-molecule near-field interactions. There are two types of mobile molecules in nanonetwork called nanomachine and infestation. Without any loss of generality, we assume that the average critical velocity between any two molecules takes the form of
1 (4) (v j 0 +v k 0 ) 2 Thereby, the average critical velocity of two nanomachines, vnn and the average critical velocity of nanomachine and infostation, vni needed to be adhered, can be given by v jk =
vnn = Fig. 1. Nanoscale information transmission in MAMNET.
3H n μ Ac 3H i μ Ac 1 ⎛ 3H n μ Ac and vni = ⎜ + 2 2πρ n rn 2 ⎜⎝ 2πρ n rn2 2πρi ri 2
⎞ ⎟⎟ ⎠
(5)
where Hn, ρn, Hi and ρi denote the hardness coefficient and density for nanomachine and infostation respectively. Therefore, the collision rate between two nanomachines, Rnn and collision rate between nanomachine and infostation, Rni can be approximated as follows [3]: Rnn ≈
π (2rn )2v nn V
and Rni ≈
π (rn + ri )2 v ni V
(6)
where rn and ri are nanomachine’s and infostation’s radius, respectively. V denotes to the volume size of nanomachines, by assumption V >> rn and ri > rn. B. Adhesion probability Adhesion occurs via binding molecules on the surface of two nanomachine and depends on the contact area. Full adhesion happens when the velocity of nanomachine reaches its critical value, as derived in Eq.(2). Hence, the probability of n bonds at time t, Pa (t) can be given by [14] ⎛ Am ⎞ Pa (t ) = ⎜ c min ⎟[ p(t )]n [1 − p(t )]Ac mmin −n ⎝ n ⎠
(7)
where mmin is the minimum surface density of bonding molecules. p(t) is the probability of forming one bond and is given by [14]. A simplified expression of adhesion probability can be derived, provided that the kinetic probability rates are constants [14]. If adhesion of nanomachines needs a minimum of n bonds, the probability of adhesion at contact time, τc is given by [14]: n −1
Pa (τ c ) = 1 − ∑ pi (τ c )
(8)
i =0
III.
NEURO-SPIKE COMMUNICATION
Among the existing intercellular communication models in living cells, the communication between neuron cells is the fastest one. For instance, Glutamatergic synapses can generate a postsynaptic current in less than 0.5ms after the arrival of the presynaptic action potential [8]. Thereby, the neuron system is considered a rich biological environment into studying the performance of SISO for synaptic transmission, where the neurotransmitter is used to transmit nanoscale packet information from one neuron to another. There are two wellknown types of neurotransmitters, namely, chemical and electrical. We focus on the neurotransmitter, which is transmitted by chemical means. According to [4], this scenario is referred to as neurospike communication and it is composed of three terminals, namely presynaptic, synapse and postsynaptic. The presynaptic releases a neurotransmitter packet to the synaptic cleft between neurons i.e. synapses. Therefore, the arrival pulse or action potential releases the neurotransmitters to presynaptic neuron according to release probability and afterwards the diffusion of neurotransmitter begins towards the postsynaptic neuron. The neurotransmitters bind to the receptor at postsynaptic neuron. The binding process opens the channel on postsynaptic neuron in order to allow the flow of ions to the neuron [5]. Although a neuron typically releases only one type of neurotransmitter, there are many different types of
neurotransmitter. From biology perspective, there are exceptions to the rule; for instance retinal starburst amacrine cells, which release acetylcholine and GABA. On the other hand, a neuron can express many different types of receptors, each sensitive to a specific neurotransmitter. The two main types of neurotransmitter receptors are called ionotropic and metabotropic. However, the ionotropic receptors are faster and generate shorter responses than metabotropic receptors [8]. From the list of neurotransmitters released by a neuron, the action on the postsynaptic neuron is determined. This can be either excitatory (common: glutamate, acetylcholine) or inhibitory (common: GABA, glycine) [6]. IV.
NANONETWORKS PERFORMANCE ANALYSIS-BASED SISO SYSTEM
In this section, we illuminate the performance analysis of synaptic transmission in SISO molecular communication. Furthermore, we measure the performance of nanonetworkbased SISO system in terms of average packet delay, throughput and incurred traffic rate. In nanonetworks, inspired by epidemic disease spreading [9], nanomachines can be found in three various states, i.e. infected, susceptible and recovered. Thereby, within a nanomachine, when a packet (i.e., infected in state I) collides and adheres with another nanomachine that does not have a copy of the packet information (i.e., susceptible in state S), it forwards it to this nanomachine. A nanomachine is considered to be recovered (i.e., recover in state R) after it has offloaded the packet to infostation. The classical epidemic SIR model is analyzed by a Markov model as illustrated in Fig.2. We can deduce the differential equation that represents the SIR system as follows [10]: dI (t ) = β × S (t ) × I (t ) − γ × I (t ) dt
(9)
We consider refining to [3], for the purposes of accurate collision, adhesion and transmission procedures representation, based on the above description for molecular neurospike communication, β factor represents the rate of packet spreading among nanomachines. Hence, β is computed as Rnn×Pa×Pt. Additionally, γ represents the rate at which infected nanomachines become recovered. Therefore, it contains infostation and nanomachine collision, adhesion and transmission rates. As a result, γ can be given by the following formula, Rni×Pa×Pt Let Nn denote the total number of nanomachines in the nanonetwork and Td is defined as a random variable, corresponding to the time elapsed from first generation of information packet by a nanomachine to the time that packet is first offloaded to an infostation. Initially, we consider a SISO i.e. single packet in the system.
Fig. 2. Markov model for classical SIR model.
At t=0 only one nanomachine is infected, i.e., I(0)=1, S(0)=Nn-1. Until offloading, the entire number of nanomachines Nn will be either contained in the I(t) state or S(t) state, i.e., S(t)+I(t)=Nn, R(t)=0 for t
