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Ad Hoc Networks 11 (2013) 2541–2555
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Ad Hoc Networks
journal homepage: www.elsevier .com/locate /adhoc
Energy and spectrum-aware MAC protocol for perpetualwireless nanosensor networks in the Terahertz Band
1570-8705/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.adhoc.2013.07.002
⇑ Corresponding author.E-mail addresses: [email protected] (P. Wang), jmjornet@buffalo.
edu (J.M. Jornet), [email protected] (M.G. Abbas Malik), [email protected] (N. Akkari), [email protected] (I.F. Akyildiz).
1 This paper was funded by King Abdulaziz University, under Grant No.(11-15-1432/HiCi). The authors, therefore, acknowledge technical andfinancial support of KAU.
Pu Wang a,⇑,1, Josep Miquel Jornet b,1, M.G. Abbas Malik c,1, Nadine Akkari c,1, Ian F. Akyildiz c,d,1
a Department of Electrical Engineering and Computer Science, Wichita State University, Wichita, KS 67260-0083, USAb Department of Electrical Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260, USAc Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabiad Broadband Wireless Networking Laboratory, School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA30332, USA
a r t i c l e i n f o
Article history:Received 12 June 2013Accepted 16 July 2013Available online 25 July 2013
Keywords:NanosensorsNanonetworksMACTerahertz BandEnergy harvesting
a b s t r a c t
Wireless NanoSensor Networks (WNSNs), i.e., networks of nanoscale devices with unprec-edented sensing capabilities, are the enabling technology of long-awaited applications suchas advanced health monitoring systems or surveillance networks for chemical and biologi-cal attack prevention. The peculiarities of the Terahertz Band, which is the envisionedfrequency band for communication among nano-devices, and the extreme energy limita-tions of nanosensors, which require the use of nanoscale energy harvesting systems, intro-duce major challenges in the design of MAC protocols for WNSNs. This paper aims to designenergy and spectrum-aware MAC protocols for WNSNs with the objective to achieve fair,throughput and lifetime optimal channel access by jointly optimizing the energy harvestingand consumption processes in nanosensors. Towards this end, the critical packet transmis-sion ratio (CTR) is derived, which is the maximum allowable ratio between the transmissiontime and the energy harvesting time, below which a nanosensor can harvest more energythan the consumed one, thus achieving perpetual data transmission. Based on the CTR, first,a novel symbol-compression scheduling algorithm, built on a recently proposed pulse-based physical layer technique, is introduced. The symbol-compression solution utilizesthe unique elasticity of the inter-symbol spacing of the pulse-based physical layer to allowa large number of nanosensors to transmit their packets in parallel without inducing colli-sions. In addition, a packet-level timeline scheduling algorithm, built on a theoretical band-width-adaptive capacity-optimal physical layer, is proposed with an objective to achievebalanced single-user throughput with infinite network lifetime. The simulation resultsshow that the proposed simple scheduling algorithms can enable nanosensors to transmitwith extremely high speed perpetually without replacing the batteries.
� 2013 Elsevier B.V. All rights reserved.
1. Introduction with very specific functionalities, such as computing, data
Nanotechnology is providing a new set of tools to theengineering community to create nanoscale components
storing, sensing and actuation. Advanced nano-devicescan be created by integrating several of these nano-compo-nents in a single entity. An early application of these nano-devices is in the field of nanosensing. Nanosensors takeadvantage of the unique properties of novel nanomaterialsto detect new types of events at the nanoscale. WNSNs, i.e.,networks of nanosensors, will enable advanced applica-tions of nanotechnology in the biomedical field (e.g., intra-body health monitoring and drug delivery systems), inenvironmental research (e.g., agriculture plague and air
2542 P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555
pollution control), and in defense and military technology(e.g., surveillance against new types of biological andchemical attacks at the nanoscale).
The peculiarities of nanosensors introduce many chal-lenges in the realization of WNSNs. On the one hand, theminiaturization of classical antennas to meet the sizerequirements of nanosensors would impose the use of veryhigh operating frequencies (hundreds of Terahertz), whichwould limit the feasibility of WNSNs. To overcome thislimitation, the use of graphene-based nano-antennas andnano-transceivers has been recently proposed[10,23,17,25]. As a result, nanosensors are expected tocommunicate in the Terahertz Band (0.1–10 THz). The Ter-ahertz Band suffers from a very high propagation loss,which drastically limits the communication range of nano-sensors due to their expectedly very limited power and en-ergy. At the same time, though, it provides a very largebandwidth, which can be used to develop simple but yetefficient modulation and medium sharing schemes.
On the other hand, the very limited amount of energythat nano-batteries can hold and the unfeasibility to man-ually recharge or replace them, have motivated the devel-opment of novel nanoscale energy harvesting systems[27,6,4]. Nanoscale power generators convert vibrational,fluidic, electromagnetic or acoustic energy into electricalenergy. When using energy harvesting systems, the energyof nanosensors does not just decrease with time, but hasboth positive and negative fluctuations. Therefore, ratherthan minimizing the energy consumption, a communica-tion system should optimize the use of the energy in thenano-battery by capturing its temporal fluctuations. Ulti-mately, WNSNs can achieve perpetual operation if the en-ergy consumption process and the energy harvestingprocess are jointly optimized.
Due to the transmission at very high speed in the Ter-ahertz Band and the expectedly very high number ofnanosensors in WNSNs willing to simultaneously commu-nicate, novel Medium Access Control (MAC) protocols areneeded to regulate the access to the channel and to coor-dinate and synchronize the transmissions among nano-devices. Classical MAC protocols cannot directly be usedin WNSNs because they do not capture (i) the limitedprocessing capabilities of nanosensors, which requiresthe development of ultra-low-complexity protocols [2];(ii) the peculiarities of the Terahertz Band [12], i.e., verylarge distant-dependent bandwidth (bandwidth is not aproblem anymore, but synchronization is) and very highpropagation loss (very limited transmission range); and,(iii) temporal energy fluctuations of nanosensors due tothe behavior of power nano-generators [9]. Therefore,there is a need to revise the traditional assumptions inMAC design and propose new solutions tailored to thisparadigm.
In this paper, we propose an energy and spectrumaware MAC protocol to achieve perpetual WNSNs. First,we propose to take advantage of the hierarchical networkarchitecture of WNSNs and shift the complexity of theMAC protocol towards more resourceful nano-controllers.In our solution, the nano-controller regulates the accessto the channel of the nanosensors, by following a TimeDivision Multiple Access (TDMA) approach. To guarantee
a fair, throughput and lifetime optimal access to the chan-nel, the nano-controller takes into account the datarequirements and energy constraints of the different nano-sensors willing to communicate. Moreover, this is done fortwo different possible physical layers, namely, a morepractical physical layer based on a recent proposedpulse-based scheme for nanoscale communications, and atheoretical bandwidth-adaptive capacity-optimal physicallayer. The system model and an overview of the proposedsolution are explained in Section 3 and Section 4,respectively.
As the essential building block of the proposed MACsolution, the throughput-and-lifetime optimal schedulehas to be designed, which aims to find an optimal trans-mission order for the nanosensors so that the networkthroughput is maximized, while maintaining the infinitenetwork lifetime. Towards this end, we first derive animportant system design parameter, namely, the criticalpacket transmission ratio (CTR). The CTR is the maximumallowable ratio between the transmission time and the en-ergy harvesting time, below which the nanosensor nodecan harvest more energy than the consumed one, thusachieving perpetual data transmission. Thanks to the pecu-liarities of the Terahertz Band and the nanoscale energyharvesting process, it is revealed that the CTR exhibits aunique distance-dependent nature so that nanosensors atdifferent locations possess different CTR. The definitionand the details on the computation of the CTR are ex-plained in Section 5.
Based on the CTR, a novel symbol-compression basedMAC solution, built on the pulse-based physical layer, isintroduced. The symbol-compression solution utilizes theunique elasticity of the inter-symbol spacing to allowmultiple nanosensors to transmit their packets in paral-lel without inducing any transmission collisions. Basedon this symbol-compression solution, a sub-optimalsymbol-compression scheduling algorithm is proposed,which can assign each nanosensor with different setsof transmission slots in such a way that all nanosensorsachieve their near-maximum single-user throughput,simultaneously, while maintaining their transmission ra-tios below the CTR for energy balancing. Different fromthe pulse-based physical layer, we reveal that there existthree unique properties of the capacity-optimal physicallayer, namely, (i) non-overlapped packet transmissions,(ii) nonexistence of throughput-and-lifetime optimalschedules, and (iii) the single-user throughput unbal-ance. Then, based on these properties, a packet-leveltimeline scheduling algorithm is proposed to achievethe balanced single-user throughput with the infinitenetwork lifetime. The algorithms are presented inSection 6.
The remainder of this paper is organized as follows. InSection 2, we review the recent literature related to MACprotocols for WNSNs. In Section 3, we describe the nano-sensor model and network model used in our analysis. InSection 4, we provide an overview of the proposed energyand spectrum-aware MAC protocol. In Section 5, we ana-lytically obtain the energy harvesting rate and the energyconsumption rate for the two proposed physical layers,and compute the CTR. We present the optimal throughput
P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555 2543
and lifetime scheduling algorithms in Section 6 and evalu-ate their performance in Section 7. Finally, we conclude thepaper in Section 8.
2. Related work
There are not many MAC solutions for WNSNs for thetime being. In [13], we proposed the PHLAME, the firstMAC protocol for ad hoc nanonetworks. In this protocol,nano-devices such as nanosensors are able to dynami-cally choose different physical layer parameters basedon the channel conditions and the energy of the nano-de-vices. These parameters were agreed between the trans-mitter nano-device and the receiver nano-device bymeans of a handshaking process. However, there aretwo limitations in the PHLAME. On the one hand, asshown in the paper, the use of a handshake process canlimit the real potential of the Terahertz Band. On theother hand, nanosensors might not have enough compu-tational resources to dynamically find the optimal com-munication parameters.
Existing MAC protocols for macroscale wireless sensornetworks or ad hoc networks are not adequate forWNSNs, because they do not capture the peculiarities ofthe Terahertz Band or the capabilities of nano-devicesand, in particular, of nanoscale energy harvesting systems.On the one hand, for the time being and to the best of ourknowledge, there are no MAC protocols for TerahertzBand communications. The closest wireless communica-tion technology is the use of the 5 GHz transmission win-dow at 60 GHz, which has been recently included in theIEEE 802.11ad [8,7]. This system adopts a very similar linklayer as the entire IEEE 802.11 standard. However, it iswell known that the use of the classical handshake pro-cess limits the achievable throughput and latency of thistechnology. The main reason for this is the fact that whentransmitting at very high bit-rate and usually with direc-tional antennas, interference problems (e.g., hidden ter-minal problem) are not the main constraint, but themain challenge is to achieve tight synchronization amongthe devices. Some other MAC protocols for 60 GHz com-munication systems can be found in the literature [24],but these are usually only minor deviations from thestandard.
On the other hand, energy harvesting systems also af-fect the way in which MAC protocols should be designed.However, existing MAC protocols for energy harvestingWireless Sensor Networks (WSNs) [22,28] do not capturethe peculiarities of nanoscale energy harvesting systems.For example, in [22], the authors investigate the perfor-mance of SMAC in a solar-energy-powered WSN. In partic-ular, the impact of the sensors duty cycle on the averageenergy in the sensors battery and the achievable through-put is investigated by starting from an analytical model ofenergy harvester. However, solar energy might not be al-ways available to nanosensors, the efficiency of nanoscalephotovoltaic cells remains unknown, and the physicallayer of nanosensors is totally different to that of classicalsensors. In [28], two dynamic duty-cycle schedulingschemes (called DSR and DSP) are described. In DSR, each
sensor node is permitted to fine-tune its duty-cycle basedon the current amount of remaining energy only. Onceagain, however, this solution does not take the particularenergy harvesting process at the nanoscale or the behaviorof the Terahertz Band channel. From this, it is clear that anew MAC policy for WNSNs is needed.
3. System model
In this section, we summarize the main peculiarities ofnanosensors that affect the design of protocols for WNSNsas well as the envisioned network model of WNSNs.
3.1. Nanosensor model
The capabilities of nanosensors introduce major con-straints in the design of protocols for WNSNs. In particular,
� Nanosensors will have very limited computationalcapabilities. As a result, nanosensors are not capable ofhandling complicated communication protocols. Nano-processors are being enabled by the development ofsmaller transistors. The smallest transistor that has beenexperimentally tested to date is based on a thin graphenestrip, which is made of just 10 by 1 carbon atoms [19].These transistors are not only smaller, but also able tooperate at much higher frequencies (up to a few THz).However, the complexity of the operations that a nano-processor will be able to handle depends on the numberof transistors in the chip, thus, on its total size. We cap-ture this peculiarity in our model by defining a hierarchi-cal network architecture and shifting the protocolcomplexity from the nanosensors to more resourcefulnano-controllers [2], as we will explain in Section 3.2.� Nanosensors will be able to communicate over the
Terahertz Band(0.1–10 THz) by using novel nano-antennas [10,15,23] and nano-transceivers [5,17,21,25],which exploit the unique properties of novel nanomate-rials such as graphene. The Terahertz Band channel sup-ports the transmission at very high bit-rates (up to a fewTerabits per second) but only over very short distances(below 1 m) [12,18]. Due to molecular absorption, i.e.,the process by which part of the EM energy of a wave isconverted into kinetic energy internal to vibrating gas-eous molecules, the available transmission bandwidthof the Terahertz Band shows a very unique distance-dependent behavior. In particular, the available trans-mission bandwidth can shrink from almost 10 THz atfew millimeters to just a few tens of Gigahertz at a fewcentimeters. We capture this peculiarity in our modelby considering novel bandwidth-adaptive communica-tion schemes, as we will explain in Section 5.� Nanosensors will require energy harvesting nano-
systems for continuous operation. The amount ofenergy that can be stored in the nanosensor batteriesis extremely low. As a result, nanosensors can onlycomplete a very few tasks with a single battery charge.Due to the impossibility to manually recharge orreplace the batteries of the nanosensors, novel energyharvesting nano-systems have been developed[27,6,4]. In contrast to the classical battery-powered
2544 P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555
devices, the energy of the self-powered devices does notjust decrease until the battery is empty, but it has bothpositive and negative fluctuations. As a result, the life-time of energy harvesting networks can tend to infinityprovided that the energy harvesting and the energyconsumption processes are jointly designed. We cap-ture this peculiarity in our model by jointly analyzingthe energy consumption process due to communicationin the Terahertz Band and the energy harvesting processby means of a piezoelectric nano-generator, as weexplain in Section 5.
3.2. Network model
Due to the limitations of individual nanosensors, in or-der to enable large-scale nanosensor networks, a hierarchi-cal network architecture is required, where the wholenetwork is partitioned into a set of clusters. Each clusteris locally coordinated by a nanocontroller with more ad-vanced capabilities and, thus, the complexity of any proto-col or algorithm can be pushed towards the nano-controller side. In addition, the nano-controller can be usedto guarantee the required physical layer synchronizationfor communication at very high data-rates in the TerahertzBand. As first described in [2],the nano-controller is ex-pected to have more capabilities than a simple nanosensor,at the expense of a much larger size.
4. Overview of energy and spectrum-aware MAC
The Terahertz Band supports the transmission at veryhigh bit-rates. MAC protocols that involve heavy signaling(e.g., classical handshaking process with conventionalRequestToSend and ClearToSend packet exchange) may limitthe achievable throughput of Terahertz Band communica-tion networks, especially if an external device, in this casethe nanocontroller, can take care of the synchronizationamong nano-devices. For this, we propose a dynamicscheduling scheme based on TDMA, which is tailored tothe capabilities of the nanosensors and the peculiaritiesof the Terahertz Band.
In this scheme, each nanosensor is dynamically as-signed variable-length transmission time slots. The lengthof the slots is related to the amount of data it needs totransmit, the distance and channel conditions betweenthe nanosensor and the nanocontroller, and the energy inthe battery of the nanosensor, as we will detail next. Whennot transmitting, the nanosensor is sleeping. The energyharvesting process by which the nanosensors can replenishtheir batteries is performed in both transmission andsleeping timeslots. The objective is to optimally assigntransmission and sleeping timeslots among nanosensorsin such a way that the harvested energy and the consumedenergy are balanced for each nanosensor, thus leading toinfinite network lifetime. Besides the everlasting networkoperation, the proposed scheduling algorithm also needsto ensure the throughput optimality so that all nanosen-sors can achieve their respective maximum single-userthroughput simultaneously.
Before determining how the time slots can be optimallyallocated to different nanosensors, we define the timeframe structure considered in our analysis. Each frame isdivided in three fixed-length sub-frames: Down Link (DL),Up Link (UL) and Random Access (RA). In the DL, the nano-controller broadcasts (BC) general information and can alsosend targeted data or commands to specific nanosensors.Different nanosensors have slots with different lengths.The DL can also be used to send wake up preambles to acti-vate specific nanosensors or all of them (BC). In the UL,nanosensors send data to the nanocontroller. As in theDL, different nanosensors might have slots with differentlengths. Finally, in the RA, nanosensors can require theslots to the nanocontroller for the next frame, or can ex-change information among them in an ad hoc fashion ifthe protocol supports it.
In our analysis, we focus on the UL, as the transmissionof information is the process that is most affected by thepower and energy limitations of nanosensors. In our sce-nario, when nanosensor that needs to transmit data tothe nanocontroller will inform the latter by sending a re-quest in the RA sub-frame. The transmission requestshould specify the nanosensor ID, amount of data, andremaining energy. On its turn, the nanocontroller will usethe received request as well as the measured channel con-ditions to optimally determine the way that the nanosen-sor should proceed. This is notified to the nanosensor inthe next frame DL.
5. Critical packet transmission ratio
Since all the nanosensors should directly communicatewith the nanocontroller, to achieve the above design objec-tives (not to consume more energy than the available oneand make sure a fair use of the resources among nanosen-sors), we need first to derive the critical packet transmis-sion ratio (CTR) at different distances. The CTR is definedas the ratio between the duration of the transmission slotand the total duration of the transmission timeslot andthe sleeping timeslot. Below this CTR, the sensor nodecan harvest more energy than the consumed one, thusachieving perpetual data transmission.
To determine the CTR, we need to evaluate the packetenergy consumption rate and packet energy harvestingrate, respectively. In our analysis, we consider two differ-ent communication schemes to compute the energy con-sumption rate. First, we consider TS-OOK [11], a recentlyproposed communication scheme for nano-devices basedon the transmission of femtosecond-long pulses by follow-ing an on–off keying modulation spread in time. Second,we consider the use of a capacity-optimal communicationscheme, which will serve to determine the upper bound interms of performance.
5.1. Energy consumption rate for TS-OOK-basedcommunication
In light of the state of the art in graphene-based nano-electronics, we consider first the use of TS-OOK [11], a re-cently proposed communication scheme for nano-devices,
P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555 2545
which is based on the transmission of very short pulses,just one-hundred-femtosecond long, by following an on–off keying modulation spread in time. These pulses canbe generated and detected with compact nano-transceiv-ers based on graphene and high-electron-mobility materi-als such as Gallium Nitride or compounds of Gallium-Arsenide [14,20,17,1,26].
The functioning of TS-OOK is as follows. The symbol ‘‘1’’is transmitted by using a one-hundred-femtosecond-longpulse and the symbol ‘‘0’’ is transmitted as silence, i.e.,the nano-device remains silent. The time between symbolsts is much longer than the symbol duration tp, i.e., b = ts/tp� 1. The reason for this is twofold. On the one hand,due to technology limitations, pulses cannot be emittedin a burst. On the other hand, the separation of pulses intime allows for the relaxation of the vibrating moleculesin the channel [12]. During the time between symbols, adevice can either remain idle or receive other incominginformation flows. Therefore, TS-OOK enables simple mul-tiple-access policies.
We next derive the energy consumption rate whenusing TS-OOK. First, the energy per pulse in TS-OOK is con-stant and equal to Ep. This value is a technology constraintand, according to the state of the art in Terahertz Bandpulse emitters [14,20,17,1,26], Ep is in the order of a fewaJ (10�18 J). This value corresponds to a peak pulse trans-mission power in the order of a few lW. Note that, duringthe transmission of ‘‘0’’s, no energy is consumed.
From [11], the maximum achievable information rate IRwith TS-OOK in bit/symbol as a function of the transmis-sion distance d is given by,
IRðdÞ ¼maxX
�X1
m¼0
pmlog2pm
(
�Z X1
m¼0
pmffiffiffiffiffiffiffiffiffiffiffiffiffi2pNmp exp �1
2ðy� amðdÞÞ2
NmðdÞ
!
� log2
X1
n¼0
pn
pm
ffiffiffiffiffiffiffiffiffiffiffiffiffiNmðdÞNnðdÞ
s
� exp �12ðy� anðdÞÞ2
NmðdÞþ 1
2ðy� amðdÞÞ2
NmðdÞ
!!dy
);ð1Þ
where X = {p0,p1} refers to the transmitter source proba-bility distribution, pm refers to the probability of transmit-ting symbol m = {0,1}, i.e., the probability to stay silent orto transmit a pulse, respectively, and am and Nm stand forthe amplitude of the received symbol and the total noisepower associated to the transmitted symbol m, which de-pend on the transmission distance and are obtained byusing the Terahertz Band channel model in [12]. Note thatIR is not always achieved for the equiprobable sourcedistribution X (p0 = p1 = 0.5). This is a consequence ofthe Terahertz Band channel asymmetric noise behavior[11].
Based on these, we define the energy consumption ratekcon�tsook in J/s as
kcon�tsookðdÞ ¼ kbitðdÞ1
IRðdÞ Epulsep̂1ðdÞ; ð2Þ
where kbit is the transmission bit-rate in bit/s, IR is theachievable information rate in bit/symbol, Epulse is the en-ergy per pulse consumption and p̂1 is the optimal probabil-ity to transmit a pulse for which the IR is achieved. Notethat kbit should not exceed the achievable information ratein bit/s, i.e.,
kbitðdÞ 6 RtsookðdÞ ¼BbIRðdÞ; ð3Þ
where B is the maximum bandwidth (i.e., 10 THz in ouranalysis), b is the spreading factor, and Rtsook is the maxi-mum transmission rate in bit/s and IR is the maximumachievable information rate in bit/symbol given by (1).
5.2. Energy consumption rate for capacity-optimalbandwidth-adaptive communication
Aimed at obtaining theoretical bounds for the perfor-mance of our MAC solution for WNSNs, we consider nextthe use of a capacity-optimal bandwidth-adaptive commu-nication scheme. Indeed, the Terahertz Band channel has avery peculiar behavior with distance. On the one hand, asin any wireless communication scheme, the path-loss suf-fered by a propagating signal increases with the transmis-sion distance. Therefore, as the distance between ananosensor and the nanocontroller increases, a higherpower is needed to guarantee a target Signal-to-Noise Ra-tio (SNR) at the receiver. On the other hand, due to molec-ular absorption, the available transmission bandwidthdrastically decreases with distance. As a result, a longertransmission time is needed to transmit the same amountof information. Therefore, the energy per bit consumptionincrease with distance is twofold, i.e., a higher power isneeded over a longer timeslot.
In order to mathematically capture this behavior, weproceed as follows. In this first case, we consider thatnanosensors can make use of dynamic power control.Therefore, the transmission power P to guarantee a targetSNR at the receiver is given by
PðdÞ ¼Z
B3dBðdÞSðd; f Þdf ¼ SNR
ZB3dBðdÞ
Aðd; f ÞSNðd; f Þdf ; ð4Þ
where d refers to the transmission distance, B3dB is the 3 dBbandwidth, Sopt is the optimal power spectral density(p.s.d.) of the transmitted signal, f stands for frequency, Ais total path-loss and SN is the noise p.s.d.
The total path-loss A in (4) can be written as [12]
Aðd; f Þ ¼ c4pdf0
� �2
expð�kðf ÞdÞ; ð5Þ
where d refers to the transmission distance, f stands for thefrequency, f0 is the design center frequency, c is the speedof light in the vacuum, and k is the molecular absorptioncoefficient,
kðf Þ ¼X
i
pp0
TSTP
TQ iriðf Þ; ð6Þ
where p refers to the system pressure in Kelvin, p0 is thereference pressure, TSTP is the temperature at standardpressure, Qi is the number of molecules per volume unit
2546 P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555
of gas i and ri is the absorption cross-section of gas i. Moredetails on how to compute the molecular absorption cross-section r can be found in [12].
The noise in the Terahertz Band is mainly contributedby the molecular absorption noise. This type of noise isgenerated by vibrating gaseous molecules which reradiatepart of the energy that have been previously absorbed.Therefore, this noise is correlated to the transmitted signal.From [12], the total molecular absorption noise p.s.d. SN iscontributed by the atmospheric noise SN0 [3] and the in-duced noise SN1 , and can be obtained as
SNðd; f Þ ¼ SN0 ðd; f Þ þ SN1 ðd; f Þ; ð7Þ
SN0 ðf Þ ¼ limd!1
kBT0ð1� expð�kðf ÞdÞÞ cffiffiffiffiffiffiffi4pp
f0
!2
; ð8Þ
SN1 ðd; f Þ ¼ Sðf Þð1� expð�kðf ÞdÞÞ c4pdf0
� �2
; ð9Þ
where d refers to the transmission distance, f stands for thefrequency, kB is the Boltzmann constant, T0 is the roomtemperature, k is the molecular absorption coefficient in(6), c is the speed of light in the vacuum, f0 is the designcenter frequency, and S is the p.s.d. of the transmittedsignal.
The 3 dB bandwidth B3dB as a function of the transmis-sion distance d is defined as the range of frequencies suchthat
f jAðd; f ÞSNðd; f Þ 6 2Aðd; f0ðdÞÞSNðd; f0ðdÞÞf g; ð10Þ
where f0 is the center frequency and also depends on thetransmission distance.
To compute the capacity of the Terahertz Band underthis scheme, we proceed as follows. First, note that the in-duced noise N1 (9) depends on the p.s.d. of the transmittedsignal S as well as on the absorption coefficient of the chan-nel k. By properly selecting S; SN1 can become negligibleand thus SN � SN0 . Similarly to the water filling principle,by allocating the power of the transmitted signal only atthose frequencies at which the resulting noise is lower,we can maximize the achievable information rate or capac-ity. By considering the resulting molecular absorptionnoise in (7) to be additive and Gaussian, the maximumtransmission bit-rate C can be written as
CðdÞ ¼Z
B3dBðdÞlog2 1þ Sðd; f ÞA�1ðd; f Þ
SN0 ðd; f Þ
!df
¼ B3dBðdÞlog2ð1þ SNRÞ; ð11Þ
where B3dB stands for the 3 dB bandwidth in (10), S is thepower spectral density of the transmitted signal, A is thechannel path-loss and SN0 is the noise p.s.d.
The average energy per bit consumption Ebit�opt as afunction of the transmission distance d can be obtained as
Ebit�optðdÞ ¼PðdÞCðdÞ ¼
SNRR
B3dBðdÞAðd; f ÞSN0ðd; f Þdf
B3dBðdÞlog2ð1þ SNRÞ : ð12Þ
Finally, we define the energy consumption rate kcon�opt in J/s for the optimal communication scheme as
kcon�optðdÞ ¼ kbitðdÞEbit�optðdÞ; ð13Þ
where d refers to distance, kbit is the bit transmission rateand Ebit�opt is the energy per bit consumption in (12). Notethat kbit should not exceed the transmission rate Ropt orcapacity of the system given by (11):
kbitðdÞ 6 RoptðdÞ ¼ CðdÞ: ð14Þ
5.3. Energy harvesting rate
As introduced in Section 3, nanosensors require energyharvesting systems to replenish their batteries. Amongstothers, one of the main alternatives is to use novel piezo-electric nano-generators [27]. A piezoelectric nano-genera-tor converts vibrational and kinetic energy into electricityby exploiting the piezoelectric behavior of Zinc Oxidenanowires. Every time that the ZnO nanowires are com-pressed or released, a small electric current is generated.This can be used to recharge an ultra-nano-capacitor afterproper rectification. Our starting point for our analysis isthe model introduced in [9], which can accurately repro-duce experimental measurements.
We are interested in the energy harvesting rate, i.e., thespeed at which the battery is replenished, kharv. The energyin battery can be written as
Ebatt ¼12
V2g Ccap 1� exp � DQ
VgCcapncycle
� �� �; ð15Þ
where Vg is the generator voltage, Ccap refers to the ultra-nano-capacitor capacitance, and DQ is the electric chargeharvested per cycle.
From this, the energy harvesting rate in J/s is obtainedas:
kharv ¼ kcycle@Ebatt
@ncycle
¼ 12
CcapV2g 2
DQVgCcap
exp � DQVgCcap
ncycle
� ��
�2DQ
VgCcapexp �2
DQVgCcap
ncycle
� ��; ð16Þ
where kcycle is the vibration frequency or compression-re-lease rate of the ZnO nanowires, and the rest of parametershave already been defined.
5.4. Critical packet transmission ratio
The CTR kc can be obtained by taking into account thatthe energy harvested during a time slot of length T is largerthan the energy consumed during the transmission timeTtx:
kharvT P kconTtx: ð17Þ
Thus,
kcðdÞ ¼ kharv
kconðdÞð18Þ
where kcon = kcon�opt in (13) for capacity-optimal communi-cation and kcon = kcon�tsookin (2) for TS-OOK-basedcommunication.
P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555 2547
6. Throughput-and-lifetime optimal scheduling
As introduced in the previous section, the critical packettransmission ratio determines the percentage of time ananosensor can transmit so that it can ensure the balancebetween the harvested and the consumed energies. In thissection, based on this CTR, we study the throughput-and-lifetime optimal scheduling problem, which aims to findan optimal transmission schedule for the nanosensors sothat the network throughput is maximized, while main-taining the infinite network lifetime. To this end, we pro-pose the optimal scheduling algorithms for TS-OOK-based and capacity-optimal nano-communication, respec-tively. The proposed algorithms can assign each nanosen-sor with different sets of transmission slots in such a waythat all nanosensors achieve their maximum single-userthroughput, simultaneously, while maintaining theirtransmission ratios below the critical ones for energy bal-ancing. Specifically, the throughput-and-lifetime optimalscheduling problem can be formally defined as follows.First, the following notations are introduced.
Si the transmission schedule of sensor iRi the maximum achievable date rate of sensor isi,j the start time of the jth packet of sensor i in Si
fi,j the finish time of the jth packet of sensor i in Si
C the total transmission schedule, i.e., C =S
i6MSi
LC the length of the transmission scheduleNC
i the total number of packets sent by sensor i in C
Definition 1 (Total Transmission Schedule). Let the trans-mission schedule Si of each nanosensor ni be denoted bya triplet
Si si;j; fi;j j6NCi;NC
i
� �: ð19Þ
Then, the total transmission schedule can be defined as
C ¼ Si fsi;j; fi;jgj6NCi;NC
i
� �n oi6M
: ð20Þ
Definition 2 (Maximum single-user throughput). The max-imum single-user throughput K is defined as the maxi-mum data rate a nanosensor can achieve to guaranteethe infinite network lifetime, i.e., for a nanosensor i at adistance di from nanocontroller
Ki ¼ RikcðdiÞ; ð21Þ
where kc(di) is the CTR given in (18) and Ri is the maximumachievable date rate, i.e., Ri = Ropt for capacity optimal com-munication given in (14) and Ri = Rtsook for TS-OOK commu-nication given in (3).
Now, the throughput-and-lifetime optimal schedulingcan be formally defined as follows.
Definition 3 (Throughput-and-Lifetime Optimal Scheduling(TLOS) problem). Given M nanosensors, find a transmissionschedule Si for each nanosensor ni so that the totaltransmission schedule C satisfies the following conditions
1. Non-Collision: no nanosensor starts its transmissionduring the transmissions of any other nanosensors.
2. Throughput Optimality: each nanosensor has a trans-mission schedule Si 2 C, by which it can achieve themaximum single-user throughput Ki defined in Defini-tion 2, i.e.,
ð9CÞð8ni; i 6 MÞ :
P|6NC
iðfi;j � si;jÞLC
¼ kcðdiÞ:
and consequently
Ki ¼ RikcðdiÞ;8ni; i 6 M: ð22Þ
3. Lifetime Optimality: each nanosensor can sufficientlyrecharge itself so that it has enough energy for the nextpacket transmission, i.e.,
si;j � si;j�1 P Ti;8i 6 M; j 6 NCi ; ð23Þ
where Ti is the minimum transmission period (MTP) perpacket for the balanced energy consumption and harvest-ing, i.e.,
Ti ¼Nbits
RikcðdiÞ
: ð24Þ
Remark 1. In the above definition, conditions (1) and (2)guarantee that the network throughput is maximized byallowing all the nanosensors approach their respective sin-gle-user throughput simultaneously, without allowing anyinter-user transmission collisions. The condition (3)ensures that the nanosensor network has the infinite net-work lifetime by letting each nanosensor achieve the bal-anced energy consumption and harvesting.
In the rest of this section, we present the optimal algo-rithms to solve the throughput-and-lifetime optimalscheduling problem under two scenarios: (1) TS-OOK com-munication and (2) capacity-optimal communication.
6.1. Symbol-compression scheduling for TS-OOK
As introduced in Section 5.1, TS-OOK is a communica-tion scheme based on the transmission of a train of veryshort symbols (pulse as ‘‘1’’ and silence as ‘‘0’’) with fixedlength equal to one hundred femtoseconds. However, asintroduced in Section 5.1, the inter-symbol spacing ts ofTS-OOK, i.e., the time separation between two consecutivesymbols, shows great elasticity. The unique elasticity of TS-OOK paves the way to a novel MAC scheme for nanosensornetworks, namely, symbol-compression communication.
The basic idea of this scheme is that based on the inter-symbol spacing diversity of nanosensors, the packet trans-missions of multiple nanosensors can be performed simul-taneously or in parallel by compressing or interleaving thesymbol transmissions of multiple nanosensors within aproper time interval. This interval is much shorter thanthe total time of sequentially sending each nanosensor’spacket back to back. An example of symbol-compressioncommunication is shown in Fig. 1. Consider two nanosen-sors with different transmission rates. By properly arrang-ing the symbol transmission time, the two nanosensors can
Nano sensor 2
Nano controller
Nano sensor 1
p t ts
1
ts2
Fig. 1. Symbol-compression communication using TS-OOK.
2548 P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555
transmit with their respective transmission rate withoutcausing any symbol collisions.
Based on the symbol compression communication, wenext propose a throughput and lifetime optimal schedulingalgorithm by allocating the symbol transmissions of nano-sensors in the optimal time instances so that the condi-tions given in Definition 3 are satisfied. The pseudo codeof the proposed algorithm is given in Algorithm 1 withthe steps summarized as follows.
Step I (Line 1–2 of Algorithm 1): for each nanosensor ni,which is di away from nanocontroller, calculatethe number of symbols (NoS) per packet Ns
i andthe MTP per packet Ti, Specifically, we have
Nsi ¼
Nbits
IRiðdiÞ; ð25Þ
where IRi dið Þ, given in (1), is the maximum achievableinformation rate of nanosensor ni with TS-OOK in bit/sym-bol. Combining (24) and (3) yields
Ti ¼Nbitsb
IRiðdiÞBkci
; ð26Þ
where B is the maximum bandwidth, b is the spreadingfactor or ratio between the time between symbols ts andthe symbol duration tp. Then, the rounded MTP T�i is de-fined as the nearest multiple of tp, i.e.,
T�i ¼Ti
tp
� �tp; ð27Þ
Consequently, the length of the transmission schedule LC isdefined as the least common multiple (LCM) of therounded MTP of the nanosensors, i.e.,
LC ¼ LCMðT�1; T�2; . . . ; T�MÞ: ð28Þ
Step II (Line 3–5 of Algorithm 1): for each nanosensor ni,define the transmission period per symbol (TPPS)as follows
T 0i ¼T�i
Nsi � 1
; ð29Þ
which, by combining (25) and (27), yields
T 0i ¼Nbitsts
BIRiðdiÞkci tp2
& ’tpIRiðdiÞ
Nbits; ð30Þ
where B is the maximum bandwidth (i.e., 10 THz in ouranalysis). Arrange nanosensors {n1, . . . , nM} in a decreasingorder of T0i, i.e., if i < j, then T0i > T0j. Then, assign each nano-sensor ni a priority pi = i. By this way, the sensor with thelongest TTPS T0i has the lowest priority pi.Step III (Line 6–16 of Algorithm 1): assume the symbol of
each nanosensor ni arrives at the period T0i. Foreach time slot sj of the schedule C, the nanocon-troller decides which sensor has the right to trans-mit during sj, based on its associated countercounti and priority pi. Specifically, among all nano-sensors with nonzero counti, the nanosensor withthe highest priority pi owns the transmission rightduring sj and thus sj is assigned to the transmis-sion schedule Si of nanosensor ni. Initially, allcounters {counti} are set as zero and then counti
is updated at every time slot sj. If a symbol ofnanosensor ni arrives during sj, set Ci = 1. Other-wise, two scenarios can happen. If nanosensor ni
wins the transmission right during sj, then setcounti = 0, and otherwise, keeps counti unchanged.
Algorithm 1. Symbol-Compression Scheduling
1:
Compute Nsi and Ti, "ni6M;l l2:
T�i Titp tp; LC LCMðT�1; . . . ; T�MÞ3:
T 0i T�iNsi
4:
ffngi6MjT0i < T 0j;8i > jg5:
pi i, "i 6M 6: Associate each sensor ni with a schedule Si and acounter counti
7:
j 0; Si £, counti 1, "i 6M 8: while jtp6 LC do
9: if pi == maxi6Mpi and counti == 1 then 10: Si Si [ {sj}; counti 0 11: end if 12: if 9m 2 Nþ : jTs6 mT 0i 6 ðjþ 1ÞTs then
13: counti 1 14: end if 15: j j + 1 16: end whileThe following Theorem defines the conditions underwhich the proposed symbol-compression algorithm leadto a throughput and lifetime near optimal schedule,i.e., each nanosensor has unlimited lifetime with thenear-optimal transmission ratio k�i , i.e.,
k�i ¼Ns
i � 1Ns
i
kcðdiÞ ð31Þ
and the near-maximum single-user throughput K�i , i.e.,
K�i ¼ k�i Ri ¼Ns
i � 1Ns
i
Ki; ð32Þ
where Ki is the maximum single-user throughput given in(21).
P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555 2549
Theorem 1. Consider M nanosensors. The schedule C yieldedfrom Algorithm 1 is throughput-and-lifetime near-optimal, if
maxi6M
tp
T 0i6
1r þM
with r ¼max
i6MT 0i
mini6M
T 0ið33Þ
and T0i is the TPPS defined in (30).
Remark 2. The above Theorem implies that if the numberof nanosenors is less than 1/(maxi6Mtp/ T 0i) � r, the symbol-compression algorithm can generate a throughput-and-lifetime near-optimal schedule. As shown in Fig. 2, T 0i isof 104 order in picosecond and r, the ratio between themaxðT 0iÞ and minðT 0iÞ is less than two. In addition, the sym-bol duration or the pulse width tp can be as small as 0.1picosecond. This means that the proposed scheduling algo-rithm can allow a large number of nanosensors (e.g., in theorder of 105) to operate at their respective near-maximumsingle-user throughput.
Proof Theorem 1. First, it is easy to show that finding thethroughput-and-lifetime near-optimal schedule is equiva-lent to finding the throughput and lifetime optimal sche-dule with the optimal throughput equal to K�i in (32).Then, we can show that the throughput-and-lifetime opti-mal scheduling (TLOS) problem (given in Definition 3) canbe reduced into a non-preemptive periodic task scheduling(NPTS) problem. Next, we prove that the rate monotonicscheduling algorithm for NPTS is a generalized version ofthe proposed symbol-compression scheduling algorithmfor TLOS. Consequently, the schedulability condition ofthe rate monotonic scheduling can lead to the optimalitycondition of the symbol-compression scheduling.
Given a set of nanosensors {ni}i6M, for each nanosensorni, we first convert the throughput optimality and lifetimeoptimality defined in Definition 3 into a periodic taskmodel tkiðTA
i ; TEi ; T
Di Þ, where TA
i is the task arrival period, TEi
is the task execution time and TDi is the relative deadline of
the task, which is the maximum allowable time betweenthe task arrival and the task completion. Because our
10−4 10−3 10−2 10−1 1001.35
1.4
1.45
1.5
1.55
1.6
1.65x 104
Distance [m]
T i′ [ps]
Fig. 2. The transmission period per symbol (TPPS) as a function ofdistance.
algorithm is a symbol-level scheduling approach, each taskrepresents a symbol. Then, the symbol transmissions of allthe nanosensors can be denoted by a set of periodic tasks,i.e.,
TK ¼ ftkiðTAi ; T
Ei ; T
Di Þ; i ¼ 1;2; . . . ;Mg: ð34Þ
Consider a particular nanosensor ni, it has Nsi symbols per
packet. First, we have
TEi ¼ tp: ð35Þ
Then, according to Definition of 3(2), to guarantee thethroughput optimality, it is sufficient to let nanosensor ni
finish sending Nsi symbols for every Ti seconds, where Ti
is the minimum transmission period (MTP) given in (24).This implies
TAi ¼
Ti
Nsi
and TDi ¼ TA
i ð36Þ
and if the deadline TDi can be met for every task, by com-
bining (36) and (24), it follows that nanosensor ni canachieve the maximum single-user throughput, i.e.,
K�i ¼TE
i
TDi
RtsookðdiÞ ¼Ns
i tp
Ti¼ Ki: ð37Þ
Next, according to Definition of 3(3), to guarantee the life-time optimality, it is sufficient to ensure the following twoconditions are met: (1) the time difference Ts
i between thefirst symbol of ni’s current packet and that of its previouspacket is larger than Ti; (2) the symbol transmissions ofni are evenly scattered within Ts
i . To this end, we let
TDi ¼
Ti
Nsi � 1
; ð38Þ
which ensures that under any scheduling algorithms, itfollows
Tsi ¼ Ni
Ti
Nsi � 1
> Ti: ð39Þ
For the sake of design simplicity, let
TAi ¼ TD
i ¼Ti
Nsi � 1
; ð40Þ
This, combining (29) and the fact that
Ti � tp and T�i ¼Ti
tp
� �tp � Ti; ð41Þ
yields
TDi � T 0i: ð42Þ
If every task is finished before the deadline TDi , it follows by
combining (40) and (24) that ni achieve near-maximumsingle-user throughput
K�i ¼TE
i
TDi
RtsookðdiÞ ¼ðNs
i � 1Þtp
Ti¼ Ns
i � 1Ns
i
Ki: ð43Þ
Finally, according to Definition of 3(1), to guarantee non-collisions among nanosensors, preemptions are not al-lowed during any scheduling algorithms, which means as
2550 P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555
long as a nanosensor begins to transmit a symbol, duringthis symbol transmission, no other nanosensors can bescheduled to transmit.
Based on the above modeling, finding a throughput-and-lifetime near-optimal schedule is equivalent to solvingthe non-preemptive periodic task scheduling problem,which aims to find a feasible task schedule for the taskset TK ¼ ftkiðTA
i ; TEi ; T
Di Þ; i ¼ 1;2; . . . ;Mg, by which all tasks
complete their execution before their respective deadlines,while no preemptions are allowed. Given a task set, it hasbeen proven in [16] that the rate monotonic schedulingalgorithm, which assigns the highest priority to the taskwith the shortest deadline TD
i , is effective to find thefeasible schedule. Based on the pseudo code in Algorithm1, it can be shown that the proposed symbol-compressionalgorithm can be reduced to the rate monotonic schedulingalgorithm. According to Theorem 4 in [16], a task setTK ¼ ftkiðTA
i ; TEi ; T
Di Þ; i ¼ 1;2; . . . ;Mg is schedulable under
the rate monotonic scheduling, i.e., there is a feasibleschedule for the task set by performing the rate monotonicscheduling, if
maxi6M
TEi
TDi
61
r þMwith r ¼
maxi6M
TDi
mini6M
TDi
: ð44Þ
This, combining (35) and (42) completes the proof. h
6.2. Timeline scheduling for capacity-optimal communication
In this section, we first present three properties of thecapacity-optimal communications, namely, (1) non-over-lapped packet transmissions, (2) nonexistence of through-put-and-lifetime optimal schedules, and (3) single-userthroughput unbalance. Then, based on these properties,we propose a packet-level timeline scheduling algorithmto achieve the balanced single-user throughput with theinfinite network lifetime.
6.2.1. Non-overlapped packet transmissionsDifferent from the pulse-based communication, the
capacity-optimal communication cannot perform symbol-level scheduling because the waveform that conveys thesymbols has to be arbitrary so that the maximum trans-mission bit-rate given in (11) can be achieved. This impliesthat under the capacity-optimal communication, the trans-mission durations of different nanosensors cannot be over-lapped. In other words, when one nanosensor istransmitting a packet. all other nanosensors are not al-lowed to transmit. Consequently, different from the sym-bol-level scheduling for pulse-based physical layertechnique, the scheduling has to be performed on the pack-et-to-packet level for the capacity-optimal case.
6.2.2. Nonexistence of the throughput-and-lifetime optimalschedule
The following Theorem defines the conditions underwhich the throughput-and-lifetime optimal schedule doesnot exist under the capacity-optimal communication.
Theorem 2. If there exists at least one nanosensor residingwithin the distance D of the nanocontroller, where
D ¼ arg maxd>0
kharv > kcon�optðdÞ; ð45Þ
then no scheduling algorithms can yield the throughput-and-lifetime optimal schedule under the capacity-optimalcommunication.
Remark 3. The above Theorem indicates that there mayexist an algorithm to generate the throughput-and-lifetimeoptimal schedule only if all nanosensors are at least D faraway from the nanocontroller. However, because the min-iature nature of nanosensors, generally, the nanosensorsare deployed randomly. Therefore, it is impossible to pre-vent the nanosensors being deployed within the range ofD of the nanocontroller. Moreover, the numerical analysisgiven in Fig. 4(a) in Section 7 shows that such D indeedexists for the capacity-optimal communication. This indi-cates that the throughput-and-lifetime optimal schedulenormally do not exist under the capacity-optimalcommunication.
Remark 4. It is worth to notice that the condition given in(45) is also applicable for the nonexistence of throughput-and-lifetime optimal schedule for TS-OOK. However, thenumerical analysis given in Fig. 3(a) in Section VII showskharv < kcon�opt(d) holds for any d > 0, This means that thedistance threshold D does not exist for TS-OOK. Therefore,given an arbitrary set of nanosensors with any deploymenttopology, the throughput-and-lifetime optimal schedulemay exist.
Proof Theorem 2. Similar to the proof of Theorem 1, wemodel the packet transmissions of nanosensors as a setof periodic tasks TK ¼ ftkiðTA
i ; TEi ; T
Di Þ; i ¼ 1;2; . . . ;Mg. Spe-
cifically, both the task arrival time TAi and task deadline
TDi are equal to Ti = Nbits/Rik
c(di), the minimum transmissionperiod (MTP) per packet defined in (24). The task executiontime TE
i is equal to the packet transmission time of nano-sensor i, i.e., TE
i ¼ Nbits=Ri. Based on this model, the taskset TK is schedulable only if
Pi6MTE
i =TDi 6 1. Since
TEi =TD
i ¼ kcðdiÞ, this implies that no throughput-and-life-time optimal schedule exists if
Pi6MkcðdiÞ > 1. This, com-
bining the fact kc(di) = kharv/kcon�opt, completes theproof. h
6.2.3. Single-user throughput unbalanceTheorem 2 indicates that under the capacity-optimal
communication, the nanosensors can be divided into twogroups: near-region sensors and far-region sensors. Thenear-region sensors, which are within the distance D ofthe nanocontroller, always have their energy harvestingrate kharv larger than their energy consumption ratekcon�opt. This indicates that the near-region sensors canoperate at their maximum achievable data rate withoutspending extra sleep time recharging their batteries.According to Definition 2, this implies that the maximum
10−4 10−3 10−2 10−1 100 10−4 10−3 10−2 10−1 1006.2
6.4
6.6
6.8
7
7.2
7.4x 10−3
Distance [m]
λc 108
1010
Distance [m]
Maximum single−user throughputMaximum achievable data rate
10−4 10−3 10−2 10−1
5
5.5
6
6.5
7x 107
Distance [m]
thro
ughp
ut [b
its/s
] Symbol−compression schedulingMaximum single user
Dat
a ra
te V
S. T
hrou
ghpu
t [b
its/s
]
106
Fig. 3. Symbol compression scheduling for TS-OOK.
P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555 2551
single-user throughput Knear(d) of a near-region sensor canapproach its maximum achievable data rate Ropt, i.e.,
KnearðdÞ ¼ RoptðdÞ;8d < D: ð46Þ
In contrary to the near-region sensors, the far-region sen-sors, which are at least D far away from the nanocontroller,always have their energy harvesting rate kharv less thantheir energy consumption rate kcon�opt. Therefore, the far-region sensors always need to enter the sleep state forrecharging before their next packet transmissions. This im-plies that the far-region sensors have the maximum single-user throughput Kfar(d) necessarily smaller than the max-imum achievable data rate Ropt, specifically,
KfarðdÞ ¼ kcðdÞRoptðdÞ;8d P D ð47Þ
Moreover, by analyzing Ropt given in (11), it is shown thatthe nanosensors at longer distance from the nanocontrollerhas the smaller maximum achievable data rate, i.e.,
RoptðdiÞ > RoptðdjÞ;8di < dj ð48Þ
In the light of (44)–(46), the maximum single-userthroughput of the far-region nanosensors is much smallerthan that of the near-region nanosensors, i.e.,
KnearðdiÞ � KfarðdiÞ with di < D < dj: ð49Þ
6.2.4. Packet-level timeline schedulingBased on the properties of the capacity-optimal com-
munication, we proposed a timeline scheduling algorithm,which decides the packet transmission order of the nano-sensors at a set of discrete uneven time instants with anobjective to ensure the infinite network lifetime with bal-anced single-user throughput between far-region sensorsand near-region ones. The pseudo code of the proposedalgorithm is given in Algorithm 2 with the steps summa-rized as follows.
Step I (Line 1–2 of Algorithm 2): calculate the minimumtransmission period (MTP) per packet Ti for eachnanosensors according to (24). Specifically, thenear-region nanosensor has
Ti ¼ Nbits=KnearðdiÞ ð50Þ
and the far-region nanosensor has
Ti ¼ Nbits=KfarðdiÞ: ð51Þ
Next, set the initial schedule length LC = maxi6MTi. Letdmax = maxi6Mdi. We have
LC ¼ Nbits=KfarðdmaxÞ: ð52Þ
Step 2 (Line 3–6 of Algorithm 2): associated each nano-sensor ni with a schedule Si as defined in Definition1. Set the packet counter in Si as NC
i ¼ 0. Then, cal-culate the packet transmission time
Tpki ¼ Nbits=RoptðdiÞ ð53Þ
for each nanosensor ni. Next, arrange the nanosensors {ni}-i6M in the increasing order of the maximum single-userthroughput K. Assign each nanosensor with a prioritypi = i, i.e., the nanosensor with smaller K has higherpriority.Step 3 (Line 7–14 of Algorithm 2): arrange the transmis-
sion order of nanosensors according to the prioritypi, the minimum transmission period (MTP) perpacket Ti, and the packet counter NC
i . At each sche-dule decision time s, among all nanosensors withthe smallest counter value, the nanosensor ni isscheduled to transmit at s if it satisfies three con-ditions. (1) It has the highest priority. (2) The back-ward difference between the current time s and thestart time of ni’s previous packet is not smallerthan its minimum transmission period (MTP) perpacket Ti, i.e.,
s� si;NCi
P Ti: ð54Þ
(3) The forward difference between the current time s andni’s first packet transmission time is not smaller than itsminimum transmission period (MTP) per packet Ti.
LC � sþ si;1 P Ti ð55Þ
If ni is scheduled to transmit at time s, the next scheduledecision time follows s ¼ sþ Tpk
i
2552 P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555
Step 4: the step 3 is repeated until two conditions are met.(1) All nanosensors have been scheduled to trans-mit at least once, i.e., NC
i P 1;8i 6 M. (2) the cur-rent schedule decision time sn is not smallerthan the schedule length LC
Algorithm 2. Timeline scheduling
1:
Ki Knear(di), if di < D; Ki Kfar(di), if di P D; 2: Ti Nbits/Ki, "ni6M; LC max (T1, . . . , TM) 3: Tpki Nbits=RoptðdiÞ;8ni6M
4:
{{n}i6M—Ki < Kj, "i < j} 5: pi i, "i 6M 6: s 0; Si £;NCi 0;8i 6 M
7: while s 6 LC and 9i 6 M : NCi < 1 do
8: if NCi ¼¼mini6MNCi and pi == maxi6Mpi then
9:
if s� si;NCi Ti and LC � s + si,1 Ti then10:
Si Si [ fsi;NCi¼ s; fi;NCi¼ sþ Tpk
i g;
11: NCi NCi þ 1; s ¼ sþ Tpk
i ;
12: end if 13: end if 14: end while7. Performance evaluation
In this section, we evaluate the performance of the pro-posed scheduling algorithms under the pulse-based physi-cal layer and the capacity optimal physical layer,respectively. Specifically, we first analyze the critical trans-mission ratio and the maximum single-user throughput ofthe above mentioned two communication schemes. Then,we study the actual single-user throughput under the pro-posed scheduling algorithms, which approaches the maxi-mum one.
In our numerical analysis, we use the following param-eter values. Pulses in TS-OOK are modeled as the first timederivative of a one-hundred-femtosecond long Gaussianpulse with a total energy of 1 aJ (which corresponds to apeak power of 1 lW). The Terahertz Band channel is mod-eled as in [12], for a standard gaseous medium with 10% ofwater vapor molecules. The piezoelectric energy harvest-ing system has the following parameters. We consider acapacitor with Ccap = 9 nF charged at Vg = 0.42 V for thecomputation of the energy in the nano-battery (15). Forthe computation of the energy harvesting rate kharv in(16), an ambient vibration with an average time betweenvibrations tcycle = 1/50 s is considered. The amount ofcharge DQ harvested per cycle is 6 pC. The battery is fullydischarged at the beginning of a simulation.
7.1. Symbol-compression scheduling for TS-OOK
As shown in Fig. 3(a), the critical transmission ratio of thepulse-based physical layer is always much less than one.This means that under the pulse-based communication, allnanosensors have to enter the sleep state for recharging
after each packet transmission. Moreover, Fig. 3(a) indicatesthat the sleeping time of the nanosensor is orderly longerthan the transmission time. On one hand, this feature allowa large number of nanosensors to share the spectrum effec-tively without inducing inter-user collisions. On the otherhand, the long sleeping time can lead to the reduced sin-gle-user throughput. Consequently, as shown in Fig. 3(b),the maximum achievable data rate is at least two order ofmagnitude higher than the maximum single-user through-put. However, in this case, the nanosensor can still achievethe date rate around 70 Mbits/s continuously.
Based on the above maximum single-user throughput,the proposed symbol-compression algorithm, shown inAlgorithm 1, aims to find the optimal schedule so that allnanosensors can obtain their maximum single-userthroughput simultaneously. To investigate the perfor-mance of the symbol-compression scheduling algorithm,we randomly select 160 nanosensors located within the ra-dius of 0.15 m of the nanocontroller. Fig. 3(c) shows thesingle-user throughput yielded by the symbol-compres-sion based scheduling algorithm. First, it is shown thatthe maximum single-user throughput is distance-depen-dent, which means the nanosensors closer to the noncon-troller have higher maximum single-user throughput.This is due to the fact that under the pulse-based physicallayer technique, all nanosensors utilize the equitant trans-mission power for the design simplicity and consequentlythe nanosensors closer to the nanocontroller have higherSNR, therefore leading to the higher throughput. Second,as shown in Fig. 3(c), the proposed symbol-compressionalgorithm can lead to the single-user throughput very closeto the maximum one, which means that with the simplescheduling algorithm, all nanosensors can continuouslyand simultaneously convey their sensing data to the nano-controller with very high data rate up to 60 Mbits/s.
7.2. Timeline scheduling for capacity-optimal communication
Now, we investigate the performance of the timelinescheduling algorithm under the capacity-optimal physicallayer technique. As shown in Fig. 4(a), the critical transmis-sion ratio of the capacity-optimal scheme shows thephase-transition phenomenon. More specifically, It isshown that there exists a distance D of around 0.04 m,above which the critical transmission ratio is less thanone and below which the critical transmission ratio is lar-ger than one. This phenomenon indicates that all nanosen-sors residing within D meter of the nanocontroller, a.k.a.the near-region nanosensors, can harvest more energyper second than the energy consumed for data transmis-sion. Theretofore, all near-region nanosensors can transmittheir data at full speed without entering the sleeping statefor recharging. On the contrary, all nanosensors residingmore than D meter far away from the nanocontroller,a.k.a. far-region nanosensors, have a critical transmissionratio less than one, therefore having to enter the sleepingstate for recharging.
The above phase transition phenomenon can lead to theunbalanced single-user throughput for the nanosensors. Asshown in Fig. 4(b), for the near-region nanosensors, theirsingle-user throughput is equal to the maximum achiev-
10−4 10−3 10−2 10−1 10010−20
10−10
100
1010
Distance [m]
λ c
0.02 0.04 0.06 0.08 0.1 0.12 0.14108
1010
1012
1014
Distance [m]
Dat
a R
ate
vs. T
hrou
ghpu
t
Maximum achievable data rate Maximum single−user throughput
0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14108
109
1010
1011
Distance [m]
Thro
ughp
ut [b
its/s
] Maximum single−user Timeline scheduling
[bits
/s]
Fig. 4. Timeline scheduling for capacity-optimal communication.
P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555 2553
able data rate. However, for the far-region nanosensors,their single-user throughput can be five order of magni-tude smaller than their maximum achievable data rate.This means that the far-region nanosensors have orderlysmaller throughput than the near-region ones. To encoun-ter this problem, the proposed timeline scheduling aims tofind the optimal schedule so that the far-region nanosen-sors can approach their maximum single-user throughput,while the near-region nanosensors can fairly share thespectrum in such way that they can achieve relativelyequivalent throughput. As shown in Fig. 4(c), under thetimeline scheduling, the nanosensors far away the nano-controller can obtain the single-user throughput very closeto the maximum achievable one, while the nanosensorsclose to the nanocontroller can achieve the same through-put. It is worth to notice that not all the near-region nano-sensors can approach their maximum single-userthroughput under the time-line scheduling algorithm. Thisis due to the fact that for any scheduling algorithm, given aset of nanosensors, the maximum single-user throughputis achievable for all nanosensors simultaneously only ifthe sum of the critical transmission ratios of the nanosen-sors is less than one. This condition is very difficult to sat-isfy when the number of near-region nanosensorsincreases.
8. Conclusions
WNSNs will boost the applications of nanotechnologyin many fields of our society, ranging from healthcare tohomeland security and environmental protection. How-ever, enabling the communication in WNSNs is still an un-solved challenge. We acknowledge that there is still a longway to go before having autonomous nanosensors, but webelieve that hardware-oriented research and communica-tion-focused investigations will benefit from being con-ducted in parallel from an early stage. In this paper, wedeveloped energy and spectrum-aware MAC protocols forWNSNs with the objective to achieve fair, throughputand lifetime optimal channel access by jointly optimizingthe energy harvesting and consumption processes. To-
wards this end, an important system design parameter,namely, the critical packet transmission ratio (CTR) hasbeen derived, which is the maximum allowable ratio be-tween the transmission time and the energy harvestingtime, below which the nanosensor node can harvest moreenergy than the consumed one, thus achieving perpetualdata transmission. Based on the CTR, first, a novel sym-bol-compression scheduling algorithm, built on the re-cently proposed pulse-based physical layer technique, isintroduced. The symbol-compression solution utilizes theunique elasticity of the inter-symbol spacing of thepulse-based physical layer to allow multiple nanosensorsto transmit their packets in parallel without inducing anytransmission collisions. In addition, a packet-level timelinescheduling algorithm, built on a theoretical bandwidth-adaptive capacity-optimal physical layer, is proposed withan objective to achieve the balanced single-user through-put with the infinite network lifetime. In this paper, wehave considered that all the nanosensors communicate di-rectly with the nano-controller in one hop. As part of ourfuture work, we will investigate optimal decision algo-rithms for multi-hop communication and routing inWNSNs.
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Pu Wang received the B.S. degree in ElectricalEngineering from the Beijing Institute ofTechnology, Beijing, China, in 2003 and theM.Eng. degree in Computer Engineering fromthe Memorial University of Newfoundland, St.Johns, NL, Canada, in 2008. He received thePh.D. degree in Electrical and ComputerEngineering from the Georgia Institute ofTechnology, Atlanta, GA, in 2013. He is cur-rently an Assistant Professor with theDepartment of Electrical Engineering andComputer Science, Wichita State University,
Wichita, KS. He was named BWN Lab Researcher of the Year 2012,Georgia Institute of Technology. He received the TPC top ranked paperaward of IEEE DySPAN 2011. He was also named Fellow of the School of
Graduate Studies, 2008, Memorial University of Newfoundland. He is amember of IEEE. His research interests include wireless sensor networks,cognitive radio networks, nanonetworks, multimedia communications,wireless communications in challenged environment, Internet of things,and cyber-physical systems.Josep Miquel Jornet received the EngineeringDegree in Telecommunication and the Masterof Science in Information and CommunicationTechnologies from the Universitat Politcnicade Catalunya, Barcelona, Spain, in 2008. Hereceived the Ph.D. degree in Electrical andComputer Engineering from the GeorgiaInstitute of Technology, Atlanta, GA, in 2013,with a fellowship from ‘‘la Caixa’’ (2009–2010) and Fundacin Caja Madrid (2011–2012). He is currently an Assistant Professorwith the Department of Electrical Engineering
at the University at Buffalo, The State University of New York. FromSeptember 2007 to December 2008, he was a visiting researcher at theMassachusetts Institute of Technology, Cambridge, under the MIT Sea
Grant program. He was the recipient of the Oscar P. Cleaver Award foroutstanding graduate students in the School of Electrical and ComputerEngineering, at the Georgia Institute of Technology in 2009. He alsoreceived the Broadband Wireless Networking Lab Researcher of the YearAward at Georgia Institute of Technology in 2010. He is a member of theIEEE and the ACM. His current research interests are in electromagneticnanonetworks, graphene-enabled wireless communication, TerahertzBand communication networks and the Internet of Nano-Things.M.G. Abbas Malik received the Ph.D. inComputer Science degree from University ofGrenoble I, France and Master in Computa-tional Linguistics from University of Paris 7 –Denis Didrot, Fance in 2010 and 2006respectively. He also received the Mater inComputer Science degree from Punjab Uni-versity College of Information Technology,University of the Punjab, Pakistan in 2003. Heserved as Assistant Professor in COMSATSInstitute of Information Technology Lahore,Pakistan for academic year 2010–2011. Since
September 2011, he has been working as Assistant Professor in Faculty ofComputing and Information Technology, King Abdulaziz University, Jed-dah, Saudi Arabia.
Nadine Akkari received the B.S and the M.S. degrees in ComputerEngineering from University of Balamand, Lebanon, in 1997 and 1999,respectively. She received the Master degree in Networks of Telecom-munications from Saint Joseph University and the Faculty of Engineeringof the Lebanese University, Lebanon, in 2001 and Ph.D. degree inNetworking from National Superior School of Telecommunications (ENST),
P. Wang et al. / Ad Hoc Networks 11 (2013) 2541–2555 2555
France, in 2006. She is currently an assistant professor with the faculty ofComputing and Information Technology at King Abdulaziz University,Jeddah, Saudi Arabia. She is a member of IEEE. Her research interests are inwireless networks, mobility management protocols, and nanonetworks.
Ian F. Akyildiz received the B.S., M.S., andPh.D. degrees in Computer Engineering fromthe University of Erlangen-Nrnberg, Germany,in 1978, 1981 and 1984, respectively. Cur-rently, he is the Ken Byers Chair Professor inTelecommunications with the School of Elec-trical and Computer Engineering, GeorgiaInstitute of Technology, Atlanta, the Directorof the Broadband Wireless Networking (BWN)Laboratory and the Chair of the Telecommu-nication Group at Georgia Tech. Since 2013, heis a FiDiPro Professor (Finland Distinguished
Professor Program (FiDiPro) supported by the Academy of Finland) in theDepartment of Electronics and Communications Engineering, at Tampere
University of Technology, Finland, and the founding director of NCC (NanoCommunications Center). Since 2011, he is a Consulting Chair Professor atthe Department of Information Technology, King Abdulaziz University(KAU) in Jeddah, Saudi Arabia. Since 2008, he is also an honoraryprofessorwith the School of Electrical Engineering at Universitat Politcnica deCatalunya (UPC) in Barcelona, Catalunya, Spain and the founding directorof N3Cat (NaNoNetworking Center in Catalunya). He is the Editor-in-Chiefof Computer Networks (Elsevier) Journal, and the founding Editor-in-Chief of the Ad Hoc Networks (Elsevier) Journal, the Physical Communi-cation (Elsevier) Journal and the Nano Communication Networks (Else-vier) Journal. He is an IEEE Fellow (1996) and an ACM Fellow (1997). Hereceived numerous awards from IEEE and ACM. His current researchinterests are in nanonetworks, Long Term Evolution Advanced (LTE-A)networks, cognitive radio networks and wireless sensor networks.
