Energy Efficiency of an Unlicensed Wireless Network in the Presence of Retransmissions
EEnergy Efficiency of an Unlicensed WirelessNetwork in the Presence of Retransmissions
Iran Ramezanipour ˚ , Hirley Alves ˚ , Pedro. H. J. Nardelli : and Ari Pouttu ˚˚ Centre for Wireless Communications (CWC), University of Oulu, Finland : Lappeenranta University of Technology, Lappeenranta, FinlandFirstname.lastname@oulu.fi, Firstname.lastname@lut.fi
Abstract —This paper analysis the energy efficiency of anunlicensed wireless network in which retransmission is possible ifthe transmitted message is decoded in outage. A wireless sensornetwork is considered in which the sensor nodes are unlicensedusers of a wireless network which transmit its data in the uplinkchannel used by the licensed users. Poisson point process is usedto model the distributions of the nodes and the interferencecaused by the licensed users for the sensor nodes. After findingthe optimal throughput in the presence of retransmissions, wefocus on analyzing the total power consumption and energyefficiency of the network and how retransmissions, networkdensity and outage threshold affects the energy efficiency of thenetwork.
Index Terms —Poisson point process, unlicensed spectrum ac-cess, sensor networks, energy efficiency.
I. I
NTRODUCTION
Wireless sensor networks (WSNs) have gained a lot of pop-ularity during the past few decades and are being implementedin different applications such as military and medical sectorsas a mean for monitoring, processing and disseminating data[1]. The ease of implementation and being cost and energyefficient are among the reasons that have made WSNs popular.Wireless sensor nodes are small size devices that can createdense networks that are randomly positioned and deployedwhich makes them a suitable choice for inaccessible locationsor disaster relief operations as well. WSNs have different prop-erties and applications compared to the traditional wireless adhoc networks, hence, protocols and algorithms that are beingused in those networks are not valid for WSNs anymore [2].This opens up a wide field of research regarding WSNs [3].Having an energy efficient network is always challengingwhen dealing with wireless networks. WSNs are also noexception to this, specially since they usually have access toa limited power source both in terms of the available energy( ă . Ah, . V) and size [4], [5] and in many cases such asaforementioned hardly accessible locations, it is not possibleto renew the power sources for sensor networks which areusually batteries, hence, the battery life in such networks playa crucial role in the sensors lifetime which makes the energyconsumption of the network elements a very important factorthat needs to be considered when dealing with WSNs [6], [7].Although a sensor network consumes energy in all its threeareas of responsibilities which were mentioned earlier, it isthe data disseminating, which includes both transmitting andreceiving data, that consumes the most energy in a WSN. Sensor networks are usually used in short range commu-nications with low data rates and short packet size whichmakes the RF communications a suitable choice for them [8].However, designing an energy efficient WSN is always oneof the challenges engineers face since the radio technologiesare not suitable for being used in all kinds of applications[9]. Thus, in this paper, we analyze the energy efficiency ofa WSN as part of an unlicensed network which allows forretransmission in case of an outage event happening.Energy efficiency (EE) studies have become very popularduring the past years and researchers have been studying EEin different types of applications. In [10], authors study the re-duction of the energy consumption of the whole network whilein [11], [12], the energy consumption of two non-cooperativeand cooperative networks with considering different networkdensities have been studied. In [11], optimizing the packetsize is used as a mean for maximizing the energy efficiencyof the two mentioned networks. In [12], energy efficiency ofa cooperative network is studied constrained by an outagethreshold. Moreover, EE is investigated in [7] by setting anend-to-end throughput constraint on the network while in [13],by studying the throughput and outage of a full-duplex and anincremental cooperative half-duplex networks respectively.While the following studies are important and valuable,they do not consider EE of a sensor network, based on theoptimal throughput of the system, constrained by an outagethreshold. In this paper, we expand our previous works in [14],[15] to cover a more generalized model rather than focusingon only the smart grids application. We follow the samemodel described in [16], [17] where there is possibility forretransmissions of a message in case of an outage happeningin the network and it is shown that having a limited numberof retransmissions can enhance the spatial throughput andtransmission capacity of ad hoc networks. We use the samenetwork model for investigating the EE of the network byfirst optimizing the link throughput in the system subjectedto a minimum outage requirement where an outage eventhappens if the transmitted message is not decoded correctlyor is never received by the receiver. Note that the number ofretransmissions is limited and if the message is not receivedafter a certain number of retransmissions, it is dropped.The rest of the paper is divided as follows. Section IIintroduces the system model, while Section III details theproposed throughput optimization and energy efficiency anal- a r X i v : . [ c s . I T ] M a r sis. Section IV presents the numerical results and Section Vconcludes this paper.II. S YSTEM MODEL
Considering the network model introduced in [14], [15],the same model which is also shown in Fig. 1, is usedhere for the implementation of the communication networkin which the sensors transmit their data to their correspondingaggregator/controller where the following assumptions hold. ‚ Assumption 1 : A communication network consists ofboth licensed and unlicensed networks where the users ofboth of the networks share the frequency bands allocatedto the uplink channel. ‚ Assumption 2 : Licensed link is the connection linkbetween static cellular base-stations and mobile userswhile the sensor nodes with fixed positions consist ofunlicensed users which communicate with their corre-sponding controller through the uplink channel. ‚ Assumption 3 : The amount of power used by the unli-censed users (sensors) for their transmission is limited.This limitation can be enforced by the licensed networkor can also be related to the sensors’ own capabilities. ‚ Assumption 4 : In this model, it is assumed that there areno packet collisions between sensors associated with thesame aggregator/controller due to the fact that the sizeof the transmitted messages are assumed to be small andmultiple access solutions are effective for the size of theunlicensed network.By considering the above assumptions, we are able tosimplify the model to some extend. This would make theanalysis easier. The use of directional antennas in unlicensedcommunication links is justified based on Assumption 2 whichstates that the unlicensed nodes are static. This would resultin not having any orientation errors [18]. Having a limitedtransmit power based on Assumption 3 means that there isalso a limit to the maximum range that the signal sent bythe sensors can reach. Hence, the radiation pattern created bythis transmission can be modeled as a line segment with thestarting point being the sensors and the end point being limitedby the imposed power constraint.The interference in this model based on Assumptions 1, 2and 4 can have different sources. (i) from unlicensed users(sensors) to cellular base-stations, (ii) from sensors to con-troller that are not their corresponding controller and (iii) fromlicensed users (mobile users) to to aggregators/controllers.The first two interference sources can be avoided if whenimplementing the network, the position of either the licensedor unlicensed nodes are specified. Even if the positions arerandomly implemented, it is highly unlikely that there wouldbe a base station or controller in the same line as the sensors’transmitted signal.This leaves out only one source of interference in thismodel which would be (iii) from licensed users to aggre-gators/controllers. In order to be able to analyze the effectof interference on the performance of the network, we needto model the uncertainty of the interferers positions. We use
Fig. 1: An illustration of the proposed scenario, where licensed andunlicensed users share the up-link channel. The reference sensor(unlicensed transmitter) is depicted by the sensor, the controller(unlicensed receiver) by the CPU and its antenna, the handsets arethe mobile licensed users (interferers to the controller) and the bigantenna is the cellular base-station. As the sensors uses directionalantennas with limited transmit power (bold arrow), its interferencetowards the base-station can be ignored. The thin black arrowsrepresent the licensed users’ desired signal, while the red onesrepresent their interference towards the controller.
Poisson point process Φ to model the interfering nodes in thisnetwork which are distributed over an infinite two-dimensionalplane with network density λ . Details of using stochasticgeometry and Poisson point process in modeling the wirelessnetworks can be found in [19].Different metrics such as distance-dependent path-loss andfast fading is considered when modeling the wireless channel.Consider r i to be the distance between the i th interfererand the reference receiver which is located arbitrary at theorigin. Based on the Slivynak theorem, a receiver can havean arbitrary fixed position at the center of the Euclideandistance. This would make the estimation of the other elementsof the network surrounding the receiver easier [19]. In thismodel, g i is considered to be the channel gain. The referencereceiver received power then would be W g i r ´ αi where W isthe transmit power and α ą is the path-loss exponent. Thiswill result in the following signal to interference ratio (SIR ).SIR “ W s g r ´ α W p ÿ i P Φ g i r ´ αi . (1)In this equation, W p and W s denote the licensed usersand unlicensed users transmit power respectively. It shouldbe noted that although the noise is neglected here, even thepresence of the noise would not make a qualitative differenceas stated also in [20].Considering that point-to-point Gaussian codes andinterference-as-noise decoding rules [21], [22] are used in thereference link, it means that obtaining the desired spectralefficiency of log p ` β q in bits/s/Hz depends on the fact thatthe SIR is greater than a given threshold or not β (i.e SIR ą β ),Hence, the probability of an outage event happening, P out , canbe explained as the probability of SIR ď β . If a transmittedessage is decoded in outage, it is retransmitted with themaximum of m attempts, meaning that the message is droppedif it is still not successfully decoded by the receiver after ` m transmissions. Thus, the probability of a successfultransmission is calculated as P suc “ ´ P ` m out .Since the licensed users (interferers) are not static, theirposition is constantly changing in each transmission. SIR in this model can be statistically evaluated by consideringdifferent realizations of Poisson point process Φ . In order tocompute P out “ Pr r SIR ď β s for each transmission attemptby considering quasi-static channel gains (squared envelopes) g which are independent and identically distributed expo-nential random variables (Rayleigh fading) with mean , thefollowing equation is used [16]. P out “ ´ e ´ kλβ { α , (2)where k “ πr Γ ` ´ α ˘ Γ ` ` α ˘ .The throughput of the reference link T is then calculatedas [16]: T “ log p ` β q ` ¯ m ` ´ P ` m out ˘ , (3)where m is the maximum number of retransmission attempts.It should be noted that in order to find m , we use anapproximation of [23, §17] which is also explained in [24], inorder to calculate the average number of transmissions neededto successfully transmit a message ( ` ¯ m ).III. T HROUGHPUT OPTIMIZATION A ND E NERGY E FFICIENCY
Energy efficiency of a wireless network can be seen as acriteria that captures the trade-off between the total powerconsumption (PC) and the throughput of the network. Hence,we first start by defining the optimal throughput of the networkwhich is obtained by the following optimization problem:max p β,m q log p ` β q ` ¯ m ˆ ` ´ P ` m out ˘ subject to P ` m out ď (cid:15) . (4)In this problem, the throughput is constrained to a maximumacceptable error rate (cid:15) , which shows how often a messageis dropped after reaching the maximum number of allowedretransmissions. Here, the SIR threshold β ą and the numberof allowed retransmissions m P N are the design variables. Proposition 1:
The throughput T “ f p β, m q in (3) is afunction of the variables m ą and β ą . The function f isthen concave with respect to β if B T B β ă . β ˚ and m ˚ repre-sent the value of β and maximum number of retransmissionsthat maximizes the link throughput respectively : β ˚ “ ˆ ´ kλ log ´ ´ (cid:15) m ` ¯˙ α . (5) m ˚ “ max m P N log ˆ ´ kλ log ´ ´ (cid:15) m ` ¯˙ ` α ˆ ´ kλ ˙ α ´ log ´ ´ (cid:15) m ` ¯¯ α ´ ´ kλ ´ log ´ ´ (cid:15) m ` ¯¯ α . (6) Proof: As m and β are strictly positive variables andfunction T is twice differentiable in terms of β , then T isconcave if and only if B T B β ă . Eq. (5) is then attained bysolving the derivative equation B T {B β “ , whose solution is β ˚ . From (5), we find T as a function of m considering β ˚ .The optimal throughput T ˚ in terms of both m and β is thengiven by the value of m that maximizes the throughput, whichis given in (6). Moreover, from (5), we find T as a functionof m considering β ˚ . The optimal throughput T ˚ in terms ofboth m and β is then given by the value of m that maximizesthe throughput, which is given in (6). Remark 1:
The maximum number of retransmissions m ˚ is a natural number that is usually small, which makes theevaluation of (8) computationally simple.By having the optimal throughput, we can now analyzethe energy efficiency of the network. As it was mentionedearlier, the EE depends on the total power consumption andthroughput of the network where the total power consumptionof the network in its turn, includes the distance dependenttransmission power in addition to the total energy consumedby the RF components and bit rate [7], [13]. Considering theabove parameters, the total power consumption of our singlehop model is derived as:PC “ m ` ÿ P C
P A ` P C T x ` P C R x log p ` β ˚ q , (7)where P C
P A denotes the power amplifier power consumptionin a one-hop transmission which also depends on a parametercalled the drain efficiency of the amplifier. We denote thedrain efficiency by ζ which would result in P C
P A “ β ˚ ζ in this model. Moreover, log p ` β ˚ q represents the bit rate(bits/s) of the system while P C T x and P C R x are constantswhich depends on the current technologies and are equal tothe energy consumed during the transmission and receptionoperations by the internal circuitry respectively. By having theabove parameters, the EE is expressed asEE “ T ˚ PC , (8)where T ˚ denotes the optimal throughput previously calcu-lated. IV. N UMERICAL RESULTS
In this part, the numerical results of our analysis is pre-sented. It should be noted that the following parameters wereconsidered for obtaining these results. The distance betweenhe sensors and the receiver r “ meter and path-loss expo-nent α “ . Also, based on the parameter setting presented in[7], P C T x “ . mW, P C R x “ . mW and ζ “ . .Fig. 2 shows how the power consumption changes withthe density of interferers (measured in node/ m ) and outageconstraints of the network for both limited and unlimitednumber of retransmissions being allowed in the network. Wecan see that in both cases, the outage constraint has a bigimpact on the total power consumption of the network. As theoutage requirement gets stricter, meaning that a lower level ofoutage is allowed in the network (higher reliability), the totalpower consumption of the network also increases, showingthat more power is used by the network in order to have asuccessfully decoded transmission.Moreover, we can see that increasing the density of interfer-ers also affects the total power consumption. While (cid:15) “ . ,for very low density of interferers ( λ ď . ), having limitednumber of retransmissions results in having lower total powerconsumption. However, as the density of interferers increasesand expectedly the total power consumption also increases,limited and unlimited retransmissions consume almost thesame amount of energy. As the outage requirement gets looser,the range of λ for which the limited transmission consumesless energy also increases. For instance, while ( λ ď . ),having limited m means having lower energy consumptionwhen (cid:15) “ . . When the outage requirement of the systemis very loose, (cid:15) “ . , for all of the considered λ range in ouranalysis, having limited m would consume less energy, sincewhen the network density is lower, the interference level ofthe network is also lower. This means that even when m islimited, the system can achieve its expected outage constraintwithout having to consume a lot of energy, hence, havinglimited m consumes less energy, but as λ increases, the levelof interference also increases which would mean that whenhaving limited m , the system needs to use more energy inorder to reach the required (cid:15) , thus, almost the same amount ofenergy as having unlimited m would be used by the network.Fig. 3 illustrates the behavior of the energy efficiency of thenetwork with respect to λ and different outage requirements.As the optimal throughput reduces dramatically by λ , we cansee that the same thing is happening in the case of EE. As theoutage requirement gets more stringent, the system needs moreretransmission in order to reach the optimal throughput. Thismeans that if m is limited, the system can not always reachthe optimal throughput as λ increases. Since as shown in (8),EE has a direct relationship with the optimal throughput, thethroughput decrease will effect EE also, that is why we cansee that for most of the λ range, having a limited number ofretransmissions has also reduced the energy efficiency of thenetwork compared to when an unlimited number of retrans-missions is allowed. Although energy efficiency also dependson the power consumption which was shown increases with λ , this change is not as high and as effective as the decrease isthe throughput, hence, the EE eventually ends up decreasing.It is also shown in Fig. 3 that like PC, EE also has a differentbehavior when λ is very low. For those cases, having limited m .
00 0 .
05 0 .
10 0 .
15 0 .
20 0 .
25 0 .
30 0 . Density of interferers- λ P o w e r c o n s u m p t i o n - P C (cid:15) = 0 . un(cid:15) = 0 . un(cid:15) = 0 . un(cid:15) = 0 . (cid:15) = 0 . (cid:15) = 0 . Fig. 2: Power Consumption PC versus the density of interferers λ for α “ , r “ for both unlimited and limited ( m “ ) numberof retransmissions. results in having higher EE. As it was explained earlier, for low λ , the network would consumes less energy while m is limited,resulting in higher energy efficiency in the network. However,as λ increase, limited m uses as much energy as unlimited m in order to reach the required constraints, on the other hand,the throughput for the unlimited case decreases also since thenetwork can not reach the optimal throughput anymore. Allthese would eventually result in the network having lowerEE when the number of retransmissions is limited as λ andinterference level increase.It should be noted that the sharp fall and rise in Figs. 2 and 3respectively are the results of having very low λ which meanshaving a very low interference. Moreover, Fig.4 illustrates theEE behavior as a function of (cid:15) for different λ s which furtherproves our point showing that looser outage requirements andlower network densities results in a higher level of energyefficiency in the network.V. C ONCLUSION
In this paper, we analyzed the energy efficiency of awireless network where the licensed and unlicensed usersshare the uplink channel. However, the unlicensed users donot cause interference on the licensed users transmissions.In this model, retransmission is also allowed if a message isdecoded in outage. Our results showed the effect of retrans-mission and outage constraint on the power consumption andenergy efficiency of the network considering different networkdensities. It was shown that having stricter outage requirementin the network also means having higher power consumptionduring transmissions. Depending on (cid:15) and λ , having limitedretransmissions means lower power consumption or at mostas much power consumption compared to having unlimited m . We also showed that as λ increases, the energy efficiencyof the network decreases due to the decrease in the optimalthroughput. Having higher outage requirement also results inneeding more m in order to reach the T ˚ , therefore, having .
00 0 .
05 0 .
10 0 .
15 0 .
20 0 .
25 0 .
30 0 . Density of interferers- λ − − − − − − − − − − E n e r g y e ffi c i e n c y - EE (cid:15) = 0 . un(cid:15) = 0 . un(cid:15) = 0 . un(cid:15) = 0 . (cid:15) = 0 . (cid:15) = 0 . Fig. 3: Energy efficiency EE versus the density of interferers λ for α “ , r “ for both unlimited and limited ( m “ ) number ofretransmissions. − − − − Error threshold- (cid:15) − − − − − − − − − E n e r g y E ffi c i e n c y - EE λ = 0 . λ = 0 . λ = 0 . Fig. 4: Energy efficiency EE versus the error threshold (cid:15) for α “ , r “ for different densities of interferers λ while the number ofretransmissions is limited ( m “ ). limited m means having lower EE for most of the λ range.We plan to continue and improve the work done in this paperby jointly optimizing the energy efficiency and throughputconstrained by a minimum outage requirement.A CKNOWLEDGMENTS
This work is partially supported by Aka Project SAFE(Grant n.303532) and Strategic Research Council/Aka BCDCEnergy (Grant n. ).R
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