Topology-assisted techniques to relay selection for homogeneously distributed wireless sensor networks

Transcription

1 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceeings. Topology-assiste techniques to relay selection for homogeneously istribute wireless sensor networs Farroh Etezai, eyvan Zarifi, Ali Ghrayeb an Sofiene Affes ECE Department, Concoria University, Montreal, Canaa f eteza@encs.concoria.ca, aghrayeb@ece.concoria.ca INRS-EMT, Montreal, Canaa {zarifi,affes@emt.inrs.ca Abstract We consier a multi-relay amplify-an-forwar cooperative communication scheme in wireless sensor networs with uniformly istribute noes. Fixing the average total transmission power from the networ an preserving fairness among the selecte relays by constraining them to transmit with equal average powers, we aim to improve the signal reception quality at the far-fiel receiver by means of a proper choice of the relays. Assuming that the noes forwar channels are not nown, the following three relay selection schemes are propose an their performances are analyze. 1 Optimal relay selection scheme that maximizes the average SNR at the receiver by exploiting noes with the highest SNRs as relays; 2 geometry-base relay selection scheme that is energy-efficient an achieves a closeto-optimal average SNR performance at the receiver by using closest noes to the source as relays; an 3 ranom relay selection scheme that is energy-efficient an further guarantees a fair usage of all noes by ranomly selecting relays from a specific area aroun the source. By minimizing an outage probability, a strategy to etermine this area is also propose. Finally, it is shown for all relay selection schemes that the SNR variance at the receiver converges to zero as increases. I. INTRODUCTION AND MOTIVATION Exploiting multiple transmit antennas in communication networs can substantially improve the communication performance by proviing the spatial iversity an/or increasing the ata rate an the multiplexing gain. However, in many systems such as wireless sensor networs WSNs, it is impractical to implement multiple antennas at the transmitting terminals. As an alternative approach to communication with multiple transmit antennas, cooperative communication techniques in wireless sensor networs can provie iversity an multiplexing gain by means of using the existing ile noes as a virtual antenna array that relay the source transmitte signal [1], [2]. How to select the relays from the pool of available noes can have a major effect on the cooperative communication efficiency. This has motivate extensive research efforts on proposing a variety of relay selection techniques for such networs. In [3], it is propose to select the relay with the best contribution in signal-to-noise ratio SNR at the receiver. In [4], the closest noe to the receiver is selecte to cooperate with the source. Assuming that the source-relay an the relayreceiver channels are nown in all noes, the best harmonicmean single relay selection technique is propose in [5]. It can be shown that selecting the optimal relay among multiple available noes provies the full iversity orer as if all noes act as relays [5]. However, this strategy results in a rapi power epletion of the selecte relay. In contrast, using multiple relays not only can provie a full iversity orer uner fairly general assumptions, but also maes it possible to ecrease the transmission power from each iniviual relay proportionally to the number of selecte relays uner a total transmit power constraint. This, in turn, can ramatically increase the networ lifetime. For a review on some techniques to multiple relay selection refer to [6]. In spite of substantial wors on efficient relay selection techniques, there is only a limite research on eveloping relay selection strategies that tae explicitly into account the networ topology. We inten to contribute in this thrust of research by introucing energy-fair relay selection techniques in WSNs where the noes are uniformly istribute accoring to a two-imensional homogeneous Poisson process [7], [8]. We consier a two-phase amplify-an-forwar AF cooperative scheme where in the first phase the source broacasts its signal an in the secon phase noes act as relays by amplifying their receive signals an resening them to the receiver through orthogonal channels. Aiming to prolong the networ lifetime by avoiing overloaing some of the selecte relays, we choose an energy-fair approach wherein all selecte relays transmit with equal average powers. We then evelop the following three relay selection techniques for the pragmatic scenario where the noes are unaware of their forwar channels to the receiver: 1 Optimal relay selection technique where the noes with the highest SNRs are selecte as relays. Among all those techniques that o not use any information of the noes forwar channels to select the proper set of relays, this approach can provie the highest SNR at the receiver. However, it entails a large signaling overhea as the set of relays may have to be upate at the beginning of every transmission cycle. In fact, the noes bacwar channel lins can change quite ramatically in a relatively short perio of time. Therefore, when this technique is use, it may not be possible to mar some noes as inappropriate relay caniates an let them go to the sleeping moe an save energy. As such, all noes have to alternately switch between the listening an transmitting moes. This results in a significant waste of energy. 2 Geometry-base relay selection technique that is base on

2 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceeings. the fact that the variations in the networ topology are typically slower than those of the channel lins. This technique selects the closest noes to the source as relays for a preetermine number of transmission cycles an leaves all other noes in the sleeping moe to save energy. After a number of cycles passe, all noes go bac to the active moe, the new set of closest noes start to act as relays, an all other noes return to the sleeping moe. Although being energy-efficient, this technique may overexploit the noes that continuously remain close to the source in networs with a static topology. 3 Ranom relay selection technique where relays are ranomly selecte from the noes within an R-istance from the source. All other noes both within an outsie this neighborhoo remain in the sleeping moe. The relay list is upate after a preetermine number of transmission cycles to avoi overexploiting a specific set of noes. At the cost of a possibly noticeable rop in the SNR performance, this technique is both energy-efficient an fair towar the noes. For all the aforementione techniques, we erive the average SNRs at the selecte relays an at the receiver an analyze their properties. We then present a variance analysis for SNR at the receiver an show that, regarless of the use relay selection technique, the SNR variance goes to zero as grows large. We also efine an outage probability, by minimizing which, the optimal R in the ranom relay selection technique can be obtaine. The rest of the paper is organize as follows. The system escription, the transmission protocol, an the signal moel are presente in Sec. II. The relay selection techniques are formally propose an the probabilistic properties of the SNRs at the relays are analyze in Sec. III. The average an the variance of the SNR at the receiver are stuie in Sec. IV. Simulation results are presente an are compare to the analytical results in Sec. V. Concluing remars are given in Section VI. II. SYSTEM MODEL A. System escription an Transmission Protocol Consier the WSN in Fig. 1 whose noes are uniformly istribute with ensity ρ in a 2-imensional plane. The source s is one of the noes in the networ an aims to sen information to the receiver in the far-fiel. In orer to provie iversity, other noes in the networ are exploite as relays in a two-phase AF cooperative scheme. In the first phase, the source broacasts its signal. In the secon phase, noes act as relays by amplifying their receive signals an resening them to the receiver through orthogonal channels. B. Signal Moel The receive signal at the th relay in the first phase is y = p s h s, /2 s, x + n =1,..., 1 where n CN0,σ 2 is noise, p s is the transmission power from the source an x is the normalize transmitte signal. D s, is the istance between the source an the th selecte relay an 2 is the path-loss factor an varies for ifferent Phase 1 Phase 2 Fig. 1: Networ moel an the transmission protocol. channel environments. h s, is the Rayleigh faing channel between the source an the th selecte relay with the variance 1/2 per real imension. From 1, the SNR at the th relay is γ = β h s, 2 s,, 2 where β = p s /σ 2. In the secon phase, the th relay sens z = β y where β = 1 P T E { y 2 = 1 P T σ 2 =1,..., γ +1 3 is the normalization factor at the -th relay [9]. In 3, γ represents the average receive SNR at the th relay. Regarless of the technique use to select the relays, it can be observe from 3 that the average transmit power from each relay is P T /. Therefore, the average of the total transmission power from the whole networ uring the relaying phase is P T. This property guarantees an equitable power issipation from the selecte relays an further maes it possible to fairly compare the performances of ifferent relay selection schemes. The signal at the receiver ue to the th relay is y [] = β h, /2 y + n [] =1,..., 4 where n [] is the receiver noise, h, is the Rayleigh faing channel between the th relay an the receiver with the variance 1/2 per real imension, an D is the istance of the far-fiel receiver from the noes. Assume that the receiver uses the optimal maximum ratio combining MRC to estimate x from the set of signals receive from the relays. Using 1 an 4 an after some manipulation, it can be shown that the soft symbol estimate at the MRC receiver output is equal to ps α h s, y = h, D /2 s, σ α h, 2 y [] 5 where =1 α β = 1 P T σ 2 D 1 γ +1 an is the complex conjugate. It can be conclue from 4 an 5 that SNR at the receiver is given by γ = 6 θ, 7 =1

3 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceeings. where θ α h, 2 1+α h, 2 γ = α 2 h, 1+α h, 2 β h s, 2. 8 D s, III. RELAY SELECTION SCHEMES AND SNR ANALYSIS SNR at the th relay epens not only on the channel h s,, but also on the istance of the selecte relay from the source, an, therefore, on the networ topology. In this section, three ifferent relay selection schemes are introuce an SNRs of all schemes are analyze. In the following we use the superscripts o, g an r in orer to refer to the optimal, the geometry-base, an the ranom relay selection schemes, respectively. Optimal Relay Selection Aiming to maximize γ, it immeiately follows from 7 that the best relaying set is the set of noes with the largest θ. θ epens on h, which is unnown at noe an therefore cannot be irectly aopte as a measure to select the relays. However, as can be observe from 8, θ is an increasing function of γ, which is linearly proportional to h s, 2 s, that is nown at the noe. The above iscussion suggests that, being unaware of h,, the optimal relaying set is the set of noes with the largest γ. We require the following theorem to analyze the performance of the optimal relay selection scheme. Theorem 1. Consier a large WSN wherein the noes are uniformly istribute with ensity ρ an the channels between the source an relays are Rayleigh faing with variance 1/2 per real imension. Then, the cumulative probability istribution CDF of the -th largest SNR at the relays is given by 1 where F γ o 1 γ =Guγ,=e uγ uγ = 2ρπ 1 j=0 uγ j, 9 j! z 2 1 e γz β z. 10 Proof: See [10]. The integral in 10 is boune an has a close form solution for all feasible values of. Using this theorem, we can fin the probability istribution function PDF of the SNR as f γ o γ = F γ o γ/ γ an obtain the average SNR, γ o. Note that γ o epens on. Therefore, when the optimal relay selection scheme is use, each relay shoul now its inex in the relaying queue. Then β o can be etermine from 3 an be use as the normalization factor at the th relay. Among the relay selection techniques that o not have access to any information regaring the noes forwar channels, the presente scheme provies the best possible SNR at the receiver. However, as iscusse in Section I, the above optimal relay selection scheme requires all the noes to continuously 1 In all our erivations, we have assume a relay-free isc of unit raius aroun the source. propel between the transmission an listening moes an, thus, can entail a significant waste in the networ energy. Geometry-base Relay Selection In many practical scenarios, the changes in the noes positions are much slower than the variations in their channel lins. This, along with the fact that θ in 8 in inversely proportional to Ds,, motivates a relay selection technique that selects closest noes to the source as relays for a preetermine number of transmission cycles while leaving the rest of the noes in the networ in the sleeping moe. Compare to the optimal relay selection technique, the above geometry-base relay selection technique is much more energy-efficient at the cost of a potential ecrease in the signal reception quality. Note that h s, is inepenent from D s, in this scheme an we have γ g = βe { h s, 2 { E s, { = βe s,. 11 Using a similar technique as in [8], the PDF of D s, can be erive as f g D s, r = 2ρπ 1! rr2 1 1 e ρπr 2 1 It follows from 11 an 12 that γ g = 2βρπ 1! 1 r>1. 12 r 1 r e ρπr2 1 r. 13 After some simple manipulations, we obtain γ g = βρπ 2 u i+ 1 e ρπu u 1! i i=0 0 = βρπ 2 i + 1! 1! i ρπ i+, 14 i=0 where α = αα 1 α +1/!. This along with 3 inicates that the normalization factor β g also epens on. The geometry-base relay selection technique increases the networ energy-efficiency an reuces its signaling complexity compare to the optimal relay selection scheme. However, in networs with a more static topology, the geometry-base relay selection technique tens to overexploit the rarelychanging set of closest noes to the source. This can eventually result in the noes battery epletion an a networ isconnectivity. Ranom Relay Selection One approach to avoi the above problem is to ranomly select relays from Os, R, the isc of raius R centere at s, an leave all other noes both insie an outsie the isc in the sleeping moe. After a preetermine number of transmission cycles, a new set of noes is selecte from Os, R to avoi overexploiting a fixe set of noes. When the noes are ranomly selecte using to the above technique, the PDF of D s, is given by f r D s, r = 2r R 2 1 r>1. 15

4 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceeings. Exploiting the inepenency of the istance D s, an the channel h s, in this relay selection scheme, 11 an 15 can be use to obtain R γ r 2t 1 β 2lnR R 2 1 =2 = β 1 R 2 1 t =. 2R β 2 1 R Note from 16 that γ r, an, hence, βr are inepenent from. Therefore, when the ranom relay selection scheme is use, it is not require that the relays are aware of their position in the relaying queue. It can also be observe from 16 that the choice of R has a significant effect on the performance of the ranom relay selection scheme. While R shoul not be selecte very small so that there are not enough relays on Os, R, it shoul also not be selecte very large so that the selecte relays suffer from a long istance from s an a wea SNR problem. In what follows, we use the above iscussion to propose a systematic approach to select R. First, let us efine the following events: A = {There are at least relays on Os, R Ā = {There are at most 1 relays on Os, R { B = γ r γ for =1, 2,..., 17 where γ is the minimum acceptable SNR at the selecte relays an can be chosen such that a minimum communication rate between the source an the relays is guarantee. Then, we can efine the outage probability as the probability that there are at most 1 relays on Os, R or at least one of the selecte relays has a SNR less than γ. More formally, P out R =1 PrA, B =1 PrB APrA =1 1 F r γ γ 1 Pr Ā, 18 where F r γ. is the CDF of the SNR when the relays are ranomly selecte from Os, R an is given by [10] 2 R F r γ γ = R 2 t 2 1 e γt β t Therefore, P out R =1 2 R t 2 1 e γ t β 1 t R e ρπr2 1 ρπr 2 1 l l! l=0 20 where the expression insie the secon parentheses at the right-han sie of 20 is ue to the fact that if noes are uniformly istribute on a 2-imensional plane with the ensity ρ, the number of noes insie an area A on the plane is a Poisson r.v. with the parameter ρμa where μa is the P out =4 =3 =2 =1 γ =0B γ = 10B R Fig. 2: P out R as a function of R for ifferent an γ. stanar Lebesgue measure of A [8], [11]. The optimal R can then be selecte as R = arg min P outr. 21 R Fig. 2 shows P out R versus R for ifferent an =2, ρ =0.1, γ =0an 10 B, an β =25B. As can be observe from Fig. 2, each outage probability curve has a minimum point that correspons to R. IV. SNR ANALYSIS AT THE RECEIVER When MRC is use at the receiver, it is straightforwar to show that the average SNR at this terminal is given by { α h, 2 γ = E 1+α h, 2 γ. 22 =1 {{ φ As h, is a zero-mean Gaussian r.v. with the variance of 1/2 per real imension, h, 2 is a unit-mean exponentially istribute r.v. an, therefore, α x φ = 1+α x e x x =1 e 1 α 1 E 1 23 α 0 where E 1 z = e t /t t is the exponential integral. It z is of practical value to stuy the variations of γ aroun γ. Using 7 an 8 along with the facts that α is inversely proportional to an h s, an h, are inepenent r.v.s, it can be reaily shown that var = ζ + ζ 2 F, 24 γ 1 where is either o, g or r an ζ 1 an ζ 2 are two scalars inepenent from. In the following, F in the ranom, the geometry-base, an the optimal relay selection schemes are analyze an the behavior of var γ when grows large are investigate. α

5 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceeings F Fig. 3: Optimum, β = 25B,ρ =0.1, =2 Optimum, β = 25B,ρ=0.01,=2 Geometry-base, β = 25B,ρ=0.1,=2 Geometry-base, β = 25B,ρ=0.01,= F o an F g versus for ρ =0.1 an ρ =0.01. γb η s =7B η s =0B Ranom, Simulation Ranom, Analytical Geometry-base, Simulation Geometry-base, Analytical Optimum, Simulation Optimum, Analytical Fig. 4: γ versus for ρ =1, η =15B, an η s =0, 7 B. Ranom Relay Selection When the ranom relay selection scheme is use, the relays istances from the source are inepenent r.v.s an it can be shown that F r = 0 [10]. Therefore, var converges to zero with the rate O1/. Geometry-base Relay Selection In the geometry-base relay selection scheme, the relays istances from the source are not inepenent r.v.s. an we have [10] F g = 1 2 γ r m 1 m=1 l=1 The analysis of var { { E s,l D s,m E γ g s,l E { s,m. 25 requires the nowlege of f g D s,l,d s,m,, the joint PDF of D s,l an D s,m. The following theorem hols. Theorem 2. For m>l, the joint PDF of D s,l an D s,m in the geometry-base relay selection scheme is given by 26. Proof: See [10]. { Using 12 an 26, analytical expressions of E { an E s,l D s,m can be obtaine an then be use to erive F g g. Although F is a rather complicate function not brought here, simulation results shown in Fig. 3 verify that F g is a ecreasing function of for the teste values of an ρ. The latter observation along with 24 suggests that var γ g shoul converge to zero as the number of relays increases. Optimal Relay Selection When the optimal relay selection technique is use, we can efine F o = 1 β 2 2 m 1 m=1 l=1 s,l E {γ l γ m E {γ l E {γ m. 27 Note that the normalization factor β 2 in 27 is only use to mae F o g an F comparable. To analyze var γ o,we require f γ o m,γ l.,., the joint PDF of γ l an γ m. The following theorem erives the latter function. Theorem 3. For m>l, the joint PDF of γ l an γ m, the SNR of the lth an the mth relays with the highest SNRs, is given by 28. Proof: See [10]. Again, simulation results shown in Fig. 3 verify the ecreasing behavior of as grows. This observation shows F o that var γ o shoul also converge to zero as the number of relays increases. Convergence of var γ to zero implies that if is large enough, then, for any arbitrary set of realizations of D s,, h s,, an h,, γ shoul be close to γ. This confirms that γ is a sensible performance measure for the consiere cooperative WSN an the erive properties of the average SNR at the receiver also approximately hol for the instantaneous SNR at this terminal. Moreover, the above result verifies that the propose relay selection schemes effectively ecrease the signal power fluctuations at the receiver. This is an expecte effect ue to the spatial iversity provie by the inepenent channel paths. V. SIMULATIONS In this section, further numerical simulations are use to valiate the analytical results. Fig. 4 shows the analytical an the numerical γ r, γg, an γo versus for D = 1000, R =20, =2, σ 2 =1, ρ =1, η = P T /σ 2 D =15B, an two ifferent η s p s /σ 2 R =0B an 7 B. Note that η s is the average SNR on the bounary of Os, R, an, therefore, γ r η s for =1, 2,...,. The figure shows the results of averaging over 10 5 ranom realizations of the channel lins an source-relay istances. Fig. 4 further verifies that the erive average SNR expressions accurately preict their numerical counterparts.

6 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceeings. f g D s,l,d s,m r, t = 4ρπ m tt2 1 m l 1 rr2 1 l 1 t 2 r 2 m l 1 m l 1! l 1! t 2 e ρπt2 1 1 t r 0 t<r x G ux uy,m l y G uy,l y x 0 y<x f o γ m,γ l x, y = γb Ranom, Simulation Ranom, Analytical Geometry-base, Simulation 0 Geometry-base, Analytical Optimum, Simulation Optimum, Analytical η s Fig. 5: γ versus η s for ρ =1, =10, an η =15B. Fig. 5 shows the analytical an the numerical γ r, γg, an γ o versus η s for ρ = 1 an = 10. In Fig. 5, η = 15 B is also plotte as a reference. As can be observe from the figure, the numerical results very closely follow their analytical counterparts. Fig. 5 also shows that when η s is very small, γ o an γ g are consierably higher than γ r. However, increasing η s, all γ r, γg, an γo rapily increase an converge to η. This inicates that if the average SNRs at all relays are large enough, the average SNR at the receiver approaches η irrespective to the selecte relaying set. This figure also shows that γ g is very close to γ o for an extene range of η s starting as low as 20 B. This observation verifies the close-to-optimal performance of the geometry-base relay selection scheme even at a very low SNR regime. Note also that γ r enters the one-b vicinity of η at a moerate η s 5 B. VI. CONCLUSIONS We have presente the following three multiple relay selection schemes in wireless sensor networs with uniformly istribute noes in the case that the forwar channels information is not available at the relays: 1 The optimal relay selection scheme where noes with the highest instantaneous SNRs are selecte for relaying. Among all relay selection techniques that o not use any information regaring the noes forwar channels, this technique achieves the highest possible SNR at the receiver at the cost of energy-inefficiency an a consierable signaling overhea; 2 the geometry-base relay selection scheme that ignores the instantaneous channel variations an chooses closest noes to the source as relays. While achieving a close-to-optimal average SNR at the receiver, it can be substantially more energy-efficient than its optimal counterpart. The main isavantage of this scheme is the possibility of overexploiting the group of noes that stay close to the source in networs with a more static topology; an 3 the ranom relay selection scheme using which noes are ranomly selecte from an R-neighborhoo aroun the source. Defining a suitable outage probability, a metho to select R in this scheme is propose. The SNR performance at the relays an the receivers for all above relay selection schemes have been analyze. The SNR variance at the receiver has also been stuie an it has been shown that it converges to zero as the number of relays grows. Various numerical simulations have also been use to verify the analytical erivations. REFERENCES [1] A. Senonaris, E. Erip, an B. Aazhang, User cooperation isversity Part I: System escription, IEEE Trans. Commun., vol. 51, pp , Nov [2] J. N. Laneman, D. N. C. Tse, an G. W. Wornell, Cooperative iversity in wireless networs: Efficient protocols an outage behavior, IEEE Trans. Inf. Theory, vol. 50, pp , Dec [3] Y. Zhao, R. Ave, an T. J. Lim, Symbol error rate of selection amplifyan-forwar relay systems, IEEE Commun. Lett., vol. 10, pp , Nov [4] V. Sreng, H. Yaniomeroglu, an D. D. Falconer, Relay selection strategies in cellular networs with peer-to-peer relaying, in Proc. IEEE Veh. Technol. Conf. Orlano, FL, Oct [5] A. Bletsas, H. Shin, an M. Z. Win, Cooperative communications with outage-optimal opportunistic relaying, IEEE Trans. Wireless Commun., vol. 6, pp , Sep [6] Y. Jing an H. Jafarhani, Single an multiple relay selection schemes an their achievable iversity orers, IEEE Trans. Wireless Commun., vol. 8, pp , Mar [7] H. Ochiai, P. Mitran, H. V. Poor, an V. Taroh, Collaborative beamforming for istribute wireless a hoc sensor networs, IEEE Trans. Signal Process., vol. 53, pp , Nov [8] M. Haenggi, On istances in uniformly ranom networs, IEEE Trans. Inf. Theory, vol. 51, pp , Oct [9] X. Deng an A. M. Haimovich, Power allocation for cooperative relaying in wireless networs, IEEE Commun. Lett., vol.9, no.11, pp , Nov [10] F. Etezai,. Zarifi, A. Ghrayeb, an S. Affes, Decentralize relay selection schemes in uniformly istribute wireless sensor networs, IEEE Trans. Wireless Commun., submitte. [11] C. Bettstetter, On the connectivity of A Hoc networs, Computer Journal, vol. 47, no. 4, pp , July 2004.