Cross-layer Routing Optimization for Wireless Networks with Cooperative Diversity

Transcription

1 Cross-layer Routing Optimiation for Wireless Networs with Cooperative Diversity Zhiguo Ding an Kin K. Leung Department of Electrical an Electronic Engineering Imperial College Lonon, UK. {higuo.ing, Abstract In this paper, we stuy the impact of cooperative transmission on the routing ecision for wireless a-hoc networs. The influence of cooperative transmission to the wireless lin cost is first stuie at the physical layer. Then the problem of routing optimiation is investigate to unerstan the effects of improve lin cost on the routing ecision, where the close-form solution of the optimiation problem is evelope an later use as a quantitative criterion of the route selection. Our evelope analytical an simulation results show that the criteria using cooperative transmission typically yiel more efficient routes compare with the non-cooperative schemes. I. INTRODUION Future wireless communication networs are expecte to support the mixture of real-time applications, such as voice an multimeia teleconferencing, an non-real-time ata applications, such as web browsing, messaging an file transfers. Compare with wire environments, the associate communication channels an traffic patterns in mobile wireless networs are more unpreictable. Hence all of these applications impose stringent an iversie Quality of Service QoS) requirements, which cannot be satisfactorily aresse through the traitional layering networ-protocol architecture. Corresponingly, there has recently been increase interest in protocols for wireless networs to exploit the signicant interactions between various layers of the protocol stac for performance enhancements. An it has been shown that these cross-layer esigns an protocols coul be essential for wireless a-hoc an sensor networs where unpreictable variables such as noe mobility, noe ensity an networ imensions mae the iverse an stringent wireless QoS requirements ficult to satisfy. Due to the unreliability of wireless lins, it has been of interest to stuy the impacts of physical-layer techniques on the esign of upper-layers, incluing meium access control MAC), pacet scheuling, power control, routing, transport protocol, an ultimately the QoS at the application level in wireless networs. Opportunistic scheuling coul be seen as one of successful examples of cross-layer esign, where Research was sponsore by US Army Research laboratory an the UK Ministry of Defence an was accomplishe uner Agreement Number W9NF The views an conclusions containe in this ocument are those of the authors an shoul not be interprete as representing the official policies, either expresse or implie, of the US Army Research Laboratory, the U.S. Government, the UK Ministry of Defense, or the UK Government. The US an UK Governments are authorie to reprouce an istribute reprints for Government purposes notwithstaning any copyright notation hereon. scheuling protocols are esigne by taing avantage of the nowlege of wireless lin conitions [], []. Among many caniates of physical-layer techniques, multiple-input multiple-output MIMO) has receive signicant attention, which can provie spatial iversity an hence represents a powerful technique for interference mitigation an reuction [], [4]. Cooperative communication provies an alternative way to achieve spatial iversity, where single-antenna terals in a multiple-user environment share their antennas an form a cluster to assist each other with their ata transmission [5], [6]. In [7] an [8] the authors stuy the cross-layer routing protocol esign for energy-constraine networs, where the cooperative transmission technique is use to form a virtual antenna array. It is shown in [7] an [8] that the propose protocol coul yiel a ferent route compare with traitionally non-cross-layer protocols the circuit processing energy is consiere, an the two protocols will choose the same route otherwise. Recently the routing optimiation was analye by using a probabilistic lin moel [9], which points out that the broacasting nature of wireless communications shoul be utilie by routing protocols to achieve robustness at the networing level. Recall that cooperative transmission has been recognie as an effective technology to utilie such feature of wireless communications [5], [0], []. Inspire by this observation, we focus on stuying the effects of cooperative transmission on the routing ecision in this paper. The effects of cooperative transmission to the lin quality are first stuie. The problem of routing optimiation is then investigate in orer to stuy the impact of the improve lin cost to the routing ecision. The objective function of interest is to imie the total power consumption with a given en-to-en reliability constraint. The optimal solution of this optimiation problem inicates the imum total power consumption of a route in orer to satisfy the require error performance, which is then use as a criterion to compare an select the best among ferent routes. Our analytical results show that the route chosen by the cooperative criterion can consume much less transmission power compare with the route using only irect transmission. For certain path loss factors an provie that irect transmission is use only, it is observe that a source noe will prefer to communicate with its estination noe irectly, which coul result in transmission power higher than the saturation level ue to the long /08/$ IEEE

2 source-estination istance. However, it is noticeable that the cooperative criterion still maintains the preference of multihop transmission to ensure the transmission power at each lin is below the given maximum limit. II. SYSTEM ARCHITEURE In this paper, we consier a wireless a-hoc networ where noes are assume to be unormly istribute in a region with the noe ensity λ. Each noe is equippe with one omniirectional antenna element although our results can be extene to more generalie cases with multiple antennas at each noe). Time Division Multiple Access TDMA) schemes are use here for two reasons. First, in case that there are multiple source-estination pairs communicating simultaneously, the TDMA assumption coul allow us to only concentrate on one pair, an hence co-channel interference is eliate automatically. Secon, the fact that time ivision uplex channels are reciprocal naturally maes channel state information available at the transmitter. We employ a propagation moel to consier path loss, shaow faing an Rayleigh faing [], [7], []. Denote g as the wireless channel coefficient between the noes i an j an can be moelle as g = h / where is the istance between the noes i an j, / / epicts the large-scale behavior of the channel gain, is the path loss exponent an h captures the channel faing characteristics ue to the rich scattering environment. Furthermore, multiple noes are separate apart enough to assume channel faing h inepenent an ientically istribute i.i..), complex Gaussian variables with ero mean an unit variance. Traitionally, the noe i communicates irectly with the noe j in the physical layer, provie that the lin i j is elegate by the routing protocol. In this paper, we propose that each noe i tries to fin one an only one useful relay noe other than the noe j) to accomplish cooperative transmission when communicating with the noe j. Since cooperative transmission can improve the quality of the wireless lin, the existing routing protocols shoul be moie to tae such effect into account. In orer to esign such a cross-layer routing protocol, it is important to first unerstan the in of effects the physical layer technique can bring to the lin quality, which will be iscusse in etail in the next section. III. LINK COST USING COOPERATIVE TRANSMISSION This section is to unerstan how much the quality of wireless lins can be improve by using cooperative transmission an what in of physical characteristics will have the critical effects to the quality improvement. Consier a three-noe scenario with noes i an j, an a relay noe R, where the noe i wants to communicate with the noe j noe with help of the relay noe R. Such cooperative transmission consists of two stages in time [0]. At the first stage, the noe i transmits its information where both the noes j an R are ) receiving. At the secon stage, the relay ecoes an forwars the information of the noe i to the noe j ecoing is successful. Otherwise the relay will eep silent an the noe i will transmit its information once again. For TDMA schemes, such cooperative transmission consumes two times the time slots compare with irect transmission, so ata rate at each stage or time slot) is chosen to be two times of that for irect transmission. Define, ir, an as the istances among the noe i, the relay noe, an the noe j. So uring the first time slot, the noe j receives y j, = h / s i + n j, ) where s i is the information of the noe i an n j will be the white noise. An uring the secon time slot, the noe j receives h s y j, = / i + n j, h <q) / ) h / s i + n j, h q) / where q) = R an R is the ata rate in bits/s/h. The signal-to-noise ratio SNR) is efine as = E b /N 0 where E b enotes transmission energy per-bit an N 0 is the one-sie power spectral ensity of the white noise. As can be seen from ), the relay noe coul yiel no performance gain it has a poor lin with the source noe i, which means that the choice of the relay noe coul be critical to the system performance. For the reason of simplicity, the ranom choice of relaying is consiere in this paper, an the results for using istribute relay selection can be foun in []. A. Ranom Choice of Relaying Consier that a relay noe is selecte ranomly. Hence the ata rate such cooperative system is able to support can be shown as [0] h log + ) h <q) I = / / h log + [ + h ]) h q) / / / By following the steps in [0], [], [4], [5] the outage probability is also use here to evaluate error performance. Since h is assume complex Gaussian variables with ero mean an unit variance, h is an exponentially istribute / variable with parameter. So using the results in [0] irectly, we have the outage probability between the noes i an j as P = P I <R) 4) ir + ) R ) = P r [ ] ir + )R ) R +) 5)

3 where R is the ata rate in bit/s/h efine by the QoS requirement an the outage probability of irect transmission between the noes i an j is P R ) 6) Comparing 5) an 6), the necessary conition to ensure cooperative transmission is better than irect transmission is [ ] ir + )R ) R +) 7) Another scheme of interest is the traitional two-hop transmission scheme where the estination can only receive signals from the relay noe. The outage probability for such two-hop transmission is P TH = PiR ) P ) 8) R ) ir + R ) ) ir R ) where the approximation follows from 6). Comparing 6) an 4), it is evient that the use of cooperative transmission can increase the quality of wireless lins in terms of reliability or transmission power consumption. An the use of more avance cooperative protocols such as in [6], [7] shall provie more performance gain, however, such a simple ecoeforwar protocol will be use later because of its simplicity. IV. ROUTE OPTIMIZATION AND PROTOCOL DESIGN Previous evelope results show that cooperative transmission can bring some performance gain to the physical layer, specially to the quality of wireless lins. It is of interest to stuy how such such physical layer benefits can have effects to the upper layer, such as the routing protocol esign. Consier that a route has been constructe between the source an estination. The goal of interest here is to unerstan the best performance a ranom route can achieve, which can be later use as a quantitative criterion for route selecting. Without losing generality, the noes sitting on the route are enote as S... n D. Dferent to traitional routes, cooperative transmission is use to improve the lin quality when the noe i is communicating with the noe j. It is possible that a goo helping noe is not available for some pairs of the n + lins of the route. In that case, irect transmission is use instea of relying on cooperative transmission. Hence the n + lins can be categorie into two sets. One set, efine as S, inclues all lins using cooperative transmission an the other one, efine as S, inclues the lins using irect transmission. Note that S + S = n + since there are only n + lins on the route. Provie that the i j lin utilies cooperative transmission, S, efine = f P ) where is the require SNR for the lin from the noe i noe to the noe j, an f x) = R ) ir + ). 9) x Hence the transmission power for the i j lin is W = RBN 0 =RBN 0 f P ). If S, the transmission power for for the i j lin is W = RBN 0 = RBN 0 f P ), where f x) =R ) x. The problem to imie the total transmission power consumption with the constraint on the en-to-en reliability can be formulate as P,P W + W 0) S S P ) P ) P S S For small outage probability P << an P <<, we can have the following approximation P ) P ) ) S S + P S P. S So the optimiation problem can be simplie as P,P W + W ) S S + P P S P S By introucing an auxiliary variable, ) can be written as P,P, W + W ) S S P P S P S 0 P Note that the transmission power is always positive, W 0, an both f x) an f x) are monotonic ecreasing. Hence the optimiation can be solve in two stages. First we treat as a constant an solve the following two optimiation problems separately, P S W S P P P S W S P

4 4 which yiels the two solutions ) R W = RBN 0 S P ) [ ir + ) ] S 4) ) R ) S W = RBN 0 5) S The results in 4) an 5) can be obtaine by applying the Kuhn-Tucer conition in [8]. Due to the space limitation, the etails of the evelopment for the optimiation is omitte here an will be provie in in []. Note that both S W an S W now becomes functions of the auxiliary variable. The secon step is solve the following optimiation ) R ) S f ) =RBN 0 ) [ +RBN R 0 P ) S ir + )] 0 P which is ficult to solve irectly as it coul result in a equation with egree higher than. Note that f ) is a strictly convex function for 0 P since f ) 0. Hence there will only one imum for 0 P, efine as f. Provie that ) 0, it can be expecte that 0 P, otherwise P P. So in the following, the close form of will be shown as P f + ) 0 = 7) P < 0 ) / 4 an the total power consumption is + ) P W = 4 ) / / 4P ) + P 4 ) / f ) f ) f ) 0 < 0 8) ), where = RBN 0 R ) S = RBN 0 P R ) S [ ir + )] ) = RBN R [ 0 S ir + )] ) S ), ) ) an R ) 4 = RBN 0 P ). The etails of the erivation for 7) can be from the []. ) A Special Case: Consier the worst case where each i j lin can not fin a goo relay noe satisfy 7). Then all lins will use irect transmission, an hence the total power consumption will be W = 4 P 9) ) RBN 0 R ) S =. P In the case of =, it is interesting to fin that W = RBN 0 R ) S ). 0) P For the two successive lins i j l. we can have + jl il since they are three eges of a triangle. Hence the one-hop transmission from the source to the estination irectly woul be preferre by the criterion in 0). ) Route Selection: For more general cases, the quality of one route will be etere jointly by the cooperative lins as well as the irect-transmission lins. Two rules for routing ecision have been implie by the evelope results. The preference of the cooperative lins can be illustrate from the object function in 6). The power consume by cooperative 6) lins is inverse proportional to the square of the outage probability whereas the power consume by irect transmission is inverse proportional to the probability. Provie that both an P are very small an at the same orer, it can be expecte that replacing a irect-transmission lin with a cooperative lin can reuce the power consumption. The preference for multiple-hop transmission can be illustrate by the following example. Consier a route where each of its lins, i j, can fin a goo-quality helping noe in the mile of the straight line between the noes i an j. With such assumption, the total transmission power consume by the route only using one hop can be written as R ) W onehop = RBN 0 = R ) P P ) an the power consumption for the route using n-hop transmission can be shown as R ) [ ] ) W nhop = RBN 0 n P n n ) = RBN 0 n R ) n P = n / W onehop,n, which shows that the use of multiple-hop transmission can reuce the transmission power consumption. ) Numerical Results: In the following, we provie an example to show the effect of the criterion of imiing the total transmission power with the constraint of the en-to-en reliability on the routing ecision. The require ata rate is R =0.bit/s/H an SR =0m. In the first setup, there are two intermeiate noes sitting on the straight line between the source an estination with S = D = SD. The noncooperative criterion in 0) will pic up the route S D since there is no point to use multiple-hop transmission which yiels the same power consumption, but more elay. However

5 5 S D S D a) Setup : Two intermeiate noes for P > 0.04 b) Setup : Two intermeiate noes for P 0.04 S D c) Setup : Three intermeiate noes for all P Fig.. Route selection with or without cooperative transmission ). The ata rate is set as R = 0. bit/s/h, an the source-estination istance is 0m. The soli line presents the route which will be chosen by the criterion in 8), an the ash line presents the route chosen by the criterion without cooperative transmission S =0). for the criterion propose in 8), the route, S D, will be chosen for the mil requirement of the en-to-en reliability, where enotes a lin using cooperative transmission. For the highly emaning reliability requirement, the error probability coul be so small that the power consume by the irect-transmission lin D will oate the power consumption, which results the route S D as the preferre one. In Table I shows that these routes pice by the propose criterion can reuce the power consumption signicantly compare with the scheme only using irect transmission. For the secon setup, there are three intermeiate noes sitting on the straight line between the source an estination with S = D = 4 SD. The situation is much easier where the route with multi-hop transmission will be chosen, an its performance is also shown in the Table I. TABLE I NORMALIZED TRANSMIT POWER CONSUMPTION CHOSEN BY TWO CRITERIA P Direct trans., S D Setup, S D Setup, S D Setup, S D V. CONCLUSION In this paper, we have stuie the impact of cooperative transmission on the routing ecision for wireless a-hoc networs. The influence of cooperative transmission to the quality of wireless lins is iscusse first at the physical layer. The objective function of interest is to imie the total power consumption with the constraint of the en-to-en reliability. Both analytical an simulation results are provie to show that the criteria using cooperative transmission typically yiel more efficient routes than the non-cooperative schemes. At the current stage, only ranom choice of relays has been use, an it is interesting to stuy cross-layer routing using more avance cooperative protocols, such as the best-relay scheme an istribute beamforg. Furthermore, a centralie scheme is require for the propose routing selection, an hence it will be an interesting future topic to esign a istribute routing protocol with the use of the evelope quantitative criterion. REFERENCES [] C.-J. Chen an L.-C. Wang, Enhancing coverage an capacity for multiuser MIMO system by utiliing scheuling, IEEE Trans. on Wireless Communications, vol. 5, pp , May 006. [] T. Yoo an A. Golsmith, On the optimality of multiantenna broacast scheuling using ero-forcing beamforg, IEEE Journal on Select. Areas in Comm., vol. 4, pp , Mar [] G. Foschini an M. 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