TEMPORAL FAIRNESS ENHANCED SCHEDULING FOR COOPERATIVE RELAYING NETWORKS IN LOW MOBILITY FADING ENVIRONMENTS

Transcription

1 TEMPORAL FAIRNESS ENHANCED SCHEDULING FOR COOPERATIVE RELAYING NETWORKS IN LOW MOBILITY FADING ENVIRONMENTS Ingmar Hammerström, Jian Zhao, and Armin Wittneben Swiss Federa Institute of Technoogy (ETH) Zurich Communication Technoogy Laboratory, Sternwartstr. 7, CH-809 Zurich, Switzerand Emai: ABSTRACT We consider a wireess network, which consists of severa active source/destination pairs and a number of ide nodes. Mutipe nodes vounteer as reays to faciitate the communication. A nodes have ow mobiity and the fading channe is essentiay constant over the atency time scae of interest (bock fading). Conventiona adaptive scheduing techniques are either unfair or inefficient in this context. In [1] we proposed a scheduing scheme which does not compromise the quaity of service of individua source/destination inks (fairness) if the number of reay nodes is sufficienty high. In this paper we propose a simpe extension to our scheduing scheme which guarantees short-term tempora fairness among the individua inks in the network, whie achieving considerabe muti-user diversity gains. 1. INTRODUCTION The use of diversity in the spatia and tempora dimension to mitigate the effects of fading and therefore to increase the reiabiity of radio inks in wireess networks is a we known technique for systems with co-ocated antennas (space-time coding). Recenty a new concept to reaize spatia diversity has been introduced in [] and [3] caed cooperative diversity or user cooperation diversity. The main idea is to use mutipe nodes as a virtua macro antenna array, reaizing spatia diversity in a distributed fashion. In such a network severa nodes serve typicay as reays for an active source/destination pair. Reays can be cassified as either decodeand-forward (DF) or ampify-and-forward (AF) reays. AF reays, which are considered in this work, ony retransmit an ampified version of their received signas. This eads to ow-compexity reay transceivers and ower power consumption since there is no need of signa processing for decoding procedures. Moreover, AF reays are transparent to adaptive moduation techniques which may be empoyed by the source. Channe adaptive scheduing is known as an efficient means to achieve muti-user diversity gains in mutipe-access networks [4]. It is often referred to as opportunistic scheduing. A good overview about opportunistic scheduing can be found, e.g., in [5 8] and their incuded references. The authors of [5] present a framework for opportunistic scheduing with different fairness constraints. In [6] and [7] throughput optima scheduing rues are proposed by taking each users data queue status into account. An opportunistic scheduing extension for IEEE systems is presented in [8]. Channe adaptive scheduing is efficient and fair in particuar in the high mobiity regime, because the channe state varies sufficienty within the atency time scae of interest. Consequenty, each node has a fair chance to have a good ink in this time interva. However, fairness is a critica issue particuary in ow mobiity fading environments. In this case a channe adaptive scheduer, which maximizes the utiization of the shared resources, essentiay woud ony serve the source/destination pair with the best ink. At the same time the ink throughput of the remaining inks woud be sacrificed. For quaity of service (QoS) reasons, a reaistic channe adaptive scheduing scheme in this case has to operate away from the aggregate throughput optimum. In [9] an opportunistic beamforming scheme is proposed to circumvent the drawbacks of ow mobiity in channe adaptive scheduing in a centraized network. It essentiay introduces tempora variations into a quasi-static fading environment by appying time-variant weights at the co-ocated transmit antenna array. In [10] we propose a simpe diversity scheme for distributed cooperative inks with AF reays, which transates the bock fading time-invariant channe into a time-variant channe by introducing time-variant phase offsets at the reays. The main motivation for the work presented in [1] is the observation, that this time variance coud be expoited by considering severa source/destination pairs jointy for scheduing purposes. We refer to this approach as joint cooperative diversity and scheduing (). The scheme consideraby improves the utiization of the physica resources. It does not compromise the quaity of service of individua source/destination inks (fairness) if the number of reay nodes is sufficienty high. In this work we extend our scheme to the case of short-term tempora fairness guarantees [11] which makes fair opportunistic scheduing with a sma number of required reays possibe. The remainder of the paper is organized as foows: in section we describe the system mode and review our cooperative reaying scheme [10]. In section 3 we summarize our approach of channe adaptive scheduing within a cooperative network. Furthermore, we introduce the extension of our scheduing scheme to the case of tempora share fairness. Performance resuts are presented in section 4. Concusions are given in section 5. Notation: We use bod uppercase etters to denote matrices and bod owercase etters to denote vectors. Further ( ) T, ( ), ( ) stand for transpose, conjugate, and conjugate transpose of a matrix, respectivey. diag[a,...,z] denotes a diagona matrix with the eements a,...,zon its main diagona.. SYSTEM MODEL AND COOPERATIVE DIVERSITY In the foowing we describe the system mode for cooperative reaying. The described network consists of N a source/destination

2 Fig.. System mode of ampify-and-forward reay Fig. 1. Two-hop cooperative reaying network consisting of two active source/destination inks and three reays. A nodes are singe antenna nodes. pairs and N r AF reays (e.g., depicted in Fig. 1 for N a =and N r =3). Communication takes pace over two hops (or rather time-sots). In the first sot the source transmits a data packet to the reays and the destination. During the second sot the reays retransmit an ampified version of the received signas to the destination. We assume that a nodes are frame synchronous, i.e., a nodes know the sot timing. In our scenario mobiity of a nodes is ow and the channe coefficients are constant over the atency time scae of interest. We assume that the channe is time-invariant over at east one transmission cyce (bock fading). To derive an expression for the SNR at the destination the channe coefficients between source and reays (upink) for ink n are stacked in the vector h 1,n, whereas the channe coefficients between reays and destination (downink) are stacked in h,n.the direct channe between source and destination is given by h 0,n. We consider frequency-fat fading, which usuay incudes path oss, shadowing and sma-scae fading. In this paper we assume that a channe coefficients are i.i.d. compex norma random variabes CN(0,d α ),wheredis the distance between transmitter and receiver and α is the path oss exponent. Fig. shows the system mode of an AF reay. The AWGN contribution for time instance k at reay is denoted by m (k) which isassumedtobecn(0,σr). Prior to the retransmission the reay ampifies the signa with the factor g (k). To derive the mutua information between the transmitted and the [ received signas we define the gain matrix G k = diag g (k) 1,...,g(k) N r ]. The transmit power of the source is P,and the AWGN contribution at the destination is CN(0,σD). Negecting the ink index n, the mutua information is then given by [ I (k) = 1 og 1+ P h0 P ] h T G k h 1 + σd σd + σ R ht G. (1) k G k h A detaied derivation of the mutua information (1) can be found in [10]. Note that the factor 1/ accounts for the two channe uses required by the reay traffic pattern. To achieve a cooperative diversity gain with N r reays in the bock-fading environment it is possibe to code the signas at the reays by a mutipication of a data packet with a non-diagona code matrix [1]. We proposed a simper approach in [10] which essentiay transforms the spatia diversity into tempora diversity by means of a diagona matrix. This tempora diversity again can be expoited by an outer code introduced at the source. Therefore, our proposed reaying scheme is transparent with respect to adaptive moduation and transmission scheduing. For carity of exposition we briefy summarize the approach: the inear processing at the reays is time-variant, which resuts in a time-variant equivaent source/destination channe coefficient (i.e., a time-variant SNR at the destination). In a simpe embodiment the reays use a time-invariant gain and a reay-specific time-variant phase offset (phase signature sequence). Thus, the ampification gain of reay at time instance k is, e.g., given as g (k) = P R P h 1, + σ R }{{} time invariant exp(jϕ (k) ), () }{{} time variant where ϕ (k) denotes the reay-specific and time-dependent phase offset. Each reay transmits with power P R. We impose a tota power constraint P on a reays, i.e., P R = P/N r. Due to the time-variant phase-shifts at the reays the spatia diversity offered by the N r reays is transated into the tempora domain. The number of reays imits the maximum achievabe diversity order to N r, because there are ony N r independent downink channe reaizations. To expoit this tempora diversity the input signa sequence is precoded by a inear bock code (matrix mutipication) as, e.g., in [13]. Note, that the phases do not necessariy change with every transmitted symbo. We assume that one transmission cyce is divided into two time-sots (upink and downink) each divided into N b segments; N b corresponds to the ength of the phase sequences of the reays in the downink. In this work, the phase sequences are chosen as N r coumns out of an IFFT matrix. But aso random phase shifts are appropriate. Note that () provide an instantaneous reay transmit power P R and ony the phases are time-variant. It woud aso be possibe to additionay mode the transmit power as a random process which woud ensure ony an average transmit power of P R over N b phase segments. 3. ADAPTIVE SCHEDULING If we consider a wireess network with mutipe source/destination pairs which share the same physica resources the question arises which ink shoud be schedued. In genera there are two extreme optimization criteria. On one hand the scheduing entity wants to maximize the utiization of the physica resources which is usuay measured in terms of system throughput. On the other hand the fairness among a competing source/destination pairs shoud be guaranteed which can be measured in terms of ink throughput. The fairness issue in scheduing again can be divided into two cases: throughput fairness and tempora fairness. In both cases the scheduer gives a certain share of the entire resource to the users. In the first case the shared resource is the whoe system throughput. In the atter case, which is considered in this work, the shared resource is time. One scheduing scheme which assures the highest tempora fairness is the static scheduing scheme round robin (RR). The disadvantage of RR scheduing is that it does not incor-

3 1. Start at beginning of fairness window; reset a counters which represent the number of segments each source/destintion pair has been schedued.. Seect the pair which supports the highest possibe rate and increase counter for this pair. 3. If a schedued pair reached its maximum tempora share, take it out of the set of pairs which have to be schedued. 4. Go to next time segment. 5. Repeat unti end of fairness window. Tabe 1. Tempora Fairness Enhanced porate the actua channe conditions into its decisions. Therefore, it is not possibe to achieve muti-user diversity gains. In the foowing we shorty review the concept of Joint Cooperative Diversity and Scheduing () which was proposed in [1]. It is based on the artificiay introduced time-variance of the channe as described in section. It makes efficient scheduing in cooperative networks in the ow mobiity environment possibe. In [1] it has been shown that achieves the same Quaity-of-Service (QoS) requirement (defined as the 1%-outage ink throughput) as a system with static scheduing. Unfortunatey, the number of reays which are required to achieve this is reativey high and increases with the number of source/destination pairs N a. Therefore, the aim of this work is to extend the scheme to the case of tempora fairness constraints to reduce the number of required reays. For this, we propose two different approaches which need different amounts of channe knowedge at the scheduing entity. With respect to our scheduing schemes, we assume that one node of the network serves as centra scheduing entity. For iustration we assume that the feedback channe to this node is perfect without any errors Joint Cooperative Diversity and Scheduing The key idea of the work presented in [1] is to further expoit the artificiay introduced time-variance by joint consideration of severa source/destination pairs to achieve muti-user diversity. If the fading conditions of a source/destination pairs are symmetric, the proposed scheduer in [1] seects the inks on the basis of a greedy (maximum-rate) scheduing metric, i.e., the best ink in each phase segment. If the fading conditions are asymmetric the uses the metric of the proportiona fair scheduer [9]. Note that, athough fairness of expicity benefits from the artificia introduced time-variance it does not assure that each source/destination ink is schedued within one transmission cyce. ony assures tempora fairness over a infinitey arge horizon. 3.. Tempora Fairness Enhanced A straightforward extension to short-term tempora fairness for can be derived as foows. To assure tempora fairness the whoe time sequence is divided into fairness windows of ength N f. We count N f in terms of transmission cyces. N f =1, e.g., woud be the most stringent QoS requirement, because then each pair has to be schedued within one transmission cyce. Within this fairness window the scheduer chooses sequentiay over the phase segments that source/destination pair which 1. Start at beginning of fairness window; reset a counters which represent the number of segments the source/destintion pair has been schedued.. Sort the supported rates for each segment over the source/destination pairs. Cacuate the differences of the best and second-best supported rate for each segment. 3. Seect the pair and segment which has the highest difference in supported rate; mark segment as schedued; increase counter for this pair. 4. If a schedued pair reached its maximum tempora share, take it out of the competition and go back to. If not, go back to 3. Repeat unti a segments are schedued. Tabe. Pre-Seective Tempora Fairness Enhanced supports the highest possibe throughput. If one pair has reached its maximum tempora share in the actua fairness window it drops out of competition and remains inactive unti the next window. We refer to this scheduing scheme as Tempora Fairness Enhanced, or TF-. The TF- scheme is summarized in Tabe 1. Obviousy, if the first source/destination drops out of competition one order of muti-user diversity is ost, because the scheduer has ony N a 1 pairs eft to schedue. From the ast remaining source/destination pair it is not possibe to achieve any muti-user diversity gain at a. Bearing this matter in mind, it can be seen that the system throughput of TF- has to be smaer compared to considered in section Pre-Seective Tempora Fairness Enhanced Another way to guarantee short-term tempora fairness which promises a higher system throughput than the TF- benefits from the time-invariant physica channe and the deterministic phase sequences at the reays. A scheduing entity which knows the channe coefficients of the network and the phase sequences can determine the supported rates of each source/destination pair in advance for the whoe a segments within a transmission cyce. Therefore, it can maximize the system throughput subject to the amount of tempora share of each pair. This optimization probem is hard to sove and needs a ot of computations, in particuar, when thinking of a brute force search agorithm. Therefore, we introduce a scheduing agorithm which is optima for N a =and suboptima for N a >, but achieves at east a higher system throughput as TF-. We refer to this kind of scheduing scheme as Pre- Seective Tempora Fairness Enhanced, or PTF-. It is based on the concept of minimizing the oss in system throughput. This oss arises if a source/destination pair has aready reached its maximum amount or tempora share by the sequentia scheduing as, e.g, in TF-, but has higher supported rates to come within the fairness window. Therefore, PTF- schedues for every segment this pair which shows the highest throughput compared to second best pair. Starting from the segment with the highest difference, this minimizes the oss in system-throughput for N a =. The agorithm is summarized in Tabe. Obviousy the required amount of channe feedback to the scheduing entity for PTF- is much higher than for TF-. For TF- ony SNR feedback is required which can be ad-

4 3 1.4 average system throughput [bps/hz] number of source/destination pairs N a 1% outage ink throughput [bps/hz] number of source/destination pairs N a Fig. 3. Average system throughput vs. number of source/ destination pairs; N r =10, ρ = 10dB, N f =1transmission cyce. ditionay much more quantized than feedback of channe coefficients. Note that for achieving fu cooperative diversity on the ink eve it is necessary that each source/destination pair is schedued at east N r times within a transmission cyce. Furthermore, the effective fading channes seen by the ink for each schedued segment have to be uncorreated, which is ony possibe if the phase sequences are orthogona. Therefore, one necessary but not sufficient condition for fu diversity regarding the number of segments is: N b N a N r. 4. PERFORMANCE RESULTS In this section we wi present the performance resuts of our proposed scheduing schemes by means of computer simuations. Simuation Setup: We consider a network where N r reays are paced at random uniformy distributed on a disk with diameter d 0. The N a sources and destinations are paced on the border of this disk, each on opposite sides. The distance between a nodes on the border of the disk are chosen to be maximum. Therefore, the ange between two subsequent sources (or destinations) is chosen as π/n a. We assume that a channe coefficients are i.i.d. compex norma random variabes CN(0,d α ),wheredis the distance between transmitter and receiver and α =3the path oss exponent. Furthermore, we assume that the noise variance of the reays is equa to the noise variance of each destination, i.e, σr = σd = σ. The parameter ρ = P/(σ d α 0 ) denotes the average SNR of the direct ink between source and destination. Note, that because the source/destination pairs are paced on the border of the disk neary symmetrica fading conditions can be assumed for each pair, i.e., the SNR distributions at the destinations are the same for a pairs. Nevertheess, we use the proportiona fair scheduing metric [9] for the scheme. Resuts: In Fig. 3 the average system throughput of the proposed scheduing schemes vs. the number of source/destinaton pairs N a is shown for N r =10reays and a SNR of ρ = 10dB. The ength of the fairness window is set to N f =1transmission cyce, whie the number of segments per transmission cyce is set to N b = 400. The 1%-outage ink throughput for this set of parameters is depicted in Fig. 4. The 1%-outage ink throughput is the throughput each individua ink woud have in 99% of a cases within the fairness constraint window of ength N f. It is directy reated to QoS parameters ike data rate and deay. Fig. 4. 1%-outage ink throughput vs. number of source/ destination pairs; N r =10, ρ = 10dB, N f =1transmission cyce. The muti-user diversity gain with increasing number of source/destination pairs is ceary visibe in Fig. 3 for the opportunistic scheduing schemes. The system throughput of the RR scheme is independent of the number of source/destination pairs. The without tempora fairness constraints shows the highest average system throughput. But regarding the ink throughput in Fig. 4 it shows the worst performance. It is not abe to assure a nonzero 1%-outage ink throughput within N f =1transmission cyce. We ony introduced phase shifts at the reays and set an instantaneous power constraint on the reay transmit power P R. Nevertheess the introduced time-variance is not sufficient to enabe the to have a nonzero 1%-outage ink throughput. To increase the time-variance, introducing time-variant reay transmit power coud be a choice (compare to ast paragraph in section ). The TF- achieves approximatey the same outage ink throughput as the static scheduing scheme RR, because the scheduer operates sequentiay and does not predict when a certain source/destination pair has its maximum. Therefore, it is ikey that the remaining pair (a others have aready reached their maximum aowed tempora share) has to be schedued without regarding its actua supported rate. Note that this performance is a big improvement compared to. The PTF- has the goba knowedge about a channe coefficients and is therefore abe to determine when a certain source/destination pair is at maximum or minimum in advance and can therefore achieve higher outage ink throughput compared to RR and TF-, whie achieving aso the highest muti-user diversity gain with subject to tempora fairness constraints. In Fig. 5 we reax the stringent condition on the tempora fairness window size N f =1transmission cyce. We compare the average system throughput over an increased ength of N f (in terms of transmission cyces). It is shown for N a =10(soid ines) and N a = (dashed ines) source/destination pairs. It can be seen that both schemes, the TF- and the PTF- approach to the performance of the without tempora fairness constraints quite fast. Note, that the performance of the PTF- is based on perfect prediction of the variations of the physica channe which changes for every transmission cyce. In a rea system this performance woud depend on the tempora correation of the channe coefficients. The TF- on the other hand does not need this prediction and is therefore a good scheduing scheme with ower feedback requirements compared to PTF-. It has the same

5 3 1.8 average system throughput [bps/hz] ength of fairness window N f [# transmission cyces] 1% outage ink throughput [bps/hz] ength of fairness window N f [# transmission cyces] Fig. 5. Average system throughput vs. ength of fairness window N f for N a =10(soid ines) and N a =(dashed ines); N r =10, ρ = 10dB. feedback signaing requirements as without short-term fairness constraints. Therefore, from the feedback point of view there is a trade-off between tempora fairness assurance with high QoS requirements and maximum system throughput scheduing with ony ong-term tempora fairness. In Fig. 6 the 1%-outage ink throughput vs. ength of the fairness window N f is depicted. It is shown for N a =10(soid ines) and N a =(dashed ines) source/destination pairs. It can be seen that the outage ink throughput within the fairness constraint window aso increases, which is mainy due to the increased tempora diversity by the physica channe. The TF- sti performs the same as the static RR in terms of QoS and is independent of the number of active source/destination pairs. The PTF- profits most from the increased ength of the fairness constraint window N f. Particuary, it can be seen that for N a =source/destination pairs aso the without short-term tempora fairness assurance achieves a nonzero outage ink throughput for N f > transmission cyces. 5. CONCLUSIONS AND OUTLOOK We extended our in [1] presented to the case of short-term fairness guarantees. We proposed two different approaches: the TF- which ony needs SNR feedback and the PTF- which needs fu channe knowedge. We concude, that both approaches achieve at east the same QoS as a RR scheduer whie achieving considerabe muti-user diversity gains. Future work wi be concerned with the signaing which is required for scheduing and with the verification of our resuts in our RACooN Laboratory [14]. 6. REFERENCES [1] A. Wittneben, I. Hammerstroem, and M. Kuhn, Joint cooperative diversity and scheduing in ow mobiity wireess networks, in Proc. GLOBECOM, (Daas, TX), Nov. 9 Dec. 3, 004. [] N. J. Laneman, D. N. Tse, and G. W. Worne, Cooperative diversity in wireess networks: Efficient protocos and outage behavior, IEEE Trans. Inform. Theory, vo. 50, pp , Dec [3] A. Sendonaris, E. Erkip, and B. Aazhang, User cooperation diversity-part I: System description, IEEE Trans. Commun., vo. 51, pp , Nov Fig. 6. 1%-outage ink throughput vs. ength of fairness window N f for N a =10(soid ines) and N a =(dashed ines); N r =10, ρ = 10dB. [4] P. Bhagwat, P. Bhattacharya, A. Krishna, and S. Tripathi, Enhancing throughput over wireess LANs using channe state dependent packet scheduing, in Proc. IEEE INFO- COM 96, (San Francisco, CA), pp , Mar. 4 8, [5] X. Liu, E. Chong, and N. Shroff, A framework for opportunistic scheduing in wireess networks, Computer Networks, vo. 41, pp , Mar [6] M. Andrew, K. Kumaran, K. Ramanan, A. Stoyar, P. Whiting, and R. Vijayakumar, Providing quaity of service over a shared wireess ink, IEEE Commun. Mag., vo. 39, pp , Feb [7] S. Shakkottai and A. Stoyar, Scheduing for mutipe fows sharing a time-varying channe: The exponentia rue, tech. rep., Be Laboratories, Dec [8] B. Sadeghi, V. Kanodia, A. Sabharwa, and E. Knighty, Opportunistic media access for mutirate ad hoc networks, in Proc. MOBICOM, (Atanta, GA), Sep. 3 8, 00. [9] P. Viswanath, D. N. C. Tse, and R. Laroia, Opportunistic beamforming using dumb antennas, IEEE Trans. Inform. Theory, vo. 48, pp , June 00. [10] I. Hammerstroem, M. Kuhn, and A. Wittneben, Cooperative diversity by reay phase rotations in bock fading environments, in Proc. SPAWC, (Lisbon, Portuga), Ju , 004. [11] S. S. Kukarni and C. Rosenberg, Opportunistic scheduing poicies for wireess systems with short term fairness constraints, in Proc. GLOBECOM,vo.1,(SanFrancisco,CA), pp , Dec. 1 5, 003. [1] Y. Jing and B. Hassibi, Distributed space-time coding in wireess reay networks-part I: Basic diversity resuts, IEEE Trans. Wire. Comm., Juy 004. (Submitted for pubication). [13] Y. Xin, Z. Wang, and G. B. Giannakis, Space-time diversity systems based on inear consteation precoding, IEEE Trans. Wire. Comm., vo., pp , Mar [14] RACooN Laboratory of the Swiss Federa Institute of Technoogy. research/projects/racoon/introduction. htm.