Closed-Form Optimality Characterization of Network-Assisted Device-to-Device Communications

Transcription

1 Closed-Form Optimality Caracterization of Network-Assisted Device-to-Device Communications Serve Salmasi,EmilBjörnson, Slimane Ben Slimane,andMérouane Debba Department of Communication Systems, Scool of ICT, KTH Royal Institute of Tecnology, Stockolm, Sweden Signal Processing Lab, ACCESS Linnaeus Centre, KTH Royal Institute of Tecnology, Stockolm, Sweden Alcatel-Lucent Cair on Flexible Radio, SUPELEC, Gif-sur-Yvette, France {emil.bjornson, Abstract Tis paper considers te selection problem for network-assisted device-to-device DD communications wit multiple antennas at te base station. We study transmission in bot dedicated and sared frequency bands. Given te type of resources i.e., dedicated or sared, te user equipment decides to transmit in te conventional cellular or directly to its corresponding receiver in te DD. We formulate tis problem under two different objectives. Te first problem is to maximize te quality-of-service QoS given a transmit power, and te second problem is to minimize te transmit power given a QoS requirement. We derive closed-form results for te optimal decision and sow tat te two problem formulations beave differently. Taking a geometrical approac, we study te area around te transmitter were te receiving sould be to ave DD optimality, and ow it is affected by te transmit power, QoS, and te number of base station antennas. I. INTRODUCTION Emerging multimedia services and applications introduce new traffic types and user beaviors [1]. To address te iger demands imposed on wireless networks, more spectrally efficient and energy efficient approaces sould be developed. Device-to-device DD communication underlaying cellular networks is proposed to improve cell spectral and energy efficiency of te network [], [3]. In DD transmission, user equipments s communicate directly to teir intended receivers as opposed to te conventional cellular were tey communicate troug te base station. DD can bring proximity gains and reduce te transmission time. Users in te DD can transmit eiter in a separate frequency band or via spectrum saring wit cellular users. In te former case, DD communications do not interfere wit cellular users. Tis case is interesting due to its potential applications, suc as public safety and multicasting for local multimedia services and robustness to infrastructure failure. On te oter and, spectrum saring can be employed to efficiently utilize te resources wic allows for better area spectral efficiency [4]. Te gain from spectrum saring can be assured if te interference is controlled by proper selection and resource management. However, depending on te network topology and cannel conditions, it may not always be beneficial to coose te DD for a. E. Björnson is funded by te International Postdoc Grant 1-8 from Te Swedis Researc Council. Tis researc as been supported by te ERC Starting Grant 3513 MORE. Te studies [5] and [6] consider te selection problem wit power control for one DD user and one cellular C in a single antenna system. Tis problem corresponds to a coice between ortogonal resources, spectrum saring, and conventional cellular transmission for te wit DD capability. In [5], te problem is formulated for two cases: greedy sum rate maximization were te C and DD users are competing entities and sum rate maximization under a rate constraint for te C. Bot problems are solved under power/energy constraints. In [6], a similar scenario is considered were te cell sum rate in single- and multi-cell scenarios is studied under a rate constraint tat gives priority to te C. Moreover, [7] considers a scenario in wic te position of te DD transmitter and receiver are fixed, wile te C s position can cange. Two uplink transmission scenarios are investigated. In te former, te DD user and te C sare te spectrum if te DD s signal-to-interferenceand-noise ratio SINR exceeds a pre-defined tresold. In te latter, te C can also use a relay to reduce its power wile saring te spectrum wit te DD user. In bot cases, te DD user s power is fixed and te interference from te DD user to te is assumed negligible. In tis paper, we consider network-assisted DD communications were te network elps te devices to perform peer discovery, radio resource management, and resolve security issues [1], [3]. Terefore, all s ave te same priority in te network regardless of teir of operation i.e., cellular or DD. Tis is different from prior works in wic DD users ave lower priority and tus underlay cellular networks or, similarly, are considered secondary entities in a cognitive radio system. Network-assisted DD communications can guarantee certain quality-of-service QoS levels for all s. We define te selection problem as follows: given te type of resources, i.e., dedicated or sared, te decides wic operation to select, i.e., te DD or cellular. Furtermore, we take into account te effects of multiple antennas in te as it is an important feature of LTE and IMT-Advanced systems tat enables simultaneous sceduling of spatially separated users [1], [8], [9]. Te selection problem is formulated wit two objectives: maximizing te QoS for a given transmit power, and minimizing te power for a given QoS. Our closed-form results sow tat te optimal /14/$31. c 14 IEEE

2 Base station Cellular 1 Receiver g DD Transmitter 1 Fig. 1. Illustration of te system l were 1 communicates wit, eiter via te cellular or by direct transmission DD. decision based on tese two formulations beaves differently. Using a geometrical approac, we study ow te area of optimality for DD transmission is affected by te transmit power, QoS, and te number of antennas at te. II. PROBLEM FORMULATION We consider a cellular network were te single-antenna 1 would like to communicate wit te single-antenna located in te same cell. Te of tis cell is equipped wit an array of N antennas and takes care of te radio resource management. In te conventional cellular, 1 first transmit its data to te using uplink resources and ten te forwards te data to using downlink resources. However, wen 1 and are close to one anoter tere is an alternative option: te allows 1 to transmit directly to in a DD. Tis scenario is illustrated in Fig. 1. Te main question tat tis paper tries to answer is: Wen is DD preferable over cellular? To make a fair comparison, te same amount of resources is allocated to eac. We stress tat 1 transmits te wole time wen in DD as compared to alf te time in cellular. Tis important difference is illustrated in Fig.. Te DD only uses uplink resources, wile cellular uses bot uplink and downlink resources. Tis as no importance in time-division duplex TDD systems, because te ratio of uplink to downlink resources is flexible. Our analysis is also applicable in frequency-division duplex FDD systems, except in extreme ig-traffic situations. A. System Model Let 1 C N 1 denote te cannel between 1 and te, wile C N 1 is te cannel between te and.alsoletw 1 C N 1 and w C N 1 denote te unitnorm receiver and transmit beamforming vectors, respectively. Te direct link between te s is g C. See Fig. 1. For fixed cannel realizations, Gaussian codebooks, and perfect cannel knowledge at te and, te acievable spectral efficiencies in bits per cannel use are R cell p,p = 1 min log 1+ p κ I + σ H 1 w 1, log 1+ p κ I dl + H σ w p g R DD p = log 1+ I + σ for cellular and DD, respectively. Te transmit power of 1 is p, wile te transmit power of te is 1 Cellular DD Uplink transmission Downlink transmission Direct device-to-device transmission using uplink resources Fig.. By cutting out te middleman te, DD can effectively use twice te amount of resources for data transmission tan cellular. p. Te parameter κ decides weter te and can double te energy per cannel use in cellular κ =, since tey only transmits alf of te time, or if te energy is fixed κ =1. Te additive circularly-symmetric complex Gaussian noise as variance σi, i {, }. TetermIdl is te estimated interference power at in te downlink. Te terms I i, i {, } are te estimated interference powers at and te in te uplink, wic are created by oter cellular or DD users transmissions wen te allocated resource is sared. Consequently, tere is no interference wen dedicated resources are reserved for DD communications. Assumption 1. Te as muc larger power resources and interference rejection capability tan 1, tus it can make log 1+ pκ H I dl +σ w log 1+ pκ I +σ H 1 w 1 for any 1,. Consequently, we assume tat 1 can be replaced by R cell p = 1 log 1+ p κ I + σ H 1 w 1. 3 In oter words, we assume tat te uplink transmission is te limiting factor in te cellular. Tere are two main approaces to optimize te resource allocation of te transmission. Te first one is to maximize te spectral efficiency, or QoS, under a given transmit power p = p. Tis is stated matematically as maximize R R subject to max R cell p,r DDp P1 R. Alternatively, one can minimize te transmit power required to maintain a given QoS level R. Tis is stated as minimize p subject to p max R cell p,r DD p R. P As sown in [8], te optimization problems P1 and P are tigtly connected [8]: let te optimal solution to P1 wit transmit power p be denoted R, ten te optimal solution to P wit te QoS level R is exactly p. Neverteless, we sow tat tese optimization problems beave differently in terms of wen DD is preferable over cellular, and vice versa. Te analysis is provided in te next two sections. III. MAXIMIZE SPECTRAL EFFICIENCY: DDOPTIMALITY Te optimization problem P1 can be solved directly by computing max R cell p,r DDp and assigning tis value to R. Wat we would like to derive is a condition on wen R DD p R cellp ; tat is, wen DD is preferably from a QoS viewpoint. First, te optimization problem P1 is solved wen a dedicated resource is available for te, ten we extend te results for spectrum saring.

3 A. DD Optimality wit a Dedicated Resource In te dedicated resource scenario, we assume te use of optimal maximum ratio combining for reception at te in cellular : w1 MRC = 1. Terefore 1 H 1 w 1 = 1. Based on Assumption 1, DD optimality is equivalent to log 1+ p σ g 1 log 1+ p κ σ 1 1 σ σ + p σ κ g σ κ g 4. 4 Since κ {1, }, te condition 4 is trivially satisfied wenever te direct cannel is stronger tan te cannel to te i.e., wen g 1. However, te second term in 4 implies tat DD can be optimal also wen te direct cannel is weaker tan tan te cannel to te, given tat p is large enoug. To understand wen tis occurs, we solve 4 as a quadratic equation in g, wic gives g 1 σ κ σ σ + p p σ p. 5 Te inequalities 4 and 5 provide two equivalent closedform necessary and sufficient conditions for optimality of DD in P1. Te following teorem provides a sufficient condition tat is more amenable to explicit analysis. Teorem 1. Te solution to P1 is acieved by DD if g 1 σ κ σ. 6 p Proof: Te rigt-and side of 5 satisfies 1 σ κ σ + σ p p σ 1 p σ κ σ, 7 p tus te condition 6 always implies tat 5 is satisfied. Several important conclusions are drawn from Teorem 1. Firstly, increasing te power p makes DD attractive also for weaker direct cannels. Tis is explained by te fact tat we ten operate in te concave regime of te log 1 + SNR-formula were it is costly to compensate for te 1 prelog-factor of cellular by increasing te power. Secondly, te cannel gain 1 sould be proportional to te squared cannel gain g to coose cellular. Remark 1 Implementation Guidelines. Te condition in Teorem 1 provides a simple mean to implement networkassisted DD communication. Wenever a observes tat 1 and are in te same cell, 1 is informed about it. 1 will now listen to te uplink pilot signals sent by and tereby obtain g. Te cannel gain 1 is obtained in te conventional way used for cellular. Tus, 1 can evaluate eiter 4, 5, or 6 and decide wic is preferable for te moment. Te fact tat 6 only provides a sufficient condition can actually be a feature, because it removes special cases wen DD is only sligtly better tan cellular but not enoug to motivate te extra overead signaling. B. DD Optimality wit a Sared Resource So far, we ave considered a scenario in wic a dedicated cannel is allocated to te. However, if te user sares te spectrum wit oter s wic are spatially separated, tere are manifold gains in cell spectral efficiency. To address spectrum saring, it is assumed tat eac receiver can measure te interference power and treat te interference as noise. Let I ul = I +σ and I DD = I +σ. In order to solve te optimization problem P1, we follow te same approac as in Section III-A. Te equivalent of DD condition 4 becomes I ul H 1 w 1 g + p κ I DD κ IDD g 4. 8 Besides te conclusions in Section III-A, 8 sows tat DD is optimal wen te interference received at is muc smaller tan te one received at te base station, i.e., I DD I ul. By solving 8 as a quadratic equation, we ave g H 1 w 1 IDD κ IDD p I + ul p I DD p. 9 Similar to Teorem 1, a simple sufficient condition for DD optimality is g H 1 w 1 IDD κ p I. 1 ul An important conclusion from 1 is tat is more sensitive to interference wen operating in te DD. Terefore, te allocation of dedicated resources for DD is of interest in rescue operations or local entertainment services. Suc services migt operate wit multi-casting. It is straigtforward to extend our optimality conditions to te multi-cast scenario by replacing g by min k K g k,were K is te set of users tat sould receive te signal. However, we do not discuss tis case furter due to space limitations. IV. MINIMIZE TRANSMIT POWER: DDOPTIMALITY In te following, we derive DD optimality conditions for te optimization problem P. We observe tat te spectral efficiencies R cell p and R DD p increase monotonically wit p, tus P is solved wen te QoS constraint olds wit equality. Te smallest transmit power tat acieves R can be computed explicitly for eac. A. DD Optimality wit a Dedicated Resource Based on Assumption 1, we ave in cellular tat 1 log 1+ p κ σ 1 =R σ p = R 1 1 κ. 11 Te corresponding expression for DD is log 1+ p σ g = R p = R 1 σ g. 1 Te solution to P is obtained by taking te smallest value of 11 and 1. In oter words, DD is optimal wenever I ul

4 te required power for DD in 1 is smaller tan te power of cellular in 11. Tis is equivalent to σ R 1 σ g 1 R 1 13 κ and gives te following te conditions for DD optimality. Teorem. For a given R >, te solution to P is acieved by DD if and only if g 1 σ R +1σ 1 κ. 14 Hence, DD is optimal for te QoS level R if and only if σ R log 1 κ σ g Proof: Te condition in 14 is acieved directly from 13 by noting tat R 1 R 1 = R 1 R +1 = R +1.Te R 1 QoS condition in 15 is acieved by solving 14 for R. Tis teorem proves tat DD is optimal wenever te rate is above te tresold in 15. Somewat surprisingly, tis means tat DD is always optimal if we let R, irrespective of ow weak te direct cannel is but possibly at te expense of spending a lot of power. Te tresold is negative for g >κ 1 tus DD is always optimal wen te direct cannel is stronger tan te cannel to te tis is consistent wit our observations in Section III-A. B. DD Optimality wit a Sared Resource In te case of spectrum saring, te solution to P for a given R is acieved by DD if and only if g 1 I DD H R 1 w 1 κ I ul Equivalently, DD is optimal for te QoS levels R log IDD I ul H 1 w 1 κ g V. GEOMETRICAL INSIGHTS To gain some geometrical insigts on te optimality of DD, we now consider a simple pat-loss l g = c g d bg g 18 1 = Nc d b 19 were d g,d are te distances between 1 and and between 1 and te, respectively. Furtermore, c g,c,b g,b > are some arbitrary pat-loss parameters. A. Maximize Spectral Efficiency Plugging tis pat-loss l into te optimality condition for DD 6 for P1 wit dedicated resources yields d bg g N σ κc d b σ p c g were it is clear tat increasing p will make DD more probable. Tis effect is counteracted by increasing te number of antennas N, wic is explained by te array gain tat is acieved by coerent beamforming at te. For a fixed distance d between 1 and te, we can compute te circular area A around 1 were or all receivers in multi-casting sould be to enable DD. From, we ave te optimality condition b A = πd bg g πd p N σ c g σ κc 1 bg. 1 Tis area increases wit te distance from te e.g., linearly for b = b g, tus DD is more probable in large macro cells and/or wen 1 is located at te cell edge. Moreover, te area grows wit te transmit power as p 1/bg and decreases as 1/N 1/bg wit te number of antennas. In te sared spectrum case, we assume zero-forcing ZF beamforming at te to cancel te interference: I =. Tis comes at te expense of te average SNR loss H 1 w 1 = N M N 1 =N Mc d b,werem M <Niste number of interferers. Te interference experienced by and its distance from 1 depend on its coordinates x r,y r. Ten, from 1 we ave te DD optimality condition p I DD x r,y r σ c g d b N Mκc d bg g x r,y r. B. Minimize Transmit Power To gain some geometrical insigt for P, we substitute 18 and 19 into 15. Ten, we ave te optimality condition d bg g d b σ σ c g R Nc κ For a fixed d, Te circular area around 1 were and oter potential multi-cast receivers sould be is b A = πd g πd bg σ σ c g N R +1 bg. 4 κc Te area of DD depends on tree factors: d b /b g, R +1 /bg,andn /bg. Te area increases by te first two factors but is inversely proportional to te last factor. In te sared spectrum case wit ZF reception at te, te DD is optimal if te interference in te is bounded as +1σ I DD x r,y r R c g d b N Mκc d bg g x r,y r. 5 VI. NUMERICAL STUDY In tis section, we evaluate te optimal selection for different system parameters by using Monte-Carlo simulations. A single circular cell wit radius R is considered were te is located in te middle. Te distance of te DD transmitter 1 from te is fixed to R/. Different locations for te DD receiver are considered wit a minimum distance d min from 1 and from te. Te simulation parameters are given in Table I. Te cannel l accounts for te effects of pat-loss and multi-pat fading. Te pat-loss parameters

5 TABLE I SIMULATION PARAMETERS. Description Parameter Value transmit power p 15 dbm QoS R {, 4, 6, 8} bpcu Nr. of antennas at N {, 8, 1} Nr. of interferers M 7 Cell radius R 5 m Noise power N 17 dbm Noise figure at s F 5 db Carrier frequency f c GHz System bandwidt B 5 MHz Min. DD receiver distance d min 1 m Pat-loss exp. b g 4 Pat-loss exp. b 3.67 Pat-loss coeff. c g 8.3 db Pat-loss coeff. c 3.55 db Monte-Carlo realizations MC 1 are based on te non-line-of-sigt NLoS scenario in [1]. We assume Rayleig block-fading cannels were te cannels are constant during one time slot, but vary between different time slots. Eac receiver knows its cannel. Te average power is te same in bot s i.e., κ = in our simulations. A. Dedicated Resource Scenario Te scenario wen dedicated resources are allocated to 1 is considered in Fig. 3. Te top plot sows results for P1 and te bottom plot considers P. Te dased circles in Fig. 3 depict te DD optimality areas derived in 1 and 4, respectively. Wile tese expressions only consider pat-losses i.e., te average cannel gains, te corresponding probabilistic areas obtained under Rayleig fading are also illustrated in Fig. 3. We observe tat te optimal area for DD is muc larger wen te objective is maximizing te QoS as in P1, as compared to minimizing te transmit power as in P. Tis is explained by te fact tat te solution to P1 operates at full power and tus DD transmission as te uge benefit of using all its resources for transmission, instead of alf of tem as in cellular. To dig deeper into te results, Fig. 4 sows te radius of te DD optimality area for P1 versus te number of antennas and different transmit powers. As proved in te analytical part, te area of optimality increases wit te power. However, te area is reduced as te number of antennas is increased. In Fig. 5, for P, te DD optimality region also becomes small if te QoS constraint is small and wen te number of antennas is large. Tis confirms our analytic results as well. B. Spectrum Saring Scenario In te spectrum saring scenario, in addition to 1,tere exist M interfering s equally distanced from te on a circle of radius R/. For te DD receiver, we considered a grid of possible positions separated by 5m in te cell area. Fig. 6 and Fig. 7 sow te optimal of eac receiver position based on te bounds derived in and 5 using only pat-loss information. In te presence of interference, te DD optimality region in P1 is larger tan te corresponding region in P. In order to combat te interference, te DD transmitter needs to increase te power. Terefore, in P, Fig. 3. Probability of DD optimality for P1 top and P bottom wit N =8, p =15dBm, R =4,andd = 5 m. Te color sows te probability for DD optimality wen te receiving is at different locations. Te black circle is te cell boundary and te dased blue one is te boundary of DD optimality area based on only pat-loss information. it may be better to communicate troug te rater tan direct transmission. Note tat te interference at te and DD receiver ave te same importance in P. Figs. 8 9 consider fading cannels. Te probability of DD optimality is iger wen te receivers are farter away from te sources of interference and closer to teir transmitter as it is sown in Fig. 9. Te areas wit distance less tan d min to te DD transmitter and te are excluded. VII. CONCLUSIONS We investigated te problem of selection for networkassisted DD communications in single-cell scenarios wit multiple antennas at te. We formulated te problem wit two objectives: P1 maximize QoS or P minimize power. We derived closed-form conditions for te optimality of DD in bot cases. Te analytic results are evaluated and illustrated by means of Monte-Carlo simulations. Our results sow tat te two problems ave distinct differences in te resulting area of optimality for te DD. Increasing te transmit power in P1 or te QoS in P increases te area of DD optimality, because te DD ten benefits greatly from its better pre-log factor. However, increasing te number of antennas as te opposite effect. Te results are easily extended to multi-casting scenarios.

6 Radius of DD optimality region [m] p = 1 dbm p = 18 dbm p = 15 dbm p = 1 dbm Number of antennas N Fig. 4. Radius of te circular DD optimality region vs. number of antennas for P1 wit dedicated resources. Radius of DD optimality region [m] 3 5 R * = bpcu R * = 4 bpcu R * = 6 bpcu R * = 8 bpcu Number of antennas N Fig. 5. Radius of te circular DD optimality region vs. number of antennas for P wit dedicated resources DD 15 optimality region 1 1 Fig. 6. DD optimality area in te sared spectrum case wit only pat-loss information for P1 wit N =8 and M =7. 1 DD 15 optimality region 1 1 Fig. 7. DD optimality area in te sared spectrum case wit only pat-loss information for P wit N =8 and M = Fig. 8. Probability of DD optimality in te sared spectrum case wit fading for P1 wit N =8 and M =7. REFERENCES [1] R. Baldemair, E. Dalman, G. Fodor, G. Mild, S. Parkvall, Y. Selen, H. Tullberg, and K. Balacandran, Evolving wireless communications: Addressing te callenges and expectations of te future, IEEE Ve. Tecnol. Mag., vol. 8, no. 1, pp. 4 3, Mar. 13. [] K. Doppler, M. Rinne, C. Wijting, C. Ribeiro, and K. Hugl, Deviceto-device communication as an underlay to LTE-advanced networks, IEEE Commun. Mag., vol. 47, no. 1, pp. 4 49, Dec. 9. [3] G. Fodor, E. Dalman, G. Mild, S. Parkvall, N. Reider, G. Miklós, and Z. Turányi, Design aspects of network assisted device-to-device communications, IEEE Commun. Mag., vol. 5, no. 3, pp , Mar. 1. [4] G. Fodor and N. Reider, A distributed power control sceme for cellular network assisted dd communications, in Proc. IEEE Global Telecommun. Conf. GLOBECOM, Houston, TX, Dec. 11. [5] C. Yu, K. Doppler, C. Ribeiro, and O. Tirkkonen, Resource saring optimization for device-to-device communication underlaying cellular networks, IEEE Trans. Wireless Commun., vol. 1, no. 8, pp , Aug Fig. 9. Probability of DD optimality in te sared spectrum case wit fading for P wit N =8 and M =7. [6] K. Doppler, C. Yu, C. Ribeiro, and P. Jänis, Mode selection for deviceto-device communication underlaying an LTE-advanced network, in Proc. IEEE Wireless Commun. Network. Conf. WCNC, Sydney, Australia, Apr. 1. [7] Z. Liu, T. Peng, S. Xiang, and W. Wang, Mode selection for device-todevice DD communication under LTE-advanced networks, in Proc. IEEE Int. Conf. on Commun. ICC, Ottawa, Canada, Jun. 1, pp [8] E. Björnson and E. Jorswieck, Optimal resource allocation in coordinated multi-cell systems, Foundations and Trends in Communications and Information Teory, vol. 9, no. -3, pp , 13. [9] D. Gesbert, M. Kountouris, R. Heat, C. Cae, and T. Salzer, Sifting te MIMO paradigm, IEEE Signal Process. Mag., vol. 4, no. 5, pp , Sep. 7. [1] H. Xing and S. Hakola, Te investigation of power control scemes for a device-to-device communication integrated into OFDMA cellular system, in Proc. IEEE Int. Symp. on Personal, Indoor, Mobile Radio Commun. PIMRC, Istanbul, Turkey, Sep. 1, pp