Resource management for network-assisted D2D communication DEMIA DELLA PENDA

Transcription

1 Resource management for network-assisted D2D communication DEMIA DELLA PENDA Licentiate Thesis Stockhom, Sweden 2016

2 TRITA-EE 2016:035 ISSN ISBN KTH Roya Institute of Technoogy Schoo of Eectrica Engineering Department of Automatic Contro SE Stockhom SWEDEN Akademisk avhanding som med tistånd av Kungiga Tekniska högskoan framägges ti offentig granskning för aväggande av teknoogie icentiatexamen i regerteknik den 30 Mars 2016 kockan i sa E3 Kungiga Tekniska högskoan, Osquars backe 14, Stockhom. Demia Dea Penda, March A rights reserved. Tryck: Universitetsservice US AB

3 Abstract During the ast decade, the widespread use of smart devices and mobie appications has ead to a massive growth of the mobie traffic demand. Efficiency and scaabiity are therefore key criteria for the deveopment of future ceuar systems, in which device-to-device (D2D) communication is recognized as one of the promising technoogies. D2D communication aows mobie users in physica proximity to communicate directy, bypassing the base station as in conventiona ceuar networks. In this thesis, we investigate some of the possibe benefits and chaenges brought by the introduction of D2D communication in ceuar systems. In particuar, we focus on resource management techniques for network-assisted D2D communication using ceuar spectrum. Our main contributions ie in the context of mode seection, power contro and (frequency/time) resource aocation mechanisms, recognized as key techniques to reaize the promises of this technoogy. First, we investigate how the integration of D2D communication in ceuar systems operating under dynamic Time Division Dupex (TDD) can enhance their energy efficiency. We perform joint optimization of mode seection, upink/downink transmission period, and power aocation to minimize the transmission energy consumption. The resource management probems for different scenarios are formuated as mixed-integer noninear programming probems. In severa cases, we expoit the probems structure to design efficient agorithms that achieve optima soutions in poynomia time. In the remaining cases, we propose a heuristic agorithm that computes near-optima soutions whie respecting practica constraints in terms of execution times and signaing overhead. Our simuations demonstrate that D2D communications in dynamic TDD systems can yied significant energy savings and improved spectra efficiency compared to traditiona ceuar communication. Second, we study the performance of various power contro strategies appicabe to D2D communications in 3GPP LTE networks. We compare them with an utiity maximization approach that trades off spectrum efficiency and tota transmit power consumption. Our numerica resuts suggest that the LTE power contro scheme is we prepared for networkassisted D2D communications, especiay from the ceuar user perspective. However, for D2D users, the utiity based scheme can provide gains in terms of SINR and power consumption. Finay, we investigate the subcarrier aocation probem for upink transmissions in a D2D-enabed network. We focus on maximizing the aggregate transmission rate of the system. In addition to the traditiona inter-ce interference, we aso account for the intra-ce interference caused by D2D pairs reusing ceuar resources. This probem is computationay hard due to its nonconvex and combinatoria nature. However, we show that it can be described as a potentia game; hence, we can find a Nash equiibrium using iterative agorithms based on best/better response dynamics.

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5 Acknowedgements I woud ike to express my sincere gratitude to my advisor, Prof. Mikae Johansson, for his guidance, motivation and endess patience. Without his support, I woud have never written this page. Moreover, I woud ike to thank him for aways making our research group such a famiiar environment, it is a peasure to be part of it! I am aso thankfu to my co-advisor, Prof. Aexandre Proutiere, for his contributions at the beginning of this experience, and for his care during (probaby) the hardest time. I am indebted to those peope I coaborated with. In particuar, to Prof. Andrea Abrardo, Dr. Gábor Fodor, and Prof. Liqun Fu, for a the fruitfu discussions, invauabe advice and encouragement. I want to thank my ακαδημαϊκό πατέρα Dr. Themistokis Charaambous, for teaching me so many things (impossibe to ist them!), and for being aways a wise guide and a very good friend. Thank you Burak, Euhanna and Farhad for your friendship, support and memorabe funny moments we have shared. Thank you saint Arda, for your care and your magic hep in programming; Hamid, for your constant positive attitude (aso during the adventurous socia events!); Bart, for your kindness and patience in earning Itaian; Sadegh, for the countess advice and usefu discussions on technica probems; Stefan, for not making me worried"; Antonio G., for aways checking my smie! My gratitude goes to my office mates and to a the current and former coeagues. Thank you for making our department such a nice pace to work at. I want to acknowedge Chrys, Euhanna, Giuio, Hamid, Marco, Patricio, Sadegh, and Themis for proofreading parts of this thesis. I reay appreciated your hep! I own specia thanks to the Itaian famiy: Aessandra, Antonio A., Damiano, Davide, Giuio, Marco, Pier Giuseppe, Riccardo and Vaerio. A unique mixture of different Itaian favors! I wi aways keep nice memories of the time we have spent (and we wi surey spend) together. I am aso gratefu to Annei, Gerd, Hanna, Karin and Sivia for their hep with a the administrative issues. Many thanks go to my cousin Monia, for her sweet care and artistic touch", and to a my friends in Itay, in Sweden, and around the word: you are aways my source of strength and happiness! Last but not east, I want to express a my gratitude to my parents and brothers, for their constant ove and support through a my choices. Thank you for aways beieving in me more than I do, and for never making me fee too far from Home. Demia Stockhom, March v

6 Contents Acknowedgements Contents v vi Abbreviations 1 1 Introduction Opportunities for device-to-device communication D2D technoogy Chaenges of D2D-enabed networks Outine and contributions Reated work on RRM techniques for D2D-enabed networks Mode seection Power contro Time/frequency resource aocation Joint RRM Summary System mode, probem formuation, and assumptions System mode Probem formuation and performance metrics Assumptions Mode seection and resource aocation in dynamic TDD system System mode and assumptions Probem statement Minimizing the energy consumption with Fu Orthogonaity Minimizing the energy consumption with D2D Resource Sharing Numerica resuts Summary Power contro schemes for D2D communication 53 vi

7 Contents vii 5.1 LTE upink power contro Power contro based on utiity maximization Mode seection and RB aocation: the MinInterf agorithm Numerica resuts Summary Subcarrier aocation in muti-ce D2D network System mode and assumptions Probem statement Preiminaries on potentia games Game formuation for the muti-ce D2D RA Impementation guideines Numerica resuts Summary Concusion and future works Concusions Future works A The customized design in the B&B method 85 Bibiography 87

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9 Abbreviations BS BW CL CSI D2D DL FDD FO ITU LTE MCS NE OFDMA OFPC OL PC QoS RB RRM RS Rx SINR SRS TDD Tx UE UL Base Station Bandwidth Cosed Loop Channe State Information Device-to-Device Downink Frequency-Division Dupex Fu Orthogonaity Internationa Teecommunications Union Long Term Evoution Moduation and Coding Scheme Nash Equiibrium Orthogona Frequency Division Mutipexing Open Loop with Fractiona Path Loss Compensation Open Loop Power Contro Quaity of Service Resource Bock Radio Resource Management Resource Sharing Receiver Signa-to-Interference-Pus-Noise Ratio Sounding Reference Signa Time-Division Dupex Transmitter User Equipment Upink 1

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11 Chapter 1 Introduction The mobie communications sector has experienced an exposive growth during the ast decade, both in the number of mobie subscribers and in the data traffic demands. Voice traffic dominated the mobie networks for many years. However, the spread of smart devices and the massive usage of mobie appications made the data traffic increase dramaticay. Today, the goba monthy data traffic is more than seventeen times the voice traffic, as reported in [1]. Richer web contents, mutimedia fie sharing, audio and, above a, high-definition video streaming, are factors that wi continue raising the amount of traffic in future wireess networks. According to Cisco s atest Visua Networking Index report, the goba mobie data traffic wi increase neary tenfod from 2014 to 2019 (see Figure 1.1), with an average traffic generated by a singe smartphone cose to 4.0 GB per month, a fivefod increase compared to the 2014 monthy average of 819 MB [2]. Another contribution to the goba mobie traffic growth wi be aso given by the spread of wireess devices accessing mobie networks for new appications beyond persona communications (e.g., machine-type-communication) [3]. The need to support this traffic exposion is certainy the main chaenge of next generation ceuar system, referred to as the fifth generation (5G). 5G networks are meant to provide, among other targets, 1000 times arger mobie data voume per area, 10 to 100 times higher user data rate, and to serve 10 to 100 times more connected devices than current ceuar systems [4 6]. Designing wireess networks abe to fufi these ambitious specifications, whie taking into account constraints in terms of cost, energy, and radio spectrum, is a chaenging goa for both industry and academia. According to the EU fagship 5G project METIS 1, future systems shoud meet the new communication requirements by means of the evoution of existing technoogies, compemented by new radio concepts [5]. Existing approaches that operators can everage today in order to further increase the system capacity can be grouped into three main categories: i) increased radio spectrum (e.g., by moving to higher frequencies), ii) improvement in ink efficiency by means of advanced communication 1 Mobie and Wireess Communications Enabers for the Twenty-Twenty Information Society [7] 3

12 4 Introduction ,3 Exabytes per month Figure 1.1: Overa mobie data traffic is expected to grow to 24.3 exabytes (10 18 bytes) per month by 2019, neary a tenfod increase over This figure is a modification of Fig.1 in [2]. technoogies such as muti-antenna transmissions (MIMO), and iii) densification of the network by increasing the density of base stations (BSs) and reducing the ce size [4, 8, 9]. In particuar, the depoyment of smaer ces as part of heterogeneous networks is a common soution to enhance capacity in highy popuated areas (i.e., business districts, universities, mas, etc.). This because smaer ces manage higher-quaity inks and aow for increased spatia reuse [10, 11]. However, extreme densification needs appropriate interference management and can ead to arge infrastructure costs and operating expenses. Besides ce shrinking, another approach to the network densification for future 5G systems is represented by device-to-device (D2D) communication: a radio technoogy which aows users in cose proximity to estabish a direct oca ink, bypassing the base station. D2D communication in a ceuar networks brings severa benefits to both the mobie users and the network operators. For this reason, it is drawing a growing attention by 3GPP LTE 2 standard. First, mobie users can experience high data rates and ow atency, saving power and energy because of the direct short-range communication and its potentiay favourabe propagation condition. Second, the ce coverage can be extended and the capacity per area improved without increasing the infrastructure cost. In fact, ce-edge users, usuay experiencing poor performance, can communicate directy or by means of a reay. In the atter case, both a D2D communication and a connection to the ceuar infrastructure is estabished. Third, by aowing spectrum reuse between traditiona ceuar communications and direct D2D communications, spectrum efficiency can be enhanced, accommodating a arger number of concurrent transmissions [13 15]. Finay, since D2D communication offers 2 3rd Generation Partnership Project Long Term Evoution [12].

13 1.1. Opportunities for device-to-device communication 5 the opportunity for oca management of short-distance transmissions, it aows for data offoading from the base station, which aeviates network congestion and traffic management effort at the centra network nodes [16, 17] Apart from a these promising advantages, the integration of D2D communication in future wireess networks opens up aso new chaenges, as it wi be described ater in this chapter. The objective of this thesis consists in proposing resource management techniques for D2D-enabed networks, aiming at tacking some of the chaenges and at vaidating the potentia of this technoogy. 1.1 Opportunities for device-to-device communication We point out some exampes where D2D communication is foreseen to both improve the performance of existing proximity-based services and to open up new uses. Socia and commercia services. The use of direct communication between nearby devices is promoted by the increasing popuarity of proximity-based services [18], for which conventiona upink/downink transmissions might be inefficient. An exampe is given by oca information sharing in crowded paces (e.g., in a stadium or at a concert), where many users request for the same popuar content; or when groups of peope in the same area (e.g., in a shopping center or in a campus) want to communicate with each other. Another appication is mobie mutipayer gaming, for which high speed, ow-atency and battery ifetime are important constraints. D2D communication is aso foreseen as a potentia new channe for oca promotions or advertisement from stores and restaurants to nearby users, and for oca broadcast of information about pubic transportation services, such as train schedues in a subway station or fight updates in airports [19 21]. Athough a these proximity-services can be impemented on existing technoogies (e.g. Buetooth), they generay cannot provide arge range of operation, high security and quaity of service guarantee, as ceuar networks can. Pubic safety. D2D communication represents an attractive option for pubic safety organisations 3, such as poice, fire and rescue services that are demanded to intervene after a natura disaster (e.g., earthquake or hurricane) or during crowded events (e.g., Oympic Games) [23, 24]. In these situations, the ceuar network might fai because of the damage of the infrastructures or because of the high congestion and overoad due to the intense communication [25]. Thereupon, D2D-enabed devices represent a soution to convey important information over reiabe shortrange communications between first responders, who must aways be connected with each other and with the oca and remote command centers to receive and send timey information. Additionay, D2D communication can be used by peope in 3 The US government has aready expressed its interest to move to LTE for future pubic safety communications, and 3GPP LTE standards aim at meeting the pubic safety appication requirements aso by means of D2D communication [22].

14 6 Introduction an emergency status to notify nearby responders and/or next of kin about their whereabouts and condition. Traffic safety and D2D reay. Vehice-to-vehice (V2V) communication is a technoogy supporting cooperation between vehices in cose proximity, in order to avoid accidents and to improve the traffic management. Due to its strict requirements in terms of reiabiity and atency of the communication, it turns out that D2D communication naturay fits the purpose [26]. Another emerging technoogy for wireess ceuar networks is the so-caed Machine-to-Machine (M2M) communication, which aows a arge number of devices to attach to the ceuar network for appications ike arge scae environment sensing, heath monitoring, etc. [27]. Such devices are usuay ow-powered; therefore, a reiabe D2D ink between them and a smart device can be used as a reay to the ceuar infrastructure. This exampe shows the possibiity to extend the D2D concept to mobie reaying, which may be empoyed for supporting the communication of devices ocated in areas with poor ceuar coverage [28]. Figure 1.2 iustrates the main conceptua use-cases foreseen for D2D communications. More use-cases descriptions can be found in [29]. SHARE SHARE Traffic safety SHARE Reaying Specia offer Content sharing Socia and commercia services Gaming Pubic safety Figure 1.2: Representative use-cases of D2D communication in ceuar networks. 1.2 D2D technoogy D2D communication can be impemented as either sef-organized D2D communication or network-assisted D2D communication, depending on the invovement of the ceuar infrastructure in the direct communication set-up. Sef-organized D2D communication is simiar to the traditiona ad-hoc networks and expoits the unicensed spectrum. This approach is usuay motivated by its

15 1.2. D2D technoogy 7 imited overhead and easy depoyment. Therefore, it finds appication when the ceuar infrastructure is not operative, such as in case of natura disaster. Network-assisted D2D communication, on the other hand, represents the case when the BS assists the D2D communication by means of contro signaing and resource management. As a consequence, the network can coordinate D2D and ceuar communications and mitigate the mutua interference. However, the coordination might require high signaing overhead and compex centraized resource management. For this reason, different eves of network support can be assumed, with the goa of achieving a good trade-off between compexity/signaing overhead and guaranteed performance. For exampe, D2D users can be supported by the network during the discovery phase, and then they manage the radio resources and schedue their transmission autonomousy [30]. Based on how users access the spectrum, D2D communications can be further divided in the foowing categories (see Figure 1.3 for iustration): In-band D2D: D2D users expoit the icensed spectrum aocated to the ceuar operator, experiencing a high contro from the BS, and hence with more guarantees on the communication performance. In-band D2D communication branches out into two subcategories: - Underay in-band D2D (shared mode): Most of the works in iterature suggest to use the same ceuar spectrum for both D2D and ceuar users in order to increase the spectrum efficiency. In this case, the interference among concurrent transmissions must be carefuy managed. - Overay in-band D2D (dedicated mode): To eiminate intra-ce interference between ceuar and D2D communications, the icensed spectrum can be divided into two non-overapping parts; one part is used for ceuar communications, whie the other is assigned to the D2D users. Out-band D2D: In this case direct communications use unicensed spectrum, avoiding interference with ceuar inks. In this thesis we focus on in-band network-assisted D2D communication, which we beieve being the most innovative concept in the context of short distance wireess communications. Out-band and sef-organized D2D communication, in fact, has aready been expoited by technoogies such as, for exampe, Buetooth and Wi-Fi Direct. Both these technoogies work in the unicensed Industria, Scientific and Medica (ISM) bands, which can be subject to unexpected interference and, therefore, to poor communication performance, especiay when the usage density is high. Differing from these conventiona approaches, network-assisted D2D in-band communication utiizes icensed spectrum with quaity of service guarantees, thanks to the interference management of the ceuar spectrum. Moreover, network-assisted D2D devices can take advantage of the synchronization of the network during the discovery process, which means that the devices do not need to constanty

16 8 Introduction D2D communication In-band Out-band Underay Overay Ceuar D2D WiFi-D & BT Freq. Ceuar D2D WiFi-D & BT Freq. Ceuar D2D WiFi-D & BT Freq. Ceuar spectrum ISM spectrum Ceuar spectrum ISM spectrum Ceuar spectrum ISM spectrum Figure 1.3: Cassification of D2D communication based on the spectrum access. scan for avaiabe access points or other Buetooth users nearby. This is especiay advantageous in reducing the power consumption and proonging the battery ifetime of the mobie equipment. D2D communication aso aows for a arger device coverage and discovery area than existing technoogies, due to the possibiity to transmit with higher power (up to 250 mw for D2D communication, compared to around 100 mw for Buetooth communication). Finay, we reca that one of the main benefits of D2D communication in ceuar networks is the offoading of the oca traffic from the BS in crowded areas. In Buetooth and Wi-Fi, this direct pairing is estabished by the end users. In network-assisted D2D communication, instead, this operation may be transparent to the users and activated directy by the network when it is needed (and possibe). A brief comparison of the main features of Buetooth, Wi-Fi Direct and in-band D2D is isted in Tabe 1.1. Tabe 1.1: Comparison of D2D technoogies Feature In-band D2D Wi-Fi Direct Buetooth Standardization 3GPP LTE IEEE Buetooth SIG a Frequency band Licensed band for LTE-A Unicensed ISM band Unicensed ISM band Interference contro yes no no Max transmission distance 1000 m 200 m m Max data rate 1 Gbps 250 Mbps 24 Mbps a Specia Interest Group.

17 1.3. Chaenges of D2D-enabed networks Chaenges of D2D-enabed networks The integration of D2D capabiities in ceuar networks poses new technica chaenges and design probems. In the foowing we give a brief overview of the most evident ones. Mode seection. A natura question in the context of D2D communication is under which condition two users shoud communicate through a direct ink rather than via the BS. For in-band D2D it aso invoves the decision on whether D2D users shoud be in shared mode or in dedicated mode. Design issues reated to the mode seection probem incude the decision on: the performance measure that one wishes to optimize; what agorithms shoud be used; what measurements are avaiabe; and the frequency of the measurements and mode seection updates. Furthermore, to reaize the fu potentia of D2D communication, especiay for underay D2D communication where the interference becomes an issue, the mode seection shoud be done jointy with other radio resource management decisions, such as power and subcarrier aocation. However, the joint optimization generay eads to chaenging probem formuations, as it wi be discussed in Chapter 2. Spectrum use and interference management. Since obtaining more icensed bandwidth is a significant and costy chaenge for the operators, an efficient use of the avaiabe spectrum is required, especiay by means of appropriate coordination of the interference. Interference management is a chaenging issue especiay in underay D2D communication. In that case, in fact, there is not ony the inter-ce mutipe-access interference due to frequency reuse between neighbour ces, but aso intra-ce interference due to the presence of D2D connections. Such an effect can become severe due to the random positions of the D2D transmitters and receivers. In cassica ceuar systems, interfering users are ocated at a distance that amounts to at east the ce radius. By introducing D2D inks, interfering transmissions can operate at any distance, potentiay jeopardizing the system performance. Baancing performance, computationa compexity and signaing overhead. Designing optima resource aocation agorithms that operate with both imited computationa compexity and imited signaing overhead is a chaenging target. In many cases, in fact, agorithms for resource aocation poicies require to sove optimization probems that are nonconvex, combinatoria, mixed integer noninear, etc. This can be highy time consuming, not scaabe, and thus not manageabe in rea systems. Additionay, optima soutions often everage on the fu channe status information of a invoved inks and/or on the exchange of information among the nodes. This might be aso impractica due to the corresponding signaing. Therefore, the main chaenge consists in finding a good trade-off between optimaity and

18 10 Introduction appicabiity, choosing among separate versus joint optimization and centraized versus distributed approaches. Peer discovery and synchronization. Peer discovery consists in searching for potentia users nearby to communicate with. For sef-organized D2D communication, the discovery can be done by the existing procedures for ad-hoc networks, e.g., [31]. Users searching for a peer can broadcast their identity periodicay so that other users in proximity can identify their presence and decide to set up a D2D communication. However, due to the ack of synchronization, the receiver shoud aways monitor the channe to not miss the discovery signas from other transmitters. This becomes an important issue in terms of time and energy efficiency, because the istening phase can significanty drain the battery of the mobie devices [19]. For in-band network-assisted D2D communication, instead, the synchronization given by the ceuar infrastructure can hep the discovery phase. However, there is no standardized signaing exchange between the mobie users, which indeed needs to be propery designed. There is an on-going research effort in tacking these and other chaenges in the context of D2D networks. This thesis is part of this effort, focusing on the first three aforementioned aspects. 1.4 Outine and contributions This thesis investigates on how to improve the performance of D2D-enabed systems by means of proper design and coordination of radio resource management techniques. Specificay, we recognize the importance of mode seection, power contro and resource (time/frequency) aocation to reaize the promises of D2D communication. The outine of the thesis, together with the pubications supporting the contributions, is as foows. In Chapter 2 we present an overview on resource management techniques for network-assisted D2D communication, referring to reated works in iterature. Chapter 3 describes the genera network mode and motivates the main design choices used in the thesis. Chapter 4 presents a mode seection and resource (time and power) aocation agorithm for energy efficient D2D networks. It is based on: Demia Dea Penda, Liqun Fu and Mikae Johansson, Mode seection for energy efficient D2D communications in dynamic TDD systems, in IEEE Internationa Conference on Communications (ICC), Demia Dea Penda, Liqun Fu and Mikae Johansson, Energy efficient D2D communications in dynamic TDD systems, submitted to IEEE Transactions on Communications (under review).

19 1.4. Outine and contributions 11 Chapter 5 examines the performance of the egacy LTE power contro too-box and benchmarks it against an utiity optima iterative scheme. This chapter incudes part of the materia in: Gábor Fodor, Demia Dea Penda, Marco Beeschi, Mikae Johansson and Andrea Abrardo, A comparative study of power contro approaches for device-to-device communications, in IEEE Internationa Conference on Communications (ICC), Marco Beeschi, Gábor Fodor, Demia Dea Penda, Aidia Pradini, Mikae Johansson, Andrea Abrardo, Benchmarking Practica RRM Agorithms for D2D Communications in LTE Advanced, in Wireess Persona Communications (Springer), Chapter 6 considers the subcarrier aocation probem for upink transmissions in a a muti-ce network, based on: Demia Dea Penda, Andrea Abrardo, Marco Moretti, and Mikae Johansson, Potentia games for subcarrier aocation in muti-ce networks with D2D communications, in IEEE Internationa Conference on Communications (ICC), Finay, in Chapter 7 we concude the thesis with a summary of the main contributions and a discussion on potentia directions for future work.

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21 Chapter 2 Reated work on RRM techniques for D2D-enabed networks The introduction of D2D communication in egacy ceuar systems creates a need for revisiting the existing radio resource management (RRM) techniques to make the best possibe use of the technoogy. RRM for D2D communication in ceuar networks consists of three key decisions: mode seection, that is, deciding if a user equipment (UE) shoud communicate directy or via the base station (BS); power contro, namey, setting the transmit power; and (time/frequency) resource aocation, i.e., assigning the physica resource bocks (RBs) to the users. These three resource management techniques are not independent. For exampe, if we want to minimize the energy consumption, the optima mode seection is affected by the assigned transmit powers, and by the abiity to aocate physica resources with imited interference. In genera, choosing the communication mode for a user pair invoves the decision on whether the D2D candidate pair shoud share the physica resources with other communications. This decision naturay eads to the foowing questions: i) Which inks shoud share the same resources and thus interfere with each other? ii) Which power eve shoud be assigned to the transmitters in order to imit the mutua interference? Fig. 2.1 iustrates the interpay of the mode seection, power, and resource aocation in a simpe exampe. It is cear from this exampe that the RRM decisions shoud be taken jointy to guarantee an optima performance. However, the joint optimization formuation usuay turns to be computationay difficut, and it might require a system knowedge that is very costy to acquire. Thus, many papers in the iterature consider the three probems separatey or ony partiay jointy; see Fig The aim of this chapter is to describe the mode seection, power contro and resource aocation probems for D2D-enabed ceuar networks, and to give a brief overview on the soution approaches proposed in iterature. 13

22 14 Reated work on RRM techniques for D2D-enabed networks UE 1 RB 1 RB 2 UE 2 RB 2 UE 2 RB 1 UE 1 BS UE 3? UE 3 Ceuar mode? D2D mode with dedicated resource? D2D mode with shared resource? RB 3 RB 3 RB 1 or RB 2? Which power? Figure 2.1: Iustrative exampe of the interpay of mode seection, power contro and time/frequency resource aocation. In the considered exampe, mode seection needs to be performed for the transmitter indicated by UE 3, assuming that ceuar users UE 1 and UE 2 are aready assigned to RB 1 and RB 2, respectivey. The mode seection decision assigns to UE 3 one of the three possibe modes: ceuar mode, D2D mode with dedicated resource or D2D mode with shared resource. In the atter case, proper resource aocation and power contro agorithms are needed to seect the RB and the transmit power that imits the mutua interference between the D2D an ceuar communications on the same RB. Mode Seection [32 37] [44, 45] [46] Power Contro [38 40] [50 54] [47 49] Time/Freq. Resource Aocation [41 43] Figure 2.2: The three main RRM probems for D2D communication in ceuar networks and some of the reated soutions in iterature. 2.1 Mode seection Mode seection is the probem of choosing whether two users shoud communicate through a direct ink, using dedicated or shared resources, rather than via the BS.

23 2.1. Mode seection 15 The optima mode seection depends on the performance measure to optimize (e.g., sum rate, transmit power, energy consumption and system capacity), and on the state information avaiabe when making the decision (e.g., physica distance, channe quaity of the inks, interference eve). The simpest and most intuitive mode seection agorithms base their decision on the path oss, which is directy reated to the physica distance between the nodes. In [40], for exampe, the D2D mode is activated if the path oss of the users forming the D2D pair is smaer than a given threshod. A mode seection approach that accounts for both D2D ink distance (r d ) and ceuar distance (r c ) is proposed in [55]. Here, D2D mode is seected if T d rd α rc α, where α is the path oss exponent and T d is a bias factor to contro the traffic offoading from the ceuar infrastructure to the D2D communication. By seecting arge vaues of T d, in fact, more user pairs are forced to communicate in D2D mode. Another exampe of distance-dependent mode seection can be found in [33], for a sighty different scenario, where severa fixed reay nodes are considered to hep ceuar communication, and the mode seection for the D2D pair is among underay or overay D2D communication. Different spectrum sharing methods for the D2D mode, and different upink servers for the ceuar users (BS or reay nodes) bring various combinations of communication modes. The proposed agorithm picks the mode with the highest sum rate. Mode seection based on channe quaity rather than ony ink distance is proposed in [46]. The agorithm takes into account both the quaity of the invoved inks and the different interference eves occurring when the D2D pair shares the upink or downink resource with a ceuar transmission. The objective of this scheme is to maximize the sum rate whie satisfying SINR constraints on active ceuar inks. The authors aso investigate the extension of their method to the muti-ce scenario, where the interference from other ces might affect the decision. However, the signaing oad of the scheme increases significanty. Severa works on mode seection assume singe antenna system and constraints that give priority to the ceuar users [32, 46]. Differenty, the authors of [36] take into account the effect of mutipe antennas at the BS and give the same priority to a users, regardess of their communication mode. They consider two different approaches to optimize the mode seection: maximizing the rate for a given transmit power and the dua probem of minimizing the power to maintain a given rate. They derive cosed-form soutions and show that even if the two probems are tighty connected, they behave differenty in terms of seected communication mode. Most of the anaysis in the iterature focus on the simpified scenario of an isoated ce [32, 33, 36, 46], assuming that inter-ce interference is mitigated by other interference management mechanism in order to dea with more tractabe probems. In a muti-ce system, in fact, the mode seection probem becomes more compex not ony for the additiona interference, but because it might aso invove the BS-user association. The joint probem of mode seection and BS association has recenty been considered in [37]. In this work, the author aims at maximizing the perceived SINR at the receivers, imiting the max number of users that each BS can support. The integer programming probem is soved to optimaity by means of

24 16 Reated work on RRM techniques for D2D-enabed networks a graph-based approach. It is worth mentioning that around the mode seection probem there are severa design issues to consider: how often the communication mode shoud be updated, what channe state information is needed, and at which frequency this information shoud be reported. The timescae for the mode seection, in fact, cannot be too coarse because the wireess channe might change rapidy, and, on the other hand, the necessary signaing overhead shoud be minima. 2.2 Power contro Power contro is used in ceuar networks to assign transmit powers to the users, such that a desired data rate is supported. In the third generations of mobie teecommunications technoogy (3G), power contro was a critica component, especiay for the upink transmission to hande the near-far probem. This is because concurrent communications to the BS are nonorthogona and high power transmitted by users cose to the BS (typicay at the ce center) can overwhem the weak transmissions from the ce edge. In 4G systems, intra-ce interference is not an issue because upink transmissions use orthogona resources. Therefore, the power contro mechanism mainy compensates for path oss and shadowing on a sow basis. Fast scheduing procedures, on the other hand, are taking over the (primary) roe of the power contro mechanism to increase the user data rate [12, 56]. However, the introduction of D2D communication in future 5G system, reusing ceuar spectrum, might reinstate the importance of the power contro. This is because of its potentia to hande the new intra-ce interference scenarios, and to reduce the power consumption of short-ink communications. In D2D-enabed networks, ceuar users are often considered as those with the highest priority to whom a certain communication quaity must be aways guaranteed. The most intuitive way to reduce the interference from D2D communications to ceuar communications consists in imiting the transmit power of D2D users. The authors of [38] anayze this probem for the singe ce scenario. The idea is to set the power of the transmitting D2D user such that the SINR degradation of the ceuar user from the SNR (i.e., without interference) is imited to 3 db. The authors of [39] aso mitigate the interference from the D2D transmissions on upink ceuar resources reducing the power of the D2D transmitter by means of a back-off parameter. Since a ow D2D transmit power transates into a sma range of the D2D ink, the power of the ceuar users is aso increased by to compensate for the interference and thus imit this drawback. Different LTE power contro schemes for the hybrid ceuar and D2D system are evauated in [40]. The study is mainy based on simuations but shows good insights into the impact of the different approaches. For exampe, the fixed transmit power scheme is very simpe, but it does not work we in the context of D2D communication due to the possibe arge dynamic range of the D2D SINR (i.e., it might provide too good performance for some users, meanwhie too bad performance

25 2.3. Time/frequency resource aocation 17 for some other users). On the other hand, when considering the fixed SNR target scheme, the seection of the SNR target vaue affects both the aocated transmit power and the fina SINR of the interfering transmissions. Agreeing upon the fact that the mode seection criterion is crucia, authors concude that the cosed oop LTE power contro with a dynamic tuning step can be a suitabe for D2D users. Nevertheess, the standaone power contro scheme is not an efficient soution to avoid the strong mutua interference between different types of communication, hence it needs to be compemented by mode seection, resource scheduing and ink adaptation. Joint mode seection and power aocation formuations can be found in [44, 45]. The agorithm proposed in [44] maximizes the power efficiency of the system, which is defined as the ratio between the sum rate and the sum transmit power of a users, for a possibe modes. Then, it seects the mode with the highest vaues. The drawback of this agorithm is that it is based on an exhaustive search over a possibe mode combinations of the users. A joint admission contro, mode seection and power contro is proposed in [45], which attempts to maximize the tota throughput and number of admitted users in the system. The probem is formuated as a mixed integer noninear probem. Due to its combinatoria nature, the soution compexity increases exponentiay with the number of user pairs. However, the authors expoit the probem structure to appy a inearization technique that gives guaranteed ɛ-optima resuts. 2.3 Time/frequency resource aocation Assigning particuar time/frequency resources to the users in the system is important not ony for taking advantage of the possibe frequency diversity among channes, but aso for increasing the spectrum efficiency and the system capacity through inteigent resource reuse. Frequency resource aocation strategies based on distance-constraints between possibe interfering users (ceuar and D2D) are proposed in [41] and [42], where the main idea is to avoid the coexistence on the same resource of ceuar and D2D users when they are too cose to each other. Considering the spectrum reuse probem from an optimization perspective usuay eads to nonconvex and mixed integer formuations, where an optima soution is in genera very hard to achieve, even for sma-sized networks. Optima resuts are obtained in very specia situations, as, for exampe, in [32]. Here, a simpified mode of ony one ceuar user and one D2D pair is considered for the joint power and resource aocation that maximizes the throughput. Other works imit the resource aocation anaysis to a singe ce case, considering different objectives with different system constraints. The sum rate maximization probem is considered in [47] and [43]. The authors of [47] design a resource sharing strategy such that a singe D2D pair can utiize a possibe ceuar resources without jeopardize the ceuar communications. The resource aocation probem

26 18 Reated work on RRM techniques for D2D-enabed networks is formuated as a power contro probem. Even though the probem is originay nonconvex, the authors show that it can be transformed into a convex one, and soved to optimaity. The resource aocation probem in [43], instead, is formuated as a mixed integer noninear programming probem. Since it is hard to sove it within the fast scheduing period required by current systems (such as LTE), the authors aso propose an aternative heuristic agorithm. This agorithm simpy seects the resources to be shared in upink or downink as those with the owest cross gain between the interfering users. Recent works on the joint resource and power aocation probem for energy efficient D2D communication can be found in [48, 49]. Specificay, in [48], the objective is to maximize the minimum weighted energy efficiency of D2D inks, where the weights are empoyed to contro the reative priorities among the D2D inks. Each D2D ink can share resources with mutipe ceuar users. However, each ceuar resource can be reused at most by one D2D ink to imit the interference towards the ceuar communications. The probem is soved by separating the goas: authors first characterize the optima power aocation of the ceuar inks, and then transform the origina resource aocation probem into the joint resource and power aocation probem for D2D inks ony. The resource aocation probem is a mixed integer noniner programming probem, for which brunch-and-bound approach is appied to achieve the optima soution. However, aternative soutions with ower compexity and imited message exchange are aso provided. The energyefficient resource aocation probem formuated in [49] is a nonconvex combinatoria programming probem, with constraints on the resources reuse simiar to those in [48]. However, by expoiting the proprieties of fractiona programming, the authors obtain a tractabe soution with an iterative approach. Moreover, they aso propose a twoayer iterative soution approach, in which the origina joint formuation of power and resource aocation is transformed into two separate optimization probems in each iteration. Finay, the resource aocation probem in muti-ce networks is sedom addressed in iterature. Instead, most works assume that an advanced inter-ce interference mitigation scheme works on top of the per-ce resource aocation agorithms. Some exceptions are [57, 58]. In [57], the authors appy fractiona frequency reuse approach, where ceuar and D2D users use different downink frequency resources depending on their ocations within the ce area. The procedure proposed in [58] is aso based on the position of the users, together with a significant exchange of information between the users and the BSs, and between the BSs. 2.4 Joint RRM As introduced at the beginning of this chapter, and as supported by the above iterature overview, the best system performance is obtained by joint soution to the mode seection, power contro and resource aocation probems. Exampe of such joint formuations are given in [50 54]. These works are mainy deveoping

27 2.5. Summary 19 mixed-integer programming modes. In some cases they are soved off-ine with the purpose of obtaining benchmark resuts and insight into the potentia gains of D2D communication [50]. Aternative proposed soutions are: to decompose the joint probem into separated subprobems [52]; to resort to more practica heuristics [50 53], or to consider game-theoretic approaches [54]. However, numerica simuations in [50, 52] show that the proper design of heuristics can give a performance cose to the optima soutions. 2.5 Summary The use of D2D communication in ceuar networks can be enabed by smart RRM techniques, such as mode seection, power contro, and time/frequency resource aocation. The most intuitive and simpest way to seect the communication mode for a pair, and to mitigate the interference, is to consider the path oss gain (and therefore the physica distance) between the invoved users. This approach is usefu to give a geometric interpretation of the soution. However, distance-based soutions do not account for the effective quaity of the inks, affected, for exampe, by shadowing and interference. Therefore, CSI and perceived SINR are preferred as decision metric in the context of RRM strategies. Soutions based on optimization formuations ead to better system performance. However, they are often ess practica due to their compexity and required signaing overhead. This aspect is even more pronounced for the joint soution of the three RRM probems. For this reason, the existing work focuses mainy on soving the probems individuay, or on proposing practica heuristic aternatives.

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29 Chapter 3 Mode, probem formuation and assumptions In this chapter, we present the genera system mode and motivate the design choices shared by the remaining chapters of the thesis. The system mode and the anaysis approach to the radio resource management probems can be can broady cassified into two groups: instantaneous anaysis and statistica anaysis [55]. The former approach considers objective functions based on instantaneous system information (e.g., channe gains and ink distances), and the mode is used to derive instantaneous optima decisions. In this case, the possibe rapid variation of the system parameters might affect the decisions, which therefore need to be updated accordingy. The statistica approach, on the other hand, is based statistica information about the system (e.g., the distributions of the users ocations and channe gains), which are stabe over a reative onger period of time. Hence, decisions made under this assumption may not be the best soutions in a particuar point of time, but they can be optima over a onger time horizon. This thesis is based on the instantaneous anaysis, with the aim of investigating the potentia imits and gains of the considered scenarios. 3.1 System mode We consider a ceuar network consisting of a set B of base stations (BSs). Each BS is paced in the center of an hexagona ce and serves mobie users randomy paced within its ce area. We assume a set L of L transmitter-receiver pairs, each constituting a ogica ink that we abe with an integer 1, 2,..., L. A ogica ink can be a pair of ceuar users transmitting data through the serving BS, or a D2D pair communicating through a direct ink. We refer to the users in pair- as transmitter- (Tx-) and receiver- (Rx-), respectivey. See Fig. 3.1 for iustration. Taking LTE as a reference system, we assume orthogona frequency division mutipexing (OFDM) [12]. The avaiabe system bandwidth is divided into a number 21

30 22 System mode, probem formuation, and assumptions Tx- BS Rx- D2D BS D2D Tx-m Rx-m BS D2D Figure 3.1: D2D-enabed muti-ce network mode; pair- is communicating in ceuar mode whie pair-m is in D2D mode. of physica Resource Bocks (RBs) of size W Hz, and time duration of T seconds 1. We assume that each BS manages a set F of F time-frequency RBs to be assigned to the ogica inks within its own ce area. We assume that a nodes are equipped with omnidirectiona antennas, and consider a fu-buffer traffic mode where transmitters aways have unimited amount of data to send to their intended receivers. We denote by P f m the transmit power eve used by Tx- towards Rx-m on RB-f. Note that the BS can act both as transmitter and receiver, depending on whether it is invoved in a downink (DL) or upink (UL) transmission, respectivey. We consider per-ink peak-power constraints in the form 0 P f m P max, (3.1) where P max is the maximum aowabe transmit power for Tx-. Communication inks are assumed as Gaussian channes, where each receiver treats muti-user interference, due to the possibe subcarrier reuse, as additive noise. The maximum achievabe rate (ink capacity) of the data transmission from Tx- to Rx-m using RB-f is given by the Shannon capacity formua r f m = W og 1 + P f m Gf m σ 2 + Im f. (3.2) 1 In an LTE system, a RB consists of 12 consecutive subcarriers with a spacing of 15 khz, thus occupying a tota of 180 khz, for a time sot duration of 0.5 ms (norma cycic prefix case) [12].

31 3.2. Probem formuation and performance metrics 23 Here, W is the bandwidth, G f m is the channe gain between Tx- and Rx-m on RB-f, and σ 2 is the therma noise power at the receiver, assumed equa for a RBs. We indicate with γ f m = P f m Gf m σ 2 + I f m the signa-to-interference-pus-noise (SINR) perceived at Rx-m from transmission on RB-f by Tx-, where the term Im f = P f jj Gf jm, j represents the interference due to concurrent transmissions on RB-f. In the definition of the interference I f m we are assuming that the summation runs over a the users in the network, in a ces. 3.2 Probem formuation and performance metrics In this thesis, we pose radio resource management tasks as utiity maximization probems. The decision variabes depend on the specific scenario, and incude the communication mode (ceuar or D2D) assigned to each transmitter-receiver pair, the assignment of RBs to user pairs, the transmission power aocation for each user pair, and the time duration of each communication. To formay describe this generic formuation, we introduce: the mode seection vector m {0, 1} L 1, with m = 0 if pair- is assigned to ceuar mode and m = 1 if in D2D mode; the transmit power matrix P R L 2F, defined as a concatenation of matrices P c R L F and P d R L F, whose eements Pf c and P f d represent, respectivey, the power eve used by transmitter- when in ceuar mode and in D2D mode. When mode seection decision has been made, the matrix P reduces its dimensions to L F. In this case, the eement P f of P represents the power aocated to transmitter- on RB-f; the RB assignment matrix X {0, 1} L F, whose entry x f is assigned to RB-f, 0 otherwise; is 1 if transmitter- and the vector t R L 1, with t being the time duration assigned to the communication of pair-.

32 24 System mode, probem formuation, and assumptions With this notation, the genera probem formuation can be written as the foowing mixed-integer probem: maximize m,p,x,t f(m, P, X, t) subject to h i (P, X, m, t) = 0, i E g j (P, X, m, t) 0, m {0, 1} L 1, t R L 1 P R L F, X {0, 1} L F. j I (3.3) The objective function and constraints vary depending on the scenario that we consider. For exampe, inequaity constraints can represent the power imitation of the devices, the minimum rate or SINR of the transmissions, etc. The equaity constraints might be used, for exampe, as a constraint on the number of RBs assigned to the users. The definition of the objective function f( ) in (3.3) depends on the network performance we wish to optimize. In order to expore and expoit the different advantages derived by introducing D2D communication in ceuar networks, in this thesis we consider different performance metrics. Energy consumption. The growing energy bis of operators, imited battery ifetime of mobie devices and environmenta concerns ed our interest towards the probem addressed in Chapter 4, where we investigate how D2D communication can be integrated in ceuar systems to minimize the transmission energy consumption. We everage on the observation that the energy required for sending a fixed amount of data is a convex and decreasing function of the transmission duration. To guarantee a certain QoS to the communication of pair- on RB-f, we can define a traffic requirement of b nats per time frame. Let t (m ), or for short t, be the transmission time assigned to Tx-, which depends on the communication mode. Then, the minimum transmission energy required can be expressed as a function of the time duration E f (t, m, X) = (exp ( b ) 1) σ2 + I f (X) t. W t As shown in Chapter 4, the energy consumption does not depend ony on the transmission duration and the communication mode, but aso on the RB aocation poicy (which affects the perceived interference). Therefore, the objective function in probem (3.3) becomes G f f(t, m, X) = E f (t, m, X). f F L Aggregate utiity. In Chapter 5, we jointy consider two of the main gains of D2D communication: increased spectrum efficiency and reduced power consumption.

33 3.3. Assumptions 25 In doing so, we consider an aggregate utiity function that takes into account both the satisfaction eve of the users when transmitting at a certain rate, and the tota power consumption [59]. The satisfaction eve of user pair- is represented by the individua utiity u ( ), which is increasing and stricty concave in the transmission rate of pair-, referred to as s f and upperbounded by the ink capacity. We indicate with L f the set of inks sharing RB-f. The objective function is then f(p, s) = U f (P, s), f F where the per-rb utiity function is defined as U f (P, s) = L f u (s f ) ω P f L f, f F, where ω 0 is a parameter that aows to set the desired tradeoff between the two objectives. Sum rate. The optimization probem presented in Chapter 6, aims at maximizing the aggregate transmission rate when D2D reuse the ceuar resources. By assuming that mode seection and power aocation are aready been performed, the objective function becomes f(x) = og(1 + P f Gf xf σ 2 + I f (X)). f F L Fig.3.2 summarized the performance metrics optimized in this thesis. Performance metric f(m, P, X, t) Chapter 4 Energy consumption f(t, m, X) Chapter 5 Aggregate utiity f(p, s) Chapter 6 Sum rate f(x) Figure 3.2: Performance metrics considered in this thesis. 3.3 Assumptions Spectrum access. For communications in ceuar mode, we consider the channe aocation poicy of egacy LTE systems, that is, ceuar communications within the same ce are assigned to orthogona RBs so to not interfere with each other. For D2D communications, on the other hand, we investigate different aocation strategies: in Chapter 4 we consider the case where D2D communication occurs on

34 26 System mode, probem formuation, and assumptions different orthogona frequency channes than those used for ceuar communications (overay in-band D2D communication), whie in Chapters 5 and 6 we consider the case where D2D transmitters are aowed to use the RBs occupied by ceuar users (underay in-band D2D communication); see Tabe 3.2. Dupexing is an integra part of the communication design. LTE system supports both Frequency-Division Dupex (FDD) and Time-Division Dupex (TDD) to separate UL and DL traffic. FDD impies that DL and UL transmission take pace in different, sufficienty separated, frequency bands, whereas TDD impies that DL and UL transmissions take pace in different, non-overapping time sots. Legacy networks empoyed static and symmetric resource utiization, where the UL and DL were often separated in the frequency domain. However, dynamic TDD technoogy is recenty gaining popuarity for 5G networks [60 62], mainy because of its capacity to better accommodate DL/UL traffic asymmetry in dense, heterogeneous networks. Additionay, the TDD scheme aso aows to simpify the access to the channe state information (CSI) by expoiting channe reciprocity and thus reducing the feedback overhead. Other possibe advantages of TDD over FDD can be found in [63]. In Chapter 4, foowing the trend of empoying dynamic TDD for future networks, we investigate the possibe advantages of integrating D2D communication in such systems. Channe mode. The channe gain G f m in Eq.(3.2) captures the phenomenon of signa attenuation over the wireess channe, which is caused by i) the distance between transmitter and receiver (path oss), ii) the presence of arge obstaces between transmitter and receiver (shadowing), and iii) the reception of mutipe copies, attenuated and phase-shifted, of the transmitted signa (muti-path fading) [64]. Another aspect of the propagation mode is frequency-seective fading, which occurs when different frequency components of the signa experience different fading. There is currenty no standardized channe mode for D2D communication. Athough the probem formuations and the resource aocation agorithms presented in this thesis are independent of the channe mode, simuation resuts wi depend on the specific propagation mode used. In this thesis, we have used severa different channe modes, depending on the purpose of our studies. Specificay, in Chapter 4, we are interested, among other things, in obtaining a geometrica interpretation of the optima mode seection poicy. For this reason we assume that the channe gains foow the simpe path-oss mode G f m = G 0Dm α, where D m is the physica distance between Tx- and Rx-m, G 0 is the path gain at a reference distance of 1 m, and α is the path-oss exponent. This choice is aso motivated by the fact that mode seection decision for D2D communication is usuay based on sow scae fading (distance dependent path oss and shadowing) measurements, to reduce the frequency of updates of the CSI. In Chapter 5, for the sake of comparison between different D2D power contro schemes, we use the propagation mode described in [40], which is based on the micro urban channe modes from the Internationa Teecommunication Union (ITU) [65].

35 3.3. Assumptions 27 Finay, in Chapter 6, to expoit the robustness to fading of OFDM systems through adaptive user-to-subcarrier assignment, we consider a frequency seective channe, with og-norma shadowing and fast Rayeigh fading in addition to the path-oss 2. Tabe 3.1 summarizes the different channe modes considered in this thesis. Tabe 3.1: Channe modes considered in this thesis. Chapter Path oss Shadowing Fading Frequency-seective fading Chapter 4 Yes No No No Chapter 5 Yes Yes No No Chapter 6 Yes Yes Yes Yes Interference scenarios When empoying in-band underay D2D communication, intra-ce orthogonaity is ost and the characteristics of the interference in the ceuar network change. D2D inks can access either the UL or DL ceuar resource, or both. When a D2D ink is active on a radio resource used by a ceuar UL transmission, interference is induced from the UL transmitting user to the D2D receiver, and from the D2D transmitter to the BS. Simiary, when the D2D ink utiizes DL resources, interference is induced from the ceuar BS to the D2D receiver, and from the D2D transmitter to the ceuar user. Additionay, interference among mutipe D2D inks sharing the same resource must be aso taken into account, since it can deteriorate the quaity of the direct transmissions. This effect is especiay strong in crowded areas where transmitters and receivers of different D2D inks are cose to each other. With the exception of Chapter 4, this thesis focuses on underay D2D communication in the UL scenarios. This choice is very common in the iterature. Apart from reguatory requirements in some countries, the use of UL resources is motivated by the asymmetric traffic oad in the UL and DL directions and by the fact that the BS has a much better capabiity to hande interference than mobie devices [21, 67 69]. In Chapter 4, we assume dynamic TDD system and we show the advantage of aocating the fu frame duration (i.e., both UL and DL resources) to the D2D ink. A disadvantage of underay D2D communication in such system is that the receiver of the D2D ink wi perceive a rapid change of the interference power when the ceuar communication switches between UL and DL. It is difficut to compensate for this effect without resorting to compex interference management agorithms that require detaied cross-gain knowedge and have high signaing oad; this reason motivated the choice of overay D2D communication. 2 Channe gains are obtained on the basis of the mode used in RUdimentary NEtwork (RUNE) simuator, a MATLAB-based software too for performance anaysis in wireess networks, originay deveoped at Ericsson [66].

36 28 System mode, probem formuation, and assumptions The compexity of the interference management further increases in the muti-ce scenario, where there is not ony the intra-ce interference due to the presence of D2D connections, but aso the inter-ce interference due to frequency reuse between ces. The intra- and inter-ce interference in underay D2D communication using UL resources is iustrated in Fig. 3.3 for a simpe two-ce network. Ce-1 BS Data transmission Inter-ce interference Intra-ce interference Figure 3.3: Exampe of both inter-ce and intra-ce interference in the UL transmissions of ceuar network with D2D communications. For iustration purposes, we show ony the interference caused by transmissions in Ce-1. Tabe 3.2 summarizes the different interference scenarios considered in this thesis. Tabe 3.2: Spectrum access and interference cases considered in this thesis. Chapter UL/DL Resource Underay/Overay D2D Singe-/Muti-ce Chapter 4 UL & DL Overay Singe-ce Chapter 5 UL Underay Muti-ce Chapter 6 UL Underay Muti-ce

37 Chapter 4 Mode seection and resource aocation in dynamic TDD system In this chapter, we investigate how the integration of D2D communication in ceuar systems operating under dynamic TDD can enhance their energy efficiency. Performance improvement that can be obtained by integrating D2D communications in ceuar systems with fexibe TDD have ony recenty gained attention in iterature. Frameworks for D2D enhanced TDD networks are proposed in [70 72]. However, they do not account for the mode seection and focus mainy on the adaptive UL/DL sot aocation to D2D pairs, so as to baance the traffic oad, coordinate the interference, improve coverage probabiity and sum-rate. Recenty, the authors of [73] have extended the resource aocation probem introduced in [70] to incude mode seection. Yet, the mode seection decision is based on the instantaneous SINR, and not in joint consideration with the power and transmission time aocation. In this work, we jointy optimize mode seection, power aocation and UL/DL transmission period, to minimize the transmission energy consumption (from both a system and a device perspective), whie satisfying a certain rate requirement. The RRM probem for the different scenarios of interest, are formuated as MINLP. Athough they are known to be NP-hard in genera, we expoit the probem structure to design efficient agorithms that sove severa probem casses to optimaity in poynomia (and sometimes even inear) time. For the remaining cases, we propose a heuristic agorithm that computes near-optima soutions whie respecting practica constraints in terms of execution times and signaing overhead. 4.1 System mode and assumptions We consider a singe-ce network popuated by L ogica inks, each denoted by an integer 1, 2,... L, whie the BS is indexed as 0. In-ce users can communicate either in ceuar mode or in D2D mode. The mode seection poicy divides the set of a user pairs L into two subsets: D is the set of user pairs that shoud communicate in D2D mode, and C = L D the set of user pairs that shoud communicate in ceuar 29

38 30 Mode seection and resource aocation in dynamic TDD system mode. Communication in ceuar mode. We assume that the system adopts a dynamic TDD mode, where the UL and DL transmissions for a user pair occur on the same frequency channe but aternate in time. The portioning of resources for UL and DL can be reconfigured in each time frame, but it is assumed to be the same for a communications within the same ce. This intra-ce UL/DL synchronization, in fact, is of critica importance to reduce the compexity of the inter-ce interference management in muti-ce networks with dynamic TDD [60, 74, 75]. Furthermore, to prevent intra-ce interference between concurrent transmissions in ceuar mode, the BS foows the channe aocation poicy of egacy LTE systems and assigns a separate channe to each ceuar user pair (see Fig. 4.1). We denote by t u and t d the portion of the time frame aocated to the UL and DL transmissions, respectivey. Communication in D2D mode. In D2D mode, each pair can use the fu frame duration for its singe-hop transmission. A arge body of work considers underay in-band D2D communication, where D2D transmitters opportunisticay access the radio resources occupied by ceuar users. A disadvantage of underay D2D communication in TDD systems is that the receiver of the D2D ink perceives a rapid change of the interference power in one time frame when the ceuar pair switches between UL and DL transmission. It is difficut to compensate for this effect without resorting to compex interference management agorithms that require detaied cross-gain knowedge and have high signaing oad. In this paper, we therefore focus on overay in-band D2D communication, where D2D communications and ceuar communications are aocated different frequency channes so that they do not cause interference to each other (Fig. 4.1). Nevertheess, resource reuse among D2D communications has been investigated in our studies. In particuar, we consider two channe aocation strategies for D2D pairs: Fu Orthogonaity (FO): A D2D communications are assigned orthogona frequency channes. Hence, no receiver is interfered by other transmissions within the ce (Fig. 4.1(a)). D2D Resource Sharing (RS): A D2D communications are assigned to the same frequency channe, hence interfere with each other (Fig. 4.1(b)). We denote with t T the active time of pair- in D2D mode. In this work we do not consider frequency-seective fading. Therefore, for the sake of notation, we disregard the index reated to the RBs (as in Chapter 3) and define the instantaneous rates r 0, r 0 and r achieved in UL, DL and in D2D mode, respectivey, as foows: r 0 = W og (1 + P 0G 0 σ 2 ), r 0 = W og (1 + P 0G 0 σ 2 ), r = W og (1 + P G σ 2 + I ). (4.1)

39 4.1. System mode and assumptions 31 (a) Fu Orthogonaity (b) D2D Resource Sharing Figure 4.1: Frequency-time resources configuration: D2D inks can use the fu frame duration T, either on orthogona subcarriers (FO) (a), or sharing the same subcarrier (RS) (b). UL and DL duration for ceuar communications can be reconfigured at each time frame. Since we are ensuring intra-ce orthogonaity among ceuar communications, the UL and DL transmission rates are not affected by any interference. Hence, their maximum vaues correspond to maximum power transmissions, and are denoted by max max r0 and r0, respectivey. On the other hand, the maximum instantaneous rate of the D2D transmission,denoted by rmax, aso depends on the current interference eve. Rate constraint, power feasibiity and energy cost. To guarantee a certain QoS, each pair- has a traffic requirement of b nats per time frame, irrespective of the communication mode. This QoS requirement can be transated into a session rate requirement of b /T nats per second. Specificay, if pair- is in ceuar mode, the transmission times for UL and DL, aong with the corresponding instantaneous transmission rates, must satisfy r0 tu b and r0 td b. (4.2) Simiary, if pair- is in D2D mode, t and r must satisfy r t b. (4.3) The imitation on the transmission power eves, together with the session rate requirements above, entai the need to verify under which conditions the communication of a pair can be supported by the network. To this end, we introduce the concept of power-feasibiity: Definition (Power feasibiity). We say that the communication of user pair- is power-feasibe

40 32 Mode seection and resource aocation in dynamic TDD system (a) in D2D mode if r max T b ; (b) in ceuar mode if there exists a time aocation (t u, t d ) such that t d b 0 t u b r max r0 max t u + t d T., (4.4) Assumption There exists a time aocation (t u, t d ) which can support the communication of a users in ceuar mode. Remark The power-feasibiity condition (4.4) impies that t u must satisfy b r0 max t u T b r0 max Thus, under Assumption 4.1.1, it must hod that max. (4.5) { b r0 max } min{t b 0 By rewriting the power-rate reations (4.1), we find the transmission energy necessary to satisfy the session rate requirement b of pair-, for a given time aocation (t u, t d ) E 0 (t u ) = P 0 t u = (exp ( ) 1) σ2 t u, W t u G 0 b b UL, ceuar mode; r max E 0 (t d ) = P 0 t d = (exp ( ) 1) σ2 t d, DL, ceuar mode; (4.6) W t d G 0 E D2D (t, I ) = P t = (exp ( b ) 1) σ2 + I t, D2D mode. W t G These functions are convex and monotonicay decreasing in their arguments (see [76] and references therein). This observation eads to the foowing resut: Lemma When minimizing the transmission energy, optima soution must aocate the fu frame duration for communication. For the D2D mode, this impies that min E D2D t,i (t, I ) = min E D2D (T, I ). I For ceuar mode, where the energy consumption is given by the sum E 0 (t u ) + E 0 (t d ), it must hod that t u + t d = T. The transmission energy cost for communicating in ceuar mode incudes both the energy cost of the transmitting mobie device and that of the BS. However, the BS often has access to cheap and abundant energy in comparison with the user equipment, in which case it is reevant to ony focus on the device energy, aiming at proonging its battery ife. To this end, we consider the foowing two definitions of energy consumption for a generic user pair- in ceuar mode: }.

41 4.2. Probem statement 33 The System Energy consumption (SE): is the energy consumed by both Tx- in UL and the BS in DL. By Lemma 4.1.4, the minimum energy cost is obtained by minimizing which is a convex function of t u. E CELL (t u ) = E 0 (t u ) + E 0 (T t u ), (4.7) The User Energy consumption (UE): is the energy consumed by Tx- in UL transmission, disregarding the energy spent by the BS in DL, that is E CELL (t u ) = E 0 (t u ), (4.8) which is a convex and monotonicay decreasing function of t u. 4.2 Probem statement We consider the probem of minimizing the transmission energy consumption of a D2D-enabed ceuar network with dynamic TDD system, by jointy optimizing: i) the communication mode of each user pair, ii) the UL/DL time configuration, and iii) the powers aocated to a transmitters. Since we are interested in two possibe energy cost functions (SE and UE) and two channe aocation strategies for D2D communications (FO and RS), we obtain four variations of the energy minimization probem, which a can be formuated as MINLPs. Tabe 4.1 summarizes the main resuts for these four cases, with the section number for easy reference. Tabe 4.1: Four variations of the energy minimization probem and the main resuts UE FO Optima soution in inear time ( 4.3) Optima soution in poynomia time ( 4.3) RS Optima soution with B&B ( 4.4.1), Suboptima soution with heuristic ( 4.4.1) SE Optima soution with B&B ( 4.4.1) 4.3 Minimizing the energy consumption with Fu Orthogonaity In this section, we show how the jointy optima mode seection and resource (time and power) aocation with FO can be found in poynomia time, even though the overa probem is not convex. For ease of exposition, we first derive the optima soution for a singe user pair, and then extend the resuts to mutipe user pairs Singe user pair We first characterize the minimum energy cost for a pair to fufi the rate requirement when in ceuar and when in D2D mode. We show that the minima SE cost can be

42 34 Mode seection and resource aocation in dynamic TDD system found by soving a simpe convex optimization probem, whie the minima UE cost admits an expicit expression. Minimum energy cost for communication in ceuar mode. In ceuar mode, the UL/DL time aocation is chosen to minimize one of the foowing two objectives: Minimizing SE: The minimum amount of energy of pair- in ceuar mode can be determined by soving the foowing singe-variabe convex optimization probem: minimize t u E 0 (t u ) + E 0 (T t u ) (4.9a) subject to b r0 max t u T b r0 max, (4.9b) where constraint (4.9b) ensures power feasibiity in the sense of Definition Probem (4.9) can be soved efficienty using a wide variety of methods, e.g., bisection search [77]. Let t u denote the optima soution to (4.9). The energy cost of pair- in ceuar mode is then E CELL (t u) = E 0 (t u) + E 0 (T t u). (4.10) Minimizing UE: Here, the ony difference from the probem formuation in (4.9) is that the objective function reduces to E 0 (t u ). By monotonicity of the objective function, the optima soution is attained by t u = T b, with the r0 max corresponding optima energy cost E CELL (t u) = E 0 (T b r0 max ). (4.11) Minimum energy cost for communication in D2D mode. In the D2D mode, no traffic is forwarded through the BS and ony the user equipment consumes energy for the connection. The minimum energy cost foows from Lemma 4.1.4, with I = 0: E D2D = (exp ( b σ2 ) 1) T. (4.12) W T G Equation (4.12) is ony vaid when the D2D mode is power feasibe. Since we have ensured power feasibiity ony for communications in ceuar mode (Assumption 4.1.2), we need to verify that r max T b before appying (4.12). To this end, we consider the extended vaue function Ē D2D = (exp ( b σ2 ) 1) W T G T if r max T b + otherwise. (4.13)

43 4.3. Minimizing the energy consumption with Fu Orthogonaity 35 Optima mode seection poicy and resource aocation. The optima mode seection poicy for the singe user pair case, consists in first soving the convex optimization probem to estimate the minimum energy cost for ceuar mode (either for the UE or for the SE case), and then comparing it with the energy cost for D2D mode. The optima communication mode is simpy the one that requires the east amount of energy. Once the optima communication mode and the optima transmission time has been seected, the corresponding optima powers are easiy derived as b P 0 = (exp ( W t ) 1) σ2, u G 0 UL, ceuar mode; b σ2 P 0 = (exp ( W (T t 1), DL, ceuar mode; (4.14) u )) G 0 P = (exp ( b σ2 ) 1), W T G D2D mode. It is possibe to interpret the mode seection poicy in terms of the channe gain (and, so, the physica distance) between the two communicating devices. We wi expore this geometrica interpretation in 4.5 to characterize regions in the ce where D2D communication is preferabe Mutipe user pairs The main chaenge with mutipe user pairs in fuy orthogona operation is that a ceuar connections must use a common UL/DL time aocation. To formuate the joint mode seection and time aocation probem for mutipe pairs under fu orthogonaity, we introduce the mode seection vector m {0, 1} L whose entries satisfy m = and consider the foowing MINLP probem 0 if pair- is in ceuar mode, 1 if pair- is in D2D mode, (4.15) minimize m,t u subject to L =1 Ē D2D m + E CELL (t u )(1 m ) (4.16a) b r0 max T m t u T b r0 max + T m,, (4.16b) t u [0, T ], m {0, 1},. (4.16c) The objective function in (4.16) is the tota energy consumption of a the L user pairs, with E CELL (t u ) given by (4.7) or (4.8) under FO-SE or FO-UE, respectivey. Here, we assume that D2D pairs do not interfere with each other, and their minima energy consumption is the same constant vaue given in (4.13) as in the singe user

44 36 Mode seection and resource aocation in dynamic TDD system pair case. Constraints (4.16b) ensure that pair- can ony be assigned to ceuar mode if it is power feasibe in the sense of Definition Since (4.16a) is separabe in m, we can express the objective in terms of the transmission energy for each device when operating in its optima mode. In other words, we rewrite (4.16) as minimize t u [0,T ] F (t u ), (4.17) where F (t u ) = L =1 E (t u ), and E (t u ) denotes the minimum energy-cost for the singe pair- when the UL time is fixed to t u, that is E (t u ) min{ēd2d, E CELL (t u )} if t u [ b 0 Ē D2D otherwise. r max, T b r0 max ] (4.18) Equation (4.18) reveas the piecewise nature of E (t u ). For t u < b /r0 max and t u > T b, we have E r0 max (t u ) = ĒD2D, which is a finite constant if user pair- is power feasibe in D2D mode, and + otherwise. In the interva [b /r0 max, T b /r0 max ], E (t u ) is either equa to the constant ĒD2D, or given by E CELL (t u ), depending on whether and at which points the graphs of E CELL (t u ) and ĒD2D intersect. Note that the two graphs can intersect ony once if E CELL (t u ) is monotonicay decreasing (i.e. when minimizing UE) or twice if it is convex (i.e. when minimizing SE). To better describe the piecewise nature of E (t u ), we introduce = [τ min, τ max ] as the interva of t u during which E (t u ) = E CELL (t u ). If, for a pair-, such an interva does not exist (i.e., = ), this means that it is aways more efficient for the pair to operate in D2D mode. See Fig. 4.2 for an iustration. Figures 4.3 and 4.4 show the minimum energy-cost of three user pairs (obtained as in Fig. 4.2), and the corresponding F (t u ), under FO-UE and FO-SE, respectivey. Note that function F (t u ) is non-convex on the interva [0, T ]. However, the foowing emma estabishes a key property of F (t u ), usefu ater to sove Probem (4.17). Lemma (a) In the FO-SE scenario, F (t u ) is a piecewise convex function. (b) In the FO-UE scenario, F (t u ) is a piecewise decreasing function. Proof. For each pair-, if =, by its definition, E CELL (t u ) is a constant vaue on [0, T ]. Otherwise, E CELL (t u ) is a constant vaue or + in the two intervas [0, τ min ) and (τ max, T ]. During the interva [τ min, τ max ], in the FO-SE case E CELL (t u ) is a convex function of t u (given by (4.7)); in the FO-UE case, E CELL (t u ) is a monotonicay decreasing function in t u (given by (4.8)). The function F (t u ) is obtained as the sum of E CELL (t u ) of a L pairs. Hence, the whoe interva [0, T ] is divided into J 2L + 1 adjacent intervas. In the FO-UE case, F (t u ) is the sum of constants and convex functions in each interva, which makes F (t u ) piecewise convex. In the FO-UE case, on the other hand, F (t u ) is the sum of constants and monotonicay decreasing functions in each interva, which makes F (t u ) piecewise decreasing.

45 4.3. Minimizing the energy consumption with Fu Orthogonaity E CELL Ē D2D E (t u) 0.25 E CELL Ē D2D E (t u) Energy cost [J] Energy cost [J] τ min b t u r max 0 τ max T b r max 0 0 τ min b t u r max 0 τ max T b r max 0 (a) FO-UE singe ink case (b) FO-SE singe ink case Figure 4.2: Deriving E (t u ) under both the FO-UE case (a), and the FO-SE case (b), with frame duration T = 1 time unit. The time interva = [τ min, τ max ] is the intersection of the the interva [ b, T b ] for power feasibiity in ceuar mode, r 0 max r 0 max with the interva bounded by the intersection points of the graphs of E CELL (t u ). In particuar, = [ b, T b ] if the two curves intersect outside the and ĒD2D r 0 max power feasibe interva (a). [ b r 0 max r 0 max, T b r 0 max ] if at east one of the two possibe intersection points of the curves is within the power feasibe interva (b). = if the two curves never intersect E 1 (t u ) E 2 (t u ) E 3 (t u ) F(t u ) Energy cost [J] Energy cost [J] τ2 min τ min t 1 u τ1 max τ2 max (a) FO-UE three inks case: energycost functions τ2 min τ min t 1 u τ1 max τ2 max (b) FO-UE three inks case: F (t u ) Figure 4.3: FO-UE probem with the time frame duration T = 1: minimum energy-cost functions of three transmitter-receiver pairs (a), and their sum F (t u ) (b). Based on Lemma 4.3.1, the optima soution to (4.17) can be computed efficienty, everaging on the foowing resuts: Proposition (a) In the FO-SE case, et J j=1 Γ j be a partition of [0, T ]

46 38 Mode seection and resource aocation in dynamic TDD system E 1 (t u ) E 2 (t u ) E 3 (t u ) F(t u ) Energy cost [J] Energy cost [J] τ3 min τ3 max t τ min u 1 τ1 max (a) FO-SE three inks case: energycost functions τ τ min 3 min τ3 max t 1 u τ1 max (b) FO-SE three inks case: F (t u ) Figure 4.4: FO-SE probem with the time frame duration T = 1: minimum energy-cost functions of three transmitter-receiver pairs (a), and their sum F (t u ) (b). induced by the points {τ1 min, τ1 max,..., τl min, τ L max }. Then, the optima UL time aocation t u can be found by soving at most 2L 1 singe-variabe convex optimization probems of the form minimize t u Γ j E (t u ) L (b) In the FO-UE case, the optima UL time aocation t max u {τ1, τ2 max,..., τl max}. Moreover, if max{τ min } min{τ max }, then t u = min {τ max } = min{t b }. r0 max Proof. Since for each user pair-, E CELL (t u ) reaches its maximum vaue during the two intervas [0, τ min ) and (τ max, T ], F (t u ) achieves its maximum vaue in the two intervas Γ 1 = [0, min {τ min }] and Γ J = [max {τ max }, T ]. Hence, t u is not in Γ 1 and Γ J, but must be found in one of the remaining (at most) 2L 1 intervas. By Lemma 4.3.1, in the FO-SE case, F (t u ) is piecewise convex. Hence, its goba minimum can be found among its 2L 1 oca minima in each interva. In the FO-UE case we know that, from Lemma 4.3.1, F (t u ) is piecewise decreasing. Thus, its goba minimum can be found in the set L {τ min, τ max }. However, for each τ min, there is at east one component E (t u ) in the sum defining F (t u ), that decreases for t u τ min. Therefore, the goba minimum can ony be found in the set {τ max, L}. Furthermore, if max{τ min } min{τ max }, then t u = min {τ max }. Given the optima soution t u to probem (4.17), the optima mode seection vector m of Probem (4.16) is then given by setting, L: m 0 if E CELL (t u = ) ĒD2D 1 otherwise,

47 4.4. Minimizing the energy consumption with D2D Resource Sharing 39 whie the corresponding optima transmission powers are derived as in (4.14). 4.4 Minimizing the energy consumption with D2D Resource Sharing To increase the ce capacity and the spectra efficiency of the system, we now consider the D2D resource sharing strategy, where a communications in D2D mode are assigned the same channe resource. Due to the cross interference among mutipe D2D pairs, the optima soutions for this scenario are more compicated to compute. Nevertheess, we deveop a combinatoria optimization agorithm that is guaranteed to find the optima soution, and often does so very quicky. This off-ine agorithm is compemented by a heuristic, suitabe for rea-time impementation under practica signaing constraints Optima soution via MINLP The effect of the interference on the energy consumption for D2D communication appears expicity in (4.6). Due to the fixed time aocation T (see Lemma 4.1.4), minimizing the energy consumption of D2D communications is equivaent to minimizing the transmission powers. To meet the minimum rate requirement in (4.3), the transmission power of any pair- in D2D mode must be such that Introducing γ tgt = [exp ( b W T P [exp ( b W T ) 1] σ2 + I G. ) 1] as the target SINR required to satisfy the session rate requirement of pair-, and the terms η = γtgt σ 2 G re-write this inequaity as and h j = γ tgt G j G, we can P η + P jj h j. (4.19) j The joint mode seection and power/time aocation probem can now be formuated as the foowing MINLP probem: minimize m,t u,p subject to L =1 b r0 max (T P )m + E CELL (t u )(1 m ) (4.20a) T m t u T b r0 max + T m,, (4.20b) P jj h j C(1 m ) P, j, (4.20c) P P max m, (4.20d) m {0, 1} L, t u [0, T ], P 0. (4.20e)

48 40 Mode seection and resource aocation in dynamic TDD system Here, m is the mode seection vector defined in (4.15). Constraint (4.20b) ensures power feasibiity for pairs in ceuar mode, whie (4.20c) guarantees that the rate requirement is satisfied for each pair in D2D mode. Finay, (4.20c) bounds the transmit power eve. The constant C in (4.20c) is a arge number (e.g., C = max {η + P max }) ensuring that the constraint is ony enforced for users in D2D mode. The expression for E CELL (t u ) in the objective function is either (4.7) or (4.8), depending on whether we are interested in the RS-SE or RS-UE probem, respectivey. Probem (4.20) beongs to the cass of mixed booean-convex probems, where for each fixed m {0, 1} L the objective function is convex in the continuous variabes. In genera, MINLPs are NP-hard probems [78], combining the combinatoria difficuty of optimizing over discrete variabe sets, with the chaenges of handing noninear functions. Their soution times grow exponentiay with the probem dimension. In particuar, if L in (4.20) is very sma (i.e., smaer than 15), the optimization probem can be soved exacty by exhaustive enumeration of the 2 L possibe mode seection vectors. However, reaistic ceuar networks might consist of a arge number of user pairs. For this reason, we deveop a customized sover based on B&B (see, e.g., [79, 80]). Specia attention is given to deveoping nove variabe seection and branching rues, aong with efficient procedures for infeasibiity detection and performance bound computations. This sover aows us to find provaby optima soutions much more efficienty than using generic B&B sovers or naive exhaustive search. In the seque, we wi focus on agorithms that sove the RS-UE probem, considering that the mobie devices are the most energy-sensitive component of the network. However, the same approaches can be appied to the RS-SE case. A branch-and-bound approach for finding the optima soution Before describing the proposed B&B agorithm, it is convenient to introduce a definition and two usefu propositions on the feasibiity of the mode seection vector m. Let H be a non-negative matrix with entries H j = h j if j, and zero otherwise, and et us introduce the vectors P = (P, L), P max = (P max, L) and η = (η, L). For each mode seection vector m, we can define the corresponding set of pairs assigned to D2D mode and to ceuar mode as D m and C m, respectivey. Let A m denote the L D m incidence matrix, which is formed by removing the -th coumn from the L L identity matrix if m = 0. We define H m = A mha m, P m = A mp, I m = A ma m, P max m = A mp max and η m = A mη. Constraints (4.20c) and (4.20d) can be written in matrix form as (I m H m )P m η m and P m p max m, (4.21) where the inequaities are component-wise, I m = A ma m, and P max m = A mp max. The matrix H m has stricty positive off-diagona eements, and we can assume that it is irreducibe because we do not consider totay isoated groups of pairs that

49 4.4. Minimizing the energy consumption with D2D Resource Sharing 41 do not interact with each other. Let ρ(h m ) denote the argest rea eigenvaue of H m. From the Perron-Frobenius theorem [81], we have the foowing proposition: Proposition ([82] Chapter 2). For a given mode seection vector m, the necessary and sufficient condition for the existence of a positive P m to sove inequaity (I m H m )P m η m is that ρ(h m ) < 1. (4.22) Moreover, P m = (I m H m ) 1 η m is its component-wise minimum soution. Proposition provides an easy condition to verify if a mode seection vector m is feasibe. Definition (Feasibe mode seection vector). A mode seection vector m is feasibe if both condition (4.22) and (I m H m ) 1 η m P max m are verified. Proposition ([83]). If m is not feasibe, then every other mode seection vector m with additiona users assigned to D2D mode, i.e. such that { L m = 1} { L m = 1}, is not feasibe. We now use the resuts above to design a B&B agorithm that soves the MINLP probem in (4.20). When using a B&B approach, a possibe mode seection vectors m are expored through a binary tree. Each node of the tree (except the root) represents a subprobem where one of the mode seection variabes m is set to either 0 or 1. Thus, to each node corresponds a partia mode seection vector with some components aready defined (fixed) and forming the set F, whie others are sti undetermined and represent the set U. Therefore, each branch of the three corresponds to a subset of the possibe mode seection vectors. The main idea of B&B is to ony expore branches of the binary tree that have the potentia to produce better soutions than the best soution found so far, and disregard (prune) the others. This is done by computing upper and ower bounds on the optima vaue at each node. If the ower bound of a node is arger than the current upper bound, then there is no need to expore its branches. To achieve a good performance of B&B, it is essentia to seect the branching rue and tree exporation strategies carefuy, and to have efficient methods for computing good (tight) upper and ower bounds [84]. The fowchart in Fig. 4.5 summarizes the proposed B&B agorithm. It is based on the foowing four choices: 1) the computation of the initia upper bound (UB), where we assume a pairs in ceuar mode; 2) the branching rue that seects the variabe to fix at each node as the one that increases the ikeihood of finding infeasibe mode seection vectors, to expoit Proposition 4.4.3, to expoit Proposition to prune branches; 3) the tree exporation strategy that assigns the seected branching variabe to 1 first (i.e., D2D mode comes first as a choice); and, finay, 4) the computation of the upper and ower bounds (Node-UB and Node-LB) as the sum of the minimum energy cost of the pairs in F pus an upper and ower bound of the energy cost of the pairs in U, respectivey. We refer to Appendix A for a detaied description and motivation of each such choice.

50 42 Mode seection and resource aocation in dynamic TDD system Initia upper bound Move to the next unexpored node Branching step branching rue tree exporation strategy Compute bounds yes New node: is F feasibe? no Prune the branch. Move to the next unexpored node Node-LB UB? yes no Update UB if Node-UB UB no Are a nodes expored? yes Probem soved; terminate Figure 4.5: Fowchart of the B&B method. Light bue bocks represent our customized choices. Once the optima mode seection vector and the corresponding optima transmission time have been found, the power eves are obtained as in (4.14) for ceuar users, and as in Proposition for D2D users. The B&B agorithm is guaranteed to find the optima soution, and does so much faster than the exhaustive search, as shown in However, for arge networks it can sti have impractica running times. In addition, the optimization formuation assumes that a cross-gains between users are known, which in turn woud impose significant communication overhead. We therefore turn our attention to heuristics that can be run in rea-time and do not assume centraized knowedge of a the channe gains. A heuristic approach to achieve a practica sub-optima soution In this subsection, we present a heuristic agorithm that achieves a near-optima soution to (4.20) in a more practica and scaabe way than the B&B approach. Again, we focus on the UE case. The key idea of this agorithm is to first determine an initia mode seection vector, together with the corresponding power and time aocation, and then improve this soution by means of a distributed power contro agorithm based ony on oca measurements. The heuristic agorithm, described in Agorithm 1, consists of the

51 4.4. Minimizing the energy consumption with D2D Resource Sharing 43 foowing three main steps: Agorithm 1: Heuristic approach for RS-UE minimization Input: (γ tgt, G, G 0, G 0 ) L, θ Output: m, p 1 (m FO, t u (m FO ), p(m FO )) soution to FO-UE probem; 2 each D m FO acquires E CELL (t u (m FO )) from the BS; 3 p (0) p(m FO ), m (0) m FO, k = 0; 4 each D m FO computes γ (0) ; 5 convergence Fase; ; 6 whie convergence do 7 m (k+1) m (k) ; 8 for each D m (k) do 9 P (k+1) 10 if P (k+1) = γtgt P (k) ; γ (k) > min { θ T ECELL (t u (m FO )), P max } then 11 m (k+1) 0, D m (k+1) D m (k) {}; 12 each D m (k+1) computes γ (k+1) ; 13 if γ (k+1) γ tgt, D m (k+1) then 14 convergence True; 15 p p (k+1), m m (k+1) ; 1. Initia phase: We adopt the optima soution to the FO-UE probem in Section 4.3 as the initia soution, denoted by (m FO, t u (m FO ), p(m FO )). The FO-UE probem is soved by the BS. For each pair- D m FO (i.e., assigned to D2D mode), the BS aso computes the energy it woud consume if in ceuar mode, that is E CELL (t u (m FO )) from (4.8), and broadcasts m FO and (t u (m FO )) to each Tx- D m FO. E CELL The initia mode seection vector m FO is obtained under the assumption of no interference among the D2D pairs. However, under the RS scenario, a the D2D pairs share the same channe, thus m FO can be energy inefficient, or even infeasibe, due to the interference. Therefore, a distributed power contro agorithm is then executed by the D2D pairs to find a feasibe and more energy-efficient soution: 2. Iterative distributed power contro for D2D pairs: Using the iterative power contro method originay proposed by Foschini and Mijanic in [85], each Tx- in D2D mode can achieve its target SINR γ tgt by updating its transmit power as foows P (k+1) = γtgt γ (k) P (k), (4.23)

52 44 Mode seection and resource aocation in dynamic TDD system where P (0) = P(m FO ) and γ (k) is the perceived SINR for pair- D m FO in iteration-k, defined as γ (k) = P (k) G /(σ 2 + j Dm FO,j P (k) jj G j). To achieve a feasibe mode seection vector and to further reduce the energy cost, some inks in D2D mode need to switch to ceuar mode. Specificay, pair- in D2D mode wi switch to ceuar mode if its transmit power eve exceeds its maximum imit or if it is more energy efficient for it to communicate in ceuar mode, that is, if P (k) > min { θ T ECELL (t u (m FO )), P max }, (4.24) where we introduce the design parameter θ 1; see Remark During the power update (4.23), if Tx- finds that condition (4.24) is fufied, it asks the BS to switch it to ceuar mode and to assign it an orthogona frequency channe. Otherwise, it keeps updating its power according to (4.23). The BS keeps track of the pairs changing communication mode, and updates the mode seection vector. This power contro agorithm converges to the minimum power eves that the user pairs remaining in D2D mode need to fufi the rate requirement. 3. Fina phase: Once the agorithm converges, the BS recomputes the optima power/time aocation for the user pairs in ceuar mode, broadcasting this information before the data transmissions take pace. On the seection of parameter θ. The seection of parameter θ accounts for the foowing key aspects of the possibe practica impementation of the proposed heuristic agorithm: Tradeoff between signaing overhead and energy gain: Communication mode switches incur additiona signaing overhead between mobie devices and the BS to coordinate the re-aocation of radio resources. Hence, by setting θ > 1, mode switches wi occur ony if they resut in a significant energy gain. Tradeoff between channe reuse and energy consumption: Since moving a user pair from D2D mode to ceuar mode requires another orthogona channe, a arge vaue of θ can enforce more pairs to communicate in D2D mode and thus increase the channe reuse, even if this comes at the cost of a higher energy consumption due to the interference. Accounting for the mis-estimation of the energy cost: D2D pairs base their seection to switch communication mode on an under-estimate of the energy consumption in ceuar mode (Eq. (4.24)). Since the optima UL transmission time computed when Agorithm 1 has converged wi be greater or equa to the initia t u (m FO ), the actua energy consumption in ceuar mode can be arger than expected. Using θ > 1 reserves a margin for mis-estimation so that ony connections that truy gain by being in ceuar switch to ceuar.

53 4.5. Numerica resuts Numerica resuts This section presents simuation resuts that vaidate our theoretica findings and evauate our proposed agorithms. We consider a singe ce with a BS, equipped with an omnidirectiona antenna, positioned in the center. The main simuation parameters are isted in Tabe 4.2. Tabe 4.2: Simuation parameters Parameter Vaue Parameter Vaue Time frame duration 1 time unit Max power for transmitter W Ce radius 500 m Max power for the BS 40 W Frequency channe bandwidth 5 MHz Path gain at reference distance of 1m Noise power spectrum density -174 dbm/hz Path oss exponent Singe ink anaysis Geometrica interpretation. We begin by deveoping a geometrica interpretation of the optima mode seection poicy for the singe ink case, under the assumption that the channe gains foow the conventiona path oss mode introduced in Chapter 3. The aim is to interpret the soution to the mode seection probem in terms of physica distance between the communicating devices, to characterize regions of the ce where D2D mode is optima. To ensure that Assumption is satisfied, we set b to its maximum vaue that guarantees that the constraint set of Probem (4.9) is never empty, i.e., b = r max 0 r max 0 T, where the maximum rates r max r0 max +r0 max 0 and r0 max are functions of gains G 0 = G 0 D0 α and G 0 = G 0 Rce α, respectivey, with R ce being the ce radius. We first consider the UE case. D2D communication is energy-optima when Ē D2D (T ) E CELL (t u ), where ED2D (T ) and E CELL (t u ) are given by (4.11) and (4.13), respectivey. Using the path oss mode, we can transform the mode seection poicy to the foowing equivaent condition on the distances between the transmitter, the receiver and the BS: D ( (eb /W T 1)T (e b /W t u 1)t u 1/α ) κ(d 0 ) D 0 = κ(d 0 )D 0. (4.25) Note that κ is a function of D 0, since D 0 affects r0 max and thereby t u = T b /r0 max. Thus, even though we are negecting the energy cost for the DL transmission, D 0 sti infuences the optima mode seection. To characterize the region where D2D mode is preferabe, we fix the position of Tx- (and therefore D 0 ). We then vary the position of Rx- aong a circe centred at the BS, thus keeping D 0 (and κ(d 0 )) constant. Inequaity (4.25) now states that

54 46 Mode seection and resource aocation in dynamic TDD system D2D mode is preferabe when the distance between the transmitter and receiver of pair- (i.e., D ) is ess than κ(d 0 )D 0. In other words, D2D mode is more energy efficient when Tx- is ocated in the arc defined by the intersection of the circe of radius D 0 centered at the BS, and the disc of radius κ(d 0 )D 0 centered at Tx-. The D2D optima area can be constructed by tracing out these arcs for various distances between Rx- and the BS, as iustrated in Fig The vaue of κ(d 0 ), and thus the D2D optima area, decreases as Rx- gets coser to the BS. Fig. 4.7 iustrates the D2D-optima area in red, and the D2D power-feasibe area in ight bue, for two different ocations of Tx-. Athough (4.25) does not formay describe a disc around Tx-, the D2D-optima area is cose to circuar. The reason for this is the power imbaance between the user equipment and the BS (P 0 P 0 ), which makes b /r max 0 very sma, t u T and κ 1 practicay independenty of D 0. BS Tx- Rx- Rx- Figure 4.6: Dashed circes centred at the position of Tx- have radius κ(d 0 )D 0 from (4.25), and represent, for each of the two positions of Rx-, the area within which D2D mode is more energy efficient than ceuar mode for the UE case. Simiar cacuations and arguments can be made for the SE objective. In this case, E CELL (t u t u ) is given by (4.10) and the condition on the direct distance for optima D2D mode gets a bit more invoved (see [86]). In this case we have 1/α ) (e b /W T 1)T D ( (e b /W t u 1)t u Dα 0 + (eb /W t d 1)t d Dα 0 κ(d 0,D 0 ) = κ(d 0, D 0 ). (4.26) Fig. 4.8 shows representative resuts for our simuation scenario. We observe that the D2D-optima area is no onger circuar and that the D2D mode is preferabe in a arge portion of the ce. In particuar, we observe that the red arcs (D2D optimaity area) enarge as the receiver moves away from the BS. The reason is as foows. When Rx- moves towards the ce-edge, the feasibe set of Probem (4.9) reduces, becoming a singe point when the distance between the BS and Rx- equas the ce radius. In genera, we coud observe that there is a certain distance D 0 after which the optima soution (t u, t d ) to Probem (4.9) remains the same. As a

55 4.5. Numerica resuts Tx 500 Tx 0 BS 0 BS (a) Tx- is 250 m away from the BS (b) Tx- is 450 m away from the BS Figure 4.7: D2D optimaity area when minimizing the UE consumption. Red area represents the positions of Rx- for which D2D mode is more energy efficient than ceuar mode, whie ight bue disk represents the area within which Tx- can fufi the rate requirement transmitting in D2D mode with a feasibe power eve. resut, after that point, the threshod on the direct distance D for D2D optimaity starts depending ony on the parameter D 0. Since it increases with D 0, D2D mode resuts more preferabe for arger arcs. 500 Tx 500 Tx 0 BS 0 BS (a) Tx- is 250 m away from the BS (b) Tx- is 450 m away from the BS Figure 4.8: D2D optimaity area when minimizing the SE consumption. Red area represents the positions of Rx- for which D2D mode is more energy efficient than ceuar mode, whie ight bue disk represents the area within which Tx- can fufi the rate requirement transmitting in D2D mode with a feasibe power eve Mutipe ink anaysis: energy savings and agorithm performance The simuation experiments for the muti-ink case are set up as foows. We generate random network topoogies with given number of user pairs. An exampe of network with 10 user pairs is given in Fig. 4.9.

56 48 Mode seection and resource aocation in dynamic TDD system Without oss of generaity, we assume the same max transmission power eve for a mobie devices, and the same traffic requirement for a pairs, indicated with b. To ensure Assumption 4.1.2, we set b = rmax u r max d T, where r max ru max +rd max u and rd max are the maximum achievabe rate in UL and DL, respectivey, when transmitter and receiver are both at the ce edge. For a given number of user pairs, we investigate 1000 random networks and present the averaged resuts BS Figure 4.9: Network with 10 user pairs randomy paced in a ce of radius 500 m. The red squares represent the transmitters and the green circes represent the receivers. Transmitter and receiver forming a pair are abeed with the same number. Energy gain by enabing D2D communications in a FO system. To quantify the energy savings that can be obtained by expoiting D2D communications, we compare the energy cost of the optima FO-UE soution with the one when a pairs are forced to communicate in ceuar mode. For each random configuration used in our Monte Caro study, we sort the inks in order of increasing energy gain and then average over the 1000 vaues coming from the different simuations. Fig shows the resuts for networks with 10 and 30 user pairs. From Fig we observe that when D2D communication is enabed, the average per user energy saving is 40%. In particuar, one third of the pairs have an energy gain arger than 60%, and haf of the transmitters achieve an energy gain arger than 20%. We highight that the energy gain is not ony a consequence of the proximity of the users, but aso stems from the more advantageous fu time frame aocation to the singe-hop D2D connections. Performance evauation of the B&B agorithm for RS-UE. The difficuty in soving Probem (4.20) ies mainy in the possiby arge search space of integer feasibe points. Tabe 4.3 shows the average number of mode seection vectors expored by different strategies, before finding the optima soution. We compare the B&B agorithm described in Section (both with the proposed branching rue and with

57 4.5. Numerica resuts 49 Per user avg. energy saving (%) Per user avg. energy saving (%) User pairs (a) Networks with 10 user pairs User pairs (b) Networks with 30 user pairs Figure 4.10: Energy gain by enabing D2D communications in a FO system. User pairs are sorted in increasing order of the energy gain they achieve by performing mode seection, compared with traditiona communication via the BS. a random seection of the branching variabe) with the naive exhaustive enumeration agorithm, where we ony eiminate infeasibe soutions using Proposition The resuts ceary show that the customized design of the branching rues have a strong effect in reducing the run time. Tabe 4.3: Avg. number of expored integer soutions. Agorithm 10 user pairs 15 user pairs 20 user pairs 30 user pairs 40 user pairs Exhaustive search with Proposition NA a NA NA B&B - Random branching rue NA B&B - Proposed branching rue a NA (not avaiabe) denotes the case when the optima soution was not found within 8 hours on a standard PC. Performance evauation of the heuristic mode seection agorithm for RS-UE. In this section, we evauate the performance of the proposed heuristic agorithm. Fig shows the additiona energy cost of the heuristic reative to the optima soution computed using the B&B sover. For networks with 10 user pairs, the heuristic is within 10% of the optima soution for amost a network configurations; see Fig. 4.11(a). For networks with 30 user pairs (Fig. 4.11(b)), the performance of the heuristic is sighty worse. This degradation is due to the arger degree of freedom in packing D2D inks on the same frequency channe. However, the soutions are sti within the 10% suboptimaity for most configurations. Fig. 4.9 is an exampe of those few network configurations where the heuristic performs much worse than optima agorithm (indicated with a red circe in Fig. 4.11). Under FO, both pair-9 and pair-4 in Fig. 4.9 woud be assigned to D2D mode. When the heuristic initiay attempts to assign these inks to the same channe, it encounters an infeasibe configuration due to the high interference that Rx-4 perceives from

58 50 Mode seection and resource aocation in dynamic TDD system Tx-9. Therefore, ony one of the two pairs can be assigned to D2D mode. The optima decision is to et pair-4 in D2D mode, but the heuristic makes a wrong decision during the first iterations, when a temporariy high interference from Rx-9 eads pair-4 to eave the shared channe and switch to ceuar mode Additiona energy cost of the suboptima soution (%) (a) Networks with 10 user pairs Additiona energy cost of the suboptima soution (%) (b) Networks with 30 user pairs Figure 4.11: Performance evauation for different agorithms. Tota energy consumption and number of orthogona frequency channes needed to accomodate a the communication requests within the ce. Vaues are averaged over 1000 random configurations. Energy and spectra efficiency of D2D in dynamic TDD. We concude this section by a comparison of the different mode seection poicies proposed in this paper, both in terms of their energy efficiency and their spectra efficiency. Fig shows the energy-channe performance of the proposed agorithms for networks with 10 and 30 user pairs, respectivey. We note that FO-UE represents the energy-optima soution, with significant energy savings compared to the purey ceuar soution (abeed FO-ceuar mode) and the same spectra efficiency (measured in number of aocated channes). Resource sharing (RS-UE-B&B) yieds big improvements in spectra efficiency at the cost of a sight increase in energy consumption when D2D transmitters need to compensate for interference. The reason that the energy increase is so sma is that the transmission powers assigned to D2D pairs are generay sma, party because D2D pairs typicay have high direct gains (since the transmitter and receiver often are in cose proximity of each other), and party because D2D connections can use the fu frame duration (see Eq. (4.6)). These resuts demonstrate that for some user pairs, communicating in D2D mode and interfering with each other is sti more energy efficient than communicating in ceuar mode on an excusive frequency channe. Thus, in dynamic TDD systems, D2D communications have the potentia to improve both spectrum and energy efficiency over a traditiona ceuar soution. Finay, we evauate the performance of the heuristic method for different vaues of the threshod θ. As expected, arge vaues of θ decrease the number of channes used at the expense of a sighty increased

59 4.6. Summary 51 energy consumption. For this reason, θ is an important design parameter for finding a suitabe tradeoff between energy consumption and channe use. Avg. tota users energy consumption [J] RS UE Heuristic FO Ceuar Mode FO UE RS UE B&B θ=3 θ=1 Avg. tota users energy consumption [J] θ= RS UE Heuristic FO Ceuar Mode FO UE RS UE B&B θ= Number of orthogona channes Number of orthogona channes (a) Networks with 10 user pairs. (b) Networks with 30 user pairs. Figure 4.12: Performance evauation for different agorithms. Tota energy consumption and number of orthogona frequency channes needed to accomodate a the communication requests within the ce. Vaues are averaged over 1000 random configurations. 4.6 Summary We investigated the probem of energy efficient mode seection and resource (power and time) aocation for network-assisted D2D communications in dynamic TDD systems. We anayzed the probem under two frequency channe aocation strategies (with and without interference among D2D pairs) and with two objectives (tota user energy and tota system energy). For each configuration we derived the optima soution to the corresponding MINLP formuation. In particuar, for the interference free case, we demonstrated how the optima soution can be obtained in poynomia time. On the other hand, when D2D pairs interfere with each other, finding the optima soution in an efficient manner in terms of execution time and cross-gains knowedge is much harder. Therefore, a customized branch-and-bound sover was compemented by a more practica ow-compexity heuristic. Through numerica simuations, we demonstrated that significant energy savings can be achieved by expoiting the benefits brought both by the better channe gain of D2D inks, and by the adaptive transmission time of the dynamic TDD technoogy. Moreover, everaging on the observation that arge channe gain and ong transmission duration for D2D inks ead to a ow transmit power (and hence ow interference), we showed the potentia of D2D communications to improve aso the spectrum efficiency over traditiona ceuar communications. Finay, we presented anaytica characterizations of the D2D-optima areas for a transmitter-receiver pair, showing that these regions can be surprisingy arge and not necessariy circuar.

60

61 Chapter 5 Power contro schemes for D2D communication The purpose of this chapter is to anayze the performance of the 3GPP LTE power contro (PC) mechanism for UL transmission, when appied to the hybrid ceuar-d2d network. A simiar investigation has been proposed in [40]. However, differenty from that work, here we compare LTE PC schemes with a distributed PC method based on utiity maximization. Buiding on the aready standardized and widey depoyed LTE UL PC schemes faciitates not ony a smooth introduction of D2D-enabed user equipments, but woud aso hep to deveop inter-operabe soutions between different devices and network equipment. However, due to the new interference scenarios, the question naturay arises whether the avaiabe LTE PC is suitabe for D2D communication integrated in an LTE network. 5.1 LTE upink power contro In this section we give a brief overview of the LTE PC options that might be appied to D2D communication integrated in ceuar systems. The PC mechanism used in LTE system empoys a combination of open-oop and cosed-oop contro to set the UL transmit power of the user. The open-oop sets a coarse operating point for the transmit power eve, which is mainy based on the path oss estimation and shoud be suitabe for a reference moduation and coding scheme (MCS). Power eve adaptation can then be appied around this operating point by means of the cosed-oop contro, which mainy compensates for ong-term channe quaity variations 1. In LTE, in fact, fuctuations of the channe gain due to fast fading, and variations of the interference eve are expoited or compensated by fast scheduing 2 and ink adaptation, rather than by varying the transmit power. 1 The cosed-oop in LTE woud be expected to operate at no more than a few hundred Hertz [12]. 2 In LTE, fast scheduing of different users is appied at 1 ms intervas [12]. 53

62 54 Power contro schemes for D2D communication Different combinations of the open-oop and cosed-oop contro mechanisms provide different modes of operation of the LTE UL PC, which can be seected and used depending on the depoyment scenario and operator preference [12, 87]. The genera LTE PC scheme sets the transmit power P UE for the user equipment, up to a maximum eve of P max, as foows: P UE = min{ P 0 ρ PL + TF + f( TPC ) + 10 og 10 M, P max } [dbm], (5.1) OL operating point dynamic offset BW factor where ρ [0, 1] is the path oss compensation factor, PL is the path gain between the user and the BS, and M is the number of schedued RBs to the user. For the open-oop operating point, P 0 is a base power eve used to contro the SNR target γ tgt, and it is cacuated as [88]: P 0 = ρ (γ tgt + P IN ) + (1 ρ) (P max 10 og 10 M), (5.2) where P IN is the estimated noise and interference power per RB. The term ρ PL in (5.1) is the path oss compensation component. It is based on the user s estimate of the downink path oss PL. It represents the degree to which the power is adapted to compensate it, on a scae from no compensation (i.e., ρ = 0) to fu compensation (i.e., ρ = 1). Fu path oss compensation maximizes fairness for users at the ce-edge. However, it increases the inter-ce interference, thus reducing the system capacity. Compensation factors around give good tradeoff between system capacity and ce-edge data rate. Furthermore, in practice, the typica range of vaues for the base power P 0 is -126 dbm to 24 dbm per RB, whie typica vaues for γ tgt are within the range [ 5, 25] db; see [12, 88]. For the dynamic offset, TF is the MCS-dependent component 3. It aows the power per RB to be adapted according to the MCS which the user has permission to transmit. The MCS can be adjusted by the BS taking into account the instantaneous buffer status, the avaiabe power headroom and the QoS requirements of the user. The f( TPC ), on the other hand, represents the expicit transmit PC (TPC) command from the network, which is user-specific and can be accomuative or absoute. When it is accumuative, it signas a power adjustment reative to the previous eve. When it is absoute, it indicates a power offset to be appied not to the previous power eve, but to the open-oop operating point. Other possibe uses for the MCS-dependent component to dynamicay adjust the transmit power, and more detais on the TPC commands can be found in [12] LTE power contro options for D2D communication Given the genera LTE UL PC mechanism described in Section 5.1, we now consider different PC strategies for the D2D-enabed network. These strategies are obtained as different parameter settings in (5.1): 3 TF stands for Transport Format.

63 5.2. Power contro based on utiity maximization 55 Fixed Tx power: in this case there is no PC, and the transmit power of the transmitters is set to some fixed vaue P fix P max. For M = 1, this can be obtained by setting ρ = 0 and P 0 = P fix in the open-oop operating point. Fixed SNR target: this scheme fuy utiizes the path oss compensation capabiity by setting ρ = 1 and P 0 = γ tgt +P IN in the open-oop operating point. Note that the seection of the SNR target wi affect the tota transmit power and the fina SINR. Open-oop with fractiona path oss compensation (OFPC): The OFPC scheme aows users to transmit with variabe power eves, depending on their path oss. In contrast to the previous PC cases, the OFPC compensates for the fraction of the path oss by setting ρ to some suitabe vaue within the range (0, 1). Cosed-oop: in this scheme we consider the cosed-oop mechanism with the singe feedback item f( TPC ) in (5.1). This tuning step is used to compensate the difference between the measured SINR at the receiver (γ) with the desired SNR target vaue (γ tgt ). The tuning step is computed as in [40]: f( TPC ) = γ tgt γ /2 if γ tgt γ > 2 db 1 db otherwise. (5.3) For users communicating in ceuar mode with their respective serving BSs, OFPC provides a we proven aternative, typicay used in practice. It avoids the compexity and overhead associated with the dynamic offset of the cosed-oop scheme, but makes use of the fractiona path oss compensation, thus baancing between overa spectrum efficiency and ce edge performance [87]. For this reason, we assume this scheme as a defaut PC method for ceuar users. For D2D transmitters, on the other hand, we consider the four aternative PC schemes described above. We examine the performance of these four variations and benchmark them against an utiity maximizing scheme appied to a transmitters (ceuar and D2D). Fig. 5.1 summarizes the different PC options considered in this thesis. 5.2 Power contro based on utiity maximization In this section we derive a reference PC scheme for the hybrid ceuar-d2d network. The adopted framework has been introduced in [59], and further investigated in the fied of fow contro and RRM in muti-hop wireess networks in [89, 90]. Without compromising the mathematica soundness, we adopt the framework of [90] to derive a practica agorithm that is appeaing to ceuar networks with underay D2D communication. In fact, the agorithm is distributed among the user pairs and does not require any coordination or message fooding scheme between a the users and the BSs.

64 56 Power contro schemes for D2D communication Open Loop Utiity Maxim. BS Fixed Power Fixed SINR target Open Loop Cosed Loop Utiity Maxim. Figure 5.1: The user communicating in ceuar mode with its serving BS uses the standard LTE fractiona open-oop PC with path oss compensation (OFPC). For the D2D ink, we study various PC strategies that can a be easiy depoyed using the fexibe LTE PC tookit. Additionay, for benchmarking purposes, we aso consider the case when both D2D and ceuar communications are assigned transmit power according to an utiity maximization approach System mode and assumptions We consider a hybrid ceuar-d2d network, where D2D pairs communicate using the ceuar UL resources, such as the UL physica RBs in a ceuar FDD system or the UL time sots in a TDD system. We assume that the communication mode for each user pair has aready been seected, and a inks have been aready assigned to a specific RB for their communication. Transmitter-receiver pairs (ceuar user-bs and D2D transmitter-receiver, depending on the mode seection decision) are abeed with = 1,..., L. We indicate with L f L the set of pairs assigned to RB-f. To simpify the notation, in this chapter we drop the indices m, f from Eq. (3.1) and (3.2), and indicate with P the transmit power used by Tx- towards its intended receiver on the assigned RB. Simiary, we indicate with γ the SINR measured at Rx-, and with r the capacity of ink-. Both γ and r are functions of the power aocation vector P = [P ] reated to the set of inks sharing the same RB. Moreover, we denote by s the end-to-end rate for the communication between transmitter and receiver of pair-. Associated with each ink- is a function u (s ), which describes the utiity of user pair- at the communication rate s. The utiity function u is assumed to be increasing and stricty-concave. We et s = [s ] and r = [r ] denote the vectors of assigned rates and ink capacities, respectivey. Obviousy, vector s must fufi the foowing constraints: s r, s 0.

65 5.2. Power contro based on utiity maximization Probem statement It is convenient to ook at s as the vector of the rate targets, whie the capacity vector r depends on the specific power used by the interfering transmitters. For each set of inks L f sharing a given RB-f (and thereby causing interference to one another), we formuate the probem of end-to-end rate setting and power contro as: maximize P,s u (s ) ω P L f L f subject to s r (P), L f, s 0, P 0, L f. (5.4) Probem (5.4) aims at maximizing the tota utiity, whie taking into account the transmit power consumption (thus reducing the interference and proonging the ifetime of the devices) by means of a predefined weight ω 0. Constraints of Probem (5.4) ensure that the aocated rate does not exceed the capacity of the ink, which is optimized through the power aocation. It is worth noting that Probem (5.4) is not convex due to the nonconvexity of the ink capacities Soution based on probem convexification To render Probem (5.4) convex, we invoke the resuts presented in [59] and [90]. In doing so, we transform the nonnegative optimization variabes ogarithmicay, that is s e s and P e P, L f, aong with a og-transformation of the capacity constraints. The origina optimization probem is therefore converted into the foowing form maximize s, P u (e s ) ω e P subject to og(e s ) og (r (e P )), L f. (5.5) Theorem ([59], Theorem 2). The transformed Probem (5.5) is convex if the utiity functions u ( ) are a (og, x)-concave over their domain. Under the condition of Theorem 5.2.1, we can sove Probem (5.5) to optimaity. In particuar, we consider u (x) = og(x) [59], and we decompose the probem into two separate probems (namey, Probem-I and Probem-II) that are executed recursivey unti convergence. Specificay, Probem-I seects the transmit rate target, whie Probem-II seects the transmit power that fufis the given rate target. This separation of setting the rates target and corresponding power eves is detaied in the next section. For the sake of notation, in the foowing sections we wi omit to specify that the probems are soved for a inks assigned to RB-f. A decomposition approach We now reformuate Probem (5.5) as a probem in the user rates vector s, which can be soved for a given power aocation vector P. Note that the target rate vector

66 58 Power contro schemes for D2D communication s can be uniquey mapped to a target SINR vector γ tgt, as it wi be shown ater. We define Probem-I as: maximize ν( s) s (Probem-I) subject to s S, where S = { s og(e s ) og(r (e P )), } represents the set of feasibe rate vectors that, for a given power vector P, fufi the constraints of Probem (5.5). The objective function in (Probem-I) is defined as ν( s) = u (e s ) ϕ( s), where ϕ( s) represents the minimum cost in terms of the tota transmit power for reaizing a given target rate s. That is, for a given s vector, ϕ( s) is the soution of Probem-II minimize P ω e P subject to og(e s ) og (r (e P )),. (Probem-II) Soving the rate aocation probem (Probem-I). To sove (Probem-I), we disregard the feasibiity constraint and we determine the optima s by means of gradient ascent iterations. As shown in [91], (Theorem 4.2.8), by starting with a feasibe rate aocation and using a step size ɛ sma enough, the rate vector remains feasibe and approaches to optimum. We consider the gradient ascent iteration where i ν( s) = s (k+1) i = s (k) i + ɛ i ν( s (k) ), i, (5.6) [ u (e s ) ϕ( s)] = u (e si )e si i ϕ( s). (5.7) s i s i To compute (5.7), we first need to find ϕ( s) by soving (Probem-II). Since it is convex in P, we can use a Lagrangian decomposition approach. Let λ be the Lagrange mutipiers for the constraints in (Probem-II) and form the Lagrangian: L(λ, P) = ω Then, the dua probem is given by: e P + λ [ og (e s ) og (r (e P )) ]. (5.8) maximize [g(λ) = min λ P subject to λ 0. L(λ, P)] Let us assume that (λ, P ) represents the optimum soution of (Probem-II), we can now cacuate ϕ( s) from (5.8): ϕ( s) = [ωe P λ og (r (e P ))] + λ og(e s ), and s i ϕ( s) = λ i.

67 5.2. Power contro based on utiity maximization 59 Therefore, recaing (5.7), we have: i ν( s) = u (e si )e si i λ i = e si [u (e si i ) λ i ] = s i [u i (s i ) λ i ], (5.9) e si s i and the fina target rate update is: s i (k+1) = e s(k+1) i = s i (k) exp (ɛ i ν( s (k) )). Finay, combining the resut above with (5.7), we can write the rate target setting rue in the foowing form: s (k+1) i = s (k) i exp ɛ s i (k) [u i (s (k) i ) λ i (s i (k) ) ] s (k) i. (5.10) Eq. (5.10) dictates the outer-oop iterative mechanism for a certain transmitter-i. Specificay, at any iteration (k + 1), (5.10) determines the rate that shoud be targeted during the inner-oop PC described in the next section. Soving the power aocation probem (Probem-II). Given any s (k) S, the constraints in (Probem-II) correspond to require that the SINR-s of the inks exceed a target vaue, i.e., og (e s(k) ) og (r (e P )) γ (P) γ tgt ( s (k) ),, where we reca that γ (P) = G P σ 2 +I, and we define γ tgt ( s (k) ) = 2 e s (k) Therefore, for a given s, (Probem-II) can be rewritten as: W 1. (5.11) minimize P subject to ω e P γ (e P ) γ tgt ( s ),, and soved with an iterative PC scheme, as in [92]: (5.12) P (t+1) = γtgt ( s ) γ (P (t) ) P (t). (5.13) Determining the λ i -s. We can now determine the λ i -s for the outer-oop update (5.10) by expoiting the reationship between the optima P and the associated Lagrange mutipiers λ i -s. To this end, we rewrite the constraints in (5.12) as: G P γ tgt σ 2 0 P γ tgt G m P m γtgt + G m P m m G G 0,. (5.14) m σ 2

68 60 Power contro schemes for D2D communication Let H R L L and η R L be defined as foows: H = [h m ] = 1 γ tgt η = [η ] = [ γtgt σ 2 G ]. G m G if = m if m (5.15) Using this notation, we can reformuate Probem (5.12) as the foowing inear programming probem: minimize P ω1 T P subject to HP η; P 0, (5.16) with the corresponding dua probem maximize λ (LP) 0 subject to η T λ (LP) H T λ (LP) ω1, (5.17) necessary to compute the Lagrange mutipiers in Eq. (5.10) for the rate update. Constraints in Probem (5.17) can be rewritten expicity as foows: λ (LP) ω k G k γ tgt λ (LP) k k G kk ω 1,. (5.18) Moreover, by defining µ = λ(lp) ω γ tgt σ 2 G Eq. (5.18) can be interpreted as an SINR requirement, i.e., γ cc (µ) = µ G σ 2 σ 2 + G k µ k k σ k Therefore, Probem (5.17) can be reformuated as: = λ(lp) ω η, (5.19) γ tgt,. (5.20) maximize µ ω1 T µ subject to γ cc γ tgt, ; µ 0. (5.21) Simiary to Eq. (5.13), the soution µ to (5.21) can be computed according to the foowing distributed PC scheme: µ (t+1) = γtgt γ cc µ(t) µ (t),. (5.22)

69 5.2. Power contro based on utiity maximization 61 Eq. (5.22) can be interpreted as a reverse ink PC probem that is executed in the contro channe between the receiver and the transmitter of ink-. Specificay, the receiver- adapts its transmitting power µ according to Eq. (5.22), whie the transmitter- measures the experienced SINR γ cc in the corresponding contro channe. Once the iterative procedure (5.22) converges to the optimum µ, the optima dua variabes λ (LP) can be retrieved from Eq. (5.19) as λ (LP) = ωµ η 1,. (5.23) The origina noninear PC probem (Probem-II) and the corresponding LP formuation (5.16) are equivaent in the sense that there exists the foowing specific reation between their optima soutions (see [90, Theorem 5.1]) ( P, λ ) and (P, λ (LP) ): P = e P,, λ = og(1 + γtgt ) 1+γtgt P γ tgt og(2)λ (LP),. (5.24) Hence, once both P and µ are achieved by ink- by means of Eq. (5.23) and (5.24), λ can be computed as λ = og(1 + γ tgt ) 1 + γtgt γ tgt P og(2)ωµ G σ 2 γ tgt Eq. (5.25) is then used to update the user rates in Eq. (5.10).,. (5.25) Summary and impementation guideines The previous section deveoped a dua oop iterative soution approach to the convex optimization probem in (5.5). The basic idea has been to decompose the probem into separate subprobems: one in s (Probem-I) and one in P (Probem-II). The soution to (Probem-I) is represented by the outer-oop iterations, it is based on gradient iterations to obtain the SINR targets. The soution to (Probem-II) represents the inner-oop iterations and it is based on a distributed PC agorithm. Specificay, the soution of (Probem-I) at step (k), i.e., γ tgt (Probem-II) that is executed unti convergence to µ ), serves as input to and P. In turn, (Probem-II) outputs λ, that is used by a new instance of (Probem-I) at step (k + 1). The machinery of the distributed utiity maximization agorithm is shown in Fig. 5.2, whie Fig.5.3 shows the impementation of the inner- and outer-oop mechanism in the network, carifying which information must be exchanged between the transmitter and receiver of each pair and which computations must be performed by both nodes. ( s (k)

70 62 Power contro schemes for D2D communication Output : λ in Eq. (5.25) (k=2) (k=3) Probem-I (k=0) (k=1) Probem-II Update the rate according to Eq. (5.10) Update the SINR target according to Eq. (5.11) (k) tgt Output : γ ( ~ s (k) ) Compute iterativey Eq. (5.13) unti convergence to P Compute iterativey Eq. (5.22) unti convergence to µ (t) Figure 5.2: Machinery of the distributed utiity maximization agorithm. The agorithm is executed by any transmitter-receiver pair in the network, i.e., both D2D and ceuar users. At convergence, the outer-oop provides the optima SINR target (i.e., transmit rate), whie the inner-oop provides the optima associated transmit power eve. In a rea-word impementation, Eq. (5.10) is computed by any transmitter and serves as an input (through Eq. (5.11)) to the inner-oop PC: Eq. (5.13) and (5.22). In turn, the inner-oop PC dictates the rate update at the next iteration through Eq. (5.25). µ m P m Tx-m BS Rx- µ Tx- P Figure 5.3: An exampe of a D2D pair sharing a RB with a ceuar user. The D2D Tx node has a target SINR of γ tgt set by the outer oop and runs the inner oop to set the necessary transmit power P. The D2D Rx node transmits on the backward channe aso targeting an SINR target of γ tgt and runs its inner oop to find the correct transmit power eve of µ. µ is then used to find the Lagrange mutipier λ that is used to update the SINR targets. At the end of the outer oop convergence, the optima SINR targets and associated transmit power eves are reached at a transmitters. 5.3 Mode seection and RB aocation: the MinInterf agorithm Power contro agorithms described in previous sections assume that the mode seection and RB aocation have aready been executed. In order to evauate the performance of the PC schemes, we consider a centraized procedure that assigns the communication mode and the RBs to the transmitter-receiver pairs in the system. This simpe agorithm, which we ca MinInterf, expoits the proximity

71 5.3. Mode seection and RB aocation: the MinInterf agorithm 63 between D2D-candidates for the mode seection, and performs RB aocation that aims at reducing the intra-ce interference by minimizing the sum of the harmfu path gains. The MinInterf procedure is singe ce based, meaning that interference coordination between neighbouring ces is not considered. Furthermore, it assumes the fu knowedge of the path oss measurements between a transmitters and receivers within the ce. The agorithm invoves two steps. First, orthogona resources are aocated to ceuar users empoying egacy RB aocation schemes 4. Second, for each D2Dcandidate pair- in the ce, MinInterf considers two possibe cases: D2D transmission with dedicated resource. If there is an orthogona resources eft, that we indicate with RB-f, it can be assigned to the D2D-candidate so that the D2D transmission does not affect others within the same ce. In this case, mode seection is simpy performed as foows: if the direct ink gain is greater than the gain towards the BS, then the D2D mode is preferred. D2D transmission with resource reuse. When there are no unused RBs in the ce, the D2D-candidate pair- must communicate in D2D mode and reuse RBs. To reduce this intra-ce interference, for each RB-f, MinInterf considers the sum S(f) = i L f G f i + Gf i [db] (5.26) as a measure of the potentia interference that assigning the D2D pair- to RB-f causes. Here G f i represents the path gain between the D2D transmitter- and the receiver of ink(s) aready aocated to RB-f, which may be the BS and/or other D2D receiver(s). It takes into account the interference that the D2D pair produces transmitting on RB-j. G f i, on the other hand, is the path gain between the transmitter(s) aready aocated to RB-f (which can be both a ceuar-ue and/or other D2D transmitters) and the receiver- of the new D2D pair. Therefore, it is reated to the interference that the D2D receiver wi experience due to the reuse. Once expression (5.26) is computed for each avaiabe RB-f, D2D pair- is assigned to that RB corresponding to the minimum vaue. It is worth noting that the performance of the mode seection and RB aocation achieved by MinInterf are not optima. Nevertheess, numerica resuts in Section show that its interpay with the iterative PC procedure, which takes into account aso the inter-ce interference, aows to attain good performance in terms of spectrum and energy efficiency. 4 Since we are disregarding frequency seective fading, to each user it can randomy pick and assigns an avaiabe RB.

72 64 Power contro schemes for D2D communication 5.4 Numerica resuts Simuation set-up and parameters setting We consider the UL transmission of a 7-ce system, in which the number of UL RBs is 4 per ce, and a transmitter-receiver pairs in the system are assigned one RB. In each ce, we drop 2 mobie users transmitting to their respective serving BS, and 4 D2D-candidate pairs, for which a mode seection poicy assigns a communication mode between ceuar mode, D2D mode with dedicated resource and D2D mode with resource reuse. Since 4 D2D-candidate pairs are dropped in addition to the 2 ceuar users, 2 of them are forced to use D2D mode and reuse the resource with either other D2D mode users or with ceuar users. This is because we assume 4 RBs per ce accommodating 6 transmitters, and we assume that ceuar users and D2D-candidates assigned to ceuar mode must remain orthogona within a ce. To generate the foowing resuts we assumed the heuristic mode seection and RB aocation agorithm described in Section 5.3. We perform Monte Caro experiments to buid some statistics over the used transmit power and achieved SINR by ceuar users and D2D pairs, when empoying the LTE-based PC agorithms or the distributed optimization-based PC scheme. For the LTE-based scheme, we assume that ceuar users operate with OFPC with ρ = 0.8, whie D2D inks use one out of the 4 schemes described in Section For the utiity maximization-based scheme, a transmitters execute the distributed outer and inner oops-based PC, as described in Section 5.2. We consider two different vaues of ω: ω = 0.1 to consider the power consumption ess important than the achieved sum rate, and ω = 10 to simuate ow sum power operation of the system. The main simuation parameters are given in Tabe 5.1. P 0 is set according to Eq. (5.2) to correspond to γ tgt = 12.5 db. Tabe 5.1: Simuation parameters Parameter Vaue Parameter Vaue Channe Mode Micro Urban [40] Ce Radius 500 m System Bandwidth 10 MHz P IN (/MHz) -116 dbm P 0-78 dbm ρ 0.8 P max 24 dbm ω 0.1 and 10 Number of RB per user 1 Fixed SINR tgt for D2D 15 db Number of outer-oop iterations 200 Fixed Tx Power for D2D -10 dbm Number of inner-oop iterations 10 Distance between ceuar user and the BS 300 ± 50 m Number of transmitters per ce 6 Distance between D2D pairs 50 ± 25 m Numerica resuts We compare the utiity-based agorithm (in the figures indicated as Utiity max. PC) appied to a users in the system, to the four different LTE PC schemes presented

73 5.4. Numerica resuts 65 in subsection Fig. 5.4(a) shows the distribution of the transmit power eves of the ceuar users for the OFPC case and for the utiity maximizing case. When ω = 10, the utiity-based approach resuts in much ower power consumption. In contrast, when ω = 0.1, the user power consumption is much ess penaized and the overa power consumption increases. These resuts show the propriety of the utiity-based scheme to tune through a singe parameter (ω) the spectra efficiency - energy efficiency tradeoff by setting the desired system operationa point. Whie the ceuar users power consumption is ony affected by the PC agorithm appied to the ceuar users (i.e., Utiity Max PC or LTE OFPC), the achieved SINR depends aso on the PC scheme used by D2D pairs because of the resource reuse. However, Fig. 5.4(b) indicates that the different PC agorithms for D2D communications have simiar impact on the ceuar ayer. This can be expained by the short distance and consequent ow power eve used by direct inks. Having a sma impact of the D2D ayer on the ceuar ayer is a key requirement in any system that aows icensed spectrum resources to be used by D2D traffic. CDF Utiity max PC ω=0.1 Utiity max PC ω=10 LTE OFPC CDF Utiity max PC ω=0.1 Utiity max PC ω=10 Fixed Tx power Fixed SNR target Open oop Cosed oop POWER UE [dbm] (a) Transmit power distribution SINR UE [db] (b) SINR distribution Figure 5.4: Performance anaysis of ceuar users. Fig. 5.5(a) and Fig. 5.5(b) show the distribution of the transmit power and SINR eves of the D2D pairs, respectivey. Simiary to the ceuar users, the D2D transmit power eves (and achieved SINR) can be tuned by choosing different vaues of ω. However, for the D2D inks, different LTE based schemes perform quite differenty both in terms of power consumption and achieved SINR. In Fig. 5.5(a), for the very ow power region (< 0 dbm), the LTE-based schemes use ess power than the utiity-based schemes. However, for higher power D2D transmitters (> 5 dbm), the optimization-based scheme with ω = 0.1 uses ess power than any of the LTE-based methods (with the exception of the fixed transmit power case). From a practica point of view, the important region is the one above 5 dbm, since users beow this power eve do not utiize their avaiabe power resources to improve their SINR eves. For users above 10 dbm of transmit power eve, the utiity-based scheme

74 66 Power contro schemes for D2D communication with ω = 0.1 and the LTE OFPC schemes perform simiary, whie the Fixed SINR target and the Cosed Loop scheme set higher transmit power eves. Notice that the Fixed Tx Power setting appies to D2D users that actuay use the D2D mode, whie D2D-candidate users using ceuar mode use the LTE OFPC scheme, which expains the distribution curve for this PC scheme in Fig. 5.5(a). In terms of SINR, the utiity-based PC schemes outperform the LTE-based PC. The SINR gain is especiay significant for the high SINR users, where ony the fixed transmit power scheme yieds higher SINR vaues than the utiity-based approach ( with ω = 0.1). However, the fixed transmit power method is ceary unacceptabe from a fairness perspective. CDF Utiity max PC ω=0.1 Utiity max PC ω=10 Fixed Tx power Fixed SNR target Open oop Cosed oop CDF Utiity max PC ω=0.1 Utiity max PC ω=10 Fixed Tx power Fixed SNR target Open oop Cosed oop POWER D2D [dbm] (a) Transmit power distribution SINR D2D [db] (b) SINR distribution Figure 5.5: Performance anaysis of D2D users. Finay, to gain some insights into the reation between the used power eves and the resuting SINR vaues for the PC approaches under study, we consider the scatter pots of Fig Fig. 5.6(a) represents each dropped user in the Monte Caro experiments with a dot indicating the transmit power and resuting SINR vaue for that particuar user. Because of the resource reuse between ceuar and D2D users, the SINR of the ceuar users depend on the PC scheme of the D2D users. Here we can ceary see that the genera trend is that the utiity-based scheme with ω = 10 uses ower power eves for simiar user SINR performance. In other words, simiar quaity of service eve can be maintained by ower user power eves when reying on the dynamic SINR target adjusting agorithm. Fig. 5.6(b) shows the reation between the D2D transmit power eves and the D2D SINR vaues. We observe that the utiity maximizing scheme tends to aocate higher power eves to ower SINR users, so in that sense it tries to compensate for the performance of the poor users. This is the opposite of the (extreme unfair) fixed Tx power approach (horizonta ine) but not as fair as the LTE OFPC scheme in the sense of SINR equaization (cose to being horizonta in the power-sinr pane).

75 5.5. Summary 67 SINR UE [db] Utiity Max PC ω=0.1 Utiity Max PC ω=10 Fixed Tx power Fixed SNR target Open oop Cosed oop POWER UE [dbm] (a) Performance of the ceuar users SINR D2D [db] Utiity max PC ω=0.1 Utiity max PC ω=10 Fixed Tx Power Fixed SNR target Open oop Cosed oop POWER D2D [dbm] (b) Performance of the D2D users Figure 5.6: (a) Scatter pot of the used transmit power of the ceuar users and the resuting SINR vaues when using different schemes for the ceuar users and the D2D pairs. The cear tendency is that the utiity-based scheme gives simiar SINR vaues but typicay with much ess transmit power. (b) Scatter pot of the used transmit power of the D2D users and the resuting SINR vaues when using different schemes for the ceuar users and the D2D pairs. 5.5 Summary This chapter presented a distributed PC agorithm that maximizes a utiity function that takes into account the inherent tradeoff between spectrum and energy efficiency. We used this agorithm as a benchmarking too with respect to practica PC schemes based on the LTE UL PC tookit. For the mode seection and resource aocation, we proposed a heuristic agorithm (MinInterf) that attempts to reduce the intra-ce interference introduced by D2D communications, assuming fu path oss knowedge. Numerica resuts indicate that the performance of LTE PC gets cose to the utiity-based scheme (with proper seection of ω), both in terms of used transmit power eves and the resuting SINR vaues. However, there is a significant gain when empoying the optimization-based approach in terms of the SINR obtained by the D2D users. On the other hand, the LTE OFPC scheme, depending on the ω parameter of the utiity-based method, can produce higher SINR vaues for the ceuar users. These resuts suggest that the fexibe LTE PC scheme is we prepared for network-assisted D2D communications, especiay for the ceuar users perspective. For the D2D pairs, instead, the utiity-based scheme shows the possibiity of performance improvement. Moreover, its distributed design makes it appeaing for a practica impementation, where ony the design parameters are controed by the ceuar network.

76

77 Chapter 6 Subcarrier aocation in muti-ce D2D network In this chapter we assume that mode seection and transmit power aocation have aready been performed, and we focus on the subcarrier (aso referred to as RBs) aocation probem. We consider a muti-ce network, where D2D communications share the UL resources with traditiona ceuar users. In this hybrid network, resource management becomes crucia because of the combined inter- and intra-ce interference caused by D2D connections and muti-ce resource reuse. Our objective is to maximize the tota rate of the system by taking advantage of frequency diversity among channes and by propery managing the interference eve on each RB. Given the nonconvex and combinatoria formuation of the probem, we everage on the theory of potentia games to guarantee convergence to a Nash equiibrium via best and better response dynamics. Potentia games have been aready shown to be a vaid approach for resource aocation probems in muti-ce wireess systems, when maximizing user SINRs and energy efficiency [93], or when minimizing interference [94]. 6.1 System mode and assumptions We consider UL transmissions in an LTE-ike muti-ce system, where underay in-band D2D communication is enabed with the assistance of the network. We assume that communication modes and transmit powers are assigned on a sower time-scae than RBs (as in the LTE UL power contro [12]). Therefore, we consider the transmit power matrix P to be constant and known, with entries P f representing the power used by transmitter- on the assigned RB-f. The set of D2D receivers, denoted by D, can be seen as a set of virtua BSs, each serving a singe user. We introduce the notation K = B D for the set of receivers in the system. For each receiver-k K, we et C k be the set of users served by k. Thus, C k is a singeton if k D, whie it may contain many users if k B. For each k K, X k represents the RB assignment to a users that transmit to receiver-k. If 69

78 70 Subcarrier aocation in muti-ce D2D network k B, X k is the RB aocation for a UL transmissions to the BS-k. If k D, X k is the RB aocation for the transmission of D2D pair-k. We abe each eement of X k with x f, which is 1 if transmitter- C k is assigned to RB-f, 0 otherwise. Moreover, X k represents the set of aocation decisions taken by a receivers except receiver-k, and X = (X k, X k ), k K is the overa resource aocation in the system. The normaized rate (with respect to the bandwidth) in bps/hz that user- C k can achieve on RB-f is R f (X k) = og σ 2 + I f k (X k), (6.1) P f Gf k where I f k (X k) = q K/{k} m Cq P f mg f mk xf m is the interference perceived at receiverk on RB-f, which depends on the resource aocation in a ces and D2D pairs, except the one which receiver-k beongs to. Finay, we denote by F the number of RBs to be assigned to transmitter-. We assume that Ck F F, k K, so that the number of avaiabe RBs is sufficient to accommodate a communication requests. This condition can be fufied by an admission contro agorithm that decides whether to accept or reject a connection request, depending on the number of avaiabe resources. 6.2 Probem statement We consider the probem of aocating RBs to users, aiming at maximizing the aggregate system rate, whie assigning a given number of RBs to each ink and ensuring orthogonaity among ceuar transmissions within the same ce. This probem can be formay stated as the foowing integer programming probem maximize {x f } subject to f F k K R f (X k)x f C k (6.2a) x f 1, f F, k K, (6.2b) C k x f n = F n, C k, k K, (6.2c) f F x f {0, 1}, f F, C k, k K, (6.2d) where (6.2b) are the orthogonaity constraints, which are active ony for k B because C k = 1 for k D; whie (6.2c) ensure that each ink is assigned the required number of RBs. 6.3 Preiminaries on potentia games In this section we briefy introduce the theory of potentia games [95], which we wi use to design a soution for the muti-ce D2D RB aocation probem formuated in (6.2).

79 6.3. Preiminaries on potentia games 71 A strategic game can be described by a tripet G = [K, {X k }, {U k }], where K is the set of payers, X k is the set of a possibe strategies for the kth payer, and each strategy is represented by X k. The function U k (X k, X k ) denotes the payoff for payer-k. It is a scaar function that depends on the strategy taken by a payers of the game. Any change in strategy from one payer affects a the other payers. Therefore, there is a dynamic process where payers iterativey update their own strategies as a reaction to the changes in the strategy of other payers. Let us reca some usefu definitions and resuts: Definition (Best- and better-response dynamics). The best-response dynamic occurs when each payer updates its strategy by seecting the one that produces the highest utiity, assuming that the other payers do not change their current strategies. That is, given a strategy profie X = ( X k, X k ), payer-k chooses its new strategy X k X k such that X k { X k X k U k ( X k, X k ) U k (X k, X k ), X k X k }. (6.3) In the ess demanding better-response dynamics, instead, the strategy update of payer-k is defined by repacing condition (6.3) with X k { X k X k U k ( X k, X k ) U k ( X k, X k )}. (6.4) which means that the new strategy is ony assured to be better than the previous one, but it might not be the best among a possibe strategies. Definition (Exact potentia game). A strategic game G = [K, {X k }, {U k }] is an exact potentia game if there exists a function Φ X 1 X 2 X K R such that for any k K U k (X k, X k ) U k (X k, X k ) = Φ(X k, X k ) Φ(X k, X k ), (6.5) where X k and X k are two different strategies of payer-k. Any such function Φ is caed the exact potentia function of G. Definition (Nash equiibrium (NE)). Given a strategic game G = [K, {X k }, {U k }], the K-tupe (X 1, X 2,, X K ) X 1 X 2 X K is a NE if U k (X k, X k) U k (X k, X k), X k X k, k = 1,, K. Put in words: at the NE no payer has an incentive to uniateray change its strategy. Potentia games possess important properties that reate the optimizers (oca optima) of the potentia function to pure-strategy NE points of the game. Lemma ([96], Theorem 15). If Φ is a potentia function of the game G and X argmax X Φ(X) is a maximizer of the potentia function, then X is a NE of the game.

80 72 Subcarrier aocation in muti-ce D2D network Another attractive property of potentia games, whose potentia function is bounded from above, is that the iterative processes based on best and better response dynamics converge to the equiibrium set, as estabished by the foowing resut: Lemma ([96], Theorem 19). Let G be a potentia game. Then both the best response dynamic and the better response dynamic wi converge a.s. 1 to a NE in a finite number of steps. 6.4 Game formuation for the muti-ce D2D RA In this section we are interested in appying the resuts from Section 6.3 to the resource aocation probem formuated in (6.2) Soution based on best response dynamic We propose a strategic game between a receivers in the set K. The game is described by G = [K, {X k }, {U k }], where X k is the set of a possibe aocation decisions for a transmissions to receiver-k K, and U k is the utiity function of the kth payer. The atter is given by the sum of a the achievabe bit rates in the system, that is U k (X k, X k ) = f F k K R f (X k)x f. (6.6) C k Hence, U k is a scaar function corresponding to the objective in Probem (6.2). Note that, athough each payer-k aims at maximizing U k with respect to its own strategy ony, a payers utiities are chosen to be the same. This means that a payers aim at maximizing the same utiity, thus we can define Φ(X) = U k (X k, X k ), k K. (6.7) Proposition The game G = [K, {X k }, {U k }] is an exact potentia game with potentia function Φ(X) defined in (6.7). Proof. G is an identica interest game, that is, a game in which the payers utiity functions are chosen to be the same [97]. Moreover, since the potentia function is defined as equa to the payers utiity, the change in any payer s utiity equas the change in the goba utiity. This means that condition (6.5) is verified. Since G is an exact potentia game, the best response dynamic wi converge to a NE of the game (Lemma 6.3.5). Thus, given any initia resource aocation for a transmissions in the system, the payers take turn to pay the game in a sequentia 1 The amost surey (a.s.) convergence comes from the possibiity to choose the same node to pay the game over and over again. This might cause the agorithm never to converge to a NE. However, in our case this wi never happen because the payers (receivers in the network) are forced to pay in turn.

81 6.4. Game formuation for the muti-ce D2D RA 73 manner, choosing their best response strategy. This iterative process terminates when no payer is wiing to change its strategy, that is, when a NE is achieved. We now turn our attention to deriving the best response of payer-k. Given X k, payer-k updates its strategy by soving the foowing optimization probem maximize X k U k (X k, X k ) subject to x f 1, f F, C k x f = F, C k, f F x f {0, 1}, C k, f F. (6.8) The objective function in (6.8) is given in (6.6) and it can be expressed expicity as function of X k as U k (X k, X k ) = og 2 f F C k 1 + P f Gf k σ 2 + I f k (X k) xf + og PmG f f mq m C q σ 2 + Iq f (X {q,k} ) + P f Gf q xf C k q K, q k x f m, (6.9) where Iq f (X {q,k} ) = c K/{q,k} i Cc P f i Gf iq xf i is the interference eve at the qth receiver. It does not incude the effect from the use of RB-f in ce-k, which is given by Ck P f Gf q xf, instead. Probem (6.8) beongs to the famiy of noninear combinatoria optimization probems. Hence, achieving its optima soution quicky becomes prohibitive when the number of users and/or RBs increases. Another drawback is reated to the information that payers need to exchange. In fact, to compute U k (X k, X k ) in (6.9), payer-k needs to retrieve from every other payer at most 2F scaar vaues, which represent the usefu power and the interference eve measured on the assigned RB. Then, payer-k must be abe to remove the contribution from its ce to the goba interference at the other receivers (this means that the cross-ink gains between transmitters in its own ce and other receivers are known), thus obtaining Iq f (X {q,k} ) q K, q k, f F Soution based on better response dynamic The noninear nature of the Probem (6.8), together with the amount of information required to be exchanged between the payers, encourage us to redefine the utiity function of the payers.

82 74 Subcarrier aocation in muti-ce D2D network We consider a reference overa aocation strategy X. Then, the new utiity function for payer-k is defined as foows Ũ k (X k, X) = [R f ( X k )x f f F C k where + (Rm( f X q ) x f m + Rf m( X q ) m C q Iq f ( X q ) (P f Gf q xf P f Gf q xf ) )], q K, q k Rm( f X f q ) Iq f ( X q ) = PmG f mq (n 2)(PmG f f mq + Iq f ( X q ) + σ 2 )(Iq f ( X q ) + σ 2 ) (6.10) (6.11) represents the rate sensitivity to the interference variations, which can be computed at receiver-q. Ũk(X k, X) represents the first-order Tayor approximation of the users rate around the interference eve given by the reference aocation X. Since the rate is a convex function of the interference, Ũk(X k, X) is a ower bound of U k (X k, X k ). Note that this bound represents a tight approximation of the origina utiity function, under the (reasonabe) assumption that the cumuative interference experienced at each receiver is much higher than the potentia interference contribution of a singe user. We can further simpify (6.10) by subtracting constant terms that do not depend on the aocation decision of payer-k, obtaining Ũ k(x k, X) = By defining f F C k R f ( X k ) + ( Rf m( X q ) m C q Iq f ( X q ) ) (P f Gf q ) x f. (6.12) q K, q k Ẽ f ( X) = R f ( X k ) + ( Rf m( X q ) m C q Iq f ( X q ) ) (P f Gf q ), q K, q k we reformuate Probem (6.8) as foows. Given the current strategy profie X, payer-k updates its strategy by soving maximize X k subject to f F C k Ẽ f ( X)x f x f 1, f F, C k F x f = F, C k, f=1 x f {0, 1}, f F, C k, k B. (6.13)

83 6.5. Impementation guideines 75 which is now an integer inear formuation, and thus it is easier to sove than Probem (6.8) [98]. It can be seen that the main difference with (6.8) is that here we consider a given benefit for each user-resource assignment, thus removing the optimization variabes from the argument of the ogarithm function as in (6.9). Moreover, differenty from (6.8), here the objective function depends on at most F scaar vaues, to be retrieved from each other payer of the game (the rate sensitivity in (6.11) for a assigned RBs). We now show that, athough we have changed the utiity function of the game, we can sti guarantee convergence to a NE, combining Lemma with the foowing resut: Proposition Given any aocation profie X, soution X k to Probem (6.13) is such that U k (X k, X k ) U k ( X), that is X k is a better response of payer-k in game G = [K, {X k }, {Ũk}]. Proof. Since X k = argmax X k Ũ k (X k, X) = argmax Xk Ũ k (X k, X), then Ũk(X k, X) Ũ k (X k, X), X k X k. Moreover, Ũ k (X k, X) U k (X k, X k ), X k X k because of the inear approximation. By combining the two inequaities above we have U k (X k, X k ) Ũk(X k, X) Ũk( X k, X) = U k ( X k, X k ). 6.5 Impementation guideines The iterative better response dynamic requires the payers to foow a predetermined order. In this work, we assume that the BSs pay in a sequentia order, agreed upon before the gamepay. D2D receivers ocated within a given ce pay right after their serving BS in an order decided by the BS itsef, and sent to the users as a contro command. A payers start with a random and feasibe RB aocation profie. When payer-k pays, before soving Probem (6.13), it retrieves from each other payer-q in the game the vector Rmq( f X q ) q = Iq f ( X q ), f F, m C q. Its eements represent the rate sensitivity on each RB, estimated after the atest strategy profie s update. Differenty from ad-hoc networks, network-assisted D2D communications are coordinated by the BS. Therefore, we assume that each BS-b B coects the information reated to the rate sensitivity of the D2D pairs under its coverage, and sends it, together with its vector b, to the next payer (BS). In an LTE network, this communication of the rate sensitivity between the BSs can be naturay mapped onto the X2-Interface [12]; see Fig. 6.1 for iustration. When a D2D transmitter has to pay, then its serving BS is in charge of forwarding (on a contro channe) the necessary information coected from the other BSs. It is worth mentioning that the impementation of the better response dynamic requires that each receiver knows the channe gains between its intended transmitters

84 76 Subcarrier aocation in muti-ce D2D network Payer-6 [ 1, 2, 3 ] Payer-1 [ 4, 5 ] 3 Payer-2 2 Payer-3 Payer-4 5 Payer-5 Figure 6.1: Exampe of the information required to be exchanged between the payers in the better response dynamic, when payer-5 updates its strategy. and the neighbouring receivers. Channe gains between mobie users and neighbouring BSs are aready estimated in ceuar networks for handover purposes. However, the presence of D2D communications requires to modify the existing protocos in order to introduce the measurements of the channe gains aso between mobie users and neighbouring D2D receivers. 6.6 Numerica resuts To study the behavior of the proposed resource aocation agorithm based on better response dynamics, we simuate networks consisting of either 7 or 3 hexagona ces with omnidirectiona BSs and randomy paced mobie users. The number of transmissions (UL transmissions and D2D communications) is assumed to be the same in a ces. A transmitters use the same power eve and the ceuar users are assigned to a resource bocks, i.e., Ck F = F, k B. The system parameters used in the simuations are summarized in Tabe 6.1. Fig. 6.2 iustrates the convergence of the better response dynamic for a 7-ce network for different number of users. Each curve shows how the tota bit rate evoves in a singe simuation run. In this figure, one iteration corresponds to the strategy update of one payer. The simuations are initiaized from a random feasibe aocation. As expected, the potentia function increases monotonicay