FULL duplex (FD) operation in a single wireless channel. User Selection and Power Allocation in Full Duplex Multi-Cell Networks

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1 1 User Selection an Power Allocation in Full Duplex Multi-Cell Networks Sanay Goyal, Stuent Memer, IEEE, Pei Liu, Memer, IEEE, an Shivenra S. Panwar, Fellow, IEEE Astract Full uplex FD) communications has the potential to oule the capacity of a half uplex HD) system at the link level. However, in a cellular network, FD operation is not a straightforwar extension of half uplex operations. The increase interference ue to a large numer of simultaneous transmissions in FD operation an realtime traffic conitions limits the capacity improvement. Realizing the potential of FD requires careful coorination of resource allocation among the cells as well as within the cell. In this paper, we propose a istriute resource allocation, i.e., oint user selection an power allocation for a FD multi-cell system, assuming FD ase stations BSs) an HD user equipment UEs). Due to the complexity of fining the gloally optimum solution, a su-optimal solution for UE selection, an a novel geometric programming ase solution for power allocation, are propose. The propose istriute approach converges quickly an performs almost as well as a centralize solution, ut with much lower signaling overhea. It provies a hyri scheuling policy which allows FD operations whenever it is avantageous, ut otherwise efaults to HD operation. We focus on small cell systems ecause they are more suitale for FD operation, given practical self-interference cancellation limits. With practical self-interference cancellation, it is shown that the propose hyri FD system achieves nearly two times throughput improvement for an inoor multi-cell scenario, an aout 65% improvement for an outoor multi-cell scenario compare to the HD system. Inex Terms Full uplex raio, LTE, small cell, scheuling, power allocation. I. INTRODUCTION FULL uplex FD) operation in a single wireless channel has the potential to oule the spectral efficiency of a wireless point-to-point link y transmitting in oth irections at the same time. Motivate y the rapi growth in wireless ata traffic, along with concerns aout a spectrum shortage [1] [3], cellular network operators an system venors have ecome more intereste in FD operations. In legacy systems, the large ifference etween transmitte Tx) an receive Rx) signal powers ue to path loss an faing, together with imperfect Tx/Rx isolation, has riven the vast maority of systems to use either frequency ivision uplexing FDD) or time ivision uplexing TDD). FDD separates the Tx an Rx signals with filters while TDD Copyright c) 2015 IEEE. Personal use of this material is permitte. However, permission to use this material for any other purposes must e otaine from the IEEE y sening a request to pus-permissions@ieee.org. This material is ase upon work supporte y the National Science Founation uner Grant No , as well as generous support from the NYSTAR Center for Avance Technology in Telecommunications CATT), an InterDigital Communications. S. Goyal sanay.goyal@nyu.eu), P. Liu peiliu@nyu.eu), S. S. Panwar panwar@nyu.eu), are with the ECE Department, NYU Tanon School of Engineering, New York University, Brooklyn, NY. achieves this with Tx/Rx switching. Recent avances in antenna esigns an active cancellation technologies [4] [10] provie a significant step towars uiling a practical FD transceiver an meeting the proecte 2X gain in capacity [11], [12] without requiring new spectrum or setting up new cells. A comination of antenna, analog an igital cancellation circuits can remove most of the crosstalk, or self-interference, etween the Tx/Rx signal path, an allows emoulation of the receive signal while transmitting to someone else. This was emonstrate using multiple antennas positione for optimum cancellation [4], [5], an later for single antenna systems [6], [7], where as much as 110 B cancellation is reporte over an 80 MHz anwith. Cancellation ranging from 70 to 100 B with a meian of 85 B using multiple antennas has een reporte [8]. An antenna fee network, for which a prototype provie 40 to 45 B Tx/Rx isolation efore analog an igital cancellation, was escrie in [6]. However, at the network level, FD operations in a cellular network is not ust a straightforwar extension of half uplex HD) operations implemente y replacing the HD raios with a FD raio. As suggeste in our preliminary research for LTE systems [13], [14] an y others [15] [18], intra/intercell interference cause y using the same frequency in oth uplink an ownlink irections is significant, an is a maor limiting factor to the system throughput. This is ecoming a key prolem to resolve as new cellular networks ecome more heterogeneous, an network entities with ifferent capailities are loosely connecte with each other. Aitionally, realistic traffic complicates scheuling ecisions since the scheule user equipment UE) might only have active traffic in one irection at a given instant. In such a scenario, it is avantageous to scheule a secon UE in the opposite irection. In this paper, we assume the BSs are equippe with FD raios, where the aitional cost an power is most likely to e acceptale; while the UE is limite to HD operation. During FD operation in a cell, the BS scheules an uplink UE an a ownlink UE in the same time slot on the same channel. The impact on over-the-air interference ue to FD operation is illustrate in Figure 1. Consier the two-cell network in Figure 1, in which UE1 an UE3 are ownlink UEs in cell 1 an cell 2, respectively, an UE2 an UE4 are uplink UEs in cell 1 an cell 2, respectively. First, to illustrate the HD scenario, we assume synchronize cells, which means that in a given time interval all cells scheule transmissions in the same irection. In this case, orthogonal channel access in time prevents interference etween UEs an etween ase stations BSs), ut each UE accesses the channel only half the time. From Figure 1a) one can see that in HD operation, UE1

2 2 Fig. 1: Half uplex an full uplex multi-cell interference scenarios. receives interference I 1 ) from BS2, which is transmitting to UE3 at the same time. Similarly, BS1 receives interference I 2 ) from the uplink signal of UE4. During FD operation, as shown in Figure 1), the ownlink UE, UE1, not only gets interference I 1 ) from BS2, ut also gets interference I 3 an I 4 ) from the uplink signals of UE2 an UE4. Similarly, the uplink from UE2 to BS1 not only gets interference I 2 ) from UE4, ut also gets interference I 6 ) from the ownlink signal of BS2, as well as Tx-to-Rx self-interference I 5 ). The existence of aitional interference sources raises the question whether there is any net capacity gain from FD operation. The actual gain from FD operation will strongly epen on link geometries, the ensity of UEs, an propagation effects in moile channels. Therefore, FD operation will provie a net throughput gain only if the throughput across two time slots, suect to the aitional interference, is larger than the throughput in one time slot without such interference. In this paper, we focus on the esign of a istriute, interference-aware scheuler an power control algorithm that maximizes the FD gain across multiple cells, while maintaining a level of fairness etween all UEs. In such a system, FD gain can e achieve y simultaneous transmissions in uplink an ownlink irections, where the the extra FD interference woul e treate as noise. The scheuler is a hyri scheuler in the sense that it will exploit FD transmissions at the BS only when it is avantageous to o so. Otherwise, when the interference is too strong, or traffic emans ictate it, it might conuct HD operations in some cells. In the propose istriute approach, neighoring cells coorinate with each other to simultaneously select the UEs an transmit power levels to maximize the system gain. This oint UE selection an power allocation prolem is in general a non-convex, nonlinear, an mixe iscrete optimization prolem. There exists no metho to fin a gloally optimum solution for such a prolem, even for the traitional HD system scenario. We provie a su-optimal metho y separating the UE selection an power allocation proceures, using Geometric Programming GP) for power allocation. The propose istriute approach converges quickly an performs almost as well as a centralize solution which has access to gloal information, i.e., channel state information, power, etc., with much lower signaling overhea. The propose FD system improves the capacity of a ense inoor multi-cell system y nearly two times an an outoor sparse multi-cell system y aout 65%. The new signaling requirements an its overhea in the case of the FD scheuling process are also iscusse. A. Relate Work Extensive avances have een mae in esigning an implementing wireless transceivers with FD capaility [9], [10]. MAC esigns for FD IEEE systems have een presente which shows throughput gains from 1.2x to 2.0x with FD operations please refer to [19] an references therein). However, to the est of our knowlege, little has een one to unerstan the impact of such terminals on a cellular network in terms of system capacity an energy efficiency. Reviewing the literature shows that there has een significant work one on interference coorination in conventional HD systems. Various solutions [20] have een propose from static frequency allocation to ynamic istriute resource allocation to avoi or coorinate the interference among neighoring interfering cells. However, with the new FD interference as escrie in Figure 1, uplink an ownlink channel resources have to e allocate ointly to support a higher numer of simultaneous links with ifferent characteristics. Thus, the existing interference coorination methos for the HD case cannot e applie irectly to the FD case. FD operation in a single cell has een evaluate [14], [21] [26]. Barghi et al. [21] compare the traeoff etween using multiple antennas for spatial multiplexing gain an FD gain y nulling self-interference. A istriute power control metho using ust one hop information to manage UE-to-UE interference in a single FD cell with massive MIMO was propose in [25]. FD operation in a cellular system has also een investigate in the DUPLO proect [27], where a oint uplink-ownlink eamforming technique was esigne for the single small cell environment [26]. Our previous work [14] introuce a single cell hyri scheuler without transmission power optimization. Other techniques for resource allocation in a FD single cell case using matching theory, a cell partitioning metho, an game theory can e foun in [22], [23], an [24], respectively. However all these propose methos for single FD cell cannot e irectly applie to resource allocation in a multi-cell scenario.

3 3 In the case of multi-cell FD operations, centralize UE selection proceures with fixe power allocation have een propose [13], [16], [17]. Moreover, inter-bs interference is assume to e perfectly cancelle an the interference from the neighoring cell UE is ignore in [16], [17], which makes the resource allocation prolem simpler even for the multi-cell case. Uner the same assumption, an analytical expression for the achievale rates assuming Clou Raio Access Network C-RAN) operation for oth HD an FD are erive y Simeone et al. [28]. However, the assumption of ignoring interference from UEs of neighoring cells may not e appropriate in some scenarios. A cell-ege uplink UE of a neighoring cell may generate severe interference for the ownlink transmission. Choi et al. [15] propose a metho to mitigate the inter-bs interference using null forming in the elevation angle at BS antennas an a simple UE selection proceure y assuming fixe transmission powers in oth irections. Using successive convex approximation an GP, Nguyen et al. [18] provies a centralize power allocation metho for the given UEs with FD capaility. Yun et al. [29] provie a intracell oint resource allocation incluing channel allocation, UE selection, an power allocation. Further, they consiere a multi femto-cell network with an unerlying macro cell, for which they provie a coorination algorithm such that the transmit powers of femtocells an their connecte UEs are auste so that ata transmissions of the unerlying macrocell is protecte. However, they i not consier coorination to mitigate the interference among the co-channel femto cells. A high level presentation, without any technical etails, of the centralize solution we use as an upper oun has een given in [30], which was use to evaluate the performance of FD systems in an inoor multi-cell system in terms of energy efficiency. The etails of this centralize metho will e provie in Section V. Stochastic geometry ase analytical moels have also een presente [13] [31] [33] for the FD multi-cell system. The impact of resiual self-interference, ensity of FD BSs, transmit power, etc., on the performance of such FD system in terms of average spectral efficiency an coverage has een evaluate. These stochastic geometry ase analyses o not consier multi-ue iversity gain, which comes through scheuling of the appropriate UEs with power austments to mitigate interference. This is especially crucial in FD systems where, as we have ust note, the interference scenario is worse than traitional HD systems. In this paper we provie a istriute metho of interference coorination etween cells with the appropriate UE selection an power allocation for a FD enale cellular system. The key contriutions of this paper are: A oint uplink an ownlink scheuler is introuce, which maximizes network utility for a FD enale multicell network. The scheuler ointly optimizes UE selection an power allocation among multiple cells in a istriute manner. New signaling require to avoi UE-to-UE interference is iscusse. The signaling overhea is also illustrate. The paper investigates the performance of FD operations for several typical eployments use y cellular operators toay, incluing oth inoor an outoor scenarios. The remaining part of the paper is organize as follows: Section II escries the system moel an prolem formulation. The iscussion on new requirements for channel estimation is iscusse in Section III. The istriute oint UE selection an power allocation metho is given in Section IV. Section V gives the etails of a centralize metho to solve the same prolem. Section VI contains simulation etails an performance results for the propose FD scheuling algorithms. Conclusions are iscusse in Section VII. II. SYSTEM DESCRIPTION AND PROBLEM FORMULATION A. System Moel We examine FD common carrier operation applie to a resource manage LTE TDD small-cell system [34], [35]. Resiual self-interference, in general, lowers the uplink coverage an preclues the use of FD technology in a large cell. For example, consier a cell with a 1 kilometer raius. Accoring to the channel moel given in [36], the path loss at the cell ege is aroun 130 B. It means the uplink signal arriving at the BS is 130 B lower than the ownlink signal transmitte, assuming equal per channel transmission power in the uplink an ownlink irections. The receive signal to interference ratio SIR) will then e at most -20 B with the est self-interference cancellation circuit known to ate, which is capale of achieving 110 B of cancellation [7]. At such an SIR, the spectrum efficiency woul e very low. Thus we elieve FD transmission is more suitale for UEs close to ase stations, which motivates us to consier small-cell systems as more suitale caniates to eploy an FD BS. We consier a network with M cells, where Π will e use to enote the set of inices of all BSs/cells. Each UE is connecte to the nearest BS, an the numer of UEs is much larger than M. We enote y K m the set of UE inices associate with cell m, an efine N m = K m. Each of the BSs an UE evices are equippe with a single antenna. Assume that at timeslot t, t) K an ut) K enote the UEs scheule in cell in ownlink an uplink irections, respectively. In case of HD UEs, t) u t). The asean signal receive y UEs t) an u t) are given y, respectively, y t)t) = h, t) x t) + h i, }{{} t) x i t) i Π\ ata }{{} BS-to-UE interference 1) + h u i t), t) x u i t)t) + n t), i Π }{{} noise } {{ } UE-to-UE interference y u t)t) = h u t), x u t)t) + h u }{{} i t), x u i t)t) i Π\ ata }{{} UE-to-BS interference + 2) h i, x i t) + h, x + n. }{{}}{{} i Π\ }{{} self-interference noise BS-to-BS interference

4 4 In the aove equations, h {} is use to enote the complex channel response etween ifferent noes. For example, h, t) an h u i t), t) enote the channel etween BS an UE t), an the channel etween UE u i t) an UE t), respectively. It inclues path loss, small-scale faing, an shaowing. Further, x {} t) is use to enote the complex ata symol transmitte y ifferent noes. The self-interference channel at BS is enote y h, which inclues the cancellation. We moel the transmitte symols as inepenent ranom variales with zero mean an variance E{ x {} t) 2 } = p {} t) 0. The notation n t) an n enote the aitive noise at UE t) an BS, treate as complex Gaussian ranom variales with variances N t)/2 an N /2, respectively. The signal to interference plus noise SINR) for ownlink UE t) an uplink UE u t) are given y, respectively, SINR, t) = i Π\ p t) G, t) p i t) G i, t) +, p u i t)t) G u i t), t) + N t) SINR u, u t) = i Π\ p u i Π t) t) G u t), p u i t)t) G u i t), +. p i t) G i, + p t)γ + N i Π\ In the aove equations, G m,n = h m,n 2 m, n. The resiual self-interference is moele as Gaussian noise, the power of which equals the ifference etween the transmit power of the BS an the assume amount of self-interference cancellation. In 4), γ enotes the self interference cancellation level at the BS. The corresponing achievale information rate in its/s/hz is given y the following Shannon formulas, 3) 4) R, t)t) = log 21 + SINR, t)), 5) R, u ut)t) = log 21 + SINR u, u t)). 6) B. Prolem Formulation We consier a system in which there is coorination among the cells. The oective of the coorinate cells is to maximize the system throughput while maintaining a level of fairness among the UEs. We consier a proportional fairness ase allocation, which is achieve y maximizing the logarithmic sum of the average rates of all the UEs [37] [38]. In the FD system oth uplink an ownlink transmissions nee to e consiere simultaneously. The oective at timeslot t is efine as Maximize ] [logr,k t)) + logru,k t)) Π suect to: k K 0 p t) p max, 0 p k t) p u max, R,kt).R u,kt) = 0, k K, Π, 7) where R,k t), Ru,k t) are the average achieve ownlink an uplink rates of UE k in cell, enote as UE,k, until timeslot t, respectively. The first two constraints in 7) are for the transmit powers of the BSs an UEs in each cell, in which p max an p u max are the maximum powers that can e use in ownlink an uplink transmission irections, respectively. The thir constraint in 7) captures the HD nature of the UEs, where R,k t) an Ru,k t) are the instantaneous ownlink an uplink rates in timeslot t, respectively, of UE,k as efine in 5) an 6). The average achieve ata rate, for example, in ownlink, R,k t) is upate iteratively ase on the scheuling ecision in timeslot t, that is, R,k t) = { βr,k t 1) + 1 β)r,kt), if t) = UE,k, βr,k t 1), otherwise. 8) where 0 < β < 1 is a constant weighting factor, which is use to calculate the length of the sliing time winow, i.e., 1/1 β), over which the average rate is compute for each frame, with its value generally chosen close to one, e.g., 0.99 [37], [39]. The average achieve uplink rate of UE,k, R,k u t) can e similarly efine. The goal of the coorinate cells is to etermine 1) the set of co-channel UEs scheule at the same time, an 2) the power allocation for the scheule UEs, so that the overall utility efine in 7) can e maximize. Assume that S = {i, : i } K K enotes all the possile cominations of choosing two UEs, i.e., one in ownlink an one in uplink in cell, where K = K { }. is use to inclue the case of no UE selection in a irection. S = S 1 S 2 S M is the selection of all UE s in the network. Further, let Q S = {p, p }, p p max, p p u max, enote all possile comination of power levels in the ownlink an uplink in S, an Q S = [Q S1,, Q S M ]. Assume Ψt) S enotes the set of chosen UEs in oth ownlink an uplink irections in timeslot t, i.e., Ψt) = [{1t), 1 u t)},, {M t), u M t)}], where i t) = i u t) = ) inicates no UE scheule for the ownlink uplink) in cell i. This coul e the result of no ownlink uplink) eman in cell i, in the current time slot t; or, as iscusse in the next section, it coul also e ecause scheuling any ownlink uplink) transmission in cell i, in timeslot t will generate strong interference to the other UEs, lowering the total network utility. So, in each timeslot, each cell will select at most one UE in the ownlink an at most one UE in the uplink irection. Assume that Pt) = [{p 1 t), p u 1 t)t)},, {p M t), p u M t)t)}], where Pt) Q Ψt) contains the power allocation for the selecte UE comination, Ψt), in timeslot t.

5 5 Using 8), the oective function in 7) can e expresse as ] [logr,k t)) + logru,k t)) = Π k K [ { log βr, t)t 1) + 1 β)r, t)t)) Π log { βr, t)t 1))} + log 9) βr, u u t)t 1)+ 1 β)r u, u t)t)) log βr u, u t)t 1))}] + A, where A is inepenent from the ecision mae at timeslot t, an is given y A = ] [logβr,k t 1)) + logβru,k t 1)). Π k K 10) In equation 9), let us enote the first term in the summation as χ, t)t), χ, t)t) =logβr, t)t 1)+ 1 β)r, t)t)) logβr, t)t 1)), 11) which can e further written as, χ, t)t) = log 1 + w, t)t) R, t)t) ), 12) where 1 β) w, t)t) = 13) βr, t)t 1). Similarly, let us write the secon term in 9) as χ u, u ) t)t), χ u, ut)t) = log 1 + w, u t)t) R, u ut)t), 14) where 1 β) w, u t)t) = 15) βr, u u t)t 1). In the aove equations, note that, if t) = 0 u t) = 0), then χ, t)t) = 0 χu, u t)t) = 0). The overall utility of a cell e.g., cell ) is efine as Φ,{ t), ut)} t) = χ, t)t) + χu, u t)t). 16) Then the optimization prolem in 7) can e equivalently expresse as Ψt), Pt) = arg max S,Q S Φ,S t). 17) Π The aove prolem is a non-linear non-convex cominatorial optimization prolem an the optimal solution may not e feasile to compute in practice. Moreover, the aove prolem is a mixe iscrete UE selection) an continuous power allocation) optimization. Although the prolem can e optimally solve via exhaustive search, the complexity of this metho increases exponentially as the numer of cells/ues increases. We will next provie a suoptimal solution of the the aove prolem which ointly etermines the UE selection an power allocation in a istriute manner. III. CHANNEL ESTIMATION IN FULL DUPLEX MULTI-CELL NETWORKS As iscusse in Section I, in a FD multi-cell scenario, channel state information is essential to maximize FD gains. There are three ifferent types of channels to monitor I) BSto-UE or UE-to-BS channels; II) BS-to-BS channels; an III) UE-to-UE channels. Since we assume a TDD system in this paper, the channels etween any two raios in oth irections are reciprocal. Existing 3GPP protocols for HD communications alreay inclue mechanisms to monitor type I channels, in which a terminal UE) nees to estimate the channel with a BS. In 3GPP LTE, cell-specific reference signals are roacast from the BSs with their physical-layer cell ientity. UEs then use the receive reference signals to estimate the channels from the BSs an transmit channel state information CSI) reports to BSs using PUCCH an PUSCH [34] [40]. The same signal can e use at the BS receiver to estimate the channel from its neighoring BSs, i.e., type II channels. The remaining challenge for the FD multi-cell scenario is to estimate UE-to-UE interference, or type III channels, since the inter-ue interference poses a funamental challenge to exploit FD in a cellular scenario. In this paper, we propose to implement neighor iscovery at UEs to fin potential UE interferers in its neighorhoo. In 3GPP LTE, Souning Reference Signals SRS) are use for channel quality estimation at ifferent frequencies in the uplink [34]. This uplink SRS can e use y UEs to estimate the channels with other UEs in its neighorhoo [41]. In LTE, each UE is scheule on the SRS channel regularly in orer for the BS enb) to collect information for uplink channel scheuling. All UEs within a cell are informe aout the suframes that will e use for SRS. The main challenge in neighor iscovery is to istinguish etween ifferent UEs, incluing neighoring cells UEs, uring SRS transmission. This prolem can e solve y allocating ifferent SRS comination sets to neighoring cells as well as ifferent orthogonal cominations to UEs within the cell which are scheule to transmit simultaneously [34]. In aition, this allocation of SRS cominations can e passe to UEs through the ownlink share channel [41]. There are alternate ways to implement neighor iscovery, such as mechanisms propose for D2D communications [42], [43]. In this paper, for our scheuling solution we assume that each UE will e ale to estimate the channels within its neighorhoo, i.e., channels with strong UE interferers, an this information will e transmitte to its BS. The signaling overhea uring the transmission of such new UE-to-UE channel information over the air link in analyze in Section VI. IV. A DISTRIBUTED FULL DUPLEX MULTI-CELL RESOURCE ALLOCATION DFDMR) In this section we provie a istriute metho to solve 17). As iscusse in Section I, FD throughput gain is availale only uner certain propagation conitions, istances among noes in the network, an power levels. This suggests that FD operation shoul e use opportunistically, that is, with

6 6 an intelligent scheuler that scheules UEs with appropriate power levels to achieve FD operation when appropriate, an otherwise efaults to HD operation. In each timeslot, the oint UE selection an power allocation prolem 17) is solve in two steps, 1) Intra-cell UE Selection: for a given feasile power allocation, this step fins the UE or a pair of UEs in each cell with maximum overall utility, an 2) Inter-cell Coorination: for the given UE selection, this step erives the powers to e allocate to the selecte UEs through inter-cell coorination such that overall utility can e maximize. In the next susections, we iscuss oth steps in etail. A. Intra-cell UE Selection In this step, for each timeslot t, each BS selects the UE or a pair of UEs to e scheule. This is a single cell resource allocation prolem, which can e solve in multiple ways [22] [24]. Given the fact that a small cell oes not have many UEs, it is easy to perform resource allocation in a centralize manner at the BS. The BS has knowlege of the channel gains with its all UEs, which is possile through CSI reporting from its UEs [34] [40]. As iscusse in Section III, we further assume that the BS also knows the channel etween all UE pairs an thus the suset of UE pairs with strong mutual interference. The BS will assume no interference etween UE pairs for which no information is receive, presumaly ecause of a weak SRS signal. In this step, each BS Π, for the given feasile power allocation, fins the UEs which provie the maximum utility efine in 16), { t), u t)} = arg max Φ,S t). 18) S Please note that at this stage, there is no inter-cell information availale, so in the aove equation, the instantaneous rate of a UE oes not take any inter-cell interference into account. Thus, for the cell, instea of 3) an 4), the SINRs at ownlink UE i an uplink UE are calculate as SINR,i = p t) G,i p t) G,i + N i, SINR u, = p t) G, p t)γ + N, 19) where G,i enotes the channel gain estimation etween UE an UE i measure y UE i. If UE i oes not hear a strong signal from UE, this means UE i i not measure an sen the channel estimation information for UE to the BS. In that case G,i will e neglecte uring this scheuling ecision. The prolem 18) can e solve simply y the exhaustive search metho. The BS initially assumes the maximum power allocation for each UE in oth irections, an then calculates the aggregate utility for each possile comination of UEs an fins the utility maximizing UE or UEs. Since each cell performs this step inepenently, the computation complexity of this step increases only in a quaratic manner with the numer of UEs, i.e., On 2 ), which shoul not e a prolem given that a small cell typically supports a small numer of UEs. After this step, each cell has a ownlink UE, or an uplink UE, or oth to scheule in timeslot t. Once the UE selection is one, the next step is inter-cell coorination, escrie next, in which the power levels of the selecte UEs are upate such that the aggregate utility of all the UEs, as given in 17), can e maximize. B. Inter-cell Coorination This step is use to take the effect of inter-cell interference into account. In this step, the transmit power levels of all the selecte UEs are upate such that the mutual interference can e mitigate an the overall utility of the system can e maximize. The oective function of this prolem can e written as, Pt) = arg max Q Ψt) Φ,{ t), ut)} t). 20) Π Each of the BSs solves the aove prolem inepenently an erives its optimum powers. The utilities of the other BSs are estimate ase on the information receive from neighoring BSs. The etaile proceure is given elow. This proceure is complete in multiple iterations. It is assume that the information etween the BSs is exchange over the X2 interface [44]. Note that this proceure is applie at each timeslot, ut for the sake of simplifying the notation, we omit the term t in this section. 1) Initialization: Intra-cell UE selection etermines the UEs to e scheule, i.e.,, u in cell Π. At this initial step, each BS Π roacasts a message vector containing the information of weights w,, w, u ), UE IDs i ), iu )), an the channel gains G,, G u, ) with its own BS for the selecte UEs. In aition to this information, the channel gains of the selecte UEs with other BSs are also sent to the corresponing BSs. For example channel gains with BS, i.e., G,, G u,) are sent to the BS. This information is only sent once at the initialization step. Here, we use UE IDs corresponing to the value of SRS comination allocate to a UE. The UE IDs of other cells s UEs will e use at a BS to ientify an match the UE-to- UE channels estimations measure y its own cells s UEs. These IDs can e create locally at each BS y matching UEs to the allocation of SRS cominations. In aition to the aove information, after getting UE IDs information, each BS also sens some require UE-to-UE channel information as escrie further in this section. 2) Power Upate: After the initial information exchange, each iteration n 1) has two steps: First Step: Each BS calculates the total receive uplink an ownlink interference ase on the information receive uring initialization an in the previous iteration n 1). For example, in BS Π, the estimate interference in ownlink an uplink are given, respectively, y = N + I n 1) I n 1) i Π\ p n 1) i G i, + p n 1) i u i Π G u i,, 21) = p n 1) γ + N + i Π\ p n 1) u i G u i, + i Π\ p n 1) i G i,, 22)

7 7 where p n 1) {} is the power values erive in the previous iteration as iscusse in the next step; G u i, is the channel measure y UE with i u of cell i as iscusse in Section III. The UE IDs information exchange uring initialization is use uring this process. At the en of this step, the value of the estimate interference is roacast y each BS to its neighors. Secon Step: Each BS upates its transmit powers to maximize the aggregate utility sum 20), given the power levels of other transmitters at the previous iteration, an the interference information receive in the first step. At each BS Π, {p n), p n) } = arg max Φ,n 1) u,{,u }, 23) {x,y} Q {,u } Π,n 1) where Φ {} is the estimate value of the overall utility calculate at BS. It can e written as {p n), p n) } = u arg max {x,y} Q {,u } Π + log where, SINR,n 1), I n 1) I n 1) [ log 1 + w, u log SINR,n 1), u = SINR,n 1), u I n 1) u I n 1) u x G, + y p n 1) u ) G u, p n 1) 1 + w, log SINR,n 1), G, ) )], + x p n 1) )G, + y p n 1) ) G u, = y G u, + x p n 1) )γ p n 1) u + x p n 1) G u, u )G, + y p n 1) u )G u, ) ) 24) =,. =,. 25) 26) Note that in 25), the channel G u, is measure at in cell as escrie in Section III. This information is sent y BS to BS after receiving UE IDs of the selecte UEs uring the initialization process. We use GP [45], [46] to get a near-optimal solution of this nonlinear nonconvex optimization 24). GP cannot e applie irectly to the oective function given in 24), so we first convert our oective function into a weighte sum rate maximization using the following approximation. In 24), for the weight terms, let us consier w,, which is given y 13). Since we set β very close to one, an moreover, if we assume that the value of the instantaneous rate, R, will e, of the same orer as the average rate, R, then the term, 1 β)r, βr, t) will e close to zero. So, y using ln1 + x) x for x close to zero, 24) can e approximate y {p n), p n) } = u arg max {x,y} Q {,u } Π w, + w, u log SINR,n 1), u,n 1) ) log SINR, ) ). 27) Please note that oth x an y in Q {,u } have inuilt maximum power constraint given in 7). The prolem 27) can e further written as M ) 1 w, ) ) arg min 1 w, u. {x,y} =1 1 + SINR,n 1) 1 + SINR,n 1),, u suect to: 0 x p 1, 0 y max p u 1. max 28) In general, to apply GP, the optimization prolem shoul e in GP stanar form [45], [46]. In the GP stanar form, the oective function is a minimization of a posynomial 1 function; the inequalities an equalities in the constraint set are a posynomial upper oun inequality an monomial equality, respectively. In our case, in 28), constraints are monomials hence posynomials), ut the oective function is a ratio of posynomials, as shown in 29). Hence, 28) is not a GP in stanar form, ecause posynomials are close uner multiplication an aition, ut not in ivision. Accoring to [46], 28) is a signomial programming SP) prolem. In [46], an iterative proceure is given, in which 28) is solve y constructing a series of GPs, each of which can easily e solve. In each iteration 2 of the series, the GP is constructe y approximating the enominator posynomial 29) y a monomial, then using the arithmetic-geometric mean inequality an the value of {x, y} from the previous iteration. The series is initialize y any feasile {x, y}, an the iteration is terminate at the s th loop if x s x s 1 < ɛ, an y s y s 1 < ɛ, where ɛ is the error tolerance. This proceure is provaly convergent, an empirically almost always computes the optimal power allocation [46]. The new erive values are roacast y each BS to its neighoring BSs. Then the same proceure is applie starting from the Power Upate step step 2) until the termination conition escrie elow is reache. 3) Termination: The proceure ens when either a maximum numer of iterations is reache or a terminating solution is otaine. For the UE selection Ψ given y Intra-Cell UE Selection, a power allocation P Q Ψ will e a terminating solution if changing the power level of any single transmitter cannot improve the aggregate utility sum, given the 1 A monomial is a function f : R n ++ R : gp) = p a1) 1 p a2) 2 pn an), where 0 an a k) R, k = 1, 2,, n. A posynomial is a sum of monomials, fp) = J =1 p a1) 1 p a 2 p a n. 2 Please note that this iterative proceure to solve GP is an inner proceure of the main iterative proceure of the istriute Power Upate step. 2) n)

8 8 ) w, M 1 =1. 1+SINR,n 1), = I n 1) M =1, where C,n 1) C,n 1) u 1 1+SINR,n 1), u I n 1) +y p n 1) u ) G ) w, u, +y p n 1) u ) G u, +x G, C,n 1) = I n 1) = I n 1) u ) w, u ) t). +xg, +y G u, C,n 1) +xg, +y G u, +p n 1) G, p n 1) G, p n 1) G u,, p n 1) u G, p n 1) u G u, I n 1) u I n 1) u +x p n 1) )γ +x p n 1) )γ+y G u, ) w, t). C,n 1) u ) w, t). C,n 1) u +xg, +yg u, +xg, +yg u, +pn 1) u G u, ) w, u t)) 29) power levels of all other transmitters. It was oserve in the simulation results that with the aove power upate rule, the termination conition is achieve in a few iterations. V. A CENTRALIZED FULL DUPLEX MULTI-CELL RESOURCE ALLOCATION CFDMR) In this section, to evaluate the performance of our propose istriute approach against a centralize approach, we escrie a centralize solution to solve the prolem 17). We assume a centralize scheuler that has access to gloal information, i.e., channel state information, power, etc., an ointly erives the UE selection an power allocation for all the cells simultaneously. The results generate using this scheuler can e viewe as an upper oun on system performance. In this setting, as in the ecentralize prolem, the oint prolem of UE selection an power allocation 17) is solve in two steps, 1) Greey UE Selection, an 2) Centralize Power Allocation. A. Greey UE Selection In each timeslot t, for a given feasile power allocation, the centralize scheuler fins a UE or a pair of UEs in each cell to transmit, which is given as Ψt) = arg max S M Φ,{ t), ut)} t) 30) =1 In traitional HD systems, fining the optimal set of UEs is very ifferent in the ownlink an uplink irection. In the literature, the prolem aove is solve optimally in the ownlink irection [47] [49], where the interferers are the fixe BSs in the neighoring cells, assuming a synchronize HD multi-cell system. It is easy to estimate the channel gains etween each UE with the neighoring BSs. Thus, interference from the neighoring cells can e calculate without knowing the actual scheuling ecision UE selection) of the neighoring cells. In this situation, a centralize scheuler can calculate the instantaneous rate an the utility of each UE in each cell, an make the UE selection ecision for each cell optimally. In uplink scheuling, for the given power allocation, interference from the neighoring cell cannot e calculate until the actual scheuling ecision of the neighoring cell is known, ecause in this case, a UE in the neighoring cell generates the interference. This also applies to the FD system, where interference from the neighoring cell coul e from a UE or the BS or oth. To solve this prolem, we use a heuristic greey metho similar to [13], [50]. In this metho, the centralize greey algorithm runs over a ranom orer of all the cells, an selects UEs in each cell one y one. For each cell, the UE or a pair of UEs are selecte with maximum utility gain, where the utility gain is the ifference etween the gain in the marginal utility of the chosen UE or UEs an the loss in the marginal utility of selecte UEs in other cells ue to new interference generate from the the cell eing consiere. Moreover, for the UEs in the cell eing consiere, interference from only the cells for which ecision has een mae is consiere. Since this is the same metho as the one given in [13], we omit the etails of this algorithm in this paper. The complete algorithm can e foun in [51]. This algorithm gives the UE comination Ψt). B. Centralize Power Allocation In this step, for the selecte UE comination in the previous step, a centralize power allocation process is applie to fin the appropriate power levels for all UEs, so that the overall utility can e maximize as escrie in 20). In this case, similar to the Section IV-B, we use GP to solve this nonlinear nonconvex prolem, ut in a centralize manner. Since we assume the centralize scheuler has access to the to gloal information, GP is applie once 3 at the scheuler to fin the optimum power allocation for all the selecte UEs, instea of applying it inepenently at each BS as in the Section IV-B. More etails can e foun in [51] for the centralize power allocation. VI. PERFORMANCE EVALUATION In this section, we evaluate the performance of the FD system compare to a aseline HD system using the oint UE selection an power allocation presente in Sections IV an V. 3 In this case also it will e a signomial programming, which will e solve in an iterative proceure y constructing a series of GPs.

9 9 Fig. 2: a) An inoor environment with nine RRH Cells, ) An outoor environment with twelve picocells. To simulate the HD system, we consier oth synchronous as well as a ynamic TDD [36] system. In the synchronous HD setting, in a given timeslot, all cells scheule either uplink or ownlink transmission, an the numer of timeslots is ivie equally etween the uplink an ownlink transmission. In ynamic TDD, each cell has the flexiility of scheuling its UE in any irection, whichever provies larger utility at the given timeslot. The same istriute an centralize algorithms are also applie to scheule the UEs an to etermine the power allocation in these HD systems. For example, for the HD case, 27), 28), 29) will ust contain a single term for the corresponing irection instea of two terms. A. Deployment Scenarios an Simulation Parameters We consier oth inoor an outoor eployment scenarios in our simulations. For the inoor environment, a ense multi-cell system with nine inoor Remote Raio Hea RRH)/Hotzone cells, as shown in Figure 2a), is consiere. The simulation parameters, ase on 3GPP simulation recommenations for an RRH cell environment [52], are escrie in Tale I. The path loss for oth LOS an NLOS within a cell are given in Tale I, where the proaility of LOS P LOS ) is, 1 R 0.018, P LOS = exp R 0.018)/0.027) < R < 0.037, 0.5 R 0.037, 31) In 31), R is the istance in kilometers. The channel moel use etween BSs an UEs is also use etween UEs, an etween BSs for the FD interference calculations, with the ustification that BSs o not have a significant height avantage in the small cell inoor scenario consiere, an that it is a conservative assumption for the UE-to-UE interference channel. Eight ranomly istriute UEs are eploye in each cell. To simulate an outoor multi-cell scenario, the parameters relate to path loss, shaowing, an noise figure use in simulations are ase on the 3GPP simulation recommenations for outoor environments [36], an are escrie in Tale II. The proaility of LOS for BS-to-BS an BS-to-UE path loss is R is in kilometers) is P LOS = 0.5 min0.5, 5 exp 0.156/R))+ min0.5, 5 exp R/0.03)). 32) For the outoor environment, we first consiere the same ense multi-cell system as shown in Figure 2a), assuming no walls) etween the cells. However, the performance gain of FD operation in such a ense outoor environments was not sustantial ue to strong inter-cell interference when no mitigation other than scheuling an power control is applie. We therefore analyze the performance of FD operation in a sparse outoor multi-cell system with twelve ranomly roppe picocells, each with ten ranomly istriute UEs as shown in Figure 2). This eployment reflects current picocell eployment, which cover local traffic hotspots. As we escrie in Section I, since FD operation increases the interference in a network significantly, exploiting FD operation in such an inoor environment or a sparse outoor environment is more eneficial ecause of the reuction in inter-cell interference. In oth inoor an outoor scenarios, the channel anwith is 10 MHz, the maximum BS power is 24 Bm, the maximum UE power is 23 Bm, an the thermal noise ensity is Bm/Hz. In our simulations, since we use the Shannon equation to measure the ata rate, we apply a maximum spectral efficiency of 6 its/sec/hz corresponing to 64-QAM moulation) to match practical systems. BSs an UEs are assume to e equippe with single omniirectional antennas. We simulate the system with oth full uffer traffic an non-full uffer FTP traffic assumptions. In the next few sections, we present the performance of the FD system with oth istriute an centralize scheuling algorithms, an also iscuss the convergence an signaling overhea in these methos. In the following sections, we use FD@x to represent the FD system with self-interference cancellation of x B. FD@Inf means that there is no self-interference. B. On the Convergence of DFDMR In this section we stuy the convergence of the istriute scheuling algorithm presente in Section IV. Figure 3 shows the average numer of iterations require to converge. Figure 3a) shows the result for the inoor multi-cell case for

10 10 TABLE I: Simulation parameters for an inoor multi-cell scenario Parameter Noise figure Shaowing stanar eviation with no correlation) Path loss within a cell B) R in kilometers) Path loss etween two cells R in kilometers) Penetration loss Value BS: 8 B, UE: 9 B LOS: 3 B NLOS: 4 B LOS: log 10 R), NLOS: log 10 R) Max log 10 R)), log 10 R))) Due to ounary wall of an RRH cell: 20 B, Within a cell: 0 B TABLE II: Simulation parameters for an outoor multi-cell scenario Parameter Value Minimum istance etween pico BSs 40 m Raius of a picocell 40 m Noise figure BS: 13 B, UE: 9 B Shaowing stanar eviation etween BS an UE LOS: 3 B NLOS: 4 B Shaowing stanar eviation etween picocells 6 B BS-to-BS path loss R in kilometers) LOS: if R < 2/3km, P LR) = log 10 R), else P LR) = log 10 R), NLOS: P LR) = log 10 R). BS-to-UE path loss R in kilometers) LOS: P LR) = log 10 R), NLOS: P LR) = log 10 R). UE-to-UE path loss R in kilometers) If R 50m, P LR) = log 10 R), else, P LR) = log 10 R). Fig. 3: Average numer of iterations require to converge in ifferent topologies in an a) inoor multi-cell scenario, ) outoor multi-cell scenario. FD@95, FD@Inf an HD synchronous systems. We calculate the average convergence time taken over ifferent istriutions of the UEs, i.e., ifferent topologies. In the FD case, ue to higher numer of simultaneous transmissions, it takes longer to converge compare to the HD system. Moreover, ue to higher interference in FD@95, the scheuler takes longer to converge compare to the FD@Inf system. In the outoor scenario given in Figure 2), the same tren is oserve as shown in the Figure 3). In this case, results are otaine with ifferent ranom rops of pico cells. Due to higher intercell interference etween a BS an UEs as compare to the inoor scenario, a higher numer of iterations are require for the outoor scenario. C. Throughput Performance With the aove simulation settings, in the inoor case, we run our simulation for ifferent UE rops in all cells, each for a thousan timeslots, with the stanar wrap aroun topology, an generate results for oth the HD an FD systems. In this section, we simulate the system in which each UE has fulluffer traffic in oth irections; the results with the non-full uffer traffic case will e presente in Section VI-D. To show the importance of UE selection an power allocation, we first generate the results in the inoor setting for a simple centralize scheuler, i.e., roun-roin scheuler with fixe maximum transmission powers in oth irections. In the HD system HD synchronous), in each irection, each cell selects UEs in a roun-roin manner. In the FD system, in each timeslot, each cell chooses the same UE as selecte in the HD system with a ranomly selecte UE for the other irection to make an FD pair. Figures 4a) an 4) show the istriution of average ownlink an uplink throughputs, for ifferent BS self-interference cancellation capailities. In the ownlink irection, in most of the cases 70%), there is no FD gain, which is ue to the lack of any intelligent selection proceure uring FD operation. In the uplink, ue to the cancellation of self-interference, the FD system throughput is higher than the HD system. The ifference improves with increase selfinterference cancellation capaility. From a system point of view, which inclues oth uplink an ownlink, this rounroin scheuling oes not provie sufficient FD capacity gain. This emonstrates the nee for an intelligent scheuling algorithm to provie a gain uring FD operation which can enefit oth uplink an ownlink. Next, we generate results with oth the propose istriute

11 11 Fig. 4: Distriution of average ata rates for the half uplex system an full uplex system with roun-roin scheuler in an inoor multi-cell scenario. Fig. 5: Distriution of average ata rates for the half-uplex system an full uplex system with oth istriute an centralize scheuling algorithms in an inoor multi-cell scenario. an centralize oint UE selection an power allocation proceure. Figures 5a) an 5) show the istriution of average ownlink an uplink throughputs for oth istriute an centralize methos. In this plot, the istriution is only shown for HD synchronous, an system to keep the plot reaale, however Tale III contains the average throughput over all UEs for all the simulate systems. It also contains the average throughput gain of FD systems compare to the HD synchronous system. The HD system shows a narrow istriution centere near 4 Mps in oth ownlink an uplink whereas the FD system shows a wier istriution since the scheuler takes avantage of the variale nature of the interference to assign FD operation with an appropriate ata rate whenever possile. The ynamic TDD HD system has similar performance as the synchronous HD system since the same kin of channel moel is assume etween ifferent noes, an therefor there is not much ifferent in the interference experience y a noe in oth systems. In this scenario, the istriute algorithm performs nearly as well as the centralize solution for almost all the systems. In general, the throughput gain of FD system compare the HD system increases as the self-interference cancellation improves. With the higher self-interference cancellation values, the FD system nearly oules the capacity compare to the HD system. From the simulation one can also oserve the epenency etween FD/HD operation selection in our scheuler an the self-interference cancellation capaility, that is, the lower the self-interference cancellation, the fewer the numer of cells in a timeslot that are scheule in FD moe. This is verifie y counting the average numer of cells per timeslot which are in FD moe or HD moe or with no transmission as shown in Tale IV. With 75 B self-interference cancellation, on average 84% of the cells operate in FD moe, while with 105 B, 98% of the cells operate in FD moe. Note that in the HD system, in each timeslot, all cells transmit in one irection either uplink or ownlink). These results are for the centralize metho; similar results are otaine for the istriute metho. To analyze the performance of FD operation in the outoor scenario, as we mentione earlier in Section VI-A, we first simulate the ense outoor multi-cell scenario. In this case, the average throughput gain of the FD system is only 25%

12 12 TABLE III: Average throughput Mps) over all UEs of half an full uplex systems with oth istriute an centralize scheuling algorithms in an inoor multi-cell scenario. For a full uplex system, average throughput gain compare to the HD synchronous system is also given. HD HD Synchronous Dynamic TDD FD@75 FD@85 FD@95 FD@105 FD@Inf CFDMR: Downlink %) %) %) %) %) DFDMR: Downlink %) %) %) %) %) CFDMR: Uplink %) %) %) %) %) DFDMR: Uplink %) %) %) %) %) TABLE IV: Average numer of cells per slot in ifferent moes in an inoor multi-cell scenario. HD Downlink, Uplink) FD@75 FD@85 FD@95 FD@105 FD@Inf FD Moe - 84% 93% 97% 98% 98% HD Moe 100%, 100%) 16% 7% 3% 2% 2% No Transmission 0%, 0%) 0% 0% 0% 0% 0% in the ownlink an 32% in the uplink with the centralize scheuler. These gains o not vary with self-interference cancellation ecause strong inter-cell interference ominates the self-interference an ecreases the opportunities for capacity improvement ue to FD operation. These results show that it is not very eneficial to use FD raios in ense outoor environments ue to the high inter-cell interference. This oservation motivates us to investigate the performance of FD raios in sparse outoor environments. We simulate the sparse outoor multi-cell scenario as shown in Figure 2). We run our simulation for several ranom rops of twelve picocells in a hexagonal cell with a with of 500 meters. Figures 6a) an 6) show the istriution of average ownlink an uplink throughputs, an Tale V shows the average throughput over all UEs for all the systems an also the gain of the FD system as compare to the HD synchronous system. Similar to the inoor scenario, FD increases the capacity of the system significantly over the HD case, where the increase is proportional to the amount of self-interference cancellation. In this case also the istriute scheuling algorithm gives results close to the centralize algorithm. In this outoor scenario, the average throughput of a UE is lower compare to the inoor case, ut it is istriute over a wier range. Moreover, the throughput increase ue to FD operation is less than what it was in the inoor case. The reason ehin this is that the inter-cell interference etween a BS an UEs in neighoring cells is much stronger that in the inoor scenario. In this case, for the centralize algorithm, the uplink throughput is higher than the ownlink throughput, which also increases the gap etween the performance of the istriute an centralize performance in the uplink. In the centralize greey UE selection algorithm, the utility to select a UE is the ifference etween the marginal utility of the UE an the loss in the marginal utility of the selecte UEs in other cells ue to new interference generate from the UE eing consiere. In case of ownlink, for all the potential UEs in the cell eing consiere, the secon term, i.e. interference generation from their BS) to other cells will e constant, whereas, in the uplink, since the interference generation also epens on the location of the UE, oth utility gain an utility ecrement of other cells vary from UE to UE. This ifference provies more egrees of freeom for the uplink UE selection an therefore manages uplink multi-cell interference etter than ownlink case. Tale VI shows the average numer of cells per slot which are in FD moe, HD moe or with no transmission with the centralize scheuling metho. First of all, in the HD system, in contrast to the inoor scenario, we can see that some cells are not transmitting at all in some slots. This is ue to the higher inter-cell interference etween the BS an UEs in neighoring cells; the system throughput is higher when certain cells are not scheule for transmission, resulting in reuce inter-cell interference. Further, for the same reason, the average numer of cells operating in FD moe is smaller than the inoor scenario. In this case, the numer of cells in FD moe also increases with self-interference cancellation. D. Full Duplex Gain for the Non-full Buffer Traffic Moel In this section we analyze the performance of the FD system with non-full uffer FTP traffic [52]. In this case, each UE has requests to ownloa or/an uploa files of 1.25 MB. The time interval etween completion of a file transmission an an arrival of a new request is exponentially istriute with a mean of 1 secon. The elay for each UE, which is efine as the total time it experiences from the request arrival to the completion of ownloaing or uploaing a file is calculate. A significant elay improvement, ue to simultaneous ownloaing an uploaing in an FD system is oserve as shown in Tale VII, which shows the average elay a UE experiences for ifferent systems. Moreover, a UE ownloas 48%, 69%, 83%, 90%, an 92% more files an uploas 56%, 75%, 86%, 88%, an 90% more files in the FD system compare to those in the HD system with 75 B, 85 B, 95 B, 105 B, an perfect self-interference cancellation, respectively. E. Signaling Overhea In this section we compute the signaling overhea require to enale FD scheuling algorithms compare to the existing HD system. As mentione in Section III, in our FD system, each UE nees to sen the channel measurement information of its neighorhoo. In our simulations, we erive a threshol

13 13 Fig. 6: Distriution of average ata rates for the half-uplex system an full uplex system with oth istriute an centralize scheuling algorithms in an outoor multi-cell scenario. TABLE V: Average throughput Mps) over all UEs of half an full uplex systems with oth istriute an centralize scheuling algorithms in an outoor multi-cell scenario. For a full uplex system, average throughput gain compare to the HD synchronous system is also given. HD HD Synchronous Dynamic TDD FD@75 FD@85 FD@95 FD@105 FD@Inf CFDMR: Downlink %) %) %) %) %) DFDMR: Downlink %) %) %) %) %) CFDMR: Uplink %) %) %) %) %) DFDMR: Uplink %) %) %) %) %) TABLE VI: Average numer of cells per slot in ifferent moes in an outoor multi-cell scenario. HD Downlink, Uplink) FD@75 FD@85 FD@95 FD@105 FD@Inf FD Moe - 36% 50% 56% 57% 57% HD Moe 81%, 88%) 62% 48% 42% 41% 41% No Transmission 19%, 12%) 2% 2% 2% 2% 2% TABLE VII: Average elay Secons) in an inoor multi-cell scenario. HD Synchronous FD@75 FD@85 FD@95 FD@105 FD@Inf Downlink Uplink for each UE to etermine inclusion in its potential strong interferer list for UE-to-UE interference. For an UE u, given its threshol, all other such UEs for which UE-to-UE channel is higher than the threshol will e consiere as strong interferers, an UE u will sen the channel information for these UEs to its BS. A ownlink UE gets interference from oth neighoring BSs an uplink UEs. The channel measurement from the BSs is use to erive the threshol for the UE-to- UE channels for each UE. Each UE measures the channel with all its neighoring BSs an erives the average channel strength of its BS-to-UE interference channel. This average channel strength is use as the threshol for the UE-to-UE interference channel. Let us assume that on an average there are K strong UE interferers. We assume the channel information is represente y 8- its. If a UE sens this information every 2ms, which is the maximum perioic frequency of the SRS transmission of a UE [34], the total overhea in each cell, woul e 4KN m kps. In our simulations, in the inoor scenario, where N m = 8, an the average value of K oserve equals 7. The average overhea in the inoor scenario is thus 224 kps. In the outoor scenario, it is 320 kps N m = 10, K = 8). For example, for a LTE system with 10 MHz anwith an 16 QAM, where the peak LTE uplink capacity is 25.5 Mps [40], the UE-to-UE channel measurement incurs less than 2% overhea. We also compare the signaling overhea of the istriute an centralize algorithms in terms of average outoun traffic generate y each BS. In the centralize metho, the centralize scheuler nees to collect a large set of channel information from each BS, which inclues, 1) channels with other BSs, 2) channels with all the UEs in the system, 3) strong UE-to-UE channels. It also nees to collect weights of all UEs. In this case, each BS generates M + MN m + N m K) 8 its per transmission time interval TTI). In case of the istriute

14 14 approach, each BS generates 2+2+2M +K) 8 its uring initialization an 2 + 2) n I 8 its uring the iterative process, where n I is the numer of iterations. In the case of the inoor system, ase on our simulation results, if we assume K = 7, n I = 7, then for the centralize approach each BS generates 1096 its per TTI, an in the case of the istriute approach, each BS generates 456 its per TTI. VII. CONCLUSION We investigate the application of common carrier FD raios to resource manage small-cell systems in a multicell eployment. Assuming FD capale BSs with HD UEs, we present a oint uplink an ownlink scheuler which oes UE selection an power allocation to maximize the network utility in a istriute manner. It operates in FD moe when conitions are favorale, an otherwise efaults to HD moe. The propose istriute algorithm performs nearly as well as the centralize solution ut with much lower signaling overhea. 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15 15 [35] Physical channels an moulation Release 10), TS , v , June [Online]. Availale: [36] Further enhancements to lte time ivision uplex TDD) for ownlinkuplink DL-UL) interference management an traffic aaptation, TR , v , June [Online]. Availale: [37] A. L. Stolyar, On the asymptotic optimality of the graient scheuling algorithm for multiuser throughput allocation, Operations Research, vol. 53, no. 1, pp , Jan-Fe [38] H. Kim, K. Kim, Y. Han, an S. Yun, A proportional fair scheuling for multicarrier transmission systems, in Vehicular Technology Conference, VTC2004-Fall. IEEE 60th, vol. 1, Sept 2004, pp [39] A. Jalali, R. Paovani, an R. Panka, Data throughput of CDMA- HDR a high efficiency-high ata rate personal communication wireless system, in Vehicular Technology Conference Proceeings, IEEE 51st, 2000, pp [40] Physical layer proceures Release 11), TS , v11.0.0, Septemer [Online]. Availale: [41] H. Tang, Z. Ding, an B. 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Julian, Power control y geometric programming, Wireless Communications, IEEE Transactions on, vol. 6, no. 7, pp , July [47] L. Venturino, N. Prasa, an X. Wang, Coorinate scheuling an power allocation in ownlink multicell OFDMA networks, Vehicular Technology, IEEE Transactions on, vol. 58, no. 6, pp , July Sanay Goyal receive his B.Tech. egree in communication an computer engineering from the LNM Institute of Information Technology, Inia, in 2009, an his M.S. egree in electrical engineering from NYU Polytechnic School of Engineering, New York, in Currently, he is a Ph.D. caniate in the ECE Department at NYU Tanon School of Engineering. He was aware, along with Carlo Galiotto, Nicola Marchetti, an Shivenra Panwar, the Best Paper Awar in IEEE ICC His research interests are in esigning an analyzing wireless network protocols with full uplex communication, especially for the MAC layer. Pei Liu is a research assistant professor of Electrical an Computer Engineering at NYU Tanon School of Engineering. He receive his Ph.D. egree in Electrical an Computer Engineering from Polytechnic University in He receive his B.S. an M.S. egrees in electrical engineering from Xi an Jiaotong University, China, in 1997 an 2000, respectively. His research interests are in esigning an analyzing wireless network protocols with an emphasis on cross-layer optimization, especially with the PHY an MAC layers. Currently, his research topics inclue wireless communications, wireless networks, an vieo over wireless. Shivenra S. Panwar [F] is a Professor in the Electrical an Computer Engineering Department at NYU Tanon School of Engineering. He receive the B.Tech. egree in electrical engineering from the Inian Institute of Technology Kanpur, in 1981, an the M.S. an Ph.D. egrees in electrical an computer engineering from the University of Massachusetts, Amherst, in 1983 an 1986, respectively. He is currently the Director of the New York State Center for Avance Technology in Telecommunications CATT), the Faculty Director of the NY City Meia La, an memer of NYU WIRELESS. He spent the summer of 1987 as a Visiting Scientist at the IBM T.J. Watson Research Center, Yorktown Heights, NY, an has een a Consultant to AT&T Bell Laoratories, Holmel, NJ. His research interests inclue the performance analysis an esign of networks. Current work inclues wireless networks, switch performance an multimeia transport over networks. He is an IEEE Fellow an has serve as the Secretary of the Technical Affairs Council of the IEEE Communications Society. He is a co-eitor of two ooks, Network Management an Control, Vol. II, an Multimeia Communications an Vieo Coing, oth pulishe y Plenum. He has also co-authore TCP/IP Essentials: A La ase Approach, pulishe y the Camrige University Press. He was aware, along with Shiwen Mao, Shunan Lin an Yao Wang, the IEEE Communication Society s Leonar G. Araham Prize in the Fiel of Communication Systems for He was also aware, along with Zhengye Liu, Yanming Shen, Keith Ross an Yao Wang, the Best Paper in 2011 Multimeia Communications Awar. [48] W. Yu, T. Kwon, an C. Shin, Joint scheuling an ynamic power spectrum optimization for wireless multicell networks, in Information Sciences an Systems CISS), th Annual Conference on, March 2010, pp [49] S. G. Kiani, G. E. Oien, an D. Gesert, Maximizing multicell capacity using istriute power allocation an scheuling, in 2007 IEEE Wireless Communications an Networking Conference, March 2007, pp [50] I. Koutsopoulos an L. Tassiulas, Cross-layer aaptive techniques for throughput enhancement in wireless OFDM-ase networks, Networking, IEEE/ACM Transactions on, vol. 14, no. 5, pp , Oct [51] S. Goyal, P. Liu, S. Panwar, R. Yang, R. A. DiFazio, an E. Bala, Full uplex operation for small cells, CoRR, vol. as/ , [Online]. 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