User Selection and Power Allocation in Full-Duplex ...catt.poly.edu/~panwar/publications/User...

2408 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 3, MARCH 2017

User Selection and Power Allocation inFull-Duplex Multicell Networks

Sanjay Goyal, Student Member, IEEE, Pei Liu, Member, IEEE, and Shivendra S. Panwar, Fellow, IEEE

Abstract—Full-duplex (FD) communications has the potentialto double the capacity of a half-duplex (HD) system at the linklevel. However, in a cellular network, FD operation is not astraightforward extension of HD operations. The increased inter-ference due to a large number of simultaneous transmissions inFD operation and real-time traffic conditions limits the capacityfor improvement. Realizing the potential of FD requires carefulcoordination of resource allocation among the cells, as well aswithin the cell. In this paper, we propose a distributed resourceallocation, i.e., joint user selection and power allocation for an FDmulticell system, assuming FD base stations (BSs) and HD userequipment (UE). Due to the complexity of finding the globally op-timum solution, a suboptimal solution for UE selection and a novelgeometric-programming-based solution for power allocation areproposed. The proposed distributed approach converges quicklyand performs almost as well as a centralized solution but withmuch lower signaling overhead. It provides a hybrid schedulingpolicy that allows FD operations whenever it is advantageous,but otherwise, it defaults to HD operation. We focus on small-cell systems because they are more suitable for FD operation,given practical self-interference cancelation limits. With practicalself-interference cancelation, it is shown that the proposed hybridFD system achieves nearly twice the throughput improvement foran indoor multicell scenario and about 65% improvement for anoutdoor multicell scenario, compared with the HD system.

Index Terms—Full-duplex (FD) radio, Long-Term Evolution(LTE), power allocation, scheduling, small cell.

I. INTRODUCTION

FULL-DUPLEX (FD) operation in a single wireless chan-nel has the potential to double the spectral efficiency of a

wireless point-to-point link by transmitting in both directions atthe same time. Motivated by the rapid growth in wireless datatraffic, along with concerns about a spectrum shortage [1]–[3],cellular network operators and system vendors have becomemore interested in FD operations.

In legacy systems, the large difference between transmitted(Tx) and received (Rx) signal powers due to path loss and fad-ing, together with imperfect Tx/Rx isolation, has driven the vastmajority of systems to use either frequency-division duplexing

Manuscript received February 1, 2016; revised May 10, 2016; acceptedMay 11, 2016. Date of publication June 14, 2016; date of current versionMarch 10, 2017. This work was supported in part by the U.S. National ScienceFoundation under Grant 1527750, by the NYSTAR Center for AdvancedTechnology in Telecommunications, and by the InterDigital Communications.The review of this paper was coordinated by Dr. N.-D. Ðào.

The authors are with the Department of Electrical and Computer Engineer-ing, New York University Tandon School of Engineering, Brooklyn, NY 11201USA (e-mail: [email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2016.2580583

(FDD) or time-division duplexing (TDD). FDD separates theTx and Rx signals with filters, whereas TDD achieves this withTx/Rx switching. Recent advances in antenna designs and activecancelation technologies [4]–[10] have provided a significantstep toward building a practical FD transceiver and meeting theprojected 2X gain in capacity [11], [12] without requiring newspectrum or setting up new cells. A combination of antenna andanalog and digital cancelation circuits can remove most of thecrosstalk, or self-interference, between the Tx/Rx signal path andcan allow the demodulation of the received signal while trans-mitting to someone else. This was demonstrated using multipleantennas positioned for optimum cancelation [4], [5] and laterfor single-antenna systems [6], [7], where as much as 110 dBcancelation is reported over an 80-MHz bandwidth. Cancelationranging from 70 to 100 dB with a median of 85 dB using multipleantennas has been reported [8]. An antenna feed network, forwhich a prototype provided 40–45 dB Tx/Rx isolation beforeanalog and digital cancelation, was described in [6].

However, at the network level, FD operations in a cellularnetwork is not just a straightforward extension of half-duplex(HD) operations implemented by replacing the HD radios withan FD radio. As suggested in our preliminary research forLong-Term Evolution (LTE) systems [13], [14] and by others[15]–[18], intra/intercell interference caused by using the samefrequency in both uplink and downlink directions is significantand is a major limiting factor to system throughput. This isbecoming a key problem to resolve as new cellular networks be-come more heterogeneous, and network entities with differentcapabilities are loosely connected with each other. Addition-ally, realistic traffic complicates scheduling decisions since thescheduled user equipment (UE) might only have active trafficin one direction at a given instant. In such a scenario, it isadvantageous to schedule a second UE in the opposite direction.

In this paper, we assume the BSs are equipped with FDradios, where the additional cost and power is most likely to beacceptable, whereas the UE is limited to HD operation. DuringFD operation in a cell, the BS schedules an uplink UE anda downlink UE in the same time slot on the same channel.The impact on over-the-air interference due to FD operation isshown in Fig. 1. Consider the two-cell network in Fig. 1, inwhich UE1 and UE3 are downlink UEs in cells 1 and 2,respectively, and UE2 and UE4 are uplink UEs in cells 1 and 2,respectively. First, to illustrate the HD scenario, we assumesynchronized cells, which means that, in a given time interval,all cells schedule transmissions in the same direction. In thiscase, orthogonal channel access in time prevents interferencebetween UEs and between base stations (BSs), but each UEaccesses the channel only half the time. In Fig. 1(a), one can

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GOYAL et al.: USER SELECTION AND POWER ALLOCATION IN FULL-DUPLEX MULTICELL NETWORKS 2409

Fig. 1. HD and FD multicell interference scenarios.

see that, in HD operation, UE1 receives interference I1 fromBS2, which is transmitting to UE3 at the same time. Similarly,BS1 receives interference I2 from the uplink signal of UE4.During FD operation, as shown in Fig. 1(b), the downlink UE,i.e., UE1, not only gets interference I1 from BS2 but also getsinterference I3 and I4 from the uplink signals of UE2 and UE4.Similarly, the uplink from UE2 to BS1 not only gets interfer-ence I2 from UE4 but also gets interference I6 from the down-link signal of BS2, as well as Tx-to-Rx self-interference I5.The existence of additional interference sources raises the ques-tion whether there is any net capacity gain from FD operation.The actual gain from FD operation will strongly depend onlink geometries, the density of UEs, and propagation effectsin mobile channels. Therefore, FD operation will provide anet throughput gain only if the throughput across two timeslots, subject to the additional interference, is larger than thethroughput in one time slot without such interference.

In this paper, we focus on the design of a distributedinterference-aware scheduler and a power control algorithmthat maximizes the FD gain across multiple cells, while main-taining a level of fairness between all UEs. In such a system, FDgain can be achieved by simultaneous transmissions in uplinkand downlink directions, where the extra FD interference wouldbe treated as noise. The scheduler is a hybrid scheduler in thesense that it will exploit FD transmissions at the BS only whenit is advantageous to do so. Otherwise, when the interference istoo strong, or traffic demands dictate it, it might conduct HDoperations in some cells.

In the proposed distributed approach, neighboring cells co-ordinate with each other to simultaneously select the UEsand transmit power levels to maximize the system gain. Thisjoint UE selection and power allocation problem is in gen-eral a nonconvex, nonlinear, and mixed discrete optimizationproblem. There exists no method to find a globally optimumsolution for such a problem, even for the traditional HD systemscenario. We provide a suboptimal method by separating theUE selection and power allocation procedures, using geometricprogramming (GP) for power allocation. The proposed distrib-uted approach converges quickly and performs almost as wellas a centralized solution that has access to global information,i.e., channel state information (CSI), power, etc., with muchlower signaling overhead. The proposed FD system improvesthe capacity of a dense indoor multicell system by nearly twotimes and an outdoor sparse multicell system by about 65%.The new signaling requirements and their overhead in the caseof the FD scheduling process are also discussed.

A. Related Work

Extensive advances have been made in designing and im-plementing wireless transceivers with FD capability [9], [10].Medium-access-control designs for FD IEEE 802.11 systemshave been presented, which shows throughput gains from 1.2×to 2× with FD operations (see [19] and references therein).However, to the best of our knowledge, little has been done tounderstand the impact of such terminals on a cellular networkin terms of system capacity and energy efficiency.

Reviewing the literature shows that there has been significantwork done on interference coordination in conventional HDsystems. Various solutions [20] have been proposed from staticfrequency allocation to dynamic distributed resource allocationto avoid or coordinate the interference among neighboringinterfering cells. However, with the new FD interference asdescribed in Fig. 1, uplink and downlink channel resources haveto be allocated jointly to support a higher number of simul-taneous links with different characteristics. Thus, the existinginterference coordination methods for the HD case cannot beapplied directly to the FD case.

FD operation in a single cell has been evaluated [14],[21]–[26]. Barghi et al. [21] compared the tradeoff betweenusing multiple antennas for spatial multiplexing gain and FDgain by nulling self-interference. A distributed power controlmethod using just one-hop information to manage UE-to-UEinterference in a single FD cell with massive multiple-inputmultiple-output was proposed in [25]. FD operation in a cel-lular system has also been investigated in the DUPLO project[27], where a joint uplink–downlink beamforming techniquewas designed for the single-small-cell environment [26]. Ourprevious work [14] introduced a single-cell hybrid schedulerwithout transmission power optimization. Other techniques forresource allocation in an FD single cell case using matchingtheory, a cell partitioning method, and game theory can befound in [22]–[24], respectively. However, all these proposedmethods for a single FD cell cannot be directly applied toresource allocation in a multicell scenario.

In the case of multicell FD operations, centralized UE selec-tion procedures with fixed power allocation have been proposed[13], [16], [17]. Moreover, inter-BS interference is assumedperfectly canceled and the interference from the neighboringcell UE is ignored in [16] and [17], which makes the resourceallocation problem simpler even for the multicell case. Underthe same assumption, an analytical expression for the achiev-able rates assuming cloud radio access network (C-RAN) oper-ation for both HD and FD are derived by Simeone et al. [28].


However, the assumption of ignoring interference from UEs ofneighboring cells may not be appropriate in some scenarios. Acell-edge uplink UE of a neighboring cell may generate severeinterference for the downlink transmission. Choi et al. [15]proposed a method to mitigate the inter-BS interference usingnull forming in the elevation angle at BS antennas and a simpleUE selection procedure by assuming fixed transmission powersin both directions. Using successive convex approximation andGP, Nguyen et al. [18] provides a centralized power allocationmethod for the given UEs with FD capability. Yun et al. [29]provided a intracell joint resource allocation including chan-nel allocation, UE selection, and power allocation. Further,they considered a multi femtocell network with an underlyingmacrocell, for which they provided a coordination algorithmsuch that the transmit powers of femtocells and their connectedUEs are adjusted so that data transmissions of the underlyingmacrocell is protected. However, they did not consider co-ordination to mitigate the interference among the cochannelfemtocells. A high level presentation, with no technical details,of the centralized solution we use as an upper bound has beengiven in [30], which was used to evaluate the performance ofFD systems in an indoor multicell system in terms of energy ef-ficiency. The details of this centralized method will be providedin Section V.

Stochastic-geometry-based analytical models have also beenpresented [13], [31]–[33] for the FD multicell system. Theimpact of residual self-interference, density of FD BSs, transmitpower, etc., on the performance of such an FD system in termsof average spectral efficiency and coverage has been evalu-ated. These stochastic-geometry-based analyses do not considermulti-UE diversity gain, which comes through scheduling ofthe appropriate UEs with power adjustments to mitigate in-terference. This is particularly crucial in FD systems where,as we have just noted, the interference scenario is worse thantraditional HD systems.

In this paper, we provide a distributed method of interferencecoordination between cells with the appropriate UE selectionand power allocation for an FD-enabled cellular system. Thekey contributions of this paper are the following.

• A joint uplink and downlink scheduler is introduced, whichmaximizes network utility for an FD-enabled multicellnetwork.

• The scheduler jointly optimizes UE selection and powerallocation among multiple cells in a distributed manner.

• New signaling required to avoid UE-to-UE interference isdiscussed. The signaling overhead is also illustrated.

• This paper investigates the performance of FD operationsfor several typical deployments used by cellular operatorstoday, including both indoor and outdoor scenarios.

The remaining part of this paper is organized as follows.Section II describes the system model and problem formulation.The discussion on new requirements for channel estimation isdiscussed in Section III. The distributed joint UE selection andpower allocation method is given in Section IV. Section V givesthe details of a centralized method to solve the same problem.Section VI contains simulation details and performance results

for the proposed FD scheduling algorithms. Conclusions arediscussed in Section VII.

II. SYSTEM DESCRIPTION AND PROBLEM FORMULATION

A. System Model

We examine FD common carrier operation applied to a re-source managed LTE TDD small-cell system [34], [35]. Resid-ual self-interference, in general, lowers the uplink coverage andprecludes the use of FD technology in a large cell. For example,consider a cell with a 1-km radius. According to the channelmodel given in [36], the path loss at the cell edge is around130 dB. It means the uplink signal arriving at the BS is 130 dBlower than the downlink signal transmitted, assuming equal perchannel transmission power in the uplink and downlink direc-tions. The received signal-to-interference ratio (SIR) will thenbe at most −20 dB with the best self-interference cancelationcircuit known to date, which is capable of achieving 110 dB ofcancelation [7]. At such an SIR, the spectrum efficiency wouldbe very low. Thus, we believe FD transmission is more suitablefor UEs close to BSs, which motivates us to consider small-cellsystems as more suitable candidates to deploy an FD BS.

We consider a network with M cells, where Π will be used todenote the set of indices of all BSs/cells. Each UE is connectedto the nearest BS, and the number of UEs is much larger thanM . We denote by Km the set of UE indices associated with cellm, and define Nm = |Km|. Each of the BSs and UE devices areequipped with a single antenna.

Assume that at time slot t, ψdb (t) ∈ Kb and ψu

b (t) ∈ Kb

denote the UEs scheduled in cell b in downlink and uplinkdirections, respectively. In case of HD UEs, ψd

b (t) �= ψub (t).

The baseband signal received by UEs ψdb (t) and ψu

b (t) are,respectively, given by

yψdb (t)

(t) = hb,ψdb (t)

xb(t)︸︷︷︸data

+∑i∈Π\b

hi,ψdb (t)

xi(t)︸︷︷︸BS−to−UEinterference

+∑i∈Π

hψui (t),ψ

db (t)

xψui (t)(t)︸︷︷︸

UE−to−UEinterference

+nψdb (t)︸︷︷︸

noise

(1)

yψub (t)

(t) = hψub (t),b

xψub (t)(t)︸︷︷︸

data

+∑i∈Π\b

hψui (t),b

xψui (t)(t)︸︷︷︸

UE−to−BSinterference

+∑i∈Π\b

hi,bxi(t)︸︷︷︸BS−to−BSinterference

+ h′b,bxb︸︷︷︸

self−interference

+ nb︸︷︷︸noise

.

(2)

In the given equations, h{} is used to denote the com-plex channel response between different nodes. For example,hb,ψd

b (t)and hψu

i (t),ψdb (t)

denote the channel between BS b and

UE ψdb (t), and the channel between UE ψu

i (t) and UE ψdb (t),

respectively. It includes path loss, small-scale fading, and shad-owing. Further, x{}(t) is used to denote the complex data


symbol transmitted by different nodes. The self-interferencechannel at BS b is denoted by h′

bb, which includes the cancela-tion. We model the transmitted symbols as independent random

variables with zero mean and varianceE{|x{}(t)|2}Δ=p{}(t)≥0.

The notation nψdb (t)

and nb denote the additive noise at UE

ψdb (t) and BS b, treated as complex Gaussian random variables

with variances Nψdb (t)

/2 and Nb/2, respectively.The signal-to-interference-plus-noise (SINR) for downlink

UE ψdb (t) and uplink UE ψu

b (t) are given by, respectively

SINRdb,ψd

b (t)

=pb(t)Gb,ψd

b (t)∑i∈Π\b

pi(t)Gi,ψdb (t)

+∑i∈Π

pψui (t)

(t)Gψui (t),ψd

b (t)+Nψd

b (t)

(3)

SINRub,ψu

b (t)

=pψu

b (t)(t)Gψu

b (t),b∑i∈Π\b

pψui (t)

(t)Gψui (t),b +

∑i∈Π\b

pi(t)Gi,b + pb(t)γ +Nb.

(4)

In the given equations, Gm,n = |hm,n|2 ∀m,n. The residualself-interference is modeled as Gaussian noise, the power ofwhich equals the difference between the transmit power of theBS and the assumed amount of self-interference cancelation. In(4), γ denotes the self-interference cancelation level at the BS.The corresponding achievable information rate in bits/s/Hz isgiven by the following Shannon formulas:

Rdb,ψd

b (t)(t) = log2

(1 + SINRd

b,ψdb (t)

)(5)

Rub,ψu

b (t)(t) = log2

(1 + SINRu

b,ψub (t)

). (6)

B. Problem Formulation

We consider a system in which there is coordination amongthe cells. The objective of the coordinated cells is to maximizethe system throughput while maintaining a level of fairnessamong the UEs. We consider a proportional-fairness-based al-location, which is achieved by maximizing the logarithmic sumof the average rates of all the UEs [37], [38]. In the FD system,both uplink and downlink transmissions need to be consideredsimultaneously. The objective at time slot t is defined as

Maximize∑b∈Π

∑k∈Kb

[log

(Rd

b,k(t))+ log

(Ru

b,k(t))]

subject to 0 ≤ pb(t) ≤ pdmax

0 ≤ pk(t) ≤ pumax

Rdb,k(t).R

ub,k(t) = 0 ∀ k ∈ Kb ∀b ∈ Π (7)

where Rdb,k(t) and Ru

b,k(t) are the average achieved downlinkand uplink rates of UE k in cell b, which is denoted UEb,k, untiltime slot t, respectively. The first two constraints in (7) are forthe transmit powers of the BSs and UEs in each cell, in which

pdmax and pumax are the maximum power that can be used indownlink and uplink transmission directions, respectively. Thethird constraint in (7) captures the HD nature of the UEs, whereRd

b,k(t) and Rub,k(t) are the instantaneous downlink and uplink

rates in time slot t, respectively, of UEb,k as defined in (5) and(6). The average achieved data rate, for example, in downlink,Rd

b,k(t) is updated iteratively based on the scheduling decisionin time slot t, i.e.,

Rdb,k(t)=

{βRd

b,k(t−1) + (1−β)Rdb,k(t), if ψd

b (t)=UEb,k

βRdb,k(t− 1), otherwise

(8)

where 0 < β < 1 is a constant weighting factor, which isused to calculate the length of the sliding time window, i.e.,1/(1 − β), over which the average rate is computed for eachframe, with its value generally chosen close to one, e.g., 0.99[37], [39]. The average achieved uplink rate of UEb,k, Ru

b,k(t)can be similarly defined.

The goal of the coordinated cells is to determine the setof cochannel UEs scheduled at the same time and the powerallocation for the scheduled UEs so that the overall utilitydefined in (7) can be maximized.

Assume that Sb = {i, j : i �= j} ∈ K′b ×K′

b denotes all thepossible combinations of choosing two UEs, i.e., one in down-link and one in uplink in cell b, where K′

b = Kb ∪ {∅}. ∅ isused to include the case of no UE selection in a direction. S =S1 × S2 · · · × SM is the selection of all UE’s in the network.Further, let QSb = {pb, pj}, pb ≤ pdmax, and pj ≤ pumax denoteall possible combination of power levels in the downlink anduplink in Sb, and QS = [QS1 , . . . , QSM ].

Assume Ψ(t) ⊂ S denotes the set of chosen UEs inboth downlink and uplink directions in time slot t, i.e.,Ψ(t)=[{ψd

1(t), ψu1 (t)}, . . . , {ψd

M (t), ψuM (t)}], where ψd

i (t) =∅ (ψu

i (t) = ∅) indicates no UE scheduled for the downlink(uplink) in cell i. This could be the result of no downlink(uplink) demand in cell i, in the current time slot t, or asdiscussed in Section III, it could also be because schedulingany downlink (uplink) transmission in cell i, in time slot t willgenerate strong interference to the other UEs, lowering the totalnetwork utility. Therefore, in each time slot, each cell will selectat most one UE in the downlink and at most one UE in theuplink direction. Assume that P(t) = [{p1(t), pψu

1 (t)(t)}, . . . ,{pM (t), pψu

M (t)(t)}], where P(t) ⊂ QΨ(t) contains the powerallocation for the selected UE combination Ψ(t), in time slot t.

Using (8), the objective function in (7) can be expressed as∑b∈Π

∑k∈Kb

[log

(Rd

b,k(t))+ log

(Ru

b,k(t))]

=∑b∈Π

[{log

(βRd

b,ψdb (t)

(t− 1) + (1 − β)Rdb,ψd

b (t)(t)

)− log

(βRd

b,ψdb (t)

(t− 1))}

+{log

(βRb,ψu

b (t)u(t− 1)+(1 − β)Ru

b,ψub (t)(t)

)− log

(βRb,ψu

b (t)u(t− 1)

)}]+A (9)


where A is independent from the decision made at time slot tand is given by

A =∑b∈Π

∑k∈Kb

[log

(βRd

b,k(t−1))+log

(βRu

b,k(t−1))]. (10)

In (9), we denote the first term in the summation asχdb,ψd

b (t)(t)

χdb,ψd

b (t)(t) = log

(βRd

b,ψdb (t)

(t− 1)

+ (1 − β)Rdb,ψd

b (t)(t)

)− log

(βRd

b,ψdb (t)

(t− 1))

(11)

which can be further written as

χdb,ψd

b (t)(t) = log

(1 + wb,ψd

b (t)(t)Rd

b,ψdb (t)

(t))

(12)

where

wb,ψdb (t)

(t) =(1 − β)

βRdb,ψd

b (t)(t− 1)

. (13)

Similarly, let us write the second term in (9) as χub,ψu

b (t)(t),

i.e.,

χub,ψu

b (t)(t) = log

(1 + wb,ψu

b (t)(t)Rub,ψu

b (t)(t))

(14)

where

wb,ψub (t)(t) =

(1 − β)

βRub,ψu

b (t)(t− 1). (15)

In the given equations, note that if ψdb (t) = 0 (ψu

b (t) = 0),then χd

b,ψdb (t)

(t) = 0 (χub,ψu

b (t)(t) = 0). The overall utility of a

cell (e.g., cell b) is defined as

Φb,{ψdb (t),ψ

ub (t)}(t) = χd

b,ψdb (t)

(t) + χub,ψu

b (t)(t). (16)

Then, the optimization problem in (7) can be equivalentlyexpressed as

Ψ(t),P(t) = argmaxS,QS

∑b∈Π

Φb,Sb(t). (17)

The given problem is a nonlinear nonconvex combinatorialoptimization problem, and the optimal solution may not befeasible to compute in practice. Moreover, the earlier problemis a mixed discrete (UE selection) and continuous (power allo-cation) optimization. Although the problem can be optimallysolved via exhaustive search, the complexity of this methodincreases exponentially as the number of cells/UEs increases.We will then provide a suboptimal solution of the earlierproblem that jointly determines the UE selection and powerallocation in a distributed manner.

III. CHANNEL ESTIMATION IN FULL-DUPLEX

MULTICELL NETWORKS

As discussed in Section I, in an FD multicell scenario, CSI isessential to maximize FD gains. There are three different typesof channels to monitor: I) BS-to-UE or UE-to-BS channels;II) BS-to-BS channels; and III) UE-to-UE channels. Since weassume a TDD system in this paper, the channels between anytwo radios in both directions are reciprocal. Existing Third-Generation Partnership Project (3GPP) protocols for HD com-munications already include mechanisms to monitor type Ichannels, in which a terminal (UE) needs to estimate the chan-nel with a BS. In 3GPP LTE, cell-specific reference signals arebroadcast from the BSs with their physical-layer cell identity.UEs then use the received reference signals to estimate thechannels from the BSs and transmit CSI reports to BSs usingPUCCH and PUSCH [34], [40]. The same signal can be used atthe BS receiver to estimate the channel from its neighboringBSs, i.e., type II channels. The remaining challenge for theFD multicell scenario is to estimate UE-to-UE interferenceor type III channels since the inter-UE interference poses afundamental challenge to exploit FD in a cellular scenario.

In this paper, we propose to implement neighbor discoveryat UEs to find potential UE interferers in its neighborhood.In 3GPP LTE, sounding reference signals (SRSs) are used forchannel quality estimation at different frequencies in the uplink[34]. This uplink SRS can be used by UEs to estimate thechannels with other UEs in its neighborhood [41]. In LTE, eachUE is scheduled on the SRS channel regularly in order for theBS (eNB) to collect information for uplink channel scheduling.All UEs within a cell are informed about the subframes that willbe used for SRS. The main challenge in neighbor discovery is todistinguish between different UEs, including neighboring cells’UEs, during SRS transmission. This problem can be solved byallocating different SRS combination sets to neighboring cellsas well as different orthogonal combinations to UEs within thecell which are scheduled to transmit simultaneously [34]. Inaddition, this allocation of SRS combinations can be passedto UEs through the downlink shared channel [41]. There arealternate ways to implement neighbor discovery, such as mech-anisms proposed for device-to-device (D2D) communications[42], [43]. In this paper, for our scheduling solution we assumethat each UE will be able to estimate the channels within itsneighborhood, i.e., channels with strong UE interferers, and thisinformation will be transmitted to its BS. The signaling over-head during the transmission of such new UE-to-UE channelinformation over the air link in analyzed in Section VI.

IV. DISTRIBUTED FULL-DUPLEX MULTICELL

RESOURCE ALLOCATION

Here, we provide a distributed method to solve (17). Asdiscussed in Section I, FD throughput gain is available onlyunder certain propagation conditions, distances among nodesin the network, and power levels. This suggests that FD opera-tion should be used opportunistically, i.e., with an intelligentscheduler that schedules UEs with appropriate power levelsto achieve FD operation when appropriate but defaults to HD


operation if otherwise. In each time slot, the joint UE selectionand power allocation problem (17) is solved in two steps:1) intracell UE selection, i.e., for a given feasible power allo-cation, find the UE or a pair of UEs in each cell with maximumoverall utility; 2) intercell coordination, i.e., for the given UEselection, derive the power to be allocated to the selected UEsthrough intercell coordination, such that overall utility can bemaximized. In the following, we discuss both steps in detail.

A. Intracell UE Selection

In this step, for each time slot t, each BS selects the UE ora pair of UEs to be scheduled. This is a single-cell resourceallocation problem, which can be solved in multiple ways[22]–[24]. Given the fact that a small cell does not have manyUEs, it is easy to perform resource allocation in a centralizedmanner at the BS. The BS has knowledge of the channel gainswith its all UEs, which is possible through CSI reporting fromits UEs [34], [40]. As discussed in Section III, we furtherassume that the BS also knows the channel between all UE pairsand thus the subset of UE pairs with strong mutual interference.The BS will assume no interference between UE pairs forwhich no information is received presumably because of a weakSRS signal.

In this step, each BS b ∈ Π, for the given feasible powerallocation, finds the UEs that provide the maximum utilitydefined in (16), i.e.,

{ψdb (t), ψ

ub (t)

}= argmax

Sb

Φb,Sb(t). (18)

Note that, at this stage, there is no intercell informationavailable; therefore, in the given equation, the instantaneousrate of a UE does not take any inter-cell interference intoaccount. Thus, for the cell b, instead of (3) and (4), the SINRsat downlink UE i and uplink UE j are calculated as

SINRdb,i=

pb(t)Gb,i

pj(t)G̃j,i +Ni

, SINRub,j=

pj(t)Gj,b

pb(t)γ +Nb(19)

where G̃j,i denotes the channel gain estimation between UEj and UE i measured by UE i. If UE i does not hear a strongsignal from UE j, this means UE i did not measure and send thechannel estimation information for UE j to the BS. In that case,G̃j,i will be neglected during this scheduling decision. Problem(18) can be solved simply by the exhaustive search method.The BS initially assumes the maximum power allocation foreach UE in both directions and then calculates the aggregateutility for each possible combination of UEs and finds theutility maximizing UE or UEs. Since each cell performs thisstep independently, the computation complexity of this stepincreases only in a quadratic manner with the number of UEs,i.e., O(n2), which should not be a problem given that a smallcell typically supports a small number of UEs. After this step,each cell has a downlink UE, an uplink UE, or both to schedulein time slot t. Once the UE selection is done, the next stepis intercell coordination, described in the following, in which

the power levels of the selected UEs are updated such thatthe aggregate utility of all the UEs, as given in (17), can bemaximized.

B. Intercell Coordination

This step is used to take the effect of intercell interferenceinto account. In this step, the transmit power levels of all theselected UEs are updated such that the mutual interferencecan be mitigated and the overall utility of the system canbe maximized. The objective function of this problem can bewritten as

P(t) = argmaxQΨ(t)

∑b∈Π

Φb,{ψdb (t),ψ

ub (t)}(t). (20)

Each of the BSs solves the given problem independently andderives its optimum power. The utilities of the other BSs areestimated based on the information received from neighboringBSs. The detailed procedure is given in the following. Thisprocedure is completed in multiple iterations. It is assumedthat the information between the BSs is exchanged over the X2interface [44]. Note that this procedure is applied at each timeslot, but for the sake of simplifying the notation, we omit theterm t here.

1) Initialization: Intracell UE selection determines the UEsto be scheduled, i.e., ψd

b and ψub in cell b ∈ Π. At this ini-

tial step, each BS b ∈ Π broadcasts a message vector con-taining the information of weights (wb,ψd

b, wb,ψu

b), UE IDs

(id(ψdb ), id(ψ

ub )), and the channel gains (Gb,ψd

b, Gψu

b ,b) with its

own BS for the selected UEs. In addition to this information, thechannel gains of the selected UEs with other BSs are also sent tothe corresponding BSs. For example, channel gains with BS j,i.e., (Gj,ψd

b, Gψu

b ,j), are sent to the BS j. This information

is only sent once at the initialization step. Here, we use UEIDs corresponding to the value of SRS combination allocatedto a UE. The UE IDs of other cells’s UEs will be used at aBS to identify and match the UE-to-UE channels estimationsmeasured by its own cells’s UEs. These IDs can be createdlocally at each BS by matching UEs to the allocation of SRScombinations. In addition to the given information, after gettingUE ID information, each BS also sends some required UE-to-UE channel information, as described further here.

2) Power Update: After the initial information exchange,each iteration (n ≥ 1) has two steps.

First Step: Each BS calculates the total received uplink anddownlink interference based on the information received duringinitialization and in the previous iteration (n− 1). For example,in BS b ∈ Π, the estimated interference in downlink and uplinkare given, respectively, by

I(n−1)

ψdb

=Nψdb+

∑i∈Π\b

p(n−1)i Gi,ψd

b+∑i∈Π

p(n−1)ψu

iG̃ψu

i ,ψdb

(21)

I(n−1)b =p

(n−1)b γ+Nb +

∑i∈Π\b

p(n−1)ψu

iGψu

i ,b+∑i∈Π\b

p(n−1)i Gi,b

(22)


where p(n−1){} is the power values derived in the previous

iteration, as discussed in the next step, and G̃ψui ,ψ

db

is the

channel measured by UE ψdb with ψu

i of cell i, as discussed inSection III. The UE ID information exchanged during initial-ization is used during this process.

At the end of this step, the value of the estimated interferenceis broadcast by each BS to its neighbors.

Second Step: Each BS updates its transmit power to maxi-mize the aggregate utility sum (20), given the power levels ofother transmitters at the previous iteration, and the interferenceinformation received in the first step.

At each BS b ∈ Π{p(n)b , p

(n)ψu

b

}= argmax

{x,y}∈Q{ψdb,ψu

b }

∑j∈Π

Φ̃b,(n−1)

j,{ψdj ,ψ

uj } (23)

where Φ̃b,(n−1){} is the estimated value of the overall utility

calculated at BS b. It can be written as{p(n)b , p

(n)ψu

b

}= argmax

{x,y}∈Q{ψdb,ψu

b }

∑j∈Π

×[log

(1+wj,ψd

jlog2

(1 + SINRb,(n−1)

j,ψdj

))+ log

(1+wj,ψu

jlog2

(1+SINRb,(n−1)

j,ψuj

))](24)

where

SINRb,(n−1)

j,ψdj

=

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

xGb,ψd

b

I(n−1)

ψdb

+

(y−p

(n−1)ψub

)G̃

ψub,ψd

b

j = b

p(n−1)j G

j,ψdj

I(n−1)

ψdj

+(x−p

(n−1)b

)G

b,ψdj+

(y−p

(n−1)

ψub

)G̃

ψub,ψd

j

j �= b

(25)

SINRb,(n−1)j,ψu

j

=

⎧⎪⎪⎪⎨⎪⎪⎪⎩yGψu

b,b

I(n−1)

ψub

+

(x−p

(n−1)

ψdb

)γ

j = b

p(n−1)

ψuj

Gψuj,j

I(n−1)

ψuj

+(x−p

(n−1)b

)Gb,j+

(y−p

(n−1)

ψub

)Gψu

b,j

j �= b.

(26)

Note that, in (25), the channel G̃ψub ,ψ

dj

is measured at ψdj in

cell j, as described in Section III. This information is sent byBS j to BS b after receiving UE IDs of the selected UEs duringthe initialization process.

We use GP [45], [46] to get a near-optimal solution of thisnonlinear nonconvex optimization (24). GP cannot be applieddirectly to the objective function given in (24); therefore, wefirst convert our objective function into a weighted-sum-ratemaximization using the following approximation. In (24), forthe weight terms, let us consider wj,ψd

j, which is given by (13).

Since we set β very close to one, and moreover, if we assume

that the value of the instantaneous rate Rdj,ψd

jwill be of the same

order as the average rate Rdj,ψd

j, then the term (1 − β)Rd

j,ψdj/

βRdj,ψd

j (t)will be close to zero. Therefore, by using ln(1+x)≈x

for x close to zero, (24) can be approximated by{p(n)b , p

(n)ψu

b

}= argmax

{x,y}∈Q{ψdb,ψu

b }

∑j∈Π

(wj,ψd

jlog2

(1 + SINRb,(n−1)

j,ψdj

)

+wj,ψujlog2

(1+SINRb,(n−1)

j,ψuj

)).

(27)

Note that both x and y in Q{ψdb ,ψ

ub } have inbuilt maximum

power constraint given in (7). Problem (27) can be furtherwritten as

argmin{x,y}

M∏j=1

⎛⎝⎛⎝ 1

1 + SINRb,(n−1)

j,ψdj

⎞⎠wj,ψd

j

·

⎛⎝ 1

1 + SINRb,(n−1)j,ψu

j

⎞⎠wj,ψuj

⎞⎠subject to 0 ≤ x

pdmax

≤ 1, 0 ≤ y

pumax

≤ 1. (28)

In general, to apply GP, the optimization problem shouldbe in GP standard form [45], [46]. In the GP standard form,the objective function is a minimization of a posynomial1

function; the inequalities and equalities in the constraint set area posynomial upper bound inequality and monomial equality,respectively.

In our case, in (28), constraints are monomials (hence posyn-omials), but the objective function is a ratio of posynomials, asin (29), shown at the bottom of the next page. Hence, (28) is nota GP in standard form because posynomials are closed undermultiplication and addition but not in division.

According to [46], (28) is a signomial programming (SP)problem. In [46], an iterative procedure is given, in which(28) is solved by constructing a series of GPs, each of whichcan easily be solved. In each iteration2 of the series, the GPis constructed by approximating the denominator posynomial(29) by a monomial, then using the arithmetic–geometric meaninequality and the value of {x, y} from the previous iteration.The series is initialized by any feasible {x, y}, and the iterationis terminated at the sth loop if ||xs − xs−1|| < ε and ||ys −ys−1|| < ε, where ε is the error tolerance. This procedure is

1A monomial is a function f : Rn++ → R : g(p)=dpa

(1)

1 pa(2)

2 · · · pa(n)

n ,

where d ≥ 0 and a(k) ∈ R, k = 1, 2, . . . , n. A posynomial is a sum of

monomials, i.e., f(p) =∑J

j=1 djpa(1)j

1 pa(2)j

2 · · · pa(n)j

n .2Note that this iterative procedure to solve GP is an inner procedure of the

main iterative procedure of the distributed Power Update step.


provably convergent and empirically almost always computesthe optimal power allocation [46].

The new derived values are broadcast by each BS to itsneighboring BSs. Then, the same procedure is applied startingfrom the Power Update step (Step 2) until the terminationcondition described below is reached.

3) Termination: The procedure ends when either a maxi-mum number of iterations is reached or a terminating solutionis obtained. For the UE selection Ψ given by Intracell UE selec-tion, power allocation P ∈ QΨ will be a terminating solutionif changing the power level of any single transmitter cannotimprove the aggregate utility sum, given the power levels ofall other transmitters. It was observed in the simulation resultsthat with the given power update rule, the termination conditionis achieved in a few iterations.

V. CENTRALIZED FULL-DUPLEX MULTICELL

RESOURCE ALLOCATION

Here, to evaluate the performance of our proposed distributedapproach against a centralized approach, we describe a central-ized solution to solve problem (17). We assume a centralizedscheduler that has access to global information, i.e., CSI, power,etc., and jointly derives the UE selection and power allocationfor all the cells simultaneously. The results generated usingthis scheduler can be viewed as an upper bound on systemperformance. In this setting, as in the decentralized problem,the joint problem of UE selection and power allocation (17) issolved in two steps: 1) greedy UE selection and 2) centralizedpower allocation.

A. Greedy UE Selection

In each time slot t, for a given feasible power allocation, thecentralized scheduler finds a UE or a pair of UEs in each cell totransmit, which is given as

Ψ(t) = argmaxS

M∑b=1

Φb,{ψdb (t),ψ

ub (t)}(t). (30)

In traditional HD systems, finding the optimal set of UEsis very different in the downlink and uplink directions. In theliterature, the problem given is solved optimally in the downlinkdirection [47]–[49], where the interferers are the fixed BSsin the neighboring cells, assuming a synchronized HD multi-cell system. It is easy to estimate the channel gains betweeneach UE with the neighboring BSs. Thus, interference fromthe neighboring cells can be calculated without knowing theactual scheduling decision (UE selection) of the neighboringcells. In this situation, a centralized scheduler can calculatethe instantaneous rate and the utility of each UE in each cell,and make the UE selection decision for each cell optimally. Inuplink scheduling, for the given power allocation, interferencefrom the neighboring cell cannot be calculated until the actualscheduling decision of the neighboring cell is known because,in this case, a UE in the neighboring cell generates the inter-ference. This also applies to the FD system, where interferencefrom the neighboring cell could be from a UE or the BS or both.

To solve this problem, we use a heuristic greedy methodsimilar to [13], [50]. In this method, the centralized greedyalgorithm runs over a random order of all the cells and selectsUEs in each cell one by one. For each cell, the UE or a pair of

M∏j=1

⎛⎝⎛⎝ 1

1 + SINRb,(n−1)

j,ψdj

⎞⎠wj,ψd

j

·

⎛⎝ 1

1 + SINRb,(n−1)j,ψu

j

⎞⎠wj,ψuj

⎞⎠

=

⎛⎝ I(n−1)

ψdb

+(y − p

(n−1)ψu

b

)G̃ψu

b ,ψdb

I(n−1)

ψdb

+(y − p

(n−1)ψu

b

)G̃ψu

b ,ψdb+ xGb,ψd

b

⎞⎠wb,ψd

b(t)

·

⎛⎝ I(n−1)ψu

b+(x− p

(n−1)

ψdb

)γ

I(n−1)ψu

b+(x− p

(n−1)

ψdb

)γ + yGψu

b ,b

⎞⎠wb,ψd

b(t)

·M∏

j=1,j �=b

⎛⎝⎛⎝ Cb,(n−1)

ψdj

+ xGb,ψdj+ yG̃ψu

b ,ψdj

Cb,(n−1)

ψdj

+ xGb,ψdj+ yG̃ψu

b ,ψdj+ p

(n−1)j Gj,ψd

j

⎞⎠wj,ψd

j(t)

·

⎛⎝ Cb,(n−1)ψu

j+ xGb,j + yGψu

b ,j

Cb,(n−1)ψu

j+ xGb,j + yGψu

b ,j+ p

(n−1)ψu

jGψu

j ,j

⎞⎠wj,ψuj(t)⎞⎠

where

Cb,(n−1)

ψdj

= I(n−1)

ψdj

− p(n−1)b Gb,ψd

j− p

(n−1)ψu

bG̃ψu

b ,ψdj

Cb,(n−1)ψu

j= I

(n−1)ψu

j− p

(n−1)b Gb,j − p

(n−1)ψu

bGψu

b ,j (29)


Fig. 2. (a) Indoor environment with nine RRH cells. (b) Outdoor environment with 12 picocells.

TABLE ISIMULATION PARAMETERS FOR AN INDOOR MULTICELL SCENARIO

UEs are selected with maximum utility gain, where the utilitygain is the difference between the gain in the marginal utilityof the chosen UE or UEs and the loss in the marginal utility ofselected UEs in other cells due to new interference generatedfrom the cell being considered. Moreover, for the UEs in thecell being considered, interference from only the cells for whichdecision has been made is considered. Since this is the samemethod as the one given in [13], we omit the details of thisalgorithm in this paper. The complete algorithm can be foundin [51]. This algorithm gives the UE combination Ψ(t).

B. Centralized Power Allocation

In this step, for the selected UE combination in the previousstep, a centralized power allocation process is applied to find theappropriate power levels for all UEs so that the overall utilitycan be maximized as described in (20). In this case, similar tothe Section IV-B, we use GP to solve this nonlinear nonconvexproblem, but in a centralized manner. Since we assume thecentralized scheduler has access to the global information,GP is applied once3 at the scheduler to find the optimumpower allocation for all the selected UEs, instead of applyingit independently at each BS, as in Section IV-B. More detailscan be found in [51] for the centralized power allocation.

VI. PERFORMANCE EVALUATION

Here, we evaluate the performance of the FD system com-pared with a baseline HD system using the joint UE selectionand power allocation presented in Sections IV and V. Tosimulate the HD system, we consider both synchronous and

3In this case, it will also be SP, which will be solved in an iterative procedureby constructing a series of GPs.

dynamic TDD [36] systems. In the synchronous HD setting, ina given time slot, all cells schedule either uplink or downlinktransmission, and the number of time slots is divided equallybetween the uplink and downlink transmission. In dynamicTDD, each cell has the flexibility of scheduling its UE inany direction, whichever provides larger utility at the giventime slot. The same distributed and centralized algorithms arealso applied to schedule the UEs and to determine the powerallocation in these HD systems. For example, for the HD case,(27)–(29) will just contain a single term for the correspondingdirection instead of two terms.

A. Deployment Scenarios and Simulation Parameters

We consider both indoor and outdoor deployment scenariosin our simulations. For the indoor environment, a dense multi-cell system with nine indoor remote radio head (RRH)/hot-zonecells, as shown in Fig. 2(a), is considered. The simulation pa-rameters, based on 3GPP simulation recommendations for anRRH cell environment [52], are described in Table I. The pathloss for both LOS and NLOS within a cell are given in Table I,where the probability of LOS PLOS is

PLOS=

⎧⎪⎨⎪⎩1, R≤0.018

exp (−(R−0.018)/0.027), 0.018<R<0.037

0.5, R≥0.037.

(31)

In (31), R is the distance in kilometres. The channel modelused between BSs and UEs is also used between UEs andbetween BSs for the FD interference calculations, with thejustification that BSs do not have a significant height advantagein the small-cell indoor scenario considered and that it is a con-servative assumption for the UE-to-UE interference channel.Eight randomly distributed UEs are deployed in each cell.


TABLE IISIMULATION PARAMETERS FOR AN OUTDOOR MULTICELL SCENARIO

Fig. 3. (a) Average number of iterations required to converge in different topologies in (a) indoor multicell and (b) outdoor multicell scenarios.

To simulate an outdoor multicell scenario, the parametersrelated to path loss, shadowing, and noise figure used in sim-ulations are based on the 3GPP simulation recommendationsfor outdoor environments [36] and are described in Table II.The probability of LOS for BS-to-BS and BS-to-UE path loss is(R is in kilometers)

PLOS = 0.5 −min (0.5, 5 exp(−0.156/R))

+ min (0.5, 5 exp(−R/0.03)) . (32)

For the outdoor environment, we first considered the samedense multicell system, as shown in Fig. 2(a), assuming nowall(s) between the cells. However, the performance gain of FDoperation in such dense outdoor environments was not substan-tial due to strong intercell interference when no mitigation otherthan scheduling and power control is applied. We thereforeanalyzed the performance of FD operation in a sparse outdoormulticell system with 12 randomly dropped picocells, eachwith ten randomly distributed UEs as shown in Fig. 2(b). Thisdeployment reflects current picocell deployment, which coverlocal traffic hotspots. As we described in Section I, since FDoperation increases the interference in a network significantly,exploiting FD operation in such an indoor environment or asparse outdoor environment is more beneficial because of thereduction in intercell interference.

In both indoor and outdoor scenarios, the channel bandwidthis 10 MHz, the maximum BS power is 24 dBm, the maxi-mum UE power is 23 dBm, and the thermal noise density is−174 dBm/Hz. In our simulations, since we use the Shannonequation to measure the data rate, we apply a maximum spectral

efficiency of 6 bits/s/Hz (corresponding to 64-QAM modula-tion) to match practical systems. BSs and UEs are assumedequipped with single omnidirectional antennas. We simulatedthe system with both full buffer traffic and nonfull buffer FileTransfer Protocol (FTP) traffic assumptions. In the follow-ing, we present the performance of the FD system with bothdistributed and centralized scheduling algorithms, and discussthe convergence and signaling overhead in these methods.Moreover, we use FD@x to represent the FD system with self-interference cancelation of x dB. FD@Inf means that there isno self-interference.

B. On the Convergence of DFDMR

Here, we study the convergence of the distributed schedulingalgorithm presented in Section IV. Fig. 3 shows the averagenumber of iterations required to converge. Fig. 3(a) shows theresult for the indoor multicell case for FD@95, FD@Inf, andHD synchronous systems. We calculate the average conver-gence time taken over different distributions of the UEs, i.e.,different topologies. In the FD case, due to higher number ofsimultaneous transmissions, it takes longer to converge com-pared with the HD system. Moreover, due to higher interferencein FD@95, the scheduler takes longer to converge comparedwith the FD@Inf system. In the outdoor scenario given inFig. 2(b), the same trend is observed as shown in the Fig. 3(b).In this case, results are obtained with different random drops ofpicocells. Due to higher intercell interference between a BS andUEs as compared with the indoor scenario, more iterations arerequired for the outdoor scenario.


Fig. 4. Distribution of average data rates for the HD system and FD system with a round-robin scheduler in an indoor multicell scenario.

Fig. 5. Distribution of average data rates for the HD system and FD system with both distributed and centralized scheduling algorithms in an indoor multicellscenario.

C. Throughput Performance

With the given simulation settings, in the indoor case, werun our simulation for different UE drops in all cells, each fora thousand timeslots, with the standard wrap around topology,and generate results for both the HD and FD systems. Here, wesimulate the system in which each UE has full-buffer traffic inboth directions; the results with the nonfull buffer traffic casewill be presented in Section VI-D.

To show the importance of UE selection and power alloca-tion, we first generate the results in the indoor setting for asimple centralized scheduler, i.e., round-robin scheduler withfixed maximum transmission powers in both directions. In theHD system (HD synchronous), in each direction, each cellselects UEs in a round-robin manner. In the FD system, in eachtime slot, each cell chooses the same UE as selected in the HDsystem with a randomly selected UE for the other direction tomake an FD pair. Fig. 4(a) and (b) show the distribution ofaverage downlink and uplink throughputs, for different BS self-interference cancelation capabilities. In the downlink direction,in most of the cases (70%), there is no FD gain, which is due to

the lack of any intelligent selection procedure during FD oper-ation. In the uplink, due to the cancelation of self-interference,the FD system throughput is higher than the HD system. Thedifference improves with increased self-interference cancela-tion capability. From a system point of view, which includesboth uplink and downlink, this round-robin scheduling doesnot provide sufficient FD capacity gain. This demonstratesthe need for an intelligent scheduling algorithm to provide again during FD operation, which can benefit both uplink anddownlink.

Next, we generate results with both the proposed distrib-uted and centralized joint UE selection and power allocationprocedure. Fig. 5(a) and (b) shows the distribution of averagedownlink and uplink throughputs for both distributed and cen-tralized methods. In this plot, the distribution is only shownfor HD synchronous, FD@75, FD@95, and FD@Inf system tokeep the plot readable; however, Table III contains the averagethroughput over all UEs for all the simulated systems. It alsocontains the average throughput gain of FD systems comparedwith the HD synchronous system.


TABLE IIIAVERAGE THROUGHPUT (Mb/s) OVER ALL UES OF HD AND FD SYSTEMS WITH BOTH DISTRIBUTED AND

CENTRALIZED SCHEDULING ALGORITHMS IN AN INDOOR MULTICELL SCENARIO. FOR AN FD SYSTEM,AVERAGE THROUGHPUT GAIN COMPARED WITH THE HD SYNCHRONOUS SYSTEM IS ALSO GIVEN

TABLE IVAVERAGE NUMBER OF CELLS PER SLOT IN DIFFERENT MODES IN AN INDOOR MULTICELL SCENARIO

Fig. 6. Distribution of average data rates for the HD system and FD system with both distributed and centralized scheduling algorithms in an outdoor multicellscenario.

The HD system shows a narrow distribution centered near4 Mb/s in both downlink and uplink, whereas the FD systemshows a wider distribution since the scheduler takes advantageof the variable nature of the interference to assign FD operationwith an appropriate data rate whenever possible. The dynamicTDD HD system has similar performance as the synchronousHD system since the same kind of channel model is assumedbetween different nodes; therefore, there is not much differentin the interference experienced by a node in both systems. Inthis scenario, the distributed algorithm performs nearly as wellas the centralized solution for almost all the systems. In general,the throughput gain of the FD system compared with that ofthe HD system increases as the self-interference cancelationimproves. With the higher self-interference cancelation values,the FD system nearly doubles the capacity when compared withthe HD system.

From the simulation, one can also observe the dependencebetween FD/HD operation selection in our scheduler and theself-interference cancelation capability, i.e., the lower the self-interference cancelation, the fewer the number of cells in a timeslot that are scheduled in FD mode. This is verified by countingthe average number of cells per time slot, which are in FD modeor HD mode or with no transmission as shown in Table IV.With 75-dB self-interference cancelation, on average, 84% of

the cells operate in FD mode, whereas with 105 dB, 98% of thecells operate in FD mode. Note that, in the HD system, in eachtime slot, all cells transmit in one direction (either uplink ordownlink). These results are for the centralized method; similarresults are obtained for the distributed method.

To analyze the performance of FD operation in the outdoorscenario, as we mentioned earlier in Section VI-A, we firstsimulate the dense outdoor multicell scenario. In this case,the average throughput gain of the FD system is only 25%in the downlink and 32% in the uplink with the centralizedscheduler. These gains do not vary with self-interference can-celation because strong intercell interference dominates theself-interference and decreases the opportunities for capacityimprovement due to FD operation. These results show that it isnot very beneficial to use FD radios in dense outdoor environ-ments due to the high intercell interference. This observationmotivates us to investigate the performance of FD radios insparse outdoor environments.

We simulate the sparse outdoor multicell scenario as shownin Fig. 2(b). We run our simulation for several random dropsof 12 picocells in a hexagonal cell with a width of 500 m.Fig. 6(a) and (b) show the distribution of average downlink anduplink throughputs, and Table V shows the average throughputover all UEs for all the systems, as well as the gain of the


TABLE VAVERAGE THROUGHPUT (Mb/s) OVER ALL UES OF HD AND FD SYSTEMS WITH BOTH DISTRIBUTED ANDCENTRALIZED SCHEDULING ALGORITHMS IN AN OUTDOOR MULTICELL SCENARIO. FOR AN FD SYSTEM,

AVERAGE THROUGHPUT GAIN COMPARED TO THE HD SYNCHRONOUS SYSTEM IS ALSO GIVEN

TABLE VIAVERAGE NUMBER OF CELLS PER SLOT IN DIFFERENT MODES IN AN OUTDOOR MULTICELL SCENARIO

TABLE VIIAVERAGE DELAY (SECONDS) IN AN INDOOR MULTICELL SCENARIO

FD system, as compared with the HD synchronous system.Similar to the indoor scenario, FD increases the capacity of thesystem significantly over the HD case, where the increase isproportional to the amount of self-interference cancelation. Inthis case also, the distributed scheduling algorithm gives resultsclose to the centralized algorithm. In this outdoor scenario, theaverage throughput of a UE is lower compared with that of theindoor case, but it is distributed over a wider range. Moreover,the throughput increase due to FD operation is less than whatit was in the indoor case. The reason behind this is that theintercell interference between a BS and UEs in neighboringcells is much stronger that in the indoor scenario.

In this case, for the centralized algorithm, the uplink through-put is higher than the downlink throughput, which also in-creases the gap between the performance of the distributedand centralized performance in the uplink. In the centralizedgreedy UE selection algorithm, the utility to select a UE is thedifference between the marginal utility of the UE and the lossin the marginal utility of the selected UEs in other cells due tonew interference generated from the UE being considered. Inthe case of downlink, for all the potential UEs in the cell beingconsidered, the second term, i.e. interference generation (fromtheir BS) to other cells will be constant, whereas in the uplink,since the interference generation also depends on the locationof the UE, both utility gain and utility decrement of other cellsvary from UE to UE. This difference provides more degreesof freedom for the uplink UE selection and therefore managesuplink multicell interference better than downlink case.

Table VI shows the average number of cells per slot, whichare in FD mode, HD mode, or with no transmission with thecentralized scheduling method. First, in the HD system, incontrast to the indoor scenario, we can see that some cells arenot transmitting at all in some slots. This is due to the higherintercell interference between the BS and UEs in neighboringcells; the system throughput is higher when certain cells are

not scheduled for transmission, resulting in reduced intercellinterference. Further, for the same reason, the average numberof cells operating in FD mode is smaller than the indoorscenario. In this case, the number of cells in FD mode alsoincreases with self-interference cancelation.

D. Full-Duplex Gain for the Nonfull Buffer Traffic Model

Here, we analyze the performance of the FD system withnonfull buffer FTP traffic [52]. In this case, each UE hasrequests to download or/and upload files of 1.25 MB. The timeinterval between completion of a file transmission and an arrivalof a new request is exponentially distributed with a mean of 1 s.The delay for each UE, which is defined as the total time itexperiences from the request arrival to the completion of down-loading or uploading a file, is calculated. A significant delayimprovement, due to simultaneous downloading and uploadingin an FD system is observed, as shown in Table VII, whichshows the average delay that a UE experiences for differentsystems. Moreover, a UE downloads 48%, 69%, 83%, 90%, and92% more files and uploads 56%, 75%, 86%, 88%, and 90%more files in the FD system compared with those in the HDsystem with 75, 85, 95, 105 dB, and perfect self-interferencecancelation, respectively.

E. Signaling Overhead

Here, we compute the signaling overhead required to enableFD scheduling algorithms compared with the existing HDsystem. As mentioned in Section III, in our FD system, eachUE needs to send the channel measurement information of itsneighbourhood. In our simulations, we derive a threshold foreach UE to determine inclusion in its potential strong interfererlist for UE-to-UE interference. For a UE u, given its threshold,all other such UEs for which the UE-to-UE channel is higher


than the threshold will be considered strong interferers, and UEu will send the channel information for these UEs to its BS.A downlink UE gets interference from both neighboring BSsand uplink UEs. The channel measurement from the BSs isused to derive the threshold for the UE-to-UE channels for eachUE. Each UE measures the channel with all its neighboringBSs and derives the average channel strength of its BS-to-UEinterference channel. This average channel strength is used asthe threshold for the UE-to-UE interference channel. Let usassume that, on average, there are K strong UE interferers.

We assume the channel information is represented by 8 bits.If a UE sends this information every 2 ms, which is the maxi-mum periodic frequency of the SRS transmission of a UE [34],the total overhead in each cell, would be 4KNm kb/s. In oursimulations, in the indoor scenario, where Nm = 8, and theaverage value of K observed equals 7. The average overhead inthe indoor scenario is thus 224 kb/s. In the outdoor scenario, itis 320 kb/s (Nm = 10, K = 8). For example, for a LTE systemwith 10-MHz bandwidth and 16-QAM, where the peak LTEuplink capacity is 25.5 Mb/s [40], the UE-to-UE channel mea-surement incurs less than 2% overhead.

We also compare the signaling overhead of the distributedand centralized algorithms in terms of average outbound trafficgenerated by each BS. In the centralized method, the central-ized scheduler needs to collect a large set of channel informa-tion from each BS, which includes 1) channels with other BSs,2) channels with all the UEs in the system, and 3) strong UE-to-UE channels. It also needs to collect weights of all UEs. Inthis case, each BS generates (M +MNm +NmK)× 8 bitsper transmission time interval (TTI). In the case of the distrib-uted approach, each BS generates (2 + 2 + 2M +K)× 8 bitsduring initialization and (2 + 2)× nI × 8 bits during the it-erative process, where nI is the number of iterations. In thecase of the indoor system, based on our simulation results, ifwe assume K = 7, nI = 7, then for the centralized approach,each BS generates 1096 bits per TTI, and in the case of thedistributed approach, each BS generates 456 bits per TTI.

VII. CONCLUSION

We investigated the application of common carrier FD radiosto resource managed small-cell systems in a multicell deploy-ment. Assuming FD capable BSs with HD UEs, we presenta joint uplink and downlink scheduler that does UE selectionand power allocation to maximize the network utility in adistributed manner. It operates in FD mode when conditions arefavorable but defaults to HD mode if otherwise. The proposeddistributed algorithm performs nearly as well as the centralizedsolution but with much lower signaling overhead. Our simu-lation results show that an FD system using a practical designparameter of 95-dB self-interference cancelation at each BS canimprove the capacity by 90% in an indoor multicell hot-zonescenario and 60% in an outdoor multiple-picocell scenario.From these results, we conclude that, in both indoor small-celland sparse outdoor environments, FD BSs with an intelligentscheduling algorithm are able to improve capacity significantlywith manageable signaling overhead.

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Sanjay Goyal (S’16) received the B.Tech. degreein communication and computer engineering fromThe LNM Institute of Information Technology,Jaipur, India, in 2009 and the M.S. degree inelectrical engineering from New York University(NYU) Tandon School of Engineering, Brooklyn,NY, USA, in 2012. He is currently working towardthe Ph.D. degree with the Department of Electricaland Computer Engineering, NYU Tandon School ofEngineering.

His research interests include designing and an-alyzing wireless network protocols with full-duplex communications, particu-larly for the medium access control layer.

Mr. Goyal co-received the Best Paper Award at the IEEE InternationalConference on Communications in 2016, along with C. Galiotto, N. Marchetti,and S. Panwar.

Pei Liu (M’09) received the B.S. and M.S. degreesin electrical engineering from Xi’an Jiaotong Uni-versity, Xi’an, China, in 1997 and 2000, respectively,and the Ph.D. degree in electrical and computer en-gineering from New York University (NYU) TandonSchool of Engineering, Brooklyn, NY, USA, in 2007.

He is currently a Research Assistant Professorof electrical and computer engineering with NYUTandon School of Engineering. His research interestsinclude designing and analyzing wireless networkprotocols with an emphasis on cross-layer optimiza-

tion, particularly with the physical and medium access control layers; wirelesscommunications; wireless networks; and video over wireless.

Shivendra S. Panwar (F’11) received the B.Tech.degree in electrical engineering from the IndianInstitute of Technology Kanpur, Kanpur, India, in1981 and the M.S. and Ph.D. degrees in electricaland computer engineering from the University ofMassachusetts, Amherst, MA, USA, in 1983 and1986, respectively.

He spent the summer of 1987 as a Visiting Sci-entist with the IBM T. J. Watson Research Center,Yorktown Heights, NY, USA, and as a Consultantto AT&T Bell Laboratories, Holmdel, NJ, USA. He

is currently a Professor with the Department of Electrical and ComputerEngineering, New York University (NYU) Tandon School of Engineering,Brooklyn, NY. He is currently the Director of the New York State Center forAdvanced Technology in Telecommunications (CATT), the Faculty Director ofthe New York City Media Laboratory, and a member of NYU WIRELESS. Heis a Coeditor of two books, i.e., Network Management and Control, Vol. II andMultimedia Communications and Video Coding, both published by Plenum,and TCP/IP Essentials: A Lab Based Approach, published by the CambridgeUniversity Press. His research interests include the performance analysis anddesign of networks, such as wireless networks, switch performance, andmultimedia transport over networks.

Dr. Panwar has served as the Secretary of the Technical Affairs Council ofthe IEEE Communications Society. He co-received the IEEE CommunicationSociety’s Leonard G. Abraham Prize in the Field of Communication Systemsfor 2004, along with S. Mao, S. Lin, and Y. Wang. He also received the 2011Best Paper in Multimedia Communications Award, along with Z. Liu, Y. Shen,K. Ross, and Y. Wang.

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