5G Massive MIMO Architectures: Self-BackhauledSmall Cells versus Direct Access

Andrea Bonfante, Lorenzo Galati Giordano, David Lopez-Perez, Adrian Garcia-Rodriguez,Giovanni Geraci, Paolo Baracca, M. Majid Butt, and Nicola Marchetti

Abstract—In this paper, we focus on one of the key technologiesfor the fifth-generation wireless communication networks, mas-sive multiple-input-multiple-output (mMIMO), by investigatingtwo of its most relevant architectures: 1) to provide in-bandbackhaul for the ultra-dense network (UDN) of self-backhauledsmall cells (SCs), and 2) to provide direct access (DA) to userequipments (UEs). Through comprehensive 3GPP-based system-level simulations and analytical formulations, we show the end-to-end UE rates achievable with these two architectures. Differentlyfrom the existing works, we provide results for two strategiesof self-backhauled SC deployments, namely random and ad-hoc, where in the latter SCs are purposely positioned close toUEs to achieve line-of-sight (LoS) access links. We also evaluatethe optimal backhaul and access time resource partition dueto the in-band self-backhauling (s-BH) operations. Our resultsshow that the ad-hoc deployment of self-backhauled SCs closerto the UEs with optimal resource partition and with directiveantenna patterns, provides rate improvements for cell-edge UEsthat amount to 30% and tenfold gain, as compared to mMIMODA architecture with pilot reuse 3 and reuse 1, respectively.On the other hand, mMIMO s-BH underperforms mMIMO DAabove the median value of the UE rates when the effect of pilotcontamination is less severe, and the LoS probability of the DAlinks improves.

Index Terms—5G mobile communication, massive MIMO,wireless backhaul, small cell deployment, network capacity.

I. INTRODUCTION

F IFTH-generation (5G) wireless communication systemsare expected to support a 1000x increase in capacity com-

pared to existing networks [2]. Meeting this gargantuan targetwill require mobile network operators (MNOs) to leverage newtechnologies, such as massive multiple-input-multiple-output

This work was supported in part by Irish Research Council, by NokiaIreland Ltd under Grant Number EPSPG/2016/106, and by Science Founda-tion Ireland (SFI) under the European Regional Development Fund – GrantNumber 13/RC/2077.

A. Bonfante is with Nokia Bell Labs, Dublin, Ireland and with CON-NECT Centre for Future Networks, Trinity College Dublin, Ireland (e-mail:andrea.bonfante@nokia-bell-labs.com).

L. Galati Giordano, D. Lopez-Perez, and A. Garcia-Rodriguez are with Nokia Bell Labs, Dublin, Ireland (e-mails:lorenzo.galati giordano@nokia-bell-labs.com; david.lopez-perez@nokia-bell-labs.com; adrian.garcia rodriguez@nokia-bell-labs.com).

G. Geraci was with Nokia Bell Labs, Dublin, Ireland. He is now withthe Department of Information and Communication Technologies, UniversitatPompeu Fabra, Barcelona, Spain (e-mail: dr.giovanni.geraci@gmail.com).

P. Baracca is with Nokia Bell Labs, Stuttgart, Germany (e-mail:paolo.baracca@nokia-bell-labs.com).

M. M. Butt was with University of Glasgow, Glasgow, U.K. He is nowwith Nokia Bell Labs, Paris–Saclay, France (e-mail: majid.butt@nokia-bell-labs.com).

N. Marchetti is with CONNECT Centre for Future Networks, TrinityCollege Dublin, Ireland (e-mail: nicola.marchetti@tcd.ie).

A part of this paper was presented at IEEE Globecom 2018 [1].

(mMIMO), and network densification using small cells basestations (SCs) [3], [4]. More specifically, mMIMO consistsof deploying a large number of antennas at the base station(BS) to enable the simultaneous transmission to and froma multitude of terminals which are spatially multiplexed inthe same time-frequency resources [3], while network den-sification considers the deployment of a large number ofSCs up to the point of having one SC per user equipment(UE) [4]. A further step towards the practical ultra-dense SCdeployment is represented by self-backhauling (s-BH), definedas the capability for a BS to enable in the same spectrumresources both the access and the backhaul transmissions.Self-backhauling could drive the tight integration betweenmMIMO and ultra-dense SC deployment luring MNOs withthe potential of achieving the desired capacity boost at acontained investment [5]. Indeed, exploiting the large numberof spatial degrees-of-freedom (DoF) available with mMIMO toprovide sub-6 GHz in-band wireless backhauling to SCs offersmultiple advantages to MNOs: i) avoiding deployment of anexpensive wired backhaul infrastructure, ii) availing of moreflexibility in the deployment of SCs, and iii) not having topurchase additional licensed spectrum, as in the case of out-of-band wireless backhauling [6].

Those advantages motivated the Third Generation Partner-ship Project (3GPP) to include in the 5G New Radio (NR)Release 15 a new study item, which focuses on IntegratedAccess and Backhaul (IAB) network architectures – alsorefereed to as self-backhauling networks in the literature. In[7], 3GPP provides a list of use cases, in both the sub-6 GHzand above-6 GHz spectrum bands, and network architecturerequirements for the NR backhauling functionalities coupledwith the radio access network (RAN) technology.

A. Background and Related Work

Several works focused on millimeter wave (mmWave) s-BHnetworks [8], [9], which offer wide bandwidth channels to ac-commodate multiple backhaul and access links simultaneously.At the same time, various research efforts considered sub-6 GHz s-BH networks in a heterogeneous network (HetNet)environment [10]–[12], which is more suitable to providewide-area coverage through conventional macro-cells, and useself-backhauled SCs to further boost the network capacity.However, due to the scarcity of spectrum in the bands below6 GHz, the bandwidth splitting required to serve multiplebackhaul links and the inter-tier interference caused by co-channel access and backhaul operations may turn out to be

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a significant impediment to the potential adoption of s-BH insub-6 GHz HetNets [12]. In [10], [11], the authors tackled theproblem of resource allocation (such as transmission powerand time-frequency resources) of s-BH networks. In [12], theauthors considered a full-duplex (FD) technique, which onthe one hand avoids the partitioning of the spectrum betweenbackhaul and access, but on the other hand, it requires to studythe problem of the self-interference due to the possible bi-directional transmission.

Moreover, works such as [13], [14], considered macroBSs equipped with mMIMO to enhance the backhaul linkcapacity and simultaneously serve SCs and UEs. In [13], theauthors studied the UE data-rate performance as a functionof the distance between the mMIMO-BS and the s-BH SCs.However, they considered a simplified single-cell scenariowithout inter-cell interference between SCs. In [14], [15], theauthors used stochastic geometry to derive the rate coverageprobability and compute the optimal proportion of in-band andout-of-band FD SCs in the network which maximizes the UErates, and energy efficiency, respectively. Finally, the authorsin [16] investigated an optimization approach to maximize thesum-rate of the UEs under capacity constrained backhaul andby considering the length of the pilot sequences used for thechannel state information (CSI) acquisition.

B. Motivation and Contribution

In this paper, we analyze the end-to-end UE performance ofmMIMO s-BH architecture by means of theoretical analysisand 3GPP-based system-level simulations when compared tomMIMO Direct Access (DA), where mMIMO-BSs are solelydedicated to serving UEs in the absence of SCs [17]. Weconsider a realistic multi-cell setup [18], where mMIMO-BSsprovide sub-6 GHz backhauling to a plurality of half-duplex(HD) SCs overlaying the macro cellular area. In these HDsystems, a s-BH network entails sharing time-and-frequencyresources between radio access and backhaul links. We use3GPP-based system level simulations up to the point of oneSC deployed for each UE, whereas we use the analyticalframework when the SC density is much larger than theUE density. In this regime, numerical simulations becomeimpractical due to the large amount of time required andthe high computational complexity involved. Two differentstrategies of self-backhauled SC deployments are consideredas illustrated in Fig. 1. We analyze a random deployment– where SCs are uniformly distributed over a geographicalarea –, and an ad-hoc deployment – where SCs are purposelypositioned close to UEs to achieve line-of-sight (LoS) accesslinks. We would like to stress that the particular choice ofthe ad-hoc SC deployment serves two purposes: a) to studythe performance gains that can be obtained by the MNOsthrough a tailored SCs deployment, and b) to provide an upperbound of the system access performance obtained when the SClocations are coupled to the UE locations.

The contributions of the paper are as follows:1) We provide 3GPP-based system-level simulations results

on the performance of the achievable UE data-rates inmMIMO based wireless in-band s-BH with random and

ad-hoc SC deployments. Differently from the previousworks [13]–[16], our work accounts for a pathloss modelwith LoS and Non-LoS (NLoS) transitions in both back-haul and access links. The closest similar work is [13],which also compares the performance of mMIMO s-BHand mMIMO DA architectures by considering channelmodels based only on pathloss, but not accounting for thepilot contamination effect on the signal-to-interference-plus-noise ratio (SINR) when mMIMO is used. On thecontrary, we show that both the pathloss models incorpo-rating LoS and NLoS transmissions and the pilot contam-ination effect severely impact the inter-cell interferencemodeling and the system performance, making our resultsmore accurate and realistic than those presented in [13].

2) We provide an analytical model for evaluating the averagedata-rate of the backhaul and access links. We adaptthe expressions proposed in [19], [20] to model themMIMO backhaul links. Specifically, we account for theeffects of the antenna directionality and sectorization,and the effect of the beamforming gain due to themMIMO precoding. In the access link formulation, weaccount for the density of active SCs, which matchesthe numerical results obtained by simulations. We alsoemploy the analytical framework to show that, due tothe over provisioning of self-backhauled SCs, randomdeployment requires thousands of SCs to achieve thesame performance of the ad-hoc deployment.

3) We explain in details the different factors playing a keyrole in the 3GPP-based system-level results. Overall, theinsights from these results can guide the deployment offuture 5G access network.

The remainder of this paper is organized as follows. SectionII introduces the system model on which the analysis isbased; Section III presents the downlink (DL) SINR andrate expressions of the backhaul and access links; SectionIV provides the analytical signal-to-interference ratio (SIR)and average rate expressions of backhaul and access; SectionV presents the numerical results, and VI summarizes thekey findings. The following notation is used throughout thepaper. Capital and lower-case bold letters denote matrices andvectors, respectively, while [·]∗, [·]T and [·]H denote conjugate,transpose, and conjugate transpose, respectively. | · | indicatesthe absolute value. The notation E[·] indicates the expectationwith respect to a random variable (RV). We use C and R todenote complex- and real-valued numbers, respectively.

II. SYSTEM MODEL

We focus on the study of the DL performance for anhexagonal grid of mMIMO-BSs equipped with a large numberof antennas M and providing wireless backhaul links to (a)randomly deployed self-backhauled SCs, (b) ad-hoc deployedself-backhauled SCs, or (c) directly serving UEs, as illustratedin Figs. 1(a), 1(b), and 1(c), respectively. Throughout thepaper, we assume to use sub-6 GHz frequencies, which canprovide backhaul connections with a single hop to all the SCsdeployed in the coverage area of the macro cell [5].

For the mMIMO-BSs, we consider the hexagonal modelsince it represents a planned scenario of deployment where

mMIMO-BS

UE

s-BH

small cell

mMIMO-BS

UEUE

mMIMO-BS

UEUE

UE

(a) s-BH architecture with random deployment

mMIMO-BS

UE

s-BH

small cell

mMIMO-BS

mMIMO-BS

UE

UE UE

UEdψ

UE

(b) s-BH architecture with ad-hoc deployment

mMIMO-BS

UE

mMIMO-BS

UE

UE

mMIMO-BS

UEUE

UEUE

UE

(c) DA architecture

Fig. 1: Illustration of (a) s-BH architecture with random deployment,(b) s-BH architecture with ad-hoc deployment, and (c) DA architec-ture.

the BS locations are optimized to improve the SINR perfor-mance. This deployment strategy is in line with the 3GPPmethodology described in [18], which we take as a referencethroughout the paper.

For the SCs, we differentiate the modeling between therandom and the ad-hoc cases. In the first case, we modelthe SC locations with a homogeneous spatial poisson-point-process (SPPP) distribution, which we refer to as SPPP, sinceit represents an unplanned scenario of deployment, where theSCs are distributed according to a uniform distribution. Thisapproach is in line with the works such as [21], [22], andalso with the 3GPP methodology [18]. In the second case, weconsider the SC locations coupled to the UE point process,and we position the SCs at a fixed distance d with respect tothe UE locations.

While the random deployment of SCs is agnostic to theUE positions, the ad-hoc deployment of SCs requires knowing

the position of the UEs before making the deployment. Thisinformation can be obtained through predictions, for example,considering the behavior of UEs, who are likely to return tothe same place at the same time of day.

A. Macro Cell, Small Cell and User Topology

We denote by i, l, and k the mMIMO-BS in the i-th sector,the SC, and the UE, respectively. I represents the set ofmMIMO-BSs deployed in the network. Li and Li′ representthe set of SCs deployed per sector and connected to the i-th and i′-th mMIMO-BS, respectively, which provides thelargest reference signal received power (RSRP).1 Li and Li′

denote the number of SCs in the sets Li and Li′ , respectively.Furthermore, we denote by Ki the number of UEs in the setKi randomly and uniformly distributed over the area coveredby each sector. We assume that each single-antenna UE isconnected with the SC (in the s-BH network), or with themMIMO-BS (in the DA network) that provides the largestRSRP [18]. Therefore each SC serves Kl UEs in the s-BHnetwork.

Three different network deployments are presented in thefollowing:(a) s-BH architecture with random deployment: Self-

backhauled SCs are randomly and uniformly distributedover the mMIMO-BS geographical area, as shown in Fig.1(a). This scenario is used as a baseline, and followsthe set of parameters specified by the 3GPP in [18] toevaluate the relay scenario. More precisely, we considerthe UE and SC antenna heights fixed at 1.5 and 5 metersabove the ground, respectively, and channel models forthe 3GPP Case 1 Relay scenario.

(b) s-BH architecture with ad-hoc deployment: Self-backhauled SCs are positioned targeting nearby UE lo-cations.2 As shown in Fig. 1(b), we model this sce-nario by considering SCs deployed within a 2-D (two-dimensional) distance d from the UEs, and an angleψ measured from the straight segment that links UEsand their closest mMIMO-BS. ψ is chosen uniformly atrandom in [−π/2, π/2]. It is worth noting that even whenthe 2-D distance d = 0, UEs and SCs are still separatedin space because the antennas are positioned at differentheights, as specified in (a). In addition, to limit the effectof the inter-cell interference, we replace the Patch antennaat the SC with a more directive Yagi antenna, pointingdownwards to the ground (as shown by the green radiationcone in Fig. 1(b)), and therefore only illuminating theclosest UEs.

(c) DA architecture: There are no self-backhauled SCsdeployed, and the mMIMO-BSs are solely dedicated todirectly serve the UEs, as illustrated in Fig. 1(c).

1 We remark that a given SC deployed in the i-th sector might be connectedto another mMIMO-BS i′ as it provides a higher RSRP level than themMIMO-BS i.

2 We assume the possibility to realize this specific network deployment,for example by means of drone-BSs, where the drone-BSs can repositionthemselves following the locations of UEs as suggested in [23]. Althoughmentioned, the drone-BSs use-case is not the focus of this paper, and it is leftfor future investigation.

DL DataUL

PilotDL Data

Access

Backhaul

macro

layer

small cell

layer

UL

Pilot

τ

DL DataDL Data

Accesstime-slot (T)

Backhaultime-slot (T)

Rx slots

(a) Self-backhaul frame

small cell

layer

macro

layer DL DataUL

PilotDL Data

UL

PilotDL Data

UL

PilotDL Data

UL

Pilot

Accesstime-slot (T)

τ

Backhaul

Backhaul

(b) Direct access frame

Fig. 2: DL frame structure for (a) mMIMO s-BH with α = 0.5, andfor (b) mMIMO DA.

B. Frame Structure

We consider a time-division duplexing (TDD) system,where the time-slot duration T is used as a single schedulingunit in the time domain. As shown in Fig. 2(a), we partitionthe access and backhauling resources through the parameterα ∈ [0, 1]. Therefore, the fraction α of time-slots is allocatedto the backhaul links, and the fraction 1 − α of time-slotsis allocated to the access links. In the frequency domain,we divide the system bandwidth BW into Qt RBs, andwe allocate all the RBs to the backhaul links or the accesslinks. We make the following assumptions in considering thepartition of backhaul and access time-slots among the SCs andUEs:

• During the backhaul time-slots, all the associated SCs areserved by the mMIMO-BS i with M antennas, and weuse the same value of α for all the SCs. The mMIMO-BSsprecode the backhaul signals towards the single-antennaSCs, which are spatially multiplexed in the same time-frequency resources. We consider to have M DoF fora mMIMO-BS with M antennas [24], and we assumeM > E[Li] by dimensioning the number of antennasM during the mMIMO-BS deployment planning. In thecase that Li may exceed the number of antennas M , ascheduler ensures to serve only M SCs randomly pickedin the set Li. We also observed in our experiments thatPr[Li > M ], i.e. the probability that the RV Li exceedsthe number of DoF M , decays rapidly for large M , andis equal to zero for the set of system parameters adoptedin our simulations.

• During the access time-slots, the SCs schedule theirconnected UEs by using a Round Robin (RR) mechanism,which equally distributes the available Qt RBs among itsUEs.

Fig. 2(b) shows the frame structure used for the DA setup,where all the time-slots are allocated to the access links. Ineach time-slot, the mMIMO BSs precode the access signals,and the UEs are spatially multiplexed reusing the entire systembandwidth. We assume M > E[Ki] due to the system design.When Ki > M , a scheduler serves only M UEs randomlypicked in the set Ki. The same observation made above forthe backhaul applies with Ki in place of Li.

Figs. 2(a) and 2(b) also show the fraction τ of the time-slots dedicated for the transmission of the uplink (UL) pilotsequences, used for the CSI acquisition. Details about the CSIacquisition procedure will be discussed in subsection II-D.

C. Channel Model

We define as hil = [hil1, . . . , hilM ]T ∈ CM the propagationchannel between the l-th single-antenna receiver (SC in themMIMO s-BH network and UE in the mMIMO DA) and theM antennas of the i-th mMIMO-BS. The composite channelmatrix between the i-th mMIMO-BS and the receivers in thei′-th cell is represented by Hi,i′ = [hi1 · · ·hiLi′ ] ∈ CM×Li′ ,where we omit the subscript q indicating the q-th RB of thechannel matrix for notational convenience. Moreover, for themMIMO sBH architecture, we define the single-input single-output (SISO) channel between the l-th SC and the k-th UEin the q-th RB as glkq ∈ C.

The channel coefficients hilm =√βilhilm and glkq =√

βlkglkq account for both the effects of the large-scale fadingand the small-scale fading components:• We model the large-scale fading components βil, βlk ∈R+ according to the 3GPP Case 1 Relay scenario [18].For a given link, the models decide whether the channelpropagation conditions are LoS or NLoS, by consideringa distance-dependent LoS probability function, and uselog-normal distributed shadowing with different values ofstandard deviation. Because of its slow-varying character-istic, the large-scale fading does not change rapidly withtime, and it can be assumed constant over the observationtime-scale of the network.

• We model the small-scale fading components hilm, glkq ∈C, which result from multi-path, as Rician fast-fading,according to the 3GPP spatial channel model for MIMOsimulations [25], assuming a K-factor dependent on thedistance between transmitter and receiver.

Throughout the paper we assume a block-fading channelmodel, where the channel vectors of the access paths, i.e. thechannel between each antenna at the mMIMO-BS and the UE,and the channel between the SC and the UE, remain constantfor a frequency-time block corresponding to one time-slot T ,and one RB [26]–[28]. In line with the LTE numerology [29],we consider the duration of the time-slot equal to 1 ms, andthe bandwidth of the RB equal to 180 KHz. Differently, weconsider that the channel vectors of the backhaul path, i.e. thechannel between each antenna at the mMIMO-BS and the SC,is constant for a period TBH T due to the static position ofthe SCs. Moreover, we adopt a horizontal uniform linear array(ULA) for the mMIMO-BS with equally spaced antennas andJakes correlation model between antenna pairs [30].

D. Massive MIMO CSI Acquisition

To calculate the DL precoder of the mMIMO-BS, we con-sider that the channel is estimated through UL pilot sequences,assuming UL/DL channel reciprocity [3]. We also considerthat the SCs or UEs associated to the same mMIMO-BShave orthogonal pilot sequences, and define the pilot code-book with the matrix Φi = [φi1 · · ·φiLi ]

T ∈ CLi×B , whichsatisfies ΦiΦ

Hi = ILi . Here, the l-th sequence is given by

φil = [φil1, . . . , φilB ]T ∈ CB , and B denotes the pilot code-book length. Note that Li ≤ B, i.e. the number of SCs trainedby the mMIMO-BSs in the backhaul time-slots is limited bythe maximum number of orthogonal pilot sequences. Similarly,Ki ≤ B, i.e. the number of UEs trained by the mMIMO-BSsin the access time-slots is limited by the maximum number oforthogonal pilot sequences. In case Li > B or Ki > B, thescheduler assigns the pilot sequences to only B SCs or UEs,randomly selected in the sets Li and Ki.3

The matrix Yi ∈ CM×B of pilot sequences received at thei-th mMIMO-BS can be expressed as [31]

Yi =√P ulil

∑i′∈I

Hi,i′Φi′ + Ni, (1)

where P ulil is the power used for UL pilot transmission by

the l-th device, located in the i-th sector, and Ni ∈ CM×Brepresents the additive noise matrix, whose entries are modeledas independent and identically distributed complex GaussianRVs with variance σ2.

Let us denote by Hi = [hi1 · · ·hiLi ] ∈ CM×Li the channelbetween the i-th mMIMO-BS and the associated devices.During the UL training phase, the mMIMO-BS obtains anestimate of Hi by correlating the received signal with a knownpilot matrix Φi. Let us define P ⊆ I as the subset ofsectors, whose devices share identical pilot sequences withthe devices served by the i-th mMIMO-BS. In line with otherstudies [31], [32], we adopt the least-squares (LS) channelestimation since we are considering a practical system, wherethe mMIMO-BS does not have perfect knowledge of the cross-cell channel statistics. The resulting LS channel estimation canbe expressed as [31]

Hi =1√P ulil

YiΦHi = Hi +

∑i′∈P

Hi,i′ +1√P ulil

NiΦHi . (2)

The first, second and third terms on the right-hand side of (2)represent the estimated channel, a residual pilot contaminationcomponent and the noise after the pilot sequence correlation,respectively. The use of the same set of orthogonal pilotsequences among different sectors leads to the well-knownpilot contamination problem, which can severely degrade theperformance of mMIMO systems [3], [33].

Similar to [33], we consider that each uplink trainingsymbol τ contains up to 16 orthogonal pilot sequences, andwe consider its duration equal to one Orthogonal Frequency

3The assumption on the number of pilots holds since we focus on broadbandnetworks and we address the conventional use case of human-type commu-nications. Differently, the application of mMIMO to other use cases, such asMachine-Type Communication and Internet of Things, would require to revisethis assumption.

TABLE I: Pilot allocation schemes in mMIMO s-BH and mMIMODA architectures.

Architecture Backhaul links Access links

mMIMO s-BHpilot reuse for all thesectors (No pilot con-tamination)

No pilot allocation

mMIMO DA – • pilot reuse 1 (R1)• pilot reuse 3 (R3)

Division Multiplex (OFDM) symbol period of the Long TermEvolution (LTE) standard [29]. The pilot sequences are as-signed to the SCs and to the UEs, in the case of mMIMO forbackhaul and mMIMO for access, respectively.

In the mMIMO s-BH architecture, due to the static positionof the SCs, the backhaul channel vectors remain constant fora longer time than the access channel vectors, and there isno need to update the CSI every time-slot. This allows tomultiplex in time, over separate backhaul time-slots, the pilotstransmitted by the SCs in different sectors. Therefore, weassume that no pilot contamination is present in the system,and we account for a pilot overhead τ over T , equivalent inour system model to 7% of the time-slot duration.

In the mMIMO DA architecture, we use two pilot allocationschemes [33]:• In pilot reuse 1 (R1) the same set of pilot sequences is

reused in all the sectors of the network, thus introducingstrong pilot contamination. The pilot overhead to accountfor is τ over T , equivalent in our system model to 7% ofthe time-slot duration.

• In pilot reuse 3 (R3) we consider coordination betweenthe same cell sites, avoiding using the same pilot sequencefrom the adjacent sectors. This reduces the effect of thepilot contamination at the expense of increasing the pilotoverhead, which is 3× τ over T , equivalent in our systemmodel to 21% of the time-slot duration.

In Table I we summarize the different pilot allocation schemesused in mMIMO s-BH and mMIMO DA architectures.

III. DOWNLINK SINR AND USER RATE

In this section, we present the formulation for the two-hop DL data-rate in the s-BH network, which comprises theformulation for the mMIMO backhaul and the SC accessSINRs and data-rates. Moreover, we include the conventionalformulation for the data-rates in mMIMO DA network.

A. Massive MIMO Backhaul Transmission

The i-th mMIMO-BS uses the precoding matrix Wi =[wi1 · · ·wiLi ] ∈ CM×Li to serve its connected SCs duringthe backhaul time-slot. In this paper, we consider that Wi iscomputed based on the zero-forcing (ZF) criterion as [34]4

Wi = Hi

(H

H

i Hi

)−1

Di12 . (3)

4As shown in [35], among the linear methods for the mMIMO precoder,ZF and minimum mean square error (MMSE) perform better than MaximumRatio Combining (MRC). However, ZF provides a better balance betweenperformance and complexity than MMSE.

Here, the diagonal matrix Di = diag (ρi1, ρi2, . . . , ρiLi) ischosen to equally distribute the total DL power P dl

i amongthe Li receivers. In the previous expression, ρil represents thepower allocated to the l-th receiver located in the i-th sector,and TrDi = P dl

i , where TrDi is the trace of matrix Di.Under the assumption that each SC has perfect CSI avail-

able, the DL SINR of the l-th stream transmitted by the i-thmMIMO-BS can be expressed as

SINRBil =

ρil|hHilwil|2∑

j∈Lij 6=l

ρij |hHilwij |2 +

∑i′∈Ii′ 6=i

∑j∈Li′

ρi′j |hHi′lwi′j |2 + σ2

n

.

(4)The numerator of (4) contains the power of the signal intendedfor the l-th receiver, and the denominator includes the intra-cellinterference from the serving i-th mMIMO-BS, the inter-cellinterference from other mMIMO-BSs, and the power of thethermal noise at the SC receiver σ2

n.The corresponding DL backhauling rate at the l-th SC

receiver can therefore be expressed as

RBil = α

(1− τ

T

)BW log2

(1 + SINRB

il

). (5)

where α, as indicated before, represents the fraction of time-slots allocated to the backhaul links.

B. Small Cell Access Transmission

We recall from the channel model that glkq denotes the SISOchannel between the l-th SC and the k-th UE correspondingto the q-th RB. The DL SINR of the k-th UE served by thel-th SC in RB q can be expressed as

SINRAlkq =

P dll |glkq|2∑

i∈I

∑l′∈Lil′ 6=l

P dll′ |gl′kq|2 + σ2

n2

, (6)

where P dll and P dl

l′ are the transmit powers on the RB of thel-th and l′-th SCs, respectively, and σ2

n2denotes the thermal

noise power at the UE receiver.The corresponding DL access rate for UE k served by SC

l can be therefore expressed as

RAlk = (1− α)

BW

Qt

Qt∑q=1

xkq log2

(1 + SINRA

lkq

), (7)

where xkq = 1 if the q-th RB is assigned to the k-th UE, andxkq = 0 otherwise.

The potential aggregated DL access rate provided by the l-th SC is RA

l =∑Klk=1R

Alk. However, the actual aggregated DL

access rate provided by the l-th SC cannot be larger than thebackhaul DL rate, which entails that RA

l ≤ RBil , ∀l ∈ Li, and

∀i ∈ I. In this paper, we assume that the backhaul capacity isequally divided between the Kl UEs served by the l-th SC.5

5 The assumption of equally distributed backhaul capacity among the UEsmight become a drawback for the end-to-end rates, when UEs served bythe same SC have different rate requirements in the access links, and inthis case, the partition of the backhaul resources among the UEs couldbe designed according to their demands. This access-based partition of thebackhaul resources among the UEs is not the focus of this paper, and itsstudy in the context of s-BH architecture is left for future work.

Therefore, the resulting end-to-end access rate for the k-th UEcan be expressed as

Rilk = min

(RBil

Kl, RA

lk

), (8)

where the minimum is computed between the backhaul rateobtained from (5), divided by the number of UEs served bythe l-th SC, and the access rate obtained from (7).

C. Massive MIMO Direct Access Transmission

In contrast to s-BH setups, mMIMO systems providing DAdedicate all their time resources to multiplex DL data streamsto the UEs. Thus, the DL access rate of the k-th UE servedby the i-th mMIMO-BS can be expressed as

RDAik =

(1− τ

T

)BW log2

(1 + SINRDA

ik

), (9)

where the estimated channel matrix Hi = [hi1 · · · hiKi ] ∈CM×Ki between the i-th mMIMO-BS and its connected UEsis plugged into (3), to subsequently derive the DL SINR in(4), assuming that each UE has perfect CSI available, and theaccess rate in (9).

IV. ANALYTICAL SIR AND AVERAGE BACKHAUL ANDACCESS RATES

In the following, we present a tractable formulation to modelthe mMIMO s-BH network, which approximates the backhauland access SINR and data-rate expressions.

We recall from Section II that the mMIMO-BS locationsare distributed on a hexagonal grid with density λa =

3( 3√

32 R2)−1, where R = dISD√

3is the outer sector radius of

the hexagonal site, and dISD is the inter-site distance betweentwo cell sites. For the random deployment, we consider thatthe locations of SCs and UEs are drawn from two independentSPPPs Ωb and Ωu with densities λb and λu, respectively. Forthe ad-hoc deployment, we consider that the SC locationsare coupled to the UE locations drawn from a SPPPs Ωu,and we position the SCs at a fixed distance d with respectto the UE locations. The mean numbers of SCs and UEs inthe finite area of the sector are obtained as µb = λb/λa andµu = λu/λa, respectively [36]. Moreover, when consideringa dense deployment of SCs, there is a high probability thatthere are SCs unloaded, i.e. without UEs associated to them[37]. We capture this effect in the analysis by considering anactivation probability for the SC, which can be approximatedas [38]

pa ≈ 1−(

1 +λu

3.5λb

)−3.5

, (10)

where the expression(

1 + λu3.5λb

)−3.5

approximates the aver-age void probability for a typical Voronoi cell [38]. Conse-quently, the locations of the active SCs can be approximatedas SPPP Ωb with density λb = paλb derived by thinning theSC process Ωb [38]. Differently, in the ad-hoc deployment weassume pa = 1, meaning that each SC is active and servesthe nearby UE. The mean number of active SCs in a sector isobtained as µb = λb/λa.

In the following expressions, SIR is used to approximatethe SINR, since in the sub-6 GHz bands, with a systemdesign which assures signal coverage, the system operates ininterference-limited conditions, where the power of receivedinterference dominates the denominator of the SINR.

A. Average Rates of Massive MIMO Backhaul Transmission

We now provide an analytical model for evaluating theaverage data-rate of the backhaul links, given the SIR of atypical SC and the spatial distribution of SCs in the sector.Inspired by [20], we treat the SCs as UEs, and we extend theframework proposed in [19] to model the SIR by consider-ing: i) the effects of antenna directionality and sectorization,captured with the horizontal and vertical antenna patterns, andby modeling the co-site interference component; ii) the effectof the beamforming gain due to the mMIMO precoding asproposed in [14]. We make the following assumptions in ouranalytical backhaul model:• For simplicity, the backhaul channel is statistically mod-

eled by considering only the large-scale fading compo-nent, excluding shadowing statistics.

• We assume LoS propagation channel conditions fromthe serving mMIMO-BS to the SC (and from the co-site interfering mMIMO-BSs to the SC), to reflect thecharacteristics of the backhaul link, which tends to havedominant LoS conditions between SCs and the antennasof the nearest mMIMO-BSs [18]. On the other hand,we assume all the mMIMO-BSs from the surroundinginterfering sites to be in NLoS.

• We assume that the co-channel interference from themMIMO-BS to other served SCs can be reasonably ne-glected since we adopt the ZF precoder. For consistencywith the assumptions made in Section II-D and in SectionIII-A, we consider that there is no pilot contamination inthe backhaul links, and we consider that each SC hasperfect CSI available.

For the analysis that follows, r and θ denote two indepen-dent RVs, which define the distance and the angle from the SCto the serving mMIMO-BS. Note that r and θ are distributedwith uniform probability density functions (pdfs) fR(r) andfΘ(θ) in the interval [rmin,

dISD2 ] and [−π/3,+π/3], respec-

tively, where the distance rmin denotes the minimum distancebetween the mMIMO-BS and the SC.6 By convention, θ = 0indicates the boresight direction in the first sector, and suchsector is denoted as s = 1 for each hexagonal cell formed byS sectors.

The SIR of a typical SC associated to the mMIMO-BS ismodeled as

SIRB(r, θ) ≈ (M − µb + 1)

µb

P dli GaGV (r)GH,1(θ)βL(r)

I1(r, θ) + I2(r),

(11)

6We observed that for the value of rmin that we use in our simulations, therealizations of the (modified) spatial process could be statistically consideredas if they were derived from a homogeneous SPPP, since we tested thespatial randomness with the Ripley’s K-function [39], and we verified thatthe theoretical values of the SPPP are contained within the region defined bythe lower and upper envelopes given by the empirical results.

where the multiplying factor (M − µb + 1)/µb represents thebeamforming gain from mMIMO precoding.7 Ga, GV (r) andGH,s(θ) are the antenna gains of the single mMIMO-BSelement, the vertical (V), and the horizontal (H) antenna pat-terns, respectively. βL(r) = ALr−η

L

is the pathloss betweenmMIMO-BS and SC, where AL and ηL indicate the frequencydependent pathloss factor and the pathloss exponent for thebackhaul link in LoS condition, respectively, and I1(r, θ) andI2(r) are the co-site and inter-site interference components,respectively. The vertical antenna pattern is defined as [18]

GV (r)|dBi = −min

(12

(atan(

δa√r2−δ2a

)− ζtilt

ζHP

)2

, Fv

),

(12)

where δa is the difference in antenna heights between themMIMO-BS and the SC, ζtilt is the mechanical downtilt, ζHPis the half-power vertical beamwidth, and Fv is the verticalfront-back ratio. Similarly, the horizontal antenna pattern isdefined as [18]

GH,s(θ)|dBi = −min

(12

(θ − (s− 1)2π/3

θHP

)2

, Fh

),

(13)where θHP is the half-power horizontal beamwidth, and Fhis the horizontal front-back ratio.

In (11), I1(r, θ) is represented as

I1(r, θ) = P dli′ GaGV (r)

S∑s=2

GH,s(θ)βL(r), (14)

and I2(r) is approximated as [19]

I2(r) ≈ 2πλaPdli′ GaGV (2Rc − r)GHANL

ηNL − 2

×(

(2Rc − r)2−ηNL

− (Rb − r)2−ηNL), (15)

where Rb = 32dISD denotes the network boundary, Rc =

dISD2 is the inner sector radius, GH =

∫ 2π

0

∑Ss=1GH,s(θ)dθ

is the average horizontal antenna gain with respect to θ, andηNL and ANL are the pathloss exponent and the frequencydependent pathloss factor for the backhaul link in NLoScondition, respectively. Eq. (15) approximates the integrationarea used to calculate the inter-cell interference from othermacro-BSs assuming a ring formed by two concentric discscentered at the origin and with radii of 2Rc and Rb. We referto [19] for the validation of this model.

Finally, the average SC data-rate for backhaul transmissioncan be expressed as

RB = αBW

×∫ π

3

−π3

∫ Rc

rmin

log2

(1 + SIRB(r, θ)

)fR(r)fΘ(θ) dr dθ. (16)

Therefore, the results for the average SC data-rate can becomputed by numerical integration of (16).

7 Only the active SCs are spatially multiplexed in the backhaul time-slots,since those inactive are not required to backhaul the UEs data.

B. Average Rates of Small Cell Access Transmission

Inspired by the stochastic geometry analysis presented in[40], we now provide an analytical model for evaluating theaccess SIR of a typical UE at the origin, and its access averageDL data-rate. Similarly to [41], [42], we consider the impact ofthe LoS and NLoS pathloss characteristics to model the SIR.We use the same LoS probability function as in [42], however,we consider for the inter-cell interference computation thedensity of the active SCs, i.e. those with UEs associated.

We make the following assumptions in our analytical accessmodel:

• We assume that each UE connects to the nearest SC.8 Forthe random deployment, since Ωb and Ωu are two inde-pendent SPPPs, we assume that x, i.e. the distance be-tween UE and the serving SC is a RV Rayleigh distributedwith pdf fX(x) = 2πλbx exp(−λbπx2)/exp(−λbπδ2

b ),where δb denotes the difference between the SC and UEheights [40]. Differently, for the ad-hoc deployment, weassume x =

√d2 + δ2

b .• The propagation channels are represented with a com-

bination of distance-dependent pathloss and multi-pathfading, distributed as Rayleigh with an exponential powerdistribution |g|2 ∼ exp(1).9

• We adopt a probabilistic LoS channel model for the inter-cell interference, with a LoS probability expressed as [42]

PrL(x) = exp(− (x/D)2), (17)

where the parameter D is set to approximate the LoSprobability of the SC-UE 3GPP model [42].

The SIR of a typical UE at the origin associated to the SCis modeled as

SIRA(x) ≈ P dll Gb|g|2βL(x)

Iagg, (18)

where Gb is the SC antenna gain, |g|2 is the multi-path channelgain, and Iagg is the aggregated inter-cell interference.

We now use (18) to provide an expression for the ratecoverage probability, which defines the probability that the UErate is higher than a minimum target Rth. This probability canbe expressed as Pr

[SIRA(x) > γa

], where γa = 2Rthµl − 1

depends on Rth, and we approximate the number of UEsassociated with the SC serving the typical UE at the originwith the corresponding mean µl, given by 1+1.28λu/λb [43].We later show in Fig. 5(b) that the mean of the distributionof the number of UEs for a typical SC, given by λu/λb [44],matches the numerical results.

8This assumption holds in the considered range of SC densities, for whichthe probability that the closest SC is in LoS is very high, as shown by thesimulation results in Fig. 3, due to the proximity of SC to UE.

9Shadowing statistics are neglected in the analytical model, although a morecomprehensive framework can incorporate this effect in the distribution of theUE distances.

TABLE II: 3GPP-based system-level simulation parameters

mMIMO-BSs DescriptionCellular layout Wrap around hexagonal, 19 sites, 3 sec-

tors/siteDeployment Inter-site distance: 500 m, height: 32 mAntenna array Uniform Linear Array (ULA) with element

spacing 0.5λ and Jakes correlation model[30], Number of antennas per array: 64

Antenna pattern 70 H x 10 V beamwidths, 14 dBi max.,downtilt: 15

Precoder Zero-forcingTx power/Noise figure 46 dBm, 5 dBmSelf-BH SCs DescriptionDeployment Random: 4, 8, 16 SCs/sector on average,

Ad-hoc: 16 SCs/sector on average, height:5 m

Backhaul antenna pattern 5 dBi antenna gain, OmniAccess antenna pattern –Patch

80 H x 80 V beamwidths, 5 dBi max.,downtilt: 90

Access antenna pattern –Yagi

58 H x 47 V beamwidths, 10 dBi max.,downtilt: 90

Tx power/Noise figure 30 dBm, 5 dBUEs DescriptionDeployment Random, 16 UEs/sector on average, all

served, height: 1.5 mTx power/Noise figure 23 dBm, 9 dBChannel DescriptionScenario Outdoor SCs, outdoor UEsBandwidth/Time-slot 10 MHz at 2 GHz, Qt = 50 RBs, T = 1

msec.LoS probability, pathlossand shadowing

• mMIMO-BS to UE (based on 3GPPmacro to UE models as per [18])

• mMIMO-BS to SC (based on 3GPPmacro to relay models as per [18])

• SC to UE (based on 3GPP relay to UEmodels as per [18])

Fast fading Rician, distance-dependent K factorThermal noise -174 dBm/Hz power spectral density

The expressions used to evaluate the rate coverage probabil-ity are included in Appendix A. Thus, the average UE data-ratefor access transmission can be expressed as

RA = (1− α)BW

×∫ +∞

0

∫ +∞

δb

Pr[SIRA(x) > γa

]fX(x) dx dγa. (19)

Therefore, the results for the average UE data-rate can becomputed by numerical integration of (19).

In the next section, we will use this model to complementthe insights given by the 3GPP-based system-level simulations.

V. SIMULATIONS AND NUMERICAL RESULTS

In this section, we evaluate the performance of mMIMOs-BH and DA networks using 3GPP-based system-level sim-ulations and mathematical analysis.

In the mMIMO s-BH network, the different characteristicsof the backhaul and access radio links are modeled consideringthe methodology described in [18] for the 3GPP Case 1Relay scenario. As described in [18, Tab. A.2.1.1.2-3], weadopt the LoS and NLoS pathloss exponents ηL = 2.35 andηNL = 3.63 for the backhaul links, and we consider ηL = 2.09and ηNL = 3.75 for the access links. For each link, we usethe corresponding LoS probability function proposed in [18,Tab. A.2.1.1.2-3]. To simulate the backhaul links, we account

Fig. 3: LoS probability for SC backhaul links and UE access linksin s-BH networks with Random and Ad-hoc deployments.

for the SC site planning correction factor, which affects thepathloss and the LoS probability as indicated in [18, Tab.A.2.1.1.4-2]. To simulate the access links, we assume cross-correlated shadowing, with correlation coefficient ρ = 0.5at the UE location with respect to the different SCs [18,Tab. A.2.1.1.2-3]. In the simulations, we consider a Ricianfading model, and we characterize the Rician K-factor withthe model: K[dB] = 13−0.03r in dB, where r is the distancebetween transmitter and receiver in meters [25].

In the 3GPP-based system-level simulations, the channelgains (composed by pathloss, shadowing and multi-path fad-ing) are generated for all useful and interfering radio linksbetween each SC and the UEs, as well as between eachmMIMO-BS and all SCs. We collect statistics for differentnetwork realizations, each with independent deployments ofUEs and SCs. Subsequently, we measure the performance interms of the cumulative distribution functions (CDFs) of thebackhaul SC rates in (5), of the access UE rates in (7), andof the end-to-end UE rates in (8).

To compare mMIMO s-BH against mMIMO DA architec-tures, we also simulate the links between mMIMO-BSs andUEs, and compute the resulting rates in (9). In the mMIMODA network, we adopt the LoS probability function and thecorresponding exponents ηL = 2.42 and ηNL = 4.28, asindicated in [18, Tab. A.2.1.1.2-3].

Table II contains the relevant parameters used to conductthe simulation campaign.

A. Massive MIMO s-BH: Random vs. Ad-hoc Small CellDeployments

In this subsection, we analyze the 3GPP-based simulationresults for the two SC topologies described in Sec. II-A,namely the ad-hoc and random SC deployments. In both cases,µu = 16 UEs are deployed per sector on average and sched-uled in access time-slots by their serving SCs. We evaluate theimpact of densification by considering µb = 4, 8, 16 SCs persector on average for the case of random SC deployments. Inthe ad-hoc deployment, we consider µb = 16 SCs per sectoron average, and different values of the 2-D distance d fromthe UE to the SC. The resource partition α is set to 0.5, to

distribute between backhaul and access the available resourcesequally.

As a first step, we compare the LoS probability of thebackhaul and access links. The group of results in the left partof Fig. 3 shows the probability of a given SC to be in LoSwith respect to the server mMIMO-BS with different densitiesof SCs and deployments. As expected, the percentages ofbackhaul links in LoS are almost the same in both the randomand ad hoc deployments, since in the first case the SCs arerandomly distributed with respect to mMIMO-BSs, while inthe last approach the SCs are positioned in the vicinity of theUEs, which are randomly distributed with respect to mMIMO-BSs. Moreover, we can also see that the LoS probability of aUE in the s-BH architecture increases as the density of SCsincrease, reaching 100% probability of LoS channel conditionin the ad-hoc deployment, as shown by the results in the rightpart in Fig. 3. Overall, the backhaul link mainly limits thejoint backhaul-access probability of LoS-LoS conditions.

As a second step, Figs. 4(a), 5(a) and 6 analyze the data-rateperformance of the backhaul and access transmission by firstconsidering the two links separately, and then their combinedeffect on the end-to-end UE rate. The following considerationscan be made:• Backhaul link performance: Fig. 4(a) illustrates the CDFs

of the backhaul data-rates. These results show how in-creasing the number of SCs randomly deployed, andespecially with the ad-hoc deployment, the backhaul data-rate received by each SC decreases. This is due to the re-duction of the multiplying factor

[(M − µb + 1)P dl

i

]/µb

in (11), and the split of the transmit power among theactive backhaul streams. It is worth to note that only theSCs with associated UEs are active (i.e. transmitting tothe UEs), and are served via multiple backhaul links.Thus, looking at Fig. 4(b), which show the averagenumber of SCs served by the mMIMO-BS when applyingthe random and ad-hoc SCs deployment strategies, wecan better explain the results presented in Fig 4(a). Infact, while with the ad-hoc deployment almost all the16 SCs are always active, with 16 randomly deployedSCs only 10 of them are active in average, as a result ofthe UEs association procedure. As depicted in Fig. 4(b),the analytical approximation in (10) of the SC activationprobability matches the numerical results obtained bysimulations.

• Access link performance: Fig. 5(a) shows the resultsfor the access data-rate. As a general conclusion wecan see that adding more randomly deployed SCs inthe sector does not introduce a significant gain, whileopportunistically deploying one SC closer to each UE isquite beneficial. In the following, we discuss the detailsof the different factors playing a key role in these results.On the one hand, when densifying the network, the carriersignal benefits from having SCs that are more likely inclose vicinity to the served UE, even if a random SCdeployment does not always guarantee this vicinity. Also,each SC has to serve a progressively reduced number ofUEs in the access links (as indicated in Fig. 5(b)), andaccordingly in the backhaul links, which means having

(a) CDF of SC rates for backhaul links (b) Average number of active SCs served per mMIMO-BS

Fig. 4: (a) CDF of SC rates for backhaul links, and (b) average number of active SCs served in the backhaul time-slots. (b) also shows theanalytical results for the SCs activation probability in (10).

(a) CDF of UE rates for access links (b) Average number of UEs served per active SC

Fig. 5: (a) CDF of UE rates for access links, and (b) average number of UEs served in the access time-slots. (b) also shows the analyticalresults of the mean number of UEs served by an active SC, given by λu/λb.

more RBs available to allocate to each UE over differentlinks.On the other hand, adding more SCs increases the prob-ability of having a larger number of LoS interferers atthe UE side. In the random deployment, the power ofthe interference links grows faster than the carrier signalpower due to NLoS to LoS transition of the interferencelinks [41]. In the ad-hoc case, the same interference effecttakes place. However, by decreasing the distance d fromUE to SC in such a way as to ensure that the positionof the SC is always close to the served UE, the powerof the carrier signal increases faster than the interferencepower, and thus the hit in the SINR is not as significant.As a result, only a very dense deployment of random SCscould provide the same data-rate as in the case of the ad-hoc deployment. In subsection V-D, we will discuss theasymptotic behavior when increasing the density of SCs,

and quantify the number of required randomly deployedSCs to achieve this condition.From Fig. 5(a), we can observe how equipping the SCwith a more directive antenna (i.e. Yagi) with respect tothe Patch antenna further boosts the access link capacityto achieve 75 Mbps per UE at the median value. Twocomplementary effects cause this performance enhance-ment: i) the signal improvements provided by the higherantenna gain of the directive Yagi, and ii) the reducedinterference created towards neighboring UEs served byother SCs.

• End-to-end overall performance: Fig. 6 shows the end-to-end results given by the combination of the two-hop,backhaul and access, performance previously depicted inFigs. 4(a) and 5(a). Overall, the end-to-end data-rates ofthe random deployment are more limited by the accesslinks than by the backhaul links, as shown by comparing

Fig. 6: CDF of end-to-end UE rates in: (i) ad-hoc deployment of 16SCs per sector with variable UE-to-SC distance d, and (ii) randomdeployment of SCs.

the results in Figs. 6 to the one in 5(a). On the con-trary, the end-to-end data-rates of the ad-hoc deploymentoutperform the one of the random deployment, but areseverely penalized by the backhaul links, as shown bycomparing the results in Figs. 6 to the one in 4(a).Thus, the reduced backhaul capacity of the mMIMO sBHad-hoc deployment does not fully allow to exploit thepotentially high data-rate achieved in the access. Thisbehavior suggests the need to optimize the splitting ofresources between the two links. Indeed, a particularlyimportant improvement in end-to-end rates would beachieved through the allocation of more resources tobackhaul links. This is analyzed in the following section.

B. Massive MIMO s-BH: Access and Backhaul ResourceAllocation

In Fig. 7, we vary α in the range 0 ≤ α ≤ 1, and analyzethe behavior of UEs rate at the 5-th and 50-th percentiles ofthe CDF. The configurations α = 0 and α = 1 entail that allthe time-slots are allocated to the access and the backhaul,respectively. Therefore, the UE rates for these two values areequal to 0, since no resources are left for the other link.Moreover, the configuration α∗ represents the value of α thatmaximizes the UE rate. For instance, with d = 0 and Yagiantennas at the SCs, α∗ is equal to 0.85 when looking at the5-th percentile. Fig. 7 brings the following insights:• By comparing the results between Fig. 7(a) and Fig.

7(b), it is important to note that the optimal α changesfrom 0.85 to 0.75. A tradeoff exists between 5-th and50-th percentile performance, and they cannot be opti-mized simultaneously. Assuming that the network usesα = 0.85, which is the optimal value for cell-edge UEs(5-th percentile of the CDF), the median UEs (50-thpercentile of the CDF) can achieve an end-to-end rateof 19.5 Mbps, which represents a 16% reduction withrespect to the maximum end-to-end rate achievable of23.3 Mbps with α = 0.75.

(a) 5-th percentile

(b) 50-th percentile

Fig. 7: (a) 5-th, and (b) 50-th percentile of the end-to-end UE ratesas a function of the fraction α of backhaul time-slots.

• In Figs. 7(a) and 7(b), we show with dashed lines theresults of the mMIMO DA setup. A properly designedmMIMO s-BH radio resource partitioning can improvethe performance of the cell-edge UEs, and keeps the sameperformance for the UEs at the median of the CDF withrespect to mMIMO DA architecture, as shown in Figs.7(a) and 7(b), respectively. A more detailed comparisonis further developed in the next section.

C. Massive MIMO Architectures: s-BH vs. Direct Access

First, we compare the joint probability of LoS-LoS channelsin the backhaul-access legs for the s-BH network with theprobability of LoS channel in the access links for the DAnetwork. As shown in Fig. 8, there are higher joint backhaul-access LoS probabilities with respect to the access LoSprobability, 47% and 25%, respectively. Those are the caseswhere the s-BH architecture can potentially improve the UEperformance with respect to the DA architecture.

Fig. 8: LoS probability for joint backhaul-access links in s-BHnetwork and for access links in DA network.

We also compare the end-to-end UE rates resulting from the3GPP-based simulations of the mMIMO s-BH and mMIMODA networks. As shown in Fig. 9, the mMIMO s-BH networkwith the ad-hoc deployment of SCs provides better perfor-mance than the mMIMO DA network with pilot reuse 1 at thebottom of the CDF, i.e. below the 50-th percentile. In fact, pilotcontamination severely degrades the rates of UEs at the celledge in the mMIMO DA setup with pilot reuse 1. On the otherhand, in the s-BH network, due to the longer coherence time ofthe backhaul channel, TBH , with respect to the system time-slot duration, T , there is no pilot contamination, and the UEsbenefit from the proximity of SCs, which reduces the pathlossand improves the LoS propagation condition, as shown in Fig.8.

However, by adopting the pilot reuse 3 in the mMIMO DAnetwork, the pilot contamination effect reduces, and the resultsshow that the mMIMO DA performance exceeds the one ofthe mMIMO s-BH with α = 0.5, even if the pilot overhead(τ = 3 OFDM symbols) is 3 times larger with respect topilot reuse 1. The mMIMO s-BH architecture provides thesame performance as the mMIMO DA for the median UEs,only when the optimal partition α = α∗ is selected. Overall,mMIMO s-BH underperforms mMIMO DA above the medianof the UE rates, and provides rate improvements for cell-edgeUEs that amount to 30% and a tenfold gain when adoptingpilot reuse 3 and reuse 1, respectively.

D. Asymptotic Data-rate AnalysisFigs. 10(a) and 10(b) show the convergence behavior of the

backhaul and access data-rates for the random SCs deploymentwith respect to the results obtained with the ad-hoc deploymentof 16 SCs, positioned at fixed distance d = 0 with respect tothe UEs. In both cases the results are obtained by numericalintegration of (16) and (19). Fig. 10(a) show the convergenceresults of the backhaul link. The backhaul data-rate of therandom distribution (solid line) converges to the one of the ad-hoc (dashed line) when the number of SCs is 100 times largerthan the number of ad-hoc SCs (denoted by the marker “*”).Fig. 10(b) shows the convergence results of the access link.In this case, the data rate of the random (solid line) convergesto the ad-hoc (dashed line), when the number of SCs is 1000times larger than the number of SCs deployed in the ad-hoccase (marker “*”). As shown in subsection V-B, the ad-hocdeployment is the one which maximizes the end-to-end data-rates of the two-hop communication.

Fig. 9: Two types of curves are represented: (i) mMIMO DA withpilot reuse schemes 1 and 3; (ii) ad-hoc deployment of 16 SCs persector for α = 0.5 and α = α∗, at which the 50-th percentile of theend-to-end UE rate is maximized (as shown in Fig. 7(b)).

(a) Asymptotic SC data-rate for backhaul links

(b) Asymptotic UE data-rate for access links

Fig. 10: Asymptotic performance measures for backhaul and accesslinks in s-BH network when random and ad-hoc deployments of SCsare considered.

The main takeaway is summarized by the possibility forthe MNOs to explore the adoption of future dynamic SCsinfrastructures [45]. Indeed, instead of significantly over-

provisioning the number of SCs, it may be beneficial to dy-namically reposition only the active ones, trying to guaranteethe same performance that are obtained with a very densedeployment of SCs.

VI. CONCLUSION AND FUTURE WORKS

In this paper, we studied the performance results for two5G mMIMO architectures working at frequencies below 6GHz: mMIMO s-BH and mMIMO DA. In the mMIMO s-BH architecture, we analyzed two different configurations:random deployment of SCs in the coverage area of the servingmacro cell, and ad-hoc deployment of SCs in close proximityto each UE. The first takeaway of this study is that therandom SCs distribution entails deploying thousands of SCsto achieve the access link performance upper bound. On theother hand, the ad-hoc deployment benefits from the closeproximity of the SCs to the UEs, and outperforms the randomone for reasonable numbers of deployed SCs. However, theSC requires to know the UE position, and this is particularlycomplicated to realize due to mobility. The second takeawayis that an ad-hoc SCs deployment supported by mMIMO s-BHprovides rate improvements for cell-edge UEs that amount to30% and a tenfold gain as compared to mMIMO DA withpilot reuse 3 and reuse 1, respectively. This means that pilotcontamination severely impacts the UEs performance at thecell-edge, and it is better to serve the UEs with the mMIMO s-BH architecture. On the other hand, mMIMO DA outperformss-BH above the median of the UE rates, meaning that whenpilot contamination is less severe, and the LoS probability ofthe DA links improves, is better to serve the UEs with themMIMO DA architecture.

Future works will focus on improving the capacity of thebackhaul, which is currently the main limitation in the s-BH architecture at the sub-6 GHz frequencies. At first, weaim to investigate how to improve the LoS probability inthe backhaul links. This improvement can be achieved byincreasing the altitude of the s-BH SCs, for example by meansof drone-BSs hovering above the UE locations. Secondly,we aim to increase the bandwidth and limit the interferenceof the backhaul links. This can be realized by using themmWave frequencies which can simultaneously guarantee theavailability of abundant spectrum in the mmWave bands, andpartially avoid the inter-cell interference issue, due to the highdirectionality of the transmission at those carrier frequencies.

ACKNOWLEDGMENT

The authors would like to thank Dr. Jacek Kibilda for hisvaluable suggestions and helpful comments.

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APPENDIX AIn the following, we derive the expression used to evaluate

the rate coverage probability. The probability that the accessSIR is greater than a threshold γa = 2Rthµl−1, which dependson the minimum target rate Rth, is expressed as [42]

Pr[SIRA(x) > γa

]= Pr

[P dll Gb|g|2βL(x)

Iagg> γa

](a)=

LIagg

(γa

P dll Gbβ

L(x)

), (20)

where (a) follows from [41, eq. (54)] neglecting the thermalnoise as the propagation in sub-6 GHz bands is interference-limited and LIagg(s) represents the Laplace transform of Iagg,and is defined according to [41], [42] as follows

LIagg(s) = exp

(−2πλb

∫ +∞

x

PrL (u)u

1 +(sP dl

l GbβL (u)

)−1 du

)

× exp

(−2πλb

∫ +∞

x1

[1− PrL (u)

]u

1 +(sP dl

l GbβNL (u)

)−1 du

), (21)

where x1 =(ANL

AL

)ηNL−1

xηL

ηNL [42].

Andrea Bonfante (S’18) is currently Ph.D. stu-dent at Trinity College Dublin supported by IRCEnterprise Partnership Scheme and co-founded byNokia Bell Labs–Ireland. He received the B.Sc. andM.Sc. degrees in Telecommunications Engineeringfrom Politecnico di Milano, Italy, in 2009 and2012, respectively. From 2015 to 2016 he workedat Nokia Bell Labs, Dublin, Ireland, and previouslyat Azcom Technology, Milan, Italy, contributing toseveral industrial and research projects focusing onvarious wireless communication systems, such as

massive MIMO, small cell base stations and relay systems. His ongoingstudies focus on the network and system-level aspects of emerging wirelesstechnologies, including cost-effective solutions for network deployment andoptimal resource allocation for multi-hop networks. He regularly serves asreviewer for several Journals of IEEE, including IEEE TRANSACTIONSON WIRELESS COMMUNICATIONS, IEEE COMMUNICATIONS LETTERS andIEEE ACCESS. He served as TPC Member of numerous conferences andworkshops including IEEE ICC’19, IEEE VTC’19 and EuCNC’19.

Lorenzo Galati Giordano (M’15) is Member ofTechnical Staff at Nokia Bell Labs Ireland since2015. Lorenzo received the M.Sc. and the Ph.D.degrees in wireless communication from Politecnicodi Milano, Italy, in 2005 and 2010, respectively, andthe master’s degree in Innovation Management fromIlSole24Ore Business School, Italy, in 2014. He wasalso Marie-Curie Short Term Fellow at Universityof Bedfordshire (UK) in 2008, researcher associatewith the Italian National Research Council in 2010and R&D Engineer for Azcom Technology, an Ital-

ian SME, from 2010 to 2014. Lorenzo has more than 10 years of academicaland industrial research experience on wireless communication systems andprotocols, holds commercial patents and publications in prestigious books,IEEE journals and conferences. In addition, he has been Chair of IEEE WCNCCo-HetNEt 2012 workshop, editor of the book Vehicular Technologies – De-ployment and Applications by Intech, guest editor for IEEE ACCESS specialsections Networks of Unmanned Aerial Vehicles, TPC Member and reviewerfor IEEE conferences and journals. Lorenzo is also very active in organizingtutorials and industrial seminars at major IEEE conferences, like “Drone BaseStations: Opportunities and Challenges Towards a Truly “Wireless” WirelessNetwork”, which won the Most Attended Industry Program award at IEEEGlobecom 2017. During the past years, Lorenzo contributed to the Nokia F-Cell project, an innovative self-powered and auto-connected drone deployedsmall cell served by massive MIMO wireless backhaul, which received theprestigious CTIA Emerging Technology 2016 Award. Lorenzo’s current focusis on future indoor networks and next generation Wi-Fi technologies, anarea where he is contributing with pioneering works on large antenna arrayssolutions for the unlicensed spectrum.

David Lopez-Perez (M’12–SM’17) is a Senior Re-search Scientist and a Distinguished Member ofTechnical Staff (DMTS) at Nokia Bell Laborato-ries, and his main research interests are on smallcells, ultra-dense networks and unlicensed spectrumtechnologies, where he has pioneered work on LTEand Wi-Fi interworking. David is currently workingon massive MIMO, future indoor networks and thenext generation of Wi-Fi technology, IEEE802.11be.David has authored more than 135 research articles,holds over 49 patents applications, and has received

a number of prestigious awards. He is an editor of IEEE TRANSACTIONS ONWIRELESS COMMUNICATIONS.

Adrian Garcia-Rodriguez (S’13–M’17) is a Re-search Scientist in Nokia Bell Labs (Ireland), wherehe focuses on the design of next-generation 802.11technologies and UAV communications. He joinedBell Labs in 2016, after receiving the Ph.D. degree inElectrical and Electronic Engineering from Univer-sity College London (U.K.). Previously, he held re-search positions in the research institute for techno-logical development and Communication Innovation(IDeTIC) at the University of Las Palmas de GranCanaria (Spain) between 2010–2012, and in the RF

group of Nokia Bell Labs (Ireland) in 2015. Adrian is co-inventor of fourteenfiled patent families and co-author of 40+ technical publications in the areasof wireless communications and networking. On these topics, he frequentlydelivers technical tutorials (IEEE WCNC’18, IEEE ICC’18, IEEE PIMRC’18,and IEEE Globecom’18), organizes workshops and special sessions (IEEEGlobecom’17, Asilomar’18, and IEEE ICC’19), and participates in industrialseminars (IEEE Globecom’18, and IEEE ICC’19). Adrian was named anExemplary Reviewer for IEEE COMMUNICATIONS LETTERS in 2016, andboth IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS and IEEETRANSACTIONS ON COMMUNICATIONS in 2017.

Giovanni Geraci (S’11–M’14) is an Assistant Pro-fessor and Junior Leader Fellow at Universitat Pom-peu Fabra in Barcelona (Spain). He earned a Ph.D.degree from the University of New South Wales(Australia) in 2014. He gained industrial innovationexperience at Nokia Bell Labs (Ireland), where hewas a Research Scientist in 2016-2018. His back-ground also features appointments at the SingaporeUniversity of Technology and Design (Singapore) in2014-2015, the University of Texas at Austin (USA)in 2013, Supelec (France) in 2012, and Alcatel-

Lucent (Italy) in 2009. He has co-authored 50+ IEEE publications with1000+ citations, and is co-inventor of a dozen filed patent families onwireless communications and networking. He is deeply involved in theresearch community, serving as an editor for the IEEE TRANSACTIONSON WIRELESS COMMUNICATIONS and IEEE COMMUNICATIONS LETTERS,and as a workshop or special session co-organizer at IEEE Globecom’17,Asilomar’18, and IEEE ICC’19. He is also a frequent speaker and hiscontributions include a workshop keynote at IEEE PIMRC ’18, an industryseminar at IEEE ICC’19, and tutorials at IEEE WCNC’18, IEEE ICC’18,IEEE Globecom’18, and IEEE PIMRC’19. He is the recipient of the IEEEComSoc Outstanding Young Researcher Award for Europe, Middle-East &Africa 2018.

Paolo Baracca (S’11–M’13) is a Research Engineerat Nokia Bell Labs in Stuttgart, Germany, since2013. He received the B.Sc. and the M.Sc. degree inTelecommunications Engineering in 2007 and 2009,respectively, and the Ph.D. degree in InformationEngineering in 2013, all from the University ofPadova, Italy. His research interests include signalprocessing, multi-antenna techniques and schedulingfor wireless communications. He has co-authoredmore than 30 research papers, holds more than 20issued or pending patents, and regularly serves as

reviewer of IEEE journals and conferences.

M. Majid Butt (S’07–M’10–SM’15) received theM.Sc. degree in digital communications from Chris-tian Albrechts University, Kiel, Germany, in 2005,and the Ph.D. degree in telecommunications fromthe Norwegian University of Science and Technol-ogy, Trondheim, Norway, in 2011. He is a SeniorScientist 5G+ Research at Nokia Bell Labs, Paris-Saclay, France, and a Visiting Research AssistantProfessor at Trinity College Dublin, Dublin, Ire-land. Prior to that, he has held various positions atthe University of Glasgow, Glasgow, U.K., Trinity

College Dublin, Fraunhofer HHI, Berlin, Germany, and the University ofLuxembourg, Luxembourg City, Luxembourg. His current research interestsinclude communication techniques for wireless networks with a focus on radioresource allocation, scheduling algorithms, energy efficiency, and machinelearning for RAN. He has authored more than 60 peer-reviewed conferenceand journal publications in these areas. Dr. Butt was a recipient of the MarieCurie Alain Bensoussan Post-Doctoral Fellowship from the European Re-search Consortium for Informatics and Mathematics (ERCIM). He has servedas the Organizer/Chair for various technical workshops on various aspectsof communication systems in conjunction with major IEEE conferences,including Wireless Communications and Networking Conference, Globecom,and Greencom. He has been an Associate Editor for the IEEE ACCESS andthe IEEE COMMUNICATION MAGAZINE since 2016.

Nicola Marchetti (M’13–SM’15) is currently Assis-tant Professor in Wireless Communications at TrinityCollege Dublin, Ireland. He performs his researchunder the Irish Research Centre for Future Networksand Communications (CONNECT), where he leadsthe Wireless Engineering and Complexity Science(WhyCOM) lab. He received the Ph.D. in WirelessCommunications from Aalborg University, Denmarkin 2007, and the M.Sc. in Electronic Engineeringfrom University of Ferrara, Italy in 2003. He alsoholds an M.Sc. in Mathematics which he received

from Aalborg University in 2010. His collaborations include research projectsin cooperation with Nokia Bell Labs and US Air Force Office of ScientificResearch, among others. His research interests include Radio Resource Man-agement, Self-Organising Networks, Complex Systems Science and SignalProcessing for communication networks. He has authored in excess of 120journals and conference papers, 2 books and 8 book chapters, holds 3 patents,and received 4 best paper awards. He is a senior member of IEEE and servesas an associate editor for the IEEE INTERNET OF THINGS JOURNAL since2018 and the EURASIP JOURNAL ON WIRELESS COMMUNICATIONS ANDNETWORKING since 2017.