What is the Optimal Network Deployment for a Fixed Density of Antennas?
Xuefeng Yao, Ming Ding, David Lopez Perez, Zihuai Lin, Guoqiang Mao
WWhat is the Optimal Network Deploymentfor a Fixed Density of Antennas?
Xuefeng Yao ¶ , Ming Ding ‡ , David L ´ opez P ´ erez † , Zihuai Lin ¶ , Guoqiang Mao ∦ † ¶ School of Electrical and Information Engineering, University of Sydney, Australia { [email protected] } ‡ Data61, CSIRO, Australia { [email protected] } † Nokia Bell Labs, Ireland { [email protected] } ∦ School of Computing and Communication, University of Technology Sydney, Australia
Abstract —In this paper, we answer a fundamental question:when the total number of antennas per square kilometer is fixed,what is the optimal network deployment? A denser network witha less number of antennas per base station (BS) or the oppositecase. To evaluate network performance, we consider a practicalnetwork scenario with a fixed antennas density and multi-user multiple-input-multiple-output (MU-MIMO) operations forsingle-antenna users. The number of antennas in each BS iscalculated by dividing the antenna density by the BS density.With the consideration of several practical network models, i.e.,pilot contamination, a limited user equipment (UE) density andprobabilistic line-of-sight (LoS)/non-line-of-sight (NLoS) path lossmodel, we evaluate the area spectral efficiency (ASE) perfor-mance. From our simulation results, we conclude that there existsan optimal BS density for a certain UE density to maximizethe ASE performance when the antenna density is fixed. Theintuition is that (i) by densifying the network with more BSs,we can achieve a receive power gain due to the smaller distancebetween the typical UE and its serving BS; (ii) by installingmore antennas in each BS, we can achieve a beamforming gainfor UEs using MU-MIMO, although such beamforming gain isdegraded by pilot contamination; (iii) thus, a trade-off existsbetween the receive power gain and the beamforming gain, if wefix the antenna density in the network.
I. I
NTRODUCTION
Mobile data traffic is predicted to grow 1000x from now un-til 2030 [1], and dense small cell networks (SCNs) and massivemultiple input multiple output (mMIMO) are considered themajor pilar technologies to meet this ever-increasing capacitydemand in the years to come [2], [3].From 1950 to 2000, network capacity was dramatically in-creased through network densification by a factor of 2700x [1].During the first decade of 2000, the 3rd Generation Part-nership Project (3GPP) standardised the 4th-Generation (4G)Long Term Evolution (LTE) systems, which kept payingspecial attention to network densification and small cells,as an effective approach to increase capacity [2]. The firststandardisation efforts on New Radio (NR) also indicate thatnetwork densification will remain as one of the workhorsesin 5G systems. Small cells are a powerful approach to fuelfast-growing network demand due to its fundamental benefits.However, how to deploy them in a cost-effective mannerhas been a big concern for both vendors and operators, andthus of the research community. A good understanding of theperformance of dense SCNs is necessary. Up to now, many studies on dense SCNs have focusedon deriving the area spectral efficiency (ASE) performance.However, most of them only consider a limited number offactors. In [4], the authors considered a single-slope pathloss model without differentiating line-of-sight (LoS) and non-LoS (NLoS) transmissions. In [5], the authors embraced LoSand NLoS transmissions, but only considered an infinity UEdensity and a single-input single-output (SISO) system. In [6],the authors further included in the analysis a finite UE densityand an idle mode capability (IMC), which is key to achievea good performance of dense SCNs. In [7], multiple antennaswere considered while analysing coverage probability.In addition to dense SCNs, mMIMO, considered as a scaled-up version of multi-user MIMO (MU-MIMO), also has thepotential to further increase network capacity by exploiting thedegrees of freedom in the spatial domain. Indeed, mMIMOhas already been adopted as a main technology to improveASE in 5G systems [3]. It is important to note that the largerthe number of antennas, the larger the number of degreesof freedom, and thus the more multiplexing opportunities.However, when time division duplex (TDD) systems are con-sidered, due to a finite channel coherent time, the performanceof mMIMO systems may be limited by inaccurate channelstate information (CSI). Pilot contamination is considered asa major bottleneck, which occurs when the same set of uplinktraining sequences is reused across neighbouring cells [8].Other channel estimation impairments also play role.Looking at mMIMO deployment aspects, in [8], the authorsshowed that a better performance can be achieved by increas-ing the number of antennas at the BS and using a simplesignal processing. In [9], the authors analysed the uplink signalto interference plus noise ratio (SINR) and rate performancein a mMIMO system, considering a single-slope path lossmodel, without differentiating LoS and NLoS transmissions.In [10], the authors derived the downlink achievable rate inmMIMO heterogeneous cellular networks, while accountingfor LoS and NLoS transmissions and an infinity UE density.It is important to note that pilot contamination was consideredin the above three studies. However, little work has been doneon understanding the impact of the BS and UE densities inthe network capacity performance.Generally speaking and for a certain UE density, the more a r X i v : . [ c s . N I] O c t Ss and/or the more antennas per BS, if operated appropri-ately, the higher the network capacity [11]. However, up tonow, it is unclear what is the optimal network deployment,i.e., the optimal combination of the number of BSs andantennas per BS in a given area, when the antenna density(antennas/km ) is fixed. In particular, two extreme cases areof great interest: i) a dense SCN network where all BSshave a single antenna, and ii) a sparse mMIMO networkwhere many antennas are concentrated in a few BSs. Whichnetwork deployment is better in terms of the network capacityperformance?In this paper, we give a first answer to this fundamentalquestion by means of computer simulations. From our sim-ulation results, we conclude that, for a certain UE density,there exists an optimal BS density to maximise the ASEperformance when the antenna density is fixed. The intuitionis that (i) by densifying the network with more BSs, wecan achieve a receive power gain due to the smaller distancebetween the typical UE and its serving BS; (ii) by installingmore antennas in each BS, we can achieve a beamforminggain for UEs using MU-MIMO, although such gain willbe degraded by pilot contamination. Thus, a trade-off existsbetween the receive power gain and the beamforming gain, ifwe fix the antenna density in the network.The rest of this paper is structured as follows. Section IIdescribes the network scenario and the wireless system modelconsidered in this paper. Section III presents our numericalresults, with remarks shedding new light on the trade-offbetween the receive power gain and the beamforming gain,if we fix the antenna density in the network. Section IV drawsthe conclusions. Notations : We use A , a , and a to denote a matrix, a vectorand a scalar, respectively. A T and A H represent the transposeand conjugate transpose of A , respectively. C m × n denotesa set of complex numbers with a dimension of m × n . A denotes a set, while N B ( m, n ) represents a negative binomialdistribution with parameters m and n .II. SYSTEM MODEL
In this section, we present the network scenario, wirelesssystem model and pilot-aided MIMO channel estimation con-sidered in this paper.
A. Network Scenario
We consider a downlink (DL) cellular network with BSsdeployed on a plane according to a homogeneous Poissonpoint process (HPPP) Φ with a density of λ BSs/km .Active DL UEs are also Poisson distributed in the consid-ered network with a density of ρ UEs/km . Here, we onlyconsider active UEs in the network because non-active UEsdo not trigger any data transmission. The typical UE U isdeployed at the origin and its serving BS is denoted as B .Each BS is equipped with M antennas, and has a totaltransmit power of P txb , where M is calculated as the antennadensity divided by the BS density λ . Each UE is equippedwith a single antenna. In practice, a BS will enter into idle mode, if there is noUE connected to it, which reduces the interference to UEs inneighbouring BSs as well as the energy consumption of thenetwork. Since UEs are randomly and uniformly distributedin the network, the active BSs also follow another HPPPdistribution ˜Φ [12], the density of which is ˜ λ BSs/km . Notethat ˜ λ ≤ λ and ˜ λ ≤ ρ , since one UE is served by at most oneBS. Also note that a larger ρ results in a larger ˜ λ .From [12], ˜ λ can be calculated as ˜ λ = λ − (cid:16) ρqλ (cid:17) q , (1)where an empirical value of 3.5 was suggested for q [12].In this paper, we consider a pilot-aided channel estimationscheme, and assume imperfect channel state information (CSI)caused by pilot contamination. In an uplink training stage, ascheduled UE transmits a randomly assigned pilot sequence t k from the set of available training sequences T . UEs ineach BS reuse the same set of pilot sequence, i.e. the pilotreuse factor can be as high as one. However, it should benoted that the pilot reuse factor at a particular time instantstrongly depends on the number of pilot sequences and thenumber of UEs per BS. For example, a higher number ofUEs per BS implies a larger reuse factor of pilot sequences.After observing the received pilot signal, which is transmittedfrom the scheduled UE and is interfered by the other UEs inneighbouring cells using the same pilot sequence, a BS candetect the corresponding pilot and then estimate the channelby, e.g., a minimum mean square error (MMSE) estimator. B. Wireless System Model
The 3D distance between an arbitrary UE and an arbitraryBS is denoted as w = (cid:112) r + h , (2)where r is the 2D distance between an arbitrary UE and anarbitrary BS, and h is the absolute antenna height differencebetween these two. Note that the value of h is in the orderof several meters. In our simulation, the height difference isdecided according to the path loss model [13], [14].With regard to such path loss modelling, we adopt a generaland practical piecewise path loss model with respect to the 3Ddistance w proposed in [ ? ], where each segment of the pathloss function is modelled as either a LoS transmission or aNLoS one. Such path loss function is given by ζ jlk ( w ) = ζ jlk ) ( w ) , when h ≤ w ≤ d ζ jlk ) ( w ) , when d ≤ w ≤ d ... ... ζ n ( jlk ) ( w ) , when w ≥ d N , (3)where ζ n ( jlk ) ( w ) is the n -th segment of the path loss functionbetween the j -th BS and the k -th UE scheduled by the l -th BS.ach segment of path loss function is modelled by: ζ n ( w ) = (cid:40) ζ L n = A L n w − α L n , for LoS ζ NL n = A NL n w − α NL n , for NLoS , (4)where • ζ L n ( w ) and ζ NL n ( w ) , n ∈ { , , . . . , N } are the n -thsegment of the path loss functions for the LoS and theNLoS cases, respectively, • A L n and A NL n are the path loss values at a reference3D distance w = 1 for the LoS and the NLoS cases,respectively, and • α L n and α NL n are the path loss exponents for the LoS andthe NLoS cases, respectively.In addition, the piecewise probability function of that atransmitter and a receiver communicate via a LoS path whileseparated by a distance w is written as P r L = P r L ( w ) when h ≤ w ≤ d P r L ( w ) when d ≤ w ≤ d ... ... P r L n ( w ) when w ≥ d N , (5)where P r L n ( w ) is the n -th segment of the LoS probabilityfunction that the path between an arbitrary UE and an arbitraryBS is a LoS one.Based on these path loss and probabilistic LoS/NLoS mod-els, a practical UE association strategy (UAS) is consideredin this paper. A UE is associated with the BS that providesthe maximum average received signal strength (i.e. the largest ζ ( w ) ). Moreover, we assume that one M -antenna BS can atmost simultaneously schedule K U UEs in a time-frequencyresource block according to [15], where K U is given by K U = min { K T , M/ } , (6)where K T is the number of pilot sequences and M is thenumber of antennas per BS. Note that M/ is an empiricalvalue to achieve a good performance for a MU-MIMO systemin case of pilot contamination [15].For convenience, we denote a UE in each BS by the indexof its used uplink training sequence, i.e., the k -th UE is theUE that uses the k -th uplink training sequence t k , where k israndomly chosen from 1 to the maximum training sequencenumber K T . Note that the k -th UE could be an empty UEsince not all of the uplink training sequences are used upin each BS. If there are more than K U UEs connected toa BS, only up to K U of them are randomly chosen to bescheduled, which means that this BS is fully loaded and K U training sequences are used. Without loss of generality andas mentioned earlier, we consider the first UE in B as thetypical UE, denoted by U .From [16], the number of UEs per active BS canbe modelled as a Negative Binomial distribution, i.e., K ∼N B ( q, ρρ + qλ ) . However, note that only active BSs areconsidered to participate in DL transmissions and that atmost K U UEs can be served simultaneously by an active BS. Thus, the actual number of scheduled UE per active BS ˆ K can be modelled as a truncated modified Negative Binomialdistribution, i.e., ˆ K ∼ T runc
N B ∗ ( q, ρρ + qλ ) , and the PMF of ˆ K can be expressed as f ˆ K ( k ) = (cid:40) f K ( k )1 − f K (0) ≤ k ≤ K U − (cid:80) ∞ k = KU f K ( k )1 − f K (0) k . = K U , (7)where f K ( k ) is the PMF of UE number distribution (i.e., K ∼N B ( q, ρρ + qλ ) ) derived in [16], which is given by f K ( k ) = Pr [ K = k ]= Γ( k + q )Γ( k + 1)Γ( q ) (cid:18) ρρ + qλ (cid:19) k (cid:18) qλρ + qλ (cid:19) q . (8)where Γ( · ) is the Gamma function. Note that f K ( k ) satisfiesthe normalization condition: (cid:80) + ∞ k =0 f K ( k ) = 1 . C. Pilot-Aided mMIMO Channel Estimation
The channel is assumed to be invariant in a time-frequencyresource block, and change independently from block to block.The channel vector can be expressed as h ( P L ) jlk = ( ζ ( P L ) jlk ) φ jlk w jlk , (9)where ’PL’ takes the value ’L’ and ’NL’ for LoS transmissionsand NLoS transmissions, respectively, h ( P L ) jlk is the channelvector between the j -th BS and the k -th UE scheduled bythe l -th BS, w jlk is the multi-path fading vector modelledaccording to Rayleigh fading, and φ jlk is the covariance matrixof the channel. Since we consider that the channel h ( P L ) jlk isidentically and independently distributed (i.i.d.), φ jlk shouldbe an identity matrix in this case.In the uplink training stage, pilot contamination is con-sidered in our simulation. Based on the distance-dependentfractional power compensation scheme, the channel vector y ( P L )11 observed at BS B for the typical UE U is given by y ( P L )11 = (cid:113) P tx h ( P L )111 + (cid:88) l (cid:54) =1 (cid:113) P tx l h ( P L )1 l + n , (10)where l represents the l -th BS, which serves an interfering UEusing the first pilot sequence. Besides, n denotes a zero-mean additive white Gaussian noise (AWGN) vector at thetypical UE U , where the variance of each element is σ .Using the fractional power compensation [14], P tx lk is thetransmit power from the k -th UE in the l -th BS, which can beexpressed as P tx lk = P txu ( ζ ( P L ) llk ( w )) − (cid:15) , (11)where P txu is the baseline transmit power of each UE, and (cid:15) is the fraction of the path loss compensation.From the observation of the pilot signals transmitted fromUEs, BSs can estimate their channels by correlating thecorresponding pilot sequences with the observation by usingan MMSE estimator. Since the channel h ( P L )111 is modelleds i.i.d Rayleigh fading, the estimated channel ¯ h ( P L )111 can becalculated as ¯ h ( P L )111 = (cid:112) P tx ζ ( P L )111 (cid:80) l (cid:54) =1 P tx l ζ ( P L )1 l + σ y ( P L )11 . (12)Note that the estimation error of ¯ h ( PL) can be formulated by ˆ h ( P L )111 = h ( P L )111 − ¯ h ( P L )111 . (13) D. Performance Metrics
In the downlink data transmission stage, we assume that BSsapply the zero-forcing (ZF) precoder based on the estimatedchannel obtained in the uplink training stage. We assume thatthe total power of a BS is fixed, and it is equally dividedamong the served UEs.With these assumptions, the received symbol s at typicalUE U can be written as [17] s = (cid:112) P ¯ h ( P L ) H f s + (cid:112) P ˆ h ( P L ) H f s + (cid:112) P l (cid:88) ( l,k ) (cid:54) =(1 , h ( P L ) H lk f lk s lk + n , (14)where f lk is the ZF precoding vector for the k -th UE scheduledby the l -th BS, P l is the transmit power allocated by the l -thBS to each of its scheduled UE, s lk is the signal intended for k -th UE in the l -th BS, and n is the AWGN vector at thetypical UE U . Here, f lk is computed by: f lk = (cid:16) ¯ h ( PL ) Hllk ¯ h ( PL ) llk (cid:17) − ¯ h ( PL ) Hllk E (cid:40)(cid:12)(cid:12)(cid:12)(cid:12)(cid:16) ¯ h ( PL ) Hllk ¯ h ( PL ) llk (cid:17) − ¯ h ( PL ) Hllk (cid:12)(cid:12)(cid:12)(cid:12) (cid:41) . (15)In (14), the first term is the received signal and the othersare unknown at the UE. Hence, the downlink SINR at thetypical UE U can be calculated bySINR = P (cid:12)(cid:12)(cid:12) ¯ h ( P L ) H f (cid:12)(cid:12)(cid:12) P (cid:12)(cid:12)(cid:12) ˆ h ( P L ) H f (cid:12)(cid:12)(cid:12) + (cid:80) ( l,k ) (cid:54) =(1 , P (cid:12)(cid:12)(cid:12) h ( P L ) H lk f lk (cid:12)(cid:12)(cid:12) + σ . (16)We also investigate the area spectral efficiency (ASE) per-formance in bps/Hz/km , which is defined as A ASE ( γ ) = ˜ λ (cid:90) + ∞ γ log (1 + γ ) f Γ ( γ ) dγ, (17)where γ is the minimum working SINR in a practical SCN,and f Γ ( λ, γ ) is the PDF of the SINR observed at the typicalUE for a particular value of λ .III. R ESULTS AND DISCUSSION
In this section, we investigate the ASE performance withvarious network deployment strategies via simulations. Weconsider a practical two-piece path loss function and a prac-tical two-piece exponential LoS probability function, defined
Fig. 1. The ASE performance of different antenna deployment when γ =0 dB vs. UE density ρ with 500 antennas/km by [14]. In more detail, all simulation parameters are takenfrom Tables A.1-3, A.1-4, A.1-5 and A.1-7 of [14]: α L = 2 . , α NL = 3 . , A L = 10 − . , A NL = 10 − . , P tx = 24 dBm, P N = − dBm (including a noise figure of 9 dBat each UE), e = 1 . In our simulations, the total numberof antennas per square kilometre is set to 500 antennas/km and 1000 antennas/km respectively, which are practical as-sumptions for 5G [2]. In addition, we set the total numberof uplink training sequences to K T = 20 , which are reusedacross all cells. Note that the pilot reuse factor varies with theBS density and UE density in different network deployment.More specifically, the pilot reuse factor is higher in a networkwith a larger UE density or a smaller BS density since the UEnumber scheduled by each BS becomes larger. As a result, theUE density generating the pilot contamination is the productof the pilot reuse factor and the BS density. A. The ASE Performance
Figs. 1 and 2 show the ASE performance versus the UEdensity ρ for various BS densities, when the antenna densitiesare 500 antennas/km and 1000 antennas/km , respectively.Note that only UEs whose SINR is larger than γ = 0 dB areconsidered in the computation of the ASE according to (17).From Figs. 1 and 2, we can draw the following conclusions: • Network deployments with BS density λ at 50 and 100BSs/km always perform better than those at 5 and 10BS/km in term of ASE. For this BS density range, thismeans that a dense network with many BSs and a fewantennas per BS is a better solution than a sparse networkwith a few BSs and many antennas per BS. The intuitionbehind this phenomenon is that by having more BSs, thepower gain due to the short signal-link distance surpassesthe loss of beamforming gain caused by the less antennasper BS. • Note that the single antenna cases, i.e., 500 BSs/km inFig. 1 and 1000 BSs/km in Fig. 2, achieves their highestASE performance when ρ is around 100 UEs/km and ig. 2. The ASE performance of different antenna deployment when γ =0 dB vs. UE density ρ with 1000 antennas/km
200 UEs/km , respectively. This is because more BSs areactivated in a scenario with more UEs, which in turncauses a large number of interference paths to transitionfrom NLoS to LoS, which damages the overall networkperformance [6]. Moreover, as shown in Figs. 1 and 2,the single antenna case show a better performance thanthe other investigated cases at around ρ ∈ [1 , UEs/km and [1 , UEs/km , respectively. The reason is that when ρ is relatively small, the active BS density ˜ λ in eachsimulated case is almost the same, i.e., ρ , and thusbringing the limited number of active BSs closer to theUEs is a better strategy than the mMIMO one. • For the multiple-antenna deployment strategies with theBS density much less than 500 BSs/km in Fig. 1 and1000 BSs/km in Fig. 2, the ASE firstly grows dramat-ically as the UE density ρ increases, and then suffersfrom a slow growth when the UE density ρ is largerthan a threshold. The reason is that BSs are low loadedor even deactivated when the UE density ρ is small.Thus, every newly added UE can be scheduled with adecent link quality, making a significant contribution tothe ASE. In contrast, nearly all BSs are active and servingthe maximum number of UEs when ρ is large enough.Hence, it is not very likely that a newly added UE canget scheduled with an additional degree of freedom. Theworst case scenario is when BSs are fully loaded, i.e., theUE density ρ is large enough compared to the BS density λ , which results in a saturated ASE as shown in Figs. 1and 2. • From the ASE results shown in Fig.1 and Fig. 2, thereexists an optimal network deployment strategy for aspecific antenna density and UE density ρ . In more detail,when the antenna density is 500 antennas/km and ρ is600 UEs/km , the descending order of the ASE perfor-mance is 50, 100, 500, 10 and 5 BSs/km . This meansthat the optimal BS density lies between 10 BSs/km and 100 BSs/km for the case of 500 antennas/km and ρ = 600 UEs/km . Moreover, when the antenna density is Fig. 3. The ASE performance of different UE density when γ = 0 dB vs.BS density λ with 1000 antennas/km and ρ is 600 UEs/km , the descendingorder of the ASE performance is 100, 50, 10, 500and 5 BSs/km . This means that the optimal BS densitylies between 50 BSs/km and 500 BSs/km for the 1000antennas/km case when ρ = 600 UEs/km . B. The Trade-off between the BS Density and the Antennanumber per BS
Fig. 3 shows the ASE performance versus the BS den-sity λ for various UE densities. In particular, we considerfour UE densities: ρ = 50 UEs/km , ρ = 100 UEs/km , ρ = 300 UEs/km and ρ = 600 UEs/km and a total antennadensity of 1000 antennas/km . To evaluate the impact ofdifferent UE densities on the ASE performance, we keep theother assumptions and models same as before.From Fig. 3, we can observe that: • For a fixed antenna density (1000 antennas/km ) and allthe investigated UE densities, there exists an optimalnetwork deployment strategy to maximize the ASE. Theoptimal deployment is around the BS density λ =100 BSs/km with approximately 10 antennas per BS forthese UE density. The intuition is that (i) by densifyingthe network with more BSs, we can achieve a receivepower gain due to the smaller distance between the typi-cal UE and its serving BS; (ii) by installing more antennason each BS, we can achieve a beamforming gain forUEs using mMIMO, although such beamforming gain isdegraded by pilot contamination. Thus, a trade-off existsbetween the receive power gain and the beamforminggain, if we fix the antenna density in the network. • It is important to note that the larger the UE density,the better the ASE. This is because a larger UE densityresults in more UEs scheduled per square kilometer. Alsonote that the ASE performance difference between the ρ = 600 UEs/km case and the ρ = 300 UEs/km case issmaller than that between the ρ = 300 UEs/km case andthe ρ = 100 UEs/km case. This is in line with the ASEtrend shown in Fig. 1, which increases rapidly and then ig. 4. The ASE performance without pilot contamination of different UEdensity when γ = 0 dB vs. BS density λ with 1000 antennas/km suffers from a slow growth with the UE density due tothe performance saturation. • For the investigated antenna density (1000 antennas/km ),the optimal BS densities for various UE densities are thesame, i.e., around λ = 100 BSs/km , which indicates thatthe optimal network deployment might be independentof the UE density. This conjecture needs to be furtherstudied with theoretical analysis. • Note that the ASE experiences a slow decrease when BSdensity is larger than around 250 BSs/km . The reasonis that the maximum scheduled UE number per BS hasalready decreased to one according to (6), which meansthe ASE performance can not be further influenced bydecreasing the scheduled UE number per BS. C. Performance Impact of Pilot Contamination
An interesting question follows from Fig. 3 is whether thetrade-off still exists between the receive power gain and thebeamforming gain, if the pilot contamination is removed fromthe investigated MU-MIMO network (i.e., perfect channel stateinformation). To answer this question, in Fig. 4 we plot theASE performance without pilot contamination, while keepingthe other assumptions same as those for Fig. 3.From Fig. 4, we can conclude that: • Without pilot contamination, the ASE performance im-proves for all cases, thanks to the accurate CSI. • Meanwhile, the descending order of the ASE performancedoes not change if we remove the pilot contamination,which means that the trade-off still exists between thereceive power gain and the beamforming gain, regardlessof the pilot contamination phenomenon. Also note thatwithout pilot contamination, the optimal network deploy-ment shifts to the BS density around 63 BSs/km with16 antennas per BS. • The ASE performance improvement without pilot con-tamination is small when the BS density is relativelylarge, because the pilot reuse factor is small in densenetworks due to the limited number of UEs per BS. IV. C
ONCLUSION
In this paper, we have conducted a performance evaluationwith a fixed number of antennas per square kilometer. Our re-sults indicate that there exists an optimal network deploymentstrategy to maximise the ASE performance for a certain UEdensity. Intuitively speaking, a balance between (i) bringingUEs closer to BSs by densifying the network, and (ii) allowingfor more antennas per BS to achieve a higher precoding gainwith the consideration of pilot contamination, needs to befound to optimise the system performance.R
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