Attitude Estimation for Base Station AntennasBased on Downlink Channel Statistics

Cen Ling1, Yongyu He1, Xuefeng Yin1∗, Zhimeng Zhong2, Weiming Duan2, and Silvia Ruiz Boqué3

1School of Electronics and Information Engineering, Tongji University, Shanghai, China2Huawei Technology Company, China

3Department of Signal Theory and Communications, Universitat Politècnica de Catalunya, SpainEmail: {1233557, 1131704, yinxuefeng}@tongji.edu.cn, {zmzhong,weiming.duan}@huawei.com, and

silvia@tsc.upc.edu

Abstract—In this contribution, a maximum-likelihood-based ap-proach is proposed for estimating the attitudes of sectoringbase station (BS) antennas based on the power of the receivedsignals observed by multiple user equipments (UEs) in a cellularnetwork. The proposed method calculates the likelihood of theantenna attitude by taking into account both the large-scalefading statistics, i.e. path loss, shadowing, and the small-scalefading attributed to multi-path propagation. The performanceof the method is evaluated by simulations in both urban andrural scenarios, where a random-propagation-graph method isapplied to generating realistic channel impulse responses by usingdirectional antenna patterns. Results show that by using theproposed method, accurate estimates of the antenna attitude canbe obtained when the observations from more UEs are availableand the line-of-sight (LoS) condition dominates the channelsbetween the BS and the UEs.

Index Terms—Received signal power, antenna attitude,maximum-likelihood algorithm, path loss, shadow fading,multipath fading, and propagation graph modeling

I. Introduction

For wireless communications in a cellular network, inter-cell interference is one of the main reasons for deteriorationof network coverage, system capacity and traffic throughput[1]. Adjustment of antenna attitude for the BSs, i.e. theantenna’s downtilt and azimuth, is considered as a feasiblemethod of inter-cell interference reduction, and signal intensityenhancement in local areas [2].

Adapting the antenna downtilt can be performed mechani-cally, electrically, or by a combination of both approaches[3]. Technologies of Mechanical Down-Tilting (MDT) caneffectively mitigate other cells’ interferences in the directionof the antenna’s main-lobe in Frequency Division Multiple-Access (FDMA) or Time-Division Multiple Access (TDMA)networks [4]. Electronic Down Tilting (EDT) modulates theimpulse response coefficients of multiple antennas to get thesuperimposed radiation at specific directions [5].

This work is jointly supported by China fundamental education basicresearch project [Polarization characterization of wireless propagation chan-nel], the project [13510711000] - System design and demo-constructionfor cooperative networks of high-efficiency 4G wireless communicationsin urban hot-spot environments -supported by the Science and TechnologyCommission of Shanghai Municipality, the Key Program of National NaturalScience Foundation of China (Grant No. 61331009), Huawei-Tongji reserachproject [YB2013120038] - High-Frequency Wireless Propagation ChannelMeasurement Techniques, and Huawei Innovation Research Program.

Recently, advantages of the down-tilting technologies havedrawn much attention from researchers. By using the antennatilting technique proposed in [6], a coverage notch may appearat the center of horizontal beam pattern. It is desirable tointentionally direct the notch towards a cochannel BS stationin order to increase radio spectral efficiency for networks.The antenna tilting techniques can maintain the signal-to-interference power ratio beyond 12 dB, satisfying the re-quirement of quality service in digital cellular systems [7].It is also fascinating to apply antenna tilting techniques incooperative communication systems so as to alleviate inter-cell interference for both interior subscribers and those locatedat the cell edges [8]. In addition, antenna tilting is beneficialto mitigate congestions in hot-spot sectors where the traffic isunevenly distributed in the cellular network [9].

The selection of Optimal Downtilt Angle (ODA), either byEDT or MDT, rests on the terrain and antenna deployment.It has to be determined for specific sites in practice. Ananalytical expression of the approximate downtilt has beengiven as a function of site spacing, antenna height and verticalbeamwidth [10]. It was observed that the ODA auguments withthe increase of antenna height and declines with the growth ofthe cell size [11]. However, this method is not accurate enoughto take into account the impact of the realistic propagationenvironment and dynamic variation of propagation channel.

In this contribution, a novel method is proposed for estimatingthe attitude of the BS antenna. The method maximizes thelikelihood of an attitude candidate calculated based on thereceived signal power observed at multiple UEs’ locations.The fading of the received power is decomposed into thecontributions of multiple variables that follow the probabilitydensity functions (pdfs) pre-determined based on calibrationcampaigns. The attitude estimate is obtained by maximizingthe likelihood function. Simulations are conducted to evaluatethe performance of the proposed method by using the propaga-tion channel realizations created with the random-propagation-graph-based method [12].

The rest of the paper is organized as follows. In Section II, themodel of the received signal power in the UE is introduced.In Section III, the maximum-likelihood-estimation for theattitude of the BS antenna is presented. Simulation results areelaborated in Section IV for the performance assessment of

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the proposed method. Finally, conclusive remarks are given inSection V.

II. Model of the received signal power

We consider a cellular scenario in an outdoor environmentwhere the UEs are located certain distances away from theBS. The signal power transmitted by the BS is denoted withPt. The normal direction of the BS antenna is tilted bythe direction ηTx = (θTx, ϕTx), where θTx and ϕTx are tiltedangles in elevation and azimuth respectively. In this paper,we are interested at estimating ηTx which is either unknownor different from its expected value. The UEs are located inclutter environments where the local scattering is the majormechanism for wave propagation. The tilted angles of the UEs’antennas are not interested in our case.

The power of the signals Pr received by a UE located in thedirection of departure (DoD) i.e. ΩT x from the BS side can becalculated as

g(ΩTx, d; ηTx) ≈ gp(d) · gs · gm · gT x(ΩTx; ηTx) · gRx, (1)

where d is the distance between the BS and the UE, gp(d)is the path gain due to the free-space propagation and theinfluence of the terrain, gs denotes the gain of shadow fading,gm represents the gain due to multi-path fading, gT x(ΩTx; ηTx)is the BS antenna gain for the DoD i.e. ΩTx when the antennais titled by the direction ηTx, and gRx is the UE antenna gain.

The following assumptions are applied in the analysis consid-ered in the paper:

1) The shadow-fading gain gs follows a log-normal distri-bution with zero mean and standard deviation σs:

fLN(gs) =1√

2πσsgs

exp

{− ln (gs)2

2σ2s

}(2)

2) The multipath fading gm, which is uncorrelated with gs,follows the Rician distribution with parameters μm andσm:

fRi(gm) =

√gm

σ2m

exp

{−gm + μ

2m

2σ2m

}I0

{μm√

gm

σ2m

}(3)

where I0(·) denotes the zero-order modified Bessel func-tion of the first kind. Notice that the Rayleigh distri-bution is a special case of the Ricean distribution forμm = 0.

3) The BS antenna gain gT x (ΩT x; ηT x) is a deterministicfunction of DoD given ηT x .

4) The UE is located in a clutter environment in such away that the multiple paths observed by the UE havesimilar DoD, i.e. ΩT x.

5) The antenna gain gRx is identified for all UEs consideredin the estimation.

Considering that the path loss model gp(d) is a deterministicfunction of d, the joint probability of multiple observations

g = {g(ΩTx, d);ΩTx ∈ STx, d ∈ [dmin, dmax]} with STx being aportion on a sphere can be written as

f (g; ηT x) =∏

ΩTx ∈ STx

d ∈ [dmin, dmax]

f (g(ΩTx, d; ηT x))

=∏

ΩTx ∈ STxd ∈ [dmin, dmax]

fLN(gs(ΩTx, d; ηT x)) fRi(gm(ΩTx, d; ηT x)).

(4)

Here, gs(ΩTx, d; ηT x) is obtained by averaging multiple valuesof g(ΩTx, d; ηT x)/gp(d; ηT x) observed within the distance oftens of wavelengths centered at d, gm(ΩTx, d; ηT x) is cal-culated by averaging g(ΩTx, d; ηT x)/gp(d; ηT x)/gm(ΩTx, d; ηT x)observed within the distance of several wavelengths centeredat d, and dmin, dmax denote the minimum and maximumseperation between the BS and UEs respectively. The pathloss models gp (d) may exhibit different behaviors i.e. thedecay exponent constant and intercept for urban/suburban,LoS/NLoS scenarios due to the diverse propagation effects[13]. In our study, path loss models are distinguished for LoSand NLoS situations.

III. Attitude estimation technique

The problem at hand is to estimate ηTx based on the ob-servation g. From the Bayesian theorem, i.e. f (g; ηTx) =f (ηTx; g) · f (g)/ f (ηTx) where the priori probability f (ηTx) isconsidered to be uniform and f (g) = 1, the likelihood of ηTx

given g, i.e. f (ηTx; g) can be calculated as

f (ηTx; g) ∝ f (g; ηTx). (5)

Thus, the maximum-likelihood (ML) estimate of ηTx can beobtained by solving the following maximization problem:

(ηTx)ML = arg maxηTx

Λ(ηTx; g, σs, μm, σm), (6)

where Λ(ηTx; g, σs, μm, σm) is the loglikelihood function ofηTx. Under the assumption that σs, μm, σm are constant for theUEs within the coverage of the cell, the loglikelihood functioncan be calculated, by dropping the constant components as

Λ(ηTx; g, σs, μm, σm) =∫ dmax

dmin

∫STx

− ln(gs(ΩTx, d; ηTx))2

2σ2s

− gm(ΩTx, d; ηTx) + μ2m

2σ2m

+ ln I0

{μm

√gm(ΩTx, d; ηTx)

σ2m

}dΩTxdd.

(7)

This equation can be adapted to the case where σs, μm, σm aredependant on the variables (ΩTx, d). In such a case, σs, μm, σm

in (7) are substituted by their functions with respect to ΩTx

and d respectively.

Before calculating the ML estimate of ηTx as shown in (6),it is prerequisite to conduct calibration campaigns to get thecorrect estimate of the path loss model gp(d), and the modelparameters, i.e. σs, μm and σm. In the calibration campaigns,the radiation pattern of the BS antenna and its attitude areknown in advance. The path loss model is established by

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fitting a regression line to the empirical scatter plots ofthe averaged power loss expressed in dB versus the BS-UEseparation. The average power loss is calculated by takingthe arithmetic mean of the received signal power obtainedwithin the distance of hundreds of wavelength [14]. Thenthe shadow fading is calculated by removing the power losspredicted by the path loss model and taking the average of theresidue within the distance of tens of wavelength. Eventually,the multipath fading is obtained by removing both the powerloss predicted by the path loss model, and shadow fading.Then the lognormal pdf and the Rician pdf are fitted to theempirical occurrence frequency graph for the shadow fadingand multipath fading respectively.

As afore-mentioned, the path loss model may be differentdepending on whether the measured received power are ob-tained in the LoS or NLoS scenarios. Considering the factthat whether a UE is in a LoS or NLoS scenario maybe determined by analyzing the K-factor for the receivedpower [15], two path loss models can be extracted basedon the observations of UEs in the LoS and NLoS scenariosrespectively. Thus, for a calibration campaign conducted in aspecific type of environment, the estimates of the followingparameters: [nLoS, nNLoS, σs, μm, σm] are obtained, where nLoS

and nNLoS represent the path loss exponent constant in the LoSand NLoS scenarios respectively. These parameter estimatesare applied in (7) for calculating the likelihood of unknownattitude of BS antenna when the environment is with the sametype as that considered in the calibration campaign.

IV. Simulation results

Simulations are performed with synthetic channels generatedin two types of propagation environments, i.e. urban and ruralscenarios. The accuracy of the proposed estimation methodis evaluated. We used the stochastic propagation graph mod-elling approach to generate the random channel realizationsin the simulations [12]. This approach relies on the geometri-cal position, mobility and the electromagnetic properties ofrandomly distributed scatterers. It predicts channel impulseresponse (CIR) by exhaustive searching for propagation pathsconnecting transmitters and receivers. The propagation graphdisplays strong capability in modeling wave-reverberation ef-fects and owns low computational complexity compared withconventional ray-tracing techniques.

The propagation in the urban and rural environments is sim-ulated by assuming the existence of multiple scatterers asdepicted in Figure 1. The red spots in Figure 1 (a) and (b)represent the location of the transmitter. The blue spots inFigure 1 (a) and the purple spots in Figure 1 (b) denotethe scatterers which are the trees, buildings and other objectsinvolved in the propagation. It can be observed that the scat-terers are spread more horizontally in the rural environment,and more vertically in the urban scenario. The locations ofUEs, depicted in pink points in the figures, are assumed tobe known in the simulations. Parameter settings specified inthe graph-modeling simulations are listed in Table I. Notice

(a) Urban scenario

(b) Rural scenario

Figure 1. Diagram for the locations of scatterers and the BS antenna in theurban and rural scenarios. The red thick spots denote the BS and the pinksmall spots refer to the UEs.

Table IParameter settings for simulation

Scenarios Rural Urban

Bandwidth 20 MHzCarrier Frequency 2.6 GHzTotal UE Locations 1000Heights of BS antenna 25 m 6 mMax height of scatterers 5 m 10 mHeights of UEs 1 − 3 m 1 − 5 m

that in the urban environment, lower antenna height is applied,which results in more NLoS channels for UEs than in the ruralscenario.

A directional antenna is used in the BS during the simulations.Figure 2 (a) and (b) depict the magnitude in dB for theunderlying antenna radiation pattern in 3-D and 2-D viewsrespectively. It can be observed that the antenna is highlydirectional with main beam centered at azimuth of 90◦, el-evation of 45◦ and the 3-dB beamwidth is about 20◦ in bothazimuth and elevation. Channels are generated in multipleUEs’ locations by assuming different downtilts. For simplicity,the orientation ϕT x of the antenna is fixed in the azimuthdomain, and only the downtilt θT x in the elevation domainis of interest for estimation during the simulations.

In the calibration step, simulations are performed to obtain thepath loss models and the statistical parameters for shadowing

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Figure 2. 3-D and 2-D views of the directional antenna radiation patternused in simulations.

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s[d

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Figure 3. Path loss models extracted for the simulation results obtained inLoS and NLoS scenarios

and multipath fading. The CIRs are generated for multiple UEsat both LoS and NLoS conditions by using an omnidirectionalBS antenna. Figure 3 (a) and (b) illustrate the scatter plots forthe received signal power versus BS-UE separation for theLoS and NLoS scenarios respectively. The linear curves fittedto the empirical data are also illustrated. It can be observedfrom Figure 3 (a) and (b) that the empirical path loss modelsexhibit significant difference for the LoS and NLoS scenarios.This indicates the necessity of modeling the statistics of fadingin the LoS and NLoS scenarios separately. Figure 4 (a) and(b) depict the scatter plots for the simulation results of shadowfading in dB and multipath fading in linear scale respectively.It can be observed that they can be well fitted with theGaussian distribution and Rician distribution respectively. Theparameters of the fitted pdfs are reported in the legends of thefigures.

In the simulations with unknown downtilt, the directionalBS antenna is applied. The effect of the radiation patternwith specific downtilt is considered for every propagationpath between scatterers and the BS antenna. The proposedalgorithm is implemented to estimate the downtilt θT x in bothrural and urban scenarios.

Figure 5 demonstrates the loglikelihood functionsΛ(θTx; g, σs, μm, σm) when the true downtilt is θ′Tx = 4◦

in the urban and rural scenarios. It can be observed fromFigure 5 that the maxima of the loglikelihood functions inboth scenarios are found at θTx = 4◦ correctly. The likelihoodgraph obtained in the rural scenario is observed to be morepeaky than that in urban scenario. We postulate that this isdue to the fact that more UEs with LoS channels are available

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Shadow fading [dB]

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piri

cal

occu

rren

cefr

eque

ncy Simulation results

Lognormal pdf σs = 0.62 dB

(a) Shadow fading

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piri

cal

occu

rren

cefr

eque

ncy

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Simulation resultsRician pdf μm = 1.08, σm = 0.14

(b) Multipath fading

Figure 4. Scatter plots of shadow fading and multipath fading observed byUEs at LoS condition.

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1

Urban Scenario

Rural Scenario

Candidate downtilt [◦]

Λ(θ

Tx;g,σ

s,μ

m,σ

m)

Figure 5. Loglikelihood of downtilt for urban and rural scenario

in the rural than in the urban scenario.

Figure 6 (a) and (c) depict the original BS antenna radiationpatterns observed at the UEs’ locations when assuming that theLoS connection exists for both scenarios. Figure 6 (b) and (d)illustrate the estimated radiation patterns gTx(ΩT x) calculatedas follows:

gTx(ΩT X) =∫ dmax

dmin

g(ΩTx, d) − gp(d) − gs(ΩTx, d; θTx)−

gm(ΩTx, d; θTx)dd,

where θTx is the estimate of the antenna downtilt. It can beobserved from these comparison that the estimated radiationpatterns are similar with the true patterns for both rural andurban scenarios.

Figure 7 depicts the estimation errors for the urban and ruralscenarios by using the proposed method with the true tilt angle

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Figure 6. Antenna Radiation Pattern For Urban and RuralScenario

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rage

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imat

edE

rror

[Deg

]

Figure 7. Estimated Error of Tilt angles in Rural and Urban Scenarios

θTx = 1, 2, . . . , 8◦. It can be observed that in most cases, thedowntilt can be correctly estimated with acceptable errors,except for θTx = 6◦ in the urban scenario where the estimationerror appears to be significant. Our conjecture is that this isdue to less number of the UEs located in the coverage of theantenna main beam for θTx = 6◦, since in the urban scenarios,UEs are distributed only along the streets in the simulations.These results demonstrate that it is preferable to select theUEs widely spread in the cell in order to have more accurateestimates of the antenna downtilt.

V. Conclusions

In this paper, a maximum-likelihood-based algorithm has beenderived for estimating the operational specifications, such asthe tilted directions of the sectoring antennas used in theBS. In the algorithm, the received power strengths reportedby multiple UEs within the coverage of a BS or a sectorof the BS are used as the observations. The likelihood ofthe antenna attitude is calculated based on the large-scale

fading statistics for path-loss and shadowing, as well as thesmall-scale fading statistics determined by multi-path. Theperformance of the proposed method has been verified byusing simulations, where a random-propagation-graph basedmethod was applied to generating the received signal powerstrength at multiple UEs’ locations. The results demonstratedthe attitude of the BS antenna can be correctly estimated in thecase where the UEs are widely spread and the LoS scenariodominates the propagation channels.

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