IEEE TANSACTIONS ON ANTENNAS AND POPAGATION 1 Statistical Evaluation of the Azimuth and Elevation Angles Seen at the Outut of the eceiving Antenna Cezary Ziółkowski and an M. Kelner Abstract A method to evaluate the statistical roerties of the recetion angle seen at the inut receiver that considers the receiving antenna attern is resented. In articular, the imact of the direction and beamwidth of the antenna attern on distribution of the recetion angle is shown on the basis of 3D simulation studies. The obtained results show significant differences between distributions of angle of arrival and angle of recetion. This means that the resented new method allows assessing the imact of the receiving antenna attern on the correlation and sectral characteristics at the receiver inut in simulation studies of wireless channel. The use of this method also rovides an oortunity for analysis of a co-existence between small cells and wireless backhaul, what is currently a significant roblem in designing 5G networks. Index Terms Angle of arrival, angle of recetion, angle sread, antenna radiation attern, azimuthal and elevational lanes, channel models, channel modeling, directional receiving antenna, geometric channel models, half ower beamwidth. I. INTODUCTION The direction and satial shae of the attern of the receiving antenna significantly affect the statistical roerties of the signal recetion angle. These roerties that are described by robability density function (PDF) deform the correlation and sectral characteristics of the signals transmitted in wireless channels [1-3]. Therefore, maing the satial distribution of the recetion angle seen at the outut of the receiving antenna, is required to obtain the convergence of the simulation studies and actual measurements. The use of this method also rovides an oortunity for analysis of a co-existence between small cells and wireless backhaul (WB). Esecially, it will allow to evaluate the interference caused by 5G access oint towards WB receiver needed to determine a minimum distance between 5G and WB deloyments. This current and significant roblem in designing 5G networks stems from narrowbeam antenna atterns, which ensure minimizing ower consumtion and increase the range of radio links. The directivity of the receiving antenna results in a satial selection of roagation aths. Therefore, the signal arriving at the inut of the receiver is a suerosition of signals from all roagation aths and their levels are formed by the receiving antenna attern. This is the cause of differentiation of the statistical roerties of the angle of arrival (AOA) in the surroundings of the receiving antenna and the angle of recetion (AO) that is seen at the outut of the receiving antenna. In the case of an omnidirectional antenna in the azimuth lane and its large beamwidth in the elevation lane, PDF of AOA and PDF of AO are convergent. In literature, we can find many models and maing methods of the statistical roerties of angle that consider the scattering henomenon both on the azimuth and elevation lanes [4-8]. However, these models and methods focus only on maing AOA and are mainly based on omnidirectional antennas. Only a few Manuscrit received Aril 4, 017. C. Ziółkowski and. M. Kelner are with the Institute of Telecommunications, Faculty of Electronics, Military University of Technology, 00-908 Warsaw, Poland (e-mail: cezary.ziolkowski@wat.edu.l; jan.kelner@wat.edu.l). Digital Object Identifier 10.1109/TAP.018.796719 of them consider the sector antennas but merely on the transmission side and in a simlified manner [9,10]. Therefore, these models and methods can be used in simulation only in scenarios where PDFs of AOA and AO are convergent. For the sectoral and narrowbeam antennas, the effect consideration of satial filtering antenna is required to evaluate the correlation and sectral signal roerties at the inut of the receiver. 3GPP channel model gives such ossibilities but only to a limited scoe [11]. These limitations are the result of using only a few strictly defined scenarios that secify the arameters of roagation henomena. The solution that is resented in this communication, addresses this roblem and is alicable in channel simulation studies and in emirical data analysis. In this case, the develoed method enables to use any roagation scenario that is defined by the ower delay rofile (PDP) or ower delay sectrum (PDS). In addition, the consideration of the transmitter and receiver antenna atterns in the angular ower distribution is an innovative contribution of this aer. Here, we resent a method to assess the statistical roerties of AO that consider the imact of the receiving antenna attern on the direction of signal recetion in 3D, and the beamwidth of the antenna attern on PDF of AO is shown for the simulation scenarios, whose arameters are defined on the basis of the 3GPP channel model [11]. The remainder of this communication is organized as follows. The system geometry and 3D channel model for AOA generation is resented in Section II. Determination of AO and estimation of its PDF is described in Section III. The next section includes the results of the simulation studies that show the effects of the direction and beamwidth of the antenna attern on sread of AO. Section IV rovides some concluding remarks. II. 3D CHANNEL MODEL The geometrical model of the channel is used to generate sets of AOAs that describe the sace scattering of signals as a set of halfellisoids. The number and satial arameters of these half-ellisoids are defined on the basis of the ower delay rofile (PDP) or ower delay sectrum (PDS). The local extremes of these characteristics reresent signal comonents that arrive at the receiver with the same delay and form so-called time clusters. The amount and the osition in time domain of these extremes define the number and size of the individual half-ellisoids. The geometry of the channel model is shown in Fig. 1. Adoted geometry is a basis to generate the angular arameters of the roagation aths arriving at the receiver with a delay relative to the direct ath. These arameters are sets of angles in the azimuth and elevation lanes, and the levels of ower that characterize the intensity of each ath. In addition to the arameters of the aths that reresent delayed comonents of the signal, the arameters of the local scattering aths are generated. In this case, the von Mises PDF is used. As a result, we obtain the sets of the angles in the elevation Θ and azimuth Φ lanes, and ower levels P that describe each 0018-96X 017 IEEE. Personal use is ermitted, but reublication/redistribution requires IEEE ermission. See htt://www.ieee.org/ublications_standards/ublications/rights/index.html for more information.
IEEE TANSACTIONS ON ANTENNAS AND POPAGATION 5 roagation ath arriving at the receiver. N, M i N, M i N, M i, Φ, P Θ (1) i0, j1 i0, j1 i0, j1 where: i is the number of the time cluster (half-ellisoid), j is the number of comonent in the ith time cluster, N reresents the number all time clusters (half-ellisoids), and Mi means the number of the comonents (roagation aths) in the ith time cluster. The elements with i = 0 reresent the local scattering comonents. Fig. 1. Geometry of 3D channel model. This channel model is one of a few that considers the imact of radiation transmitter antenna on the statistical roerties of AOA. A detailed descrition of the generation rocedure of Θ, Φ, and P is resented in [1]. In this ublication, the evaluation of the statistical roerties of the generated sets of the angles shows the comliance with the measurement data. This justifies the use of this model to determine the angle and ower arameters of the received signal comonents in simulation studies of channel. The used geometric channel model is an extension of our revious works, i.a., [13,14]. III. ESTIMATION OF AO DISTIBUTION Evaluation of the influence of the receiving antenna at AO is based on the inut data that are Θ, Φ, P, and the ower attern of g,. The sets of the angles and owers that this antenna, reresent the arameters of the roagation aths, can be written in N, M,. This form shows that each integrated form as i i0, j1 element of this set reresents the ower that arrives at the receiver from, direction. Thus, for the jth ath of the ith halfellisoid, the signal ower,, receiving antenna exresses the following relationshi:,,,, at the outut of the g () In simulation studies, the Gaussian beam is commonly arametrized ower attern of the antennas [15,16] where: g π, Gex ex g g G means the boresight gain of the antenna, g and g reresent beamwidths of the antenna attern in the elevation and azimuth lanes, resectively. These arameters are closely related to the half ower beamwidths (HPBWs) in the resective lanes (see [15]). (3) These relationshis are the basis for the transformation of the signal ower from the surroundings of the antenna to the inut of the receiver. Let, i, j: ε ε and O, where ε ε are the neighborhoods of θ and φ, resectively. Thus,, reresents the total ower of the signal that arrives O, at the inut of the receiver from ε, ε sector. Let Q means the number of all roagation aths reaching the receiver and let in the neighborhood of ever θ and φ is at least one angle that describes the ath. Then, for Q, the size of the neighborhood aroaches zero for each angle (εθ 0 and εφ 0). Consequently, each sum related to εθ and εφ reresents the ower that falls on the elementary interval of the angle. Therefore, in the limit, we obtain the ower P, angle sectrum, O, 4ε ε, Q ε 0 ε 0 P, It means that these finite sums can be treated as an estimator of P,. Note also that the signal average ower, P0, at the inut of the receiver is estimated by N M i i0 j1 4ε ε, In ractice, we can resent, where, P Q ε 0 ε 0 P in the form P f,, 0 0 (4) (5) P (6) f means PDF of AO. On the basis of (6), the f,, is estimator of PDF of AO, f, C 0 N, O M i i0 j1,, where C0 is a normalizing constant that is associated with εθ, εφ, and 90 180 f. rovides a condition lim, d d 1 ε 0 ε 0 0 180 In the real environment, scattering henomena that occur in the elevation and azimuth lanes are indeendent. Hence, marginal PDFs of AO in the elevation and azimuth lanes can be reresented in the following forms: f K L f N M C, C N Mi i i0 j1 i0 j1 (7) (8)
IEEE TANSACTIONS ON ANTENNAS AND POPAGATION 5 (c) Fig.. Power attern of widebeam antenna for α = 30º, 0º, 60º in azimuth lane (linear scale), P ( φ ), and (c) P ( θ ) for scenario. (c) Fig. 3. Power attern of narrowbeam antenna for α = 30º, 0º, 60º in azimuth lane (linear scale), P ( φ ), and (c) P ( θ ) for scenario.
IEEE TANSACTIONS ON ANTENNAS AND POPAGATION 5 where f and f are the estimators of PDFs of AO in the elevation and azimuth lanes, resectively, K i, j: ε, L i, j: ε Cθ and Cφ fulfill conditions lim d 1 lim 180 ε 0 180 f. d 1 90 ε 0 0, whereas f and In simulation and emirical studies of channel, () and (8) are the basis for the ractical assessment of the imact of the receiving antenna attern on the statistical roerties of AO. IV. ANTENNA PATTEN PAAMETES AND PDF OF AO In this section, we show the imact of the receiving antenna on the statistical roerties of AO that is viewed from the receiver inut. Here, we focus on the changes of PDF of AO that result from changes in both the direction,, and beamwidths, HPBWθ,φ, of the transmitting and receiving antenna atterns. To include these relations we introduce following designations in the analytical f f f f, where descrition of PDFs:, HPBW, and. In the simulation studies, PDPs from 3GPP nonline-of-sight roagation scenarios [11, Table 7.7.-] are assumed to design the geometric channel model. As an examle, we used three urban macro (UMa) scenarios for 8 GHz. The scenarios 1,, and 3 are defined as short-, normal-, and long-delay rofiles [11, Table 7.7.3-] that reresent the average results of measurement camaigns in diverse urban environments. All tests are carried out at narrowbeam and widebeam antennas for 8 GHz whose arameters are as follows: the widebeam antenna G 15.0 dbi, HPBW 30. 0, and HPBW 8.8, the narrowbeam antenna G 4.5 dbi, HPBW 8. 6, and HPBW 10.9, resectively. These arameters are adoted on the basis of measurement camaigns [16-18], which aim was to assess the roagation henomena in wireless links of 5G networks. To evaluate 3D modeling rocedure, 00 Monte Carlo runs were carried out in the Matlab. In the first ste, we consider the imact of that is the angle between the signal source and receiving antenna attern direction in P, in the azimuth lane. Based on (6) and (8), the grahs of the azimuth, P, and elevation, P, lanes for the widebeam and narrowbeam antennas, and scenario are resented in Figs. and 3, resectively. In each of the figures, a case of AOA is g, on P. considered to assess the imact of P and In addition, the angular ositions of the receiving antenna atterns are shown in Figs. a) and 3 a), resectively. For the widebeam antenna, the increase of to 10º causes a decrease of 30 db and 7 db in the maximum of P and P. Whereas for the narrowbeam antenna, this reduction is 46 db and 40 db, resectively. As we can see, the change in is reflected not only in level changes, but also in the changes of the angular disersion of the receiving signal ower. For scenario, the influence of on the statistical roerties of the ower disersion that reresent PDFs, are illustrated in Fig. 4. As can be seen in Fig. 4 b), PDFs are asymmetrical for 0, which is clearly visible with increasing. To quantify the influence of on the intensity of the AO scattering henomenon, the standard deviations are used. For the elevation and azimuth lanes, these arameters are determined, resectively, as 1 n f n n f (9) n 1 n1 1 n1 n f n n f (10) n n1 1 n1 where is the number of data from the simulation results. Fig. 4. lanes. PDFs of AO for α = 30º, 0º, 60º in elevation and azimuth For the widebeam and narrowbeam antennas, the grahs of versus are shown in Fig. 5. For the widebeam and and narrowbeam transmitting antennas, the standard deviations of AOA are ( 14, 34 ), and ( 6, 19 ), resectively. Fig. 5 shows that and reach minimum for 0. It means that the beamwidth of receiving antenna limits the intensity of the ower disersion by aroximately 11, 7 and 4, 15 comared to AOA for the widebeam and narrowbeam antenna, resectively. For 30, the scattering intensity of AO significantly increases articularly in the azimuth lane. The relationshis () and (8) also rovide an oortunity to analyze the changes in PDF of AO as a function of the antenna attern beamwidth. In this case, HPBW is analyzed as a arameter of PDFs for angles in the elevation and azimuth lanes. The examle of maing the imact of the antenna attern beamwidth on PDF of
IEEE TANSACTIONS ON ANTENNAS AND POPAGATION 5 AO is considered for 0. For the widebeam and narrowbeam antennas, the grahs of PDFs of AO in the elevation and azimuth lanes are shown in Figs. 6 a) and 6 b), resectively. Additionally, PDFs of AOA at the surrounding the receiving antenna with regarding the transmitting antenna attern are resented to comare the statistical roerties of the recetion angle. It is obvious, that the AO disersion is reduced along with a decrease in the attern beamwidth of the receiving antenna. However, quantitative assessment of the effect is ossible because of the analysis of the simulation data that is resented in this communication. Here, we limit this analysis only to assess the imact of changes in the attern beamwidth in the azimuth lane. In Fig. 7, is shown as a function of HPBW for three UMa scenarios. Simulation test are erformed on the assumtions 0 and HPBW 30. Fig. 5. Grahs of σ θ(ω) and σ φ(ω) versus α for widebeam and narrowbeam antennas in elevation and azimuth lanes. Fig. 7. Grahs of σ φ(ω) versus HPBW φ for UMa scenarios (α = 0, HPBW θ = 30 ). Based on the grahs of σφ(ω) for AOA, we can see that the tye of environment significantly differentiated the intensity of the scattering henomenon. This environmental imact is already resent when the HPBWφ of the transmitting antenna exceeds 5. Alying the narrowbeam attern of the receiving antenna substantially reduces the imact of the environment on the AO distribution. In this case, the environmental imact aears only for HPBW 40 and it is insignificant comared to AOA. Fig. 6. PDFs of AO and AOA for widebeam and narrowbeam antennas in elevation and azimuth lanes. V. CONCLUSION This communication resents methods to ma and assess the imact of the receiving antenna on the statistical roerties of AO. In the case of using the receiving sector antennas, the obtained results show significant differences between PDFs of AOA and AO. This means that in both simulation and emirical studies of channel, the assessment of the correlation and sectral characteristics of the signal at the receiver inut requires consideration of the receiving antenna attern. The modeling rocedure resented in this communication, is a new method of maing the statistical characteristics of AO that considers the receiving antenna arameters and tye of roagation environment. The use of this rocessing data in simulation studies of wireless system channels significantly reduce the aroximation error of the modeling results with resect to actual measurements of signal at the outut of the receiving antenna. The develoed method gives us the oortunity to analyze the co-existence between small cells and WB, what is currently a significant roblem in designing 5G networks. The
IEEE TANSACTIONS ON ANTENNAS AND POPAGATION 5 significance of this roblem is resented in [19]. In this case, the 3GPP [11] model was used, which defines determined satial scenarios and considers antenna atterns in a simle filtering rocedure. The use of our method gives the oortunity to consider the actual environmental conditions that are defined by measurement PDPs. [19] S. Kim, E. Visotsky, P. Moorut, K. Bechta, A. Ghosh, and C. Dietrich, Coexistence of 5G with the incumbents in the 8 and 70 GHz bands, IEEE. Sel. Areas Commun., vol. 35, no. 6,. 154 168, un. 017. EFEENCES [1] G. L. Stüber, Princiles of mobile communication, 3rd ed. New York, USA: Sringer, 011. [] A. Abdi,. A. Barger, and M. Kaveh, A arametric model for the distribution of the angle of arrival and the associated correlation function and ower sectrum at the mobile station, IEEE Trans. Veh. Technol., vol. 51, no. 3,. 45 434, May 00. [3] B. T. Sieskul, C. Kuferschmidt, and T. Kaiser, Satial fading correlation for local scattering: A condition of angular distribution, IEEE Trans. Veh. Technol., vol. 60, no. 3,. 171 178, Mar. 011. [4]. Zhang, C. Pan, F. Pei, G. Liu, and X. Cheng, Three-dimensional fading channel models: A survey of elevation angle research, IEEE Commun. Mag., vol. 5, no. 6,. 18 6, un. 014. [5] A. Ahmed, S.. Nawaz, and S. M. Gulfam, A 3-D roagation model for emerging land mobile radio cellular environments, PLoS ONE, vol. 10, no. 8,. e013555, Aug. 015. [6] S.. Nawaz, M. iaz, N. M. Khan, and S. Wyne, Temoral analysis of a 3D ellisoid channel model for the vehicle-to-vehicle communication environments, Wirel. Pers. Commun., vol. 8, no. 3,. 1337 1350, an. 015. [7] A. Y. Olenko, K. T. Wong, S. A. Qasmi, and. Ahmadi-Shokouh, Analytically derived ulink/downlink TOA and -D-DOA distributions with scatterers in a 3-D hemisheroid surrounding the mobile, IEEE Trans. Antennas Proag., vol. 54, no. 9,. 446 454, Se. 006. [8] A. Y. Olenko, K. T. Wong, and S. A. Qasmi, Distribution of the ulink multiaths arrival delay and azimuth-elevation arrival angle because of bad urban scatterers distributed cylindrically above the mobile, Trans. Emerg. Telecommun. Technol., vol. 4, no.,. 113 13, Mar. 013. [9] N. M. Khan, M. T. Simsim, and P. B. aajic, A generalized model for the satial characteristics of the cellular mobile channel, IEEE Trans. Veh. Technol., vol. 57, no. 1,. 37, an. 008. [10] L. iang and S. Y. Tan, Simle geometrical-based AOA model for mobile communication systems, Electron. Lett., vol. 40, no. 19,. 103 105, Se. 004. [11] 3GPP T 38.901 V14..0 (017-09). Study on channel model for frequencies from 0.5 to 100 GHz (elease 14). 3rd Generation Partnershi Project (3GPP), Technical Secification Grou adio Access Network, Valbonne, France, Se. 017. [1] C. Ziółkowski and. Kelner, Antenna attern in three-dimensional modelling of the arrival angle in simulation studies of wireless channels, IET Microw. Antennas Proag., vol. 11, 017, to be ublished. [13] C. Ziółkowski and. M. Kelner, Estimation of the recetion angle distribution based on the ower delay sectrum or rofile, Int.. Antennas Proag., vol. 015,. e936406, Dec. 015. [14] C. Ziółkowski,. M. Kelner, L. Nowosielski, and M. Wnuk, Modeling the distribution of the arrival angle based on transmitter antenna attern, in 017 11th Euroean Conference on Antennas and Proagation (EuCAP), Paris, France, 017,. 158 1586. [15]. Vaughan and. Bach Andersen, Channels, roagation and antennas for mobile communications. London: Institution of Electrical Engineers, 003. [16] M. K. Samimi and T. S. aaort, 3-D millimeter-wave statistical channel model for 5G wireless system design, IEEE Trans. Microw. Theory Tech., vol. 64, no. 7,. 07 5, ul. 016. [17] T. S. aaort, G.. MacCartney, M. K. Samimi, and S. Sun, Wideband millimeter-wave roagation measurements and channel models for future wireless communication system design, IEEE Trans. Commun., vol. 63, no. 9,. 309 3056, Se. 015. [18] S. Sun, G.. MacCartney, M. K. Samimi, and T. S. aaort, Synthesizing omnidirectional antenna atterns, received ower and ath loss from directional antennas for 5G millimeter-wave communications, in 015 IEEE Global Communications Conference (GLOBECOM), San Diego, CA, USA, 015,. 1 7.