Modeling Power Angle Spectrum and Antenna Pattern Directions in Multipath Propagation Environment

Transcription

1 Modelng ower Angle Spectrum and Antenna attern Drectons n Multpath ropagaton Envronment Jan M Kelner and Cezary Zółkowsk Insttute of elecommuncatons, Faculty of Electroncs, Mltary Unversty of echnology, Warsaw, oland {jankelner, cezaryzolkowsk}@watedupl Abstract Most propagaton models do not consder the nfluence of antenna patterns on the parameters and characterstcs of receved sgnals hs assumpton s equvalent to the use of sotropc or omndrectonal antennas n these models Emprcal measurement results ndcate that the radaton pattern, gan and drecton of drectonal antennas sgnfcantly nfluence on propertes of the receved sgnal hs fact shows that consderaton the drectonal antennas n propagaton models s very mportant especally n the context of emergng telecommuncaton technologes such as beamformng or massve MIMO he purpose of ths paper s to present the modelng method of power angular spectrum and drecton of antenna patterns n a multpath propagaton envronment Index erms multpath propagaton, channel modelng, power angle sprectrum, power azmuth sprectrum, antenna pattern, drectonal antenna, mult-ellptcal channel model, non-lne-of-sght condtons I INODUCION A power angle spectrum (AS) s the basc characterstc used to estmate and model an angular dsperson n wreless channels AS can be determned n azmuth and elevaton planes If the model ncludes both planes, then we are talkng about 3D models [1],[],[3] In D [4],[5],[6] models, only the azmuth plane s consdered, and then the AS acronym means the power azmuth spectrum AS s a practcal channel characterstc used prmarly n emprcal measurements In the case of rado channel modelng, theoretcal characterstc, e, a probablty densty functon (DF) of angle of arrval (AOA), s more commonly used If the channel model does not consder a pattern of a recever (x) antenna, then we can assume that an omndrectonal (for a D model) or sotropc antenna s n ths model, eg, [4],[5] In ths case, AS and DF of AOA shapes are dentcal, whle the total power of a receved sgnal s proportonalty factor between these characterstcs [7] If the recevng antenna s drectonal, then we should dstngush two types of theoretcal characterstcs, e, DF of AOA seen at the x antenna nput and DF of angle of recepton (AO) seen from the x nput, e, the x antenna output [3] herefore, DF of AO and AS nclude the recevng antenna pattern wo approaches are used for AS and DF of AOA/AO modelng he frst s the geometrc channel model (GCM), whch defnes the area of scatterer locaton of sgnal components and ther densty, eg, [1],[4] he second s emprcal models, whch are based on standard statstcal dstrbutons such as Laplacan or Gaussan [6] hs model type s also used to descrbe AS n standard models, socalled reference models, such as the 3G model [8] here are also mxed models, eg [],[3],[5], where delayed scatter components of the receved sgnal are defned geometrcally, whle local scatterng components are statstcal n nature he am of the paper s to show the mpact of the drectonal antenna patterns and ther drectons on the AS n the azmuth plane In ths case, the mult-ellptcal channel model (MCM) s used for modelng [],[3] he presented results show a sgnfcant nfluence of the antenna patterns and ther drectons on the spatal dsperson and total power of the receved sgnal he analyss of ths ssue s partcularly mportant for future telecommuncaton systems, especally n the context of beamformng, massve MIMO technology, green communcatons, and 5G systems hs paper s organzed as follows In Secton II, modelng method of AS and antenna pattern drectons usng MCM s brefly descrbed Evaluaton of the nfluence of drectonal antennas on AS s presented n Secton III Secton IV contans conclusons II MODELING AS AND ANENNA AEN In MCM, three types of the receved sgnal components are present hese are the drect path component, local scatterng components occurrng near the recevng antenna, and the delayed scatterng components o descrbe the local scatterng, the von Mses dstrbuton s used he scatterers of delayed components are located on coaxal ellpses (D) [5],[7],[9] or half-ellpsods (3D) [],[3] In ths paper, the AS analyss concerns only the azmuth plane, so the followng descrpton refers only to ellpses, even n regard to lterature descrbng the 3D model he transmtter (x) and x are located n the foc of the ellpses he MCM geometry s shown n Fg 1 he basc nput data for MCM s the power delay profle (D), whch represents the power dstrbuton on tme clusters D delays defne szes of the ellpses, whle D Jan M Kelner and Cezary Zółkowsk, Modelng power angle spectrum and antenna pattern drectons n multpath propagaton envronment, n 18 1th European Conference on Antennas and ropagaton (EuCA), London, UK, , pp 1 5

2 powers descrbe the powers of ndvdual sgnal components [],[3],[5],[7],[9] For the local scatterng components, AOAs are generated based on the von Mses dstrbuton where I f l, exp cos πi s the zero-order modfed Bessel functon and s the dstrbuton parameter descrbng the ntensty of the local scatterng he resultng DF of AOA seen at the recevng antenna nput s descrbed by [],[9] Fg 1 Geometry of MCM he transmttng antenna pattern s used to generate angles of departure (AOD) [],[9] hus, the shape, halfpower beam wdth (),, and drecton of the x antenna pattern has a sgnfcant mpact on the DF of AOD, and ndrectly also on the DF of AOA In the general case, any shape of the antenna pattern may be used In ths paper, we use the Gaussan to model the man lobe of the drectonal antennas [1] g exp 4ln hus, AODs,, are generated on the bass of the DF defned as [],[9] f C g where C s constant normalzng the DF of AOD that depends on For the delayed scatterng components, AOAs,, are determned for the th ellpse and each generated AOD [9] e e 1 cos sgn arccos 1 cos, e e where e d d c s the eccentrcty of the th ellpse defned by delay for 1,,, N, N 1 s the number of tme clusters occurred n the D, d s the x-x dstance, and c s the speed of lght For the delayed scatterng components, DFs of AOA, f, are determned from the obtaned sets of AOAs d, for each ellpse hese DFs can be determned n two ways, e, based on hstograms of AOA [5] or component powers [],[9] Conducted studes show that both approaches are equvalent N 1 f f f 1 d, l, 1 1 δ where s the can factor, s the power of the th D tme cluster correspondng to the delay for,1,, N, N s the total power of the receved sgnal, and δ s the Drac delta functon In the case of the sotropc or omndrectonal antennas, the component powers of the receved sgnal are generated on the bass of unform dstrbutons defned for each clusters For delayed and local scatterng components, we have respectvely [],[5],[9] f pj f p j for, p M M p M for, j 1 M j for p, 1 M for p, 1 M j j where p j s the power of the jth path of the th cluster seen at the x antenna nput, M s the number of generated paths n the th cluster,,1,, N, and j 1,,, M In the case of the drectonal recevng antenna, AS and DF of AOD consder also ts pattern he pattern of ths antenna can be descrbed analogously to the transmttng antenna, e, Jan M Kelner and Cezary Zółkowsk, Modelng power angle spectrum and antenna pattern drectons n multpath propagaton envronment, n 18 1th European Conference on Antennas and ropagaton (EuCA), London, UK, , pp 1 5

3 g exp 4ln where and are the drecton and wdth of the man lobe of the recevng antenna pattern, respectvely he recevng antenna pattern s used to determne the power of each path seen at the x antenna output Fgures, 4, and 6 show ASs for 18, selected, and three analyzed types of antennas, e, BS, C, and G, respectvely Whle, Fgs 3, 5, and 7 present ASs for, selected, and three antenna types, e, BS, C, and G, respectvely p, j pj g, j where p, j s the power of the jth path seen at the x nput, corresponds to AOA/AO,, j he obtaned powers are used to determne the estmator of the DF of AOD that s seen at the x nput For ths purpose, we use the hstogram method for the path powers [3] f L C N M p j1, j, j p, j, j where L, j :, j ε, C s constant normalzng the DF of AO, and ε s a neghborhood of hen, we can descrbe the AS seen at the nput x as [3],[7] Fg ASs for BS, α = 18 and selected β f he AS modelng method descrbed above s used n the studes presented n ths paper III IMAC OF ANENNA AENS ON AS he mpact evaluaton of the antenna patterns on AS s carred out for the urban macro (UMa) scenaro and nonlne-of-sght (NLOS) condtons, For ths am, we use D based on the 3G tapped delay lne (DL) model, e, DL-B [8, able 77-] for the frequency range, fc 4 7 GHz, and rms delay spread, DS 363 ns [8, able 773-] hree types of antennas are analyzed, e, corner reflector (C), parabolc grd (G), and base staton antenna (BS) he s of these antennas are C 58, G 1, and BS 68 for C, G [11], and BS (Kathren 81715) [1], respectvely he x-x dstances are d 8 m and d 4 m for BS and C or G, respectvely Fg 3 ASs for BS, β = and selected α he obtaned results show that ASs are symmetrcal for cases the antennas are drected at themselves, e, for 18 and Changng the drecton of one antenna results a deformaton of the AS symmetry For BS and C, AS shapes are smlar despte dfferent dstances For BS and C, s are approxmate hus, Jan M Kelner and Cezary Zółkowsk, Modelng power angle spectrum and antenna pattern drectons n multpath propagaton envronment, n 18 1th European Conference on Antennas and ropagaton (EuCA), London, UK, , pp 1 5

4 ths parameter of the antennas have a sgnfcant nfluence on the AS shape For very selectve G, ASs are also selectve Fg 6 ASs for G, α = 18 and selected β Fg 4 ASs for C, α = 18 and selected β Fg 7 ASs for G, β = and selected α Fg 5 ASs for C, β = and selected α For 18, changes of cause major changes n the shape and orentaton of the receved AS For, changes of cause relatvely mnor changes of the AS hus, mpact of changng the recevng antenna drecton on the AS s more sgnfcantly he obtaned graphs show that the proper orentatons of the transmttng and recevng antennas sgnfcantly mpact on the AS shape, angular dsperson, and power of the receved sgnal resented approach for the AS modelng s used n [13] to modfy a path loss model for varous orentaton of drectonal antennas hs path loss model only for antennas drected at each other s shown n [11] IV CONCLUSION In ths paper, the authors presented the methodology of the AS modelng, whch consders the drectonal antennas Jan M Kelner and Cezary Zółkowsk, Modelng power angle spectrum and antenna pattern drectons n multpath propagaton envronment, n 18 1th European Conference on Antennas and ropagaton (EuCA), London, UK, , pp 1 5

5 he obtaned smulaton results show that the AS shape closely depends on the s and drectons of the antenna patterns he proposed methodology can be used to assess the mpact of nterference between antenna systems for ther dfferent orentatons hs s mportant n an electromagnetc compatblty evaluaton of radocommuncaton systems he modelng method of the drectonal antenna and AS can also be used to modfy propagaton models that do not consder the antenna patterns EFEENCES [1] A Ahmed, S J Nawaz, and S M Gulfam, A 3-D propagaton model for emergng land moble rado cellular envronments, LoS ONE, vol 1, no 8, p e13555, Aug 15 [] C Zółkowsk and J M Kelner, Antenna pattern n threedmensonal modellng of the arrval angle n smulaton studes of wreless channels, IE Mcrow Antennas ropag, vol 11, no 6, pp , May 17 [3] C Zółkowsk and J M Kelner, Statstcal evaluaton of the azmuth and elevaton angles seen at the output of the recevng antenna, IEEE rans Antennas ropag, vol 66, 18 DOI: 1119/A [4] K Wong, Y I Wu, and M Abdulla, Landmoble radowave multpaths DOA-dstrbuton: Assessng geometrc models by the open lterature s emprcal datasets, IEEE rans Antennas ropag, vol 58, no 3, pp , Mar 1 [5] C Zółkowsk and J M Kelner, Estmaton of the recepton angle dstrbuton based on the power delay spectrum or profle, Int J Antennas ropag, vol 15, p e93646, Dec 15 [6] C Zółkowsk and J M Kelner, Emprcal models of the azmuthal recepton angle art I: Comparatve analyss of emprcal models for dfferent propagaton envronments, Wrel ers Commun, vol 91, no, pp , Jul 16 [7] C Zółkowsk, Statstcal model of the angular power dstrbuton for wreless multpath envronments, IE Mcrow Antennas ropag, vol 9, no 3, pp 81 89, Feb 15 [8] 3G 3891 V14 (17-9) Study on channel model for frequences from 5 to 1 GHz (elease 14) 3rd Generaton artnershp roject (3G), echncal Specfcaton Group ado Access Network, Valbonne, France, Sep-17 [9] C Zółkowsk, J M Kelner, L Nowoselsk, and M Wnuk, Modelng the dstrbuton of the arrval angle based on transmtter antenna pattern, n 17 11th European Conference on Antennas and ropagaton (EuCA), ars, France, 17, pp [1] Vaughan and J Bach Andersen, Channels, propagaton and antennas for moble communcatons London, UK: Insttuton of Electrcal Engneers, 3 [11] J A Azevedo, F E Santos, A Sousa, and J M Agrela, Impact of the antenna drectvty on path loss for dfferent propagaton envronments, IE Mcrow Antennas ropag, vol 9, no 13, pp , Oct 15 [1] Kathren Catalogue MHz base staton antennas and antenna lne products, Kathren, 17 [13] J M Kelner and C Zółkowsk, ath loss model modfcaton for varous gans and drectons of antennas, n 18 1th European Conference on Antennas and ropagaton (EuCA), London, UK, 18, pp 1 4 Jan M Kelner and Cezary Zółkowsk, Modelng power angle spectrum and antenna pattern drectons n multpath propagaton envronment, n 18 1th European Conference on Antennas and ropagaton (EuCA), London, UK, , pp 1 5