Statistical modelling at 20 GHz for fixed wireless access systems in urban multipath environments J. Zhang, J. Richter, L.P. Ivrissimtzis and M.O. Al-Nuaimi Abstract: For fixed wireless access systems in urban areas, reflection or scattering from building surfaces can cause propagation impairments and influence system planning, deployment and quality of service. A statistical model is presented for such fixed radio links operating at microwave and mm-wave frequencies to predict the radiowave propagation characteristics. The model considers the fundamental underlying propagation, where buildings give rise to multipath due to reflection or scattering. In addition, the model accounts for the antenna properties, including relative height, orientation and radiation patterns. Overall good agreement between the statistical properties of narrowband measurements and simulations is demonstrated. 1 Introduction Broadband fixed radio access systems are intended to provide cost efficient connections for both commercial and private use. The convergence of broadcast, communication and data services has a near perfect platform, which can be facilitated in millimetre wave radio. Current research [1] shows that, in urban environments, the effect of building scatter can become a significant factor in determining the distribution of co-channel and adjacent channel interference levels. Hence, in conjunction with the radiation character- istics of the central hub and subscriber antennas, building scatter can constrain the planning and deployment of interference limited networks. In the statistical model proposed here, the total field is described as the super- position of the direct field and a number of field contributions scattered from randomly distributed surfaces representing building rooftops, walls or illuminated ground patches. Evaluation of the field amplitude distribution at the receiver location and K-factor variability describing the relative contribution of multipath rays [2] can be efficiently carried out in terms of the link design parameters. Briefly, these are the distance between the transmitter and receiver locations, radiation patterns and gains of antennas, and the statistical distribution of the position, orientation and electrical properties of the scattering surfaces. 2 Propagation model The basic fixed link geometry is depicted in Fig. 1. The radiation characteristics of the transmitter and receiver antennas are represented by their far field radiation patterns e t;r ð ^ s 1;2 Þ, in the direction of the unit vectors ^ s 1;2 , namely: E t;r ð ^ s 1;2 ; s 1;2 Þ¼ e t;r ð ^ s 1;2 Þ e jks 1;2 s 1;2 ð1Þ The tangent plane method, detailed in [3], provides an approximation of scattered signals from curved surfaces, with large scale irregularities, by projecting the rough surface onto a plane tangential to the surface curvature. The received scattered signal power is described as J ik ¼ T in T km E t n E t m e jf m 4ðs 1;m s 2;m Þ 2 q 4 q 4 2 Ds m ð2Þ where T in and T km are the tensor dyadic coefficients, E t n and E t m are the electric field matrices at the source, and s 1,m and s 2,m are the distances between the scattering point and the transmitter and receiver. Further, q ¼j qj, q ¼ k k, where k and k are wave vectors directed along the normal to the phase front of the incident and reflected waves, respectively, and Ds m is the area of scattering surface, as shown in Fig. 1. Based on the tangent plane approximation, the received field E s due to the wave scattered by a building surface of area Ds m can be shown to be proportional to E s ð ^ s 1;m ; ^ s 2;m ; s 1;m ; s 2;m Þ¼ e t ð ^ s 1;m Þ T ð ^ s 1;m ; ^ s 2;m ; R v;m ; R h;m Þ ffiffiffiffiffiffiffiffi Ds m p e t ð ^ s 2;m Þ e jkðs 1;m þs 2;m Þ s 1;m s 2;m ð3Þ where T ð ^ s 1;m ; ^ s 2;m ; R v;m ; R h;m Þ is the dyadic scattering coefficient of the surface patch Ds m and ^ s 1;m ; ^ s 2;m are the unit vectors in the directions of the transmitting and receiving antennas, or, equivalently, the direction of propagation of the incident and scattered waves. Approx- imations of the elements of the dyadic scattering coefficient, for observation angles defined by the incident ray and the average plane of the surface, can be obtained using the tangent-plane approximation over an infinite surface and plane wave incidence [3] . The detailed derivation involves the reflectivity properties of the surface, signified in (3) by the reflection coefficients R v;m ; R h;m for polarisations of the incident field that are perpendicular and parallel to the plane of incidence, respectively. In the case of a general J. Zhang, J. Richter and M.O. Al-Nuaimi are with the Radio Propagation & System Design Research Unit, School of Electronics, University of Glamorgan, Pontypidd, Wales, CF37 1DL, UK L.P. Ivrissimtzis is with Agere Systems, Kingswood, Kings Ride, Ascot, Berks, SL5 8AD, UK E-mail: [email protected]r IEE, 2005 IEE Proceedings online no. 20045065 doi:10.1049/ip-map:20045065 Paper first received 21st July and in revised form 2nd December 2004 278 IEE Proc.-Microw. Antennas Propag., Vol. 152, No. 4, August 2005
Transcript
Statistical modelling at 20 GHz for fixed wirelessaccess systems in urban multipath environments
J. Zhang, J. Richter, L.P. Ivrissimtzis and M.O. Al-Nuaimi
Abstract: For fixed wireless access systems in urban areas, reflection or scattering from buildingsurfaces can cause propagation impairments and influence system planning, deployment andquality of service. A statistical model is presented for such fixed radio links operating at microwaveand mm-wave frequencies to predict the radiowave propagation characteristics. The modelconsiders the fundamental underlying propagation, where buildings give rise to multipath due toreflection or scattering. In addition, the model accounts for the antenna properties, includingrelative height, orientation and radiation patterns. Overall good agreement between the statisticalproperties of narrowband measurements and simulations is demonstrated.
1 Introduction
Broadband fixed radio access systems are intended toprovide cost efficient connections for both commercial andprivate use. The convergence of broadcast, communicationand data services has a near perfect platform, which can befacilitated in millimetre wave radio. Current research [1]shows that, in urban environments, the effect of buildingscatter can become a significant factor in determining thedistribution of co-channel and adjacent channel interferencelevels. Hence, in conjunction with the radiation character-istics of the central hub and subscriber antennas, buildingscatter can constrain the planning and deployment ofinterference limited networks. In the statistical modelproposed here, the total field is described as the super-position of the direct field and a number of fieldcontributions scattered from randomly distributed surfacesrepresenting building rooftops, walls or illuminated groundpatches. Evaluation of the field amplitude distribution at thereceiver location and K-factor variability describing therelative contribution of multipath rays [2] can be efficientlycarried out in terms of the link design parameters. Briefly,these are the distance between the transmitter and receiverlocations, radiation patterns and gains of antennas, and thestatistical distribution of the position, orientation andelectrical properties of the scattering surfaces.
2 Propagation model
The basic fixed link geometry is depicted in Fig. 1.The radiation characteristics of the transmitter andreceiver antennas are represented by their far field radiation
patterns et;rðs1;2Þ, in the direction of the unit vectorss1;2, namely:
Et;rðs1;2; s1;2Þ ¼ et;rðs1;2Þ
e�jks1;2
s1;2ð1Þ
The tangent plane method, detailed in [3], provides anapproximation of scattered signals from curved surfaces,with large scale irregularities, by projecting the roughsurface onto a plane tangential to the surface curvature. Thereceived scattered signal power is described as
Jik ¼TinT �kmEt
nE�tm e�jfm
4ðs1;ms2;mÞ2q4
q42
Dsm ð2Þ
where Tin and Tkm are the tensor dyadic coefficients, Etn and
Etm are the electric field matrices at the source, and s1,m and
s2,m are the distances between the scattering point and the
transmitter and receiver. Further, q ¼ jqj, q ¼ k� k, wherek and k are wave vectors directed along the normal to thephase front of the incident and reflected waves, respectively,and Dsm is the area of scattering surface, as shown in Fig. 1.
Based on the tangent plane approximation, the receivedfield Es due to the wave scattered by a building surface ofarea Dsm can be shown to be proportional to
where T ðs1;m; s2;m; Rv;m;Rh;mÞ is the dyadic scatteringcoefficient of the surface patch Dsm and s1;m; s2;m are theunit vectors in the directions of the transmitting andreceiving antennas, or, equivalently, the direction ofpropagation of the incident and scattered waves. Approx-imations of the elements of the dyadic scattering coefficient,for observation angles defined by the incident ray and theaverage plane of the surface, can be obtained using thetangent-plane approximation over an infinite surface andplane wave incidence [3]. The detailed derivation involvesthe reflectivity properties of the surface, signified in (3) bythe reflection coefficients Rv;m;Rh;m for polarisations of theincident field that are perpendicular and parallel to theplane of incidence, respectively. In the case of a general
J. Zhang, J. Richter and M.O. Al-Nuaimi are with the Radio Propagation &System Design Research Unit, School of Electronics, University of Glamorgan,Pontypidd, Wales, CF37 1DL, UK
L.P. Ivrissimtzis is with Agere Systems, Kingswood, Kings Ride, Ascot, Berks,SL5 8AD, UK
scattering centre, the dyadic T ðs1;m; s2;m; Rv;m;Rh;mÞ can bedescribed as
T ðs1m; s2m; Rv;m;Rh;mÞ ¼Rhh Rhv
Rvh Rvv
� �ð4Þ
From (3), the total field p (scalar emf) at the receiver, beingthe superposition of direct field and a finite number (N) ofscattering fields, is given by
p¼ etðs0Þ � erð�s0Þs0
þXN
m¼1etðs1;mÞ � T ðs1;m; s2;m; Rh;m;Rv;mÞ
�ffiffiffiffiffiffiffiffiDsm
p� erðs2;mÞ
e�jfm
s1;ms2;mð5Þ
In the above, s0 is the unit vector in the line connecting thereceiver and transmitter antennas and s0 is the correspond-ing distance. At high frequencies, the phase angles fm of thescattered field components can be assumed to be randomvariables uniformly distributed in the interval [0, 2p].Examples of evaluations based on (5) are presented in [4],
and preliminary measurement results and analysis based on(5) are presented in [5].
3 Measurement and analysis of results
3.1 Measurement descriptionNarrowband field measurements at 20GHz were conductedon the University of Glamorgan campus. Figure 2 showsthe top view of the three cross-campus point-to-point radiolinks marked as A, B and C. Link A crosses severalbuildings and, as a result, is strongly affected by multipathpropagation. In link B, the received scattered field includedcontributions from a building adjacent to the receiver. Inparticular, this proximity of the receiver to the buildingresulted into a number of signal paths due to scatter to beintercepted by the sidelobes of the antenna, and hence, arelatively high degree of multipath propagation. Line ofsight (LOS) was achieved for both links with approximately2m clearance above the roofs of surrounding buildings. Inlink C, the radio path, with approximately 2.5m buildingroof clearance, resulted in a predominantly LOS link withlow levels of multipath contributions.
BFWA systems receivers will generally operate withrelatively highly directional antennas, and therefore stan-dard gain pyramidal horn antennas with well definedantenna parameters were used in the measurements. On thetransmitter side a horn antenna with 20dBi gain was used,whereas on the receiver three antennas with gains 10, 15 and20dBi were deployed. The E-plane 3dB antenna beam-width for 10, 15, 20dB standard gain horn antennas are 551,321 and 161, respectively.
During the experiments the transmitter antenna remainedfixed. The receiver antenna was displaced over anapproximate distance of 1m at a speed of 0.5 cm/s andthe resulting received field variation was recorded. Thedisplacement was carried out both in the direction of
Rx A
Rx BRx C
Tx ATx B/C
link C (100 m)
link A (290 m)link B (110 m)
Fig. 2 Top view of radio paths of crosscampus point-to-point radio linksTx A height: 4.5mRx A height: 10.5mTx B/C height: 7mRx B height: 1.6mRx C height: 3.5m
the link and perpendicular to it; however, the orientationof the main antenna beam with respect to the transmitterwas fixed.
3.2 Analysis of measurement resultsThe measured results for each link are depicted in Figs. 3–5.These Figures show the variation of normalised receivedsignal strength with antenna displacement. The signal levelshown was normalised with respect to its mean value.
Comparing the measurement results for the three links, itis apparent that links A and B show a larger signal variationwith antenna displacement than link C. Links A and B areboth comparatively strongly affected by multipath propa-gation due to building and ground scatter. Link A crossedover a considerable number of rooftops with the LOS signalalso present. Therefore many reflection paths within thepropagation channel are expected. On link B the receiverantenna was placed at relatively low height (1.6m) and inthe vicinity of a large building, resulting into strongmultipath components at the receiver. In contrast, link Cwas an unobstructed LOS link with good clearance over theroofs of the surrounding buildings and, hence, a muchsmaller variation in the received signal level has beenobserved, as shown in Fig. 5.
Furthermore, it is apparent that from the measurementresults for links B and C, antennas with higher gain at thereceiver site result in less signal variation, indicating thatnarrower beamwidths result in fewer scattered signalcomponents being received, as shown in Figs. 4 and 5.
3.3 Modelled resultsReceived signal level variation due to multipath is modelledby taking into account the signal contributions from thedirect field component and those from the various scattercentres. Statistical variation of the height and location of thescatter centres results in statistical path length differences forthe different rays, hence a statistical distribution of relativeamplitude and phase of the various signal components.
Using (5) and assuming statistical representations of atypical residential scattering environment, the resultant fieldreceived at a given position was evaluated. Such statisticalparameters included the height distribution of rooftops, thetilt and orientation of building surfaces and their reflectivity
properties [6]. Through randomly varying scattering centres,the variations of the received signal envelope can beobtained. Here, it was also assumed that the variability inthe signal level arising from the random choice of scatteringcentres (modelling) and that due to the receiver displace-ment (measurements) are statistically similar.
In particular, the model considers a simple distribution ofthe randomly distributed height of the scattering centres inthe simulations. The probability distribution function(PDF) of rooftop height is represented by a linear increasein the interval [0–ha] followed by a linear decrease over [ha–hm], where ha and hm are the average and maximum heightsof the scattering surfaces centres, respectively. Theseparameters can be readily obtained from topographicaldata analysis of the specific urban environment. Thus, the
−8
−6
−4
−2
0
2
4
6
1
sample no.
rela
tive
leve
l, dB
21 41 61 81 101 121 141
Fig. 3 Received field amplitude (normalised to mean) for link A at20 GHz
fixed receiver Rx: 20dBilongitudinal Rx: 20dBi
_________ transversal Rx: 20dBi
1 101 201 301 401 501 601 701
sample no.
a
leve
l rel
ativ
e to
mea
n, d
B
6
4
2
0
−10
−8
−6
−4
−2
−12
1 101 201 301 401 501 601 701
sample no.
b
leve
l rel
ativ
e to
mea
n, d
B6
8
10
4
2
0
−10
−8
−6
−4
−2
Fig. 4 Received field amplitude (normalised to mean) for link B at20 GHza Rx: longitudinal
position of the scattering centre is determined by randomlychoosing the height of scattering centres and the direction ofincidence, which leads subsequently to the determination ofs1;m, s2;m, s1;m and s2;m.
To provide a statistical characterisation of the radio links,the cumulative distribution function (CDF) of the receivedsignal envelope, obtained from each set of measurements,was evaluated from the variation of the received signalenvelope and subsequently compared with predictions.
The ratio of the direct field to the scattered field is calledthe K-factor, which is often represented in decibels. Thetypical distribution of the envelope of the signal with adirect field and a large number of normally distributedscattering mechanisms is Rician distribution [2]. As ameasure of how severely the investigated radio links wereaffected by multipath propagation, K-factor graphs were
produced, for both the measured and simulated datayielded by the model. To illustrate the range of K-factors foreach measurement, maximum and minimum values werecalculated. On all links, measurements were conducted forlongitudinal and transversal displacements of the receiverantenna with respect to the direction of propagation of theLOS component. Minimum and maximum K-factor valuesfor each one of the links were derived from the CDF slopesobtained from the measurement data for each case ofreceiver antenna gain. In deriving these, the CDF minimum(or maximum) slope was averaged using data sets fromboth the longitudinal and transversal measurements. On theother hand, predicted values for the K-factor were obtainedfrom the slope of the corresponding CDF curves derivedfrom the simulation data.
3.4 Cumulative distribution functions andK-factorThe CDFs of measured results, together with the predictedvalues, are shown in Figs. 6–8. Figures 6 and 7 show goodagreement between the CDFs derived from measurementdata and the prediction model for links A and B. Theagreement between the CDFs of measured and predicteddata is, however, moderately good in Fig. 8. This graphshows the CDFs for link C, which is predominantly LOS.Closer examination of the differences between the curvescorresponding to different receive antenna gains in Fig. 7reveals a smaller PDF gradient as the gain of the antennadecreases, indicating, as expected, a larger amount ofmultipath contributions to signals received by antennas withwider beamwidths. A slight overestimation of the amountof multipath propagation in the prediction model where theLOS component is more dominant is observed in Fig. 7.Here, CDFs from measurement data and prediction agreevery well for the 10dBi receiver antenna curve, withagreement being less good for higher gain antennas (15,20dBi).
Figures 9 and 10 show increasing K-factor values withincreasing antenna gain in both measurements and predic-tions, which corresponds well with expectations. The
1 103 205 307 409 511 613 715sample no.
a
leve
l rel
ativ
e to
mea
n, d
B
2.0
1.5
1.0
0.5
0
−2.0
−1.5
−1.0
−0.5
leve
l rel
ativ
e to
mea
n, d
B
2.0
1.5
1.0
0.5
0
−2.0
−1.5
−1.0
−0.5
1 105 209 313 417 521 625 729sample no.
b
Fig. 5 Received field amplitude (normalised to mean) for link C at20 GHza Rx: longitudinal
Rx: 10dBiRx: 15dBi
_________ Rx: 20dBib Rx: perpedicular
Rx: 10dBiRx: 15dBi
_________ Rx: 20dBi
level relative to mean, dB
cum
ulat
ive
dist
ribut
ion
func
tion
K =10.2 − 12.2
K =11
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0−6 −5 −4 −3 −2 −1 43210
Fig. 6 CDF of received field for link Afixed receiver Rx: 20dBilongitudinal Rx: 20dBitransversal Rx: 20dBi
predicted K-factor values fall well within the range of thosevalues derived from measurements, suggesting that themodel can successfully be used to predict K-factors of fielddistributions in a receiver location and, subsequently, inexpected levels of signal impairments due to multipath, aswell as interference.
4 Conclusion
A statistical radio propagation model for fixed point-to-point radio links at 20GHz is presented. The modelconsiders the effects of signal propagation from multiplescatter sources in the radio channel and enables theevaluation of the resultant envelope of the signal received
at a given receiver position, using a statistical description ofthe radio path environment. This in turn facilitates theestimation of the CDF of the received signal and the K-factor of the resulting Rician distribution characterisingLOS links. The model is applicable in the estimation ofsignal impairments due to multipath and co-channel oradjacent channel interference, where the interference sourcemay be situated at the frequency reuse distance or beyond,thus enabling expected levels of carrier-to-interference ratiosfor a particular underlying propagation environment to beevaluated. In comparison to deterministic ray tracingmodels, which involve intensive computations and detailedknowledge of topographical data, the proposed modelyields good predicted estimates of average signal andmultipath interference levels. However, this approachretains both amplitude and phase variation of signalcomponents, so that factors like building material properties
level relative to mean, dB
cum
ulat
ive
dist
ribut
ion
func
tion
−1.5 −1.2 −0.9 −0.6 −0.3 0 0.3 0.6 0.9 1.2 1.5
1.0
0.8
0.6
0.4
0.2
0
Fig. 8 CDF of received field for link Cmeasurement Rx: 20dBimeasurement Rx: 15dBimeasurement Rx: 10dBi
_________ simulation
Rx antenna gain, dBi
K-f
acto
r
10
1
0.18 10 12 14 16 18 20 22
Fig. 9 K-factor dependence on receiver antenna gain for link BK-factor (min-measured)K-factor (max-measured)simulation
Rx antenna gain, dBi
K-f
acto
r
8 10 12 14 16 18 20 22
100
10
1
Fig. 10 K-factor dependence on receiver antenna gain for link CK-factor (min-measured)K-factor (max-measured)simulation
level relative to mean, dB
cum
ulat
ive
dist
ribut
ion
func
tion
1.0
0.8
0.6
0.4
0.2
0−10 −8 −6 −4 −2 2 4 60
Fig. 7 CDF of received field for link Bmeasurement Rx: 10dBimeasurement Rx: 15dBimeasurement Rx: 20dBisimulation Rx: 10dBi
as well as broadband characteristics can be incorporated infuture; both are currently under investigation.
5 References
1 ACTS Project 215, ‘Cellular radio access for broadband services’(CRABS), Specification of Next-Generation of LMDS Architecture,D2P1B, February 1999
2 Papazian, P.B., Hufford, G.A., Achatz, R.J., and Hoffman, R.: ‘Studyof the multipoint distribution service radio channel’, IEEE Trans.Broadcast., 1997, 43, (2), pp. 175–184
3 Bass, F.G., and Fuks, I.M.: ‘Wave scattering from statistically roughsurfaces’ (Pergamon Press, 1979)
4 Ivrissimtzis, L.P., AL-Nuaimi, M.O., Richter, J., and Zhang, J.:‘A statistical model of the urban propagation channel in fixedwireless access systems’. International Union of Radio Science 27thGeneral Assembly URSI 2002 Maastricht, Netherlands, August 2002
5 Zhang, J., Richter, J., AL-Nuaimi, M.O., and Ivrissimtzis, L.P.:‘Measurements and modelling for fixed wireless access systems atmillimeter wave frequencies’. 12th Int. Conf. on Antennas andPropagation, ICAP, 31March–3 April 2003, University of Exeter, UK
6 Li, L.J., Wang, Y.Z., and Gong, K.: ‘Measurements of buildingconstruction materials at Ka band’, Int. J. Infrared Millim. Waves,1998, 19, (9), pp. 1293–1298
