> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE- CLICK HERE TO EDIT) < Urban Propagation Channels Mithul Thanu Muthukumar [email protected]Submitted in partial fulfillment of the requirements of ECEN 5264 Electromagnetic Absorption, Scattering, and Propagation Department of Electrical and Computer Engineering University of Colorado at Boulder May 3, 2013 ABSTRACT Abstract—This paper gives an overview of the various effects that occur in an urban propagation channel. It also provides a description of propagation models developed to study and overcome these effects in the real world so as to have a reliable microwave link. We examine one of the most generic models and prove its validity. Index Terms— Multipath, scattering, propagation modeling, diffraction, Fresnel zone, clutter, fading, path loss. 1
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Submitted in partial fulfillment of the requirements of
ECEN 5264Electromagnetic Absorption, Scattering, and Propagation
Department of Electrical and Computer EngineeringUniversity of Colorado at Boulder
May 3, 2013
ABSTRACT
Abstract—This paper gives an overview of the various effects that occur in an urban propagation channel. It also provides a description of propagation models developed to study and overcome these effects in the real world so as to have a reliable microwave link. We examine one of the most generic models and prove its validity.
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1. INTRODUCTION
n the tropospheric region which extends upto12 km above the earths surface the radio waves are transmitted and received through microwave links and between these microwave links we have a
constantly changing environment which influences the propagation characteristics of these waves. The electromagnetic radiation in this region is called as the ground waves and sky waves and similar to light these electromagnetic radiations experience various effects such as reflection, scattering, attenuation and diffraction. As to which of these effects occur, it is dependent on the surface which the electromagnetic wave encounters. If the wave impinges on an object which is comparable to its wavelength it experiences reflection. When it encounters a sharp irregular edge it undergoes diffraction and scattering is caused by objects way smaller than the wavelength of the propagating wave.
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When electromagnetic waves are propagated over extended distances they experience fading. This occurs because of the changing distance between the receiver and transmitter and the changes in the atmospheric conditions. Fading can be split into three types, fading in free space, large-scale fading or shadowing and small scale fading. It is important to measure the path loss in all the cases as it provides us with useful information to what happens to these electromagnetic radiations in a statistical sense. For each of these fading types different models have been proposed and implemented. All these models try to define the path loss component for different environments. The simplest way of defining path loss is that it’s the ratio between the received power to the transmitted power. For free space propagation the power ratio of a microwave system can be given by the Friss formulae.
, (1)
Where, Pt and Pr are the transmitted and received power and Gt and Gr are the gains of the transmitting and receiving antennas respectively. As most Rf comparison and measurements are performed in decibles and it is a consistent method to determine the signal level at any given point, we manipulate the equation to a logarithmic format to obtain the equation below [1].
L(dB) = 32.45+20log(f/fo)+20log(d/d0) (2)
The path loss is highly dependent on the environment; a dense region such as an urban city will have higher path loss compared to a suburban region. It is important to develop empirical models as they are less site specific and provide a first order modeling for a wide range of similar locations. Developing all these models consume a lot of time and cost. Hence, these models are always developed around PCS frequencies (800 MHz to 1900 Mhz) which are commercially used by cellular companies and extended over other frequencies. These empirical models are mostly applicable to outdoor environments but when we model for indoor propagation the modeling is mostly site specific with features specific to a particular building: wall thickness, construction material used, floor and ceiling material etc. Since most of the buildings have sharp edges, diffraction is a very common phenomenon in indoor propagation or in a region comprising lots of building. The diffraction losses are often calculated as a function of obstruction with respect to the first Fresnel zone. Fresnel zones are zones delimited by prolate ellipsoids of revolution with transmitter and receiver as the two foci [2]; the nth Fresnel zone is the loci of points with an excess path between (n-1)λ/2 and (n)λ/2 over the direct path. The odd Fresnel zones especially the first carry most of the propagation energy; therefore it is highly essential the designed microwave link clears this region so as to have an effective communication link.
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The weather also plays a very important role in the propagation of radio waves. Since water is a very lossy medium; large raindrops could cause significant attenuation, depolarization and scattering. Precipitation rates and probability of rain occurrence have been measured and summarized globally. In the USA the rain region pattern used is called the Crane rain region, these regional contours are used to gauge the probability of heavy rain outrages.
In this paper we try to address most of these models and and how they help us develop and maintain various microwave links in a constantly changing environment. We also discuss the effect of weather on radio wave propagation.
2.FADING CAUSED BY MULTIPATH
Fading is the phenomenon caused due to multipath. Multipath is simply rays reaching its destination through multiple paths. This is caused by the waves that are reflected by other surfaces in the environment before it reaches its destination. The best way to describe this is using a two ray model. A source ray that originates at the antenna has a direct path to its receiver and there is another ray which reaches the receiver at a different path length due to surface reflection.
Figure 1: Path loss vs distance for one slope and two slope
When we plot the path loss power vs the distance graph for a single ray and a two ray model. We can see that it is linear for a single ray and in a two ray model signals add constructively in some cases and in others phase differences causes deep fades. These fades causes loss of data in telecommunication systems.In a real world system there are going to be many number of reflected rays present between various buildings/surfaces.
Figure 2: Multipath between a Tx and Rx between multiple buildings
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The equation for the power received is given below
(3)
Where l1 and l’1 are defined below
(4)
We assume a value of 10 feet for Wt and 40 feet for Ws and obtain the plot below.
Figure 3: Plot of fades caused my multipaths
We observe as we increase the number of rays the number of fades also increases this is due to the destructive interference between multiple rays.
3. PROPAGATION MODEL IN URBAN AND SUB-URBAN CHANNELS
To overcome these fades and to provide an efficient microwave link; empirical models were designed. Extensive measurements were performed in different urban and suburban environments and were modeled into a general equation, of these the most significant empirical model was the COST 231-Hata model. This model was derived by Okumura by performing extensive measurements and was later put into equation by Hata and this model provides effective path loss estimates for large urban cells, suburban as well as rural regions[3]. The derived equation is given below
The co cf and b(hB) almost remain constant between different regions. The values of a(hM) and CM vary extensively and are modeled according to the city size and height. The data book of the COST project gives the values for different cities. Using the above model we try to design the propagation characteristics in Boulder at the University of Colorado campus. A signal generator was set up to transmit at 785 MHz frequency form the engineering center through a directional panel antenna. Various data points of receiver
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power were measured using a spectrum analyzer outside the engineering center and the readings are tabulated as below. Antenna parameters are provided in the Appendix [A1].
Table 1: Measurements of received power at various distances
These data points were fed into EDX propagation design software and the actual propagation model was designed.
Figure 4: Free space Propagation model
From the above design we can see that only 4 data points matches the actual measured values. This is because the free space propagation model only considers the decay in power with respect do distance and does not account for the fades from multipath. Now we calculate the various parameters of the COST 231 model for a suburban environment and input it in the EDX design software and run the simulation. We import the antenna lobe pattern [A2] into the simulation tool and we obtain the COST 231 propagation model and this model has managed to match 14 of the 21 different data points proving that it is an efficient sub urban propagation model. The modeling equation for the sub-urban environment in boulder is given below along with the propagation pattern.
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Where hB defines the height of the base station or the Rx antenna whick can vary from 10m to 100m, hM
height of the mobile terminal which ranges from 0 m to10 m and hb gives the average height of the building around the datapoints. For our case we assumed this to be 15-30 meters. We could only match 14 points because of approximation of height values. Model is more accurate for accurate values of assumed height. In the equation we have substituted values of c0, cf, b(hB),a(hM) and CM from the data book for a suburban terrain operation between frequency range of 500-1500 MHz for a COST 231Hata model [A3]. The software computes the Lhata and modifies the propagation model as given below and proves its validity for suburban environments by managing to obtain a closer propagation model to the actual readings.
Figure 5: COST 231 propagation model
There is another model derived from the COST 231 model called the COST 231-Walfish Ikegami Model. This model is based on the considerations of reflection and scattering above and between buildings in urban environments. It considers the LOS and the NLOS situations hence it has an additional term compared to the previous equation
LNLOS = L0 + Max0, Lrts + Lmsd (7)
The Lrts and the Lmsd are the factors representing the diffraction and scatters from rooftop to streets and Lmsd is the Multi-diffraction between buildings. This model enables us to obtain a better model for dense urban environments by tweaking the Loss equation by including additional parameters.
3. SMALL SCALE AND LARGE SCALE FADING
Small scale fading is explained by the fact that, the instantaneous received signal is a sum of many contributions coming from different directions due to the many reflections of the transmitted signal reaching the receiver [5]. In the time domain, multipath parameters can be seen as the spread of the arriving waves but in the frequency domain, the concept becomes less intuitive and relates to a coherence bandwidth, which refers to the width of the spectrum attenuated by the fade. Depending on the coherence bandwidth the wave experiences flat fading or frequency selective fading. The amplitude of the signal follows a Rayleigh fading distribution.Rayleigh fading channels are used in empirical urban studies and are
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accepted to model multipath environments with no direct line of sight. The channel amplitude follows the Rayleigh distribution:
P(α) = (2α /Ω) exp ( - α2/Ω) (8)
Where, Ω is the mean square value of α
Now moving over to large scale fading which corresponds to losses caused due to blockage such as a receiver turning into a corner or entering a building. This large-scale fading is referred to as shadowing. Large scale variations caused by shadowing follow log normal distribution, which means when they are converted to dB values they follow a Gaussian distribution.
P0(R) =1/2 erfc (-F/σ ) (9)
This is useful for calculating the edge reliability in wireless communications.
4. DIFFRACTION AND CLUTTER
Diffraction loss is a very significant component of microwave design. It depends on the path clearance, for a given path clearance the diffraction loss will vary from a minimum value for a single knife-edge obstruction to a maximum for smooth spherical obstructions [6]. Most of the microwave energy is concentrated within the first Fresnel zone and the diffraction loss is always calculated as a function of obstruction with respect to the first Fresnel zone. The dotted lines in the figure below represent the 1st 2nd and 3rd Fresnel zones. The obstruction height must always clear the first Fresnel zone or the microwave link is going to suffer clutter or diffraction loss.
Figure 6: Fresnel zone geometry
F1 the radius of the first Fresnel ellipsoid can be approximated by the following formulae.
F1 = 17.3 (d1d2/f*d)1/2 (10)
There are infinite Fresnel zone in an real world environment. The even Fresnel are generally ignored because they are totally in out of phase with the original signal and hence out the original signal and hence it is not required in the design of a radio path. The diffraction loss is small when at least 55% of the first Fresnel zone is cleared. There by using the formulae we can design systems so that it clears the 1st Fresnel zone.
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To prove this we setup an antenna to radiate at 785 Mhz frequency using an antenna at a window in the basement so there is NLOS measurement and various data points are noted on the map and measurements of received power are taken at these points. We plot the radiation characteristics using the EDX software without accounting for any of the environmental factors and considering it as a free space propagation model.
Point Rcvd Power dBm Ant angle Ant gain dBi EIRP (dBm) path loss dist (m) Received power #VALUE!1 -40.1 0 0 10 43 -93.1 100 -37.6 2
Table 2 : Received power for 785 Hz at various data points
Figure 6: Free space propagation model
Now we zoom in to the model and draw the poly lines to tweak the model and account for the region data and the average height of objects around the data points for clutter and diffraction losses [A4].
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Figure 7: Poly lines representing data points
Now we run the model and derive its propagation characteristics. The graph below compares the path loss components of both the manually obtained values and the model predicted by EDX. The blue line is the
manual measurement and the red line represents the model predicted by EDX.
Graph 1: plot of path loss for EDX model and manual measurement
From the graph we can see that the path loss of the model obtained from EDX is way lower than the manually obtained readings. This is because the EDX model accounts for the diffraction loss and clears the Fresnel zone threshold to get better power at the receiving data points represented by polylines in the model.
5.INDOOR PROPAGATION MODEL
Indoor propagation most often has to be designed by site-specific models, mainly with respect to the features specific to a particular building as it has a strong impact on wave guiding within the building. One of the simple models is the Motley-Keenan model which estimated path loss by a additive loss in terms of wall attenuation factor and floor attenuation factor.
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The model simply approximates the number of walls and floors with an average loss for each. The COST project also proposed a model for indoor penetration. This model considers the angle through which the radiation enters a building and the material used to construct the walls of the building.
6. ATMOSPHERIC ABSORBPTION AND ITS EFFECTS
Due to temperature variations in the atmosphere the water vapor content will vary thereby creating different refractive layers in the atmosphere, which will affect long range microwave links. This effect is dominant in costal regions as the humidity is high in these regions. They create a refractive gradient in the atmosphere which leads to multipath and hence fading. When we talk about humidity it directly implies to the water vapor content in the atmosphere. The atmospheric absorption is dominated by the water vapor and the oxygen content in the atmosphere. The absorption of microwave energy by oxygen is a result of magnetic dipole interactions with the incident radiation due to the oxygen molecule’s permanent magnetic dipole moment [7]. This creates transistors between the fine molecular structure levels of the allowed rotational states. The general absorption rate for oxygen molecule in terms of dB/Km is given below.
AO2 = 7.19x10-3+6.09/(f2+0.27)+4.81/(f-57)2+1.5) x f2 x10-3 (12)
The absorption of microwave energy by water vapor results from electric dipole interactions and its theoretical treatment is similar to the case discussed above. The absorption rate can be given by the following equation.
[13]
7. IMPACT OF RAIN ON RADIO CHANNELS
As we have seen in the earlier case water is a very lossy medium and as the size of the rain drop increases it tends to leave its spherical shape and transforms to more of an oblate ellipsoid. Due to this change in shape of the rain drop, its effect is more dominant in the horizontally polarized wave compared to that of the vertically polarized wave. Hence, most design engineers prefer to use the vertically polarized wave. Also, rain fades have more dominant effects on higher frequencies. Since, rain storms are a more localized phenomena it only affects a portion of the microwave link. Hence various measurements are done geographically to determine the precipitation rates and probability of rain occurrences. The commonly used rain region data is the Crain rain region map. With the help of this model it is possible to estimate the occurrence of rain over a huge geographical region and design systems accordingly. The effective path length attenuated due to rain can be defined by the equation below:
Deff = d / 1 + (d/d0) [14]
Where do = 35e-0.015R0.01 R0.01= 100mm/h.
The rain attenuation is estimated by
A0.01= deff*k*(R0.01)α [15]
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Where k and α are the constants defined by the Crain region table.
Thus, it is possible compute rain attenuations for a specific region and design an efficient microwave link.
8. CONCLUSION
In this paper we have discussed how surfaces in urban environments affects the propagation of radio waves. We managed to design empirical models to contain these propagation effects and how to establish an effective microwave link in an urban/sub-urban channel also proving their validity by using simulation tool EDX. Finally, we discuss on the propagation effects caused due to the atmosphere and rain. All these empirical models and equations do not give a 100% efficient system by they manage to address the most of the losses and provide us with a sufficiently effective radio link modeling strategy for Urban/Sub-urban propagation channels.
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[3] “Modification of Universal okumura and Hata model for radio wave propagation” ,Lida Akhoondzadeh-Asl and Narges Noori,IEEE,propagationProceedings of Asia-Pacific Microwave Conference 2007
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[5] ”Morse.colorado.edu”,Notes Thomas Schwengler.
[6]” Full-Wave Computation of Clutter for VHF Ground RADAR over Irregular Terrain”,Le pauld,Ieee, Radar, 2001 CIE International Conference on, Proceedings,p314-318.
[7] “The absorbption of radio waves by oxygen and watervapor in the atmosphere”,Straiton.a,IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, JULY 1975.
