Mobile Radio Propagation

Cellular Mobile Communications-

IV Mobile Radio Propagation Dr. Nasir D. Gohar

Mobile Radio Propagation Modeling a Radio Channel: Most difficult part in Radio System Design  Highly unpredictable as compared to fixed wireline media  Transmission path and its parameters keeps changing instantaneously

Changes in path profile Obstructions Environmental changes  Typically done statistically based on field measurements[System Specific]

Physical survey *1 Computer simulation using certain models and terrain data *2

*1

Gives some real picture of the environment and data can be incorporated to new system design and predict its performance

*2

Empirical Models and Terrain data may not be quite updated

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Propagation Models are tools used for  Prediction of received signal strength at a certain distance from Tx  Estimation of rapid fluctuations in Rx signal strength in a close spatial proximity to a particular location

Large-Scale Propagation Models  Estimation/Prediction of Rx Signal Strength* [Local Average]over larger distances from Tx[x00-xx,000 m]  Used for Coverage Area estimation

Small-Scale Propagation Models  Prediction/Estimation of rapid fluctuations** of Rx Signal Strength over a short distance [few wavelengths] and short time interval [few seconds]  Also called Fading Models * computed by averaging signal measurements taken at intervals of 5λ to 40λ [1-10 m] ** Rx signal strength may vary very rapidly (over a change of a fraction of wavelength] by as large as 30-40 db (3 to 4 orders of magnitude]

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Three Basic Mechanisms Affecting Radio Signal Propagation

 Reflection: Signal waves Impinging upon earth surface, buildings, and walls [objects quite big in size as compared to wavelength λ] get reflected  Diffraction: Signal waves get diffracted/bent around the objects, having sharp irregularities [edges], and obstructing its path between Tx and Rx

 Signal waves reach Rx behind the obstacle[a hill, a tall building, or some other structures] under its shadow  Depends on geometry of the object, amplitude, phase and polarization of the signal wave at the point of diffraction.

 Scattering: is caused by very small obstacles [as compared to signal wavelength λ] such as rough surface, foliage, lamp posts, street signs, etc.

Large-Scale Propagation Models are used to predict the receive signal power or the path loss caused by above mechanisms.

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Free Space Propagation Model  Used only when there exists a Line-Of-Sight [LOS] between Tx and Rx  Finds application in Satellite and LOS MW Radio Link Designing  It provides Path Loss PL[dB] calculations between such TX-RX as under

PL [dB] = -10 Log [ λ 2 / (4 π d)2] …………….Eqn-4.6 where λ is signal wavelength and d is distance between Tx and Rx. ASSUMPTIONS: 1. Both Tx and Rx Antennas are Unity Gain Antennas 2. There is no Loss in Feeder Cable, Duplexer, and HPA. HOW WE GET AT THIS RESULT ? T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Free Space Propagation Model[Cont’d]  Far-Field or Fraun-hofer Region: The region beyond the fraun-

hofer distance df from Tx Antenna

df = 2 D2 / λ where D is the largest linear dimension of Tx Antenna and df >> D and df >> λ .  EIRP and ERP ?  Close-in Distance: The minimum distance >= df where onward Free-Space Model gets applicable. Denoted by do.

This distance is used as a known received power reference point. Pr(d) = Pr(do) (do / d)2 …………………….. df <= do. <= d

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Free Space Propagation Model[Cont’d] EXAMPLE-4.1: Find the far field distance of an antenna with Max. physical linear dimension of 1 m and operating frequency 900 MHz.

Let us do it together EXAMPLE-4.2: A Radio Tx is rated for a Max output of 50 Watts. Express Pt in [a] dBm [b] dBW. [c] If this Tx is used in a system which employs a unity gain Tx antenna and 900 MHz carrier frequency, calculate Pr in dBm at a free-space close-in distance = 100 m. What would be Pr at 10 km from Tx. Assume unity gain Rx antenna.

Who would like to do it?

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Radiated Power and Electric Field Generated by a Small Current Carrying Element  Current carrying

z P

element produces E & M fields  E & M fields launched

L

P θr

θ d

y x

an antenna element (as shown in Fig-1) are given in Equation 1-3*.  Three field components:

Fig-1

1. Radiation field component 2. Induction field component 3. Electrostatic field component * Derivation of these equations is given in H/O # 12. T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Radiated Power and Electric Field Generated by a Small Current Carrying Element [Cont’d]

Fig-2 [a] Power Flux Density [ L << λ ]

Pd = EIRP/ 4π d2 = PtGt/ 4π d2 = E2 / Rfs = E2/ η W / m2 = |E|2 / 120π W / m2 ………. 4 Pr (d) = Pd Ae = |E|2 Ae / 120π = PtGtGrλ 2/ (4π d)2 W…5 Fig-2 [b] Electrical Model of Voltage Applied at Rx Input

Pr (d) = V2 / Rant = (Vant )2 / 4Rant ……….6 T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Radiated Power and Electric Field Generated by a Small Current Carrying Element [Cont’d] Example-4.3: Assume a Rx is working at 10 km LOS distance from an Isotropic Tx of 50W [Assume L = 1, and Gt = 1]. Rx has a gain Gr defined equal to 2. Find [a] Power received at Rx [b] Magnitude of E field induced at Rx antenna, and [c] Open circuit voltage induced at Rx input assuming that Rx antenna has a pure real Impedance of 50 ohm and is matched with that of Rx.

Let us Try.

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Three Basic Propagation Mechanisms  Reflection

Radio wave travelling from one medium to another, having different electric characteristics, gets partially reflected and partially transmitted into the second medium. Perfect Dielectric Material:  No energy absorption  ETotal = EReflected + ERefracted

Perfect Conductor Material  No energy absorption  ETotal = EReflected

Fresnel Reflection Coefficient Γ  Relates incident wave energy with reflected wave energy  Depends on material properties, wave polarization and frequency and incidence angle T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Three Basic Propagation Mechanisms  Reflection

Fresnel Reflection Coefficient Intrinsic Impedance η η = (µ/ε)1/2

Velocity of EM wave = 1/ (µε)1/2 θi = θr  Er = Γ E i Et = (1 + Γ) Ei T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Three Basic Propagation Mechanisms  Reflection

Brewster Angle An angle at which no reflection occurs in the medium of origin. Occurs when incidence angle θB is such that Γ becomes zero. Sin θB = (ε1 / ε1 + ε2 )1/2

Sin θB = (εr -1 / (εr)2 -1)1/2

Magnitude of reflection coefficients as a function of angle of incidence for εr = 4, εr = 12

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Three Basic Propagation Mechanisms  Reflection

Perfect Conductor  All Wave Energy is reflected [Maxwell’s Boundary Conditions]  θi = θr  E field in plane of incidence [Vertical Polarization], Γii = 1, thus, Er = Ei  E field normal to the plane of incidence [Horizontal Polarization], Γ1 = -1, thus, Er = -Ei

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Three Basic Propagation Mechanisms  Reflection

Ground Reflection (2-Ray) Model  Direct Path Signal and Ground-Reflected Path Signal [Fig-1] are considered  Provides a reasonably accurate prediction of large-scale signal strength [over several km distance]*  Also, used for LOS MW Radio Link Designing** Tx E LOS ht

EI

ER=EG

Fig-1: Two Ray Model

Rx hr

d

* Mobile Radio Systems using tall towers[50m] ** 3rd ray reflected from ionosphere layer is also used T.S. Rappaport Ch 4-5 NDG Notes

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Mobile Radio Propagation  Ground Reflection (2-Ray) Model[Cont’d]  EToT = ELOS + Eg  At Close-in distance, E(do, t) = Eo do Cos (ω c t)  At distance d, E(d, t) = Eo do/ d Cos ω c (t - d/c) …[1] (d >> do)  |EToT | = |ELOS + Eg|

Fig-2: Method of Images used to find path difference of ELOS and Eg T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Ground Reflection (2-Ray) Model[Cont’d]  It can be shown [as derived in class, H/O # 13] that EToT (d) = 2 Eo do / d [2π ht hr/ λ d ] We know that Pr (d) = | EToT (d)|2 . Ae/ 377 Watts EXAMPLE-4.6: A mobile station with λ/4 antenna length and gain of 2.55 dB[1.8] is located at a distance of 5 km from Base Station. The electric field strength measured at 1 km distance from the Base Station is 1 mV/m. The carrier frequency used is 900 MHz. [a] Find the length of the Mobile antenna. [b] If Base Station is using an antenna tower of height 50 m from ground level, and Mobile antenna is at 1.5 m above the ground level, find the received power at the Mobile antenna, using 2-Ray Model T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Diffraction  A Mechanism that helps wave propagation

around curved surface of earth, beyond the horizon and behind obstacles (shadow zones).  Huygen’s Principle states

all the points (obstructions) on a wave-front become point sources for production of secondary wavelets which combine(vector sum) to form a new wave-front (in the direction of propagation), and this new wave-front is called diffracted wave-front

Fig-1: A typical Urban Environment Showing Multi-path and Shadowing

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Fig-2: [a] Anther Exhibition of Shadowing Effect [b] Marine Environment Showing Shadowing and Multi-path

[a]

[b]

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Fresnel Zone In multi-path environment, obstacles on the path of radio waves cause diffraction. Fresnel, the inventor of fresnel model, postulated that the x-section of optical wavefront(electro-magnetic wave-front) is divided into zones of concentric circles, separated by λ/2. The radius of nth fresnel zone is given by Rn = [n λ d1 d2 / d1 + d2 ]1/2 ………………………………………..[1]

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Effect of Fresnel Zone Equation-1 implies two things:  For a given Tx antenna height, higher the transmission frequency, more the distance a radio signal will cover before the first fresnel zone touches the ground  For a given Tx frequency, higher the Tx antenna, more the distance a radio signal will cover before the first fresnel zone touches the ground

Fig-4: [a] Effect of Frequency on Fresnel Zones [b] Effect of Tx Antenna Height

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation Fresnel Zone Geometry

Fig-5: Knife-Edge Diffraction Geometry

Tx and Rx separated by an obstruction of infinite width Excess path length, ∆, can be obtained from Fig-5[b] ∆ ≈ h2 (d1 + d2)/ 2d1 d2……….2 The corresponding phase difference is given as θ ∆ = 2 π ∆ / λ = π h2 (d1+d2)/ λd1d2 α ≈ h (d1 + d2)/ d1 d2 θ ∆ = π v2 / 2 where v = h[2(d1+d2)/ λd1d2]1/2 v is known as Fresnel-Kirchoff Diffraction parameter. T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Knife-Edge Diffraction Model Fig-6: Knife-Edge Diffraction Geometry

Theoretical estimation modified by necessary empirical correction Difficult to predict accurately for actual complex & irregular terrain Mathematical expressions for simple cases have been derived. Knife-Edge Model represents the simplest case, one obstruction. Ed = Eo F(v) ………………..2 Gd (dB) = 20 log | F(v) |……3

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Knife-Edge Diffraction Model

Fig-7: Knife-Edge Diffraction Gain as a Function of v

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Knife-Edge Diffraction Model

Fig-4.12: Fresnel Zones for Different knife-edge Diff. Scenarios

EXAMPLE-01: Calculate the Diffraction Loss for three cases as shown in Fig-4.12. Assume λ = .33 m, d1 = d2 = 1 km and [a] h = 25 m [b] h = 0 m and [c] h = -25 m

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  Knife-Edge Diffraction Model

Fig-9: Knife-edge Geometry for Example-02

EXAMPLE-02: Calculate the Diffraction Loss for the Knife-Edge Scenario as shown Fig-9. Also, calculate the height of obstacle to get 6 dB Diff. Loss. Assume f = 900 MHz.

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  OUTDOOR PROPAGATION MODELS  Many Models, Longley-Rice Model, Durkin Model, Okummura, Hata, etc., mostly based on systematic interpretation of measurement data in the area concerned  Aim is to predict signal strength at a particular point or in a certain locality  Differ in their approach, complexity, and accuracy.  Classical and most commonly used models:

Okumura Model Hata Model Walfisch and Bertoni Model

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  OUTDOOR PROPAGATION MODELS  Okumura Model

Simplest and best in terms of accuracy [mature and land mobile radio systems] Mostly used for urban and suburban area Applicable for frequencies 150 MHz - 1920 MHz [Can be extrapolated up to 3 GHz Range covered is 1 km to 100 km Applicable antenna heights range from 30 m to 1000 m. A purely statistical model that does not provide any analytical explanation Not suitable for rural areas

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  OUTDOOR PROPAGATION MODELS  Okumura Model Provides a set of curves [Fig-1] based on extensive measurements  Application of this model

Calculate free space loss Lf Add to this, A (f, d) found from these curves Some corrections are applied for terrain type[Fig-2, Next Slide]

Fig-1 Median attenuation relative to free space (amu(f,d)), over a quasi-smooth terrain T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  OUTDOOR PROPAGATION MODELS  Okumura Model EXAMPLE-01: Using Okumura’s model, find median attenuation for d = 50 km, Tx antenna = 100 m and Rx antenna = 10 m in a suburban area. If Tx EIRP is 1 kW at 900 MHz, find the signal receive level at mobile station ( assume its antenna gain = 0 dB]. Solution: 1. Calculate LF 2. Calculate L50 3. Pr = EIRP - L50 + Gr Fig-2 Okumura Model Correction Curves T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  OUTDOOR PROPAGATION MODELS  Hata Model  Empirical formulation of Okumura Model graphical curves  Valid for 150 - 1500 MHz frequency range  Standard formula provides urban area propagation loss and corrections are applied for other areas  Tx antenna height range is limited to 30 to 200 m  Rx antenna height is limited to 3 to 10 m

 Hata Model standard formula:

 Urban Area:  Suburban Area:  Rural Area:  Mobile antenna correction factor:  Small to medium size city:  Large city:

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation

Urban area:

L50 = 69.55 + 26.16 log fc ­ 13.82 log hb­ a(hm) + (44.9­6.55 log hb) log R where fc 

frequency (MHz)

L50 

mean path loss (dB)

Hb

base station antenna height

a(hm) correction factor for mobile antenna height (dB) R

distance from base station (km)

 The range of the parameters for which Hata’s model is valid is 150 ≤ fc ≤ 1500 MHz 30 ≤ hb ≤ 200 m 1 ≤ hm ≤ 10 m 1 ≤ R ≤ 20 km T.S. Rappaport Ch 4-5

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Mobile Radio Propagation

Urban area (cont.):

 For a small or medium­sized city: a(hm)=(1.1 log fc ­ 0.7) hm ­ (1.56 log fc ­ 0.8 ) dB  For a large city: a(hm)=8.29(log 1.54 hm)2 ­ 1.1 dB,    fc ≤ 200 MHz    or 

a(hm)=3.2(log 11.75 hm)2 ­ 4.97 dB,    fc ≥ 400 MHz

 Suburban area:

2    fc   L50   =  L50( urban)  ­  2 log + 5.4      dB     28   

 Open Area:

L50 = L50(urban) ­ 4.78 (log fc)2+18.33 (log fc) ­40.94

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  OUTDOOR PROPAGATION MODELS  PCS Extension of Hata Model by EURO-COST-231  Extended version of Hata Model suitable for PCS-1800 system  Valid for 1500-2000 MHz frequency range  Standard formula provides urban area propagation loss and a correction factors are applied for mobile antenna[same as in Hata Model] and CM for city type  Tx antenna height range is limited to 30 to 200 m  Rx antenna height is limited to 1 to 10 m  Tx-Rx separation is limited to 1-20 km

 Hata-COST-231 Model standard formula:

CM : Suburban and medium size city: 0 dB Large city and Metropolitan center: 3 dB

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  OUTDOOR PROPAGATION MODELS  Walfisch and Bertoni Model  Impact of rooftops and building height is studied  IMT-R considers this Model as a candidate for IMT-2000 standard activities  This model considers free space loss plus roof-top to street diffraction and scatter loss, and multi-screen diffraction loss due to rows of the buildings [Fig-3]

Fig-3: Propagation Geometry for Walfisch and Bertoni Model

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  INDOOR PROPAGATION MODELS  Advent of PCS generated an impulse to study wave propagation inside buildings.

Main differences between outdoor and indoor wave propagation characteristics are;  The distance covered are much smaller  Within such a smaller range of Tx -Rx separation, a much larger environmental variation is encountered  Wave propagation is strongly influenced by  Building layout  Construction materials  Building type

 Same three mechanisms: Reflection, Diffraction, and Scattering are main reasons of signal propagation and attenuation  Signal level varies very quickly depending upon:

Interior doors are open or closed Antenna mounting T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  INDOOR PROPAGATION MODELS  Partition Losses: Partitions play an important role in signal propagation within buildings.

Hard Partitions: Part of building structure and immoveable partitions such as fixed internal walls, reinforced concrete between floors, etc Soft Partitions: Moveable and not spanning to the ceiling, such as office partitions

 Same Floor: A floor inside a building may have a combination of partitions, hard as well as soft partitions  Inter Floor: Mainly fixed partitions, concrete floors, external dimensions and materials of the building  Partitions Offer Wide Variety of Physical As Well As Electrical Characteristics

Difficult to apply general models to indoor radio signal propagation Some measurement data describes radio signal attenuation while

crossing various kinds of partitions or across a number of floors [See Table-4.3, 4.4, and 4.5]

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  INDOOR PROPAGATION MODELS  Partition Losses

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  INDOOR PROPAGATION MODELS  Partition Losses

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  INDOOR PROPAGATION MODELS  Partition Losses Table-4.4 and Table-4.5

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  INDOOR PROPAGATION MODELS  Log-Distance Path Loss Model Many Researchers have shown that radio signal propagation inside buildings obey distance power law given by PL(dB) = PL (do) + 10 n log (d/do) + Xσ……………Eqn. 1 Where n depends on surroundings and building type, and Xσ is a random variable depending on standard deviation σ [dB]. See Table-4.6 on next slide

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation

T.S. Rappaport Ch 4-5

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Mobile Radio Propagation  INDOOR PROPAGATION MODELS  Ericsson Multiple Breakpoint Model

Empirical Model based on measurements in a multiple floor office

building Provides an upper and lower bound on path loss Assumes that at 1 meter distance(from Tx) there is 30 dB loss at 900 MHz.

Fig-1 Ericsson In-building Path Loss Model

T.S. Rappaport Ch 4-5

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