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Home , Fresnel zone, Multipath propagation, Radio wave, Wave propagation

Chapter 2: Propagation Fundamentals

M.Sc. Sevda Abadpour Dr.-Ing. Marwan Younis

INSTITUTE OF RADIO ENGINEERING AND

KIT – The Research University in the Helmholtz Association www.ihe.kit.edu Scope of the (Today‘s) Lecture

D Effects during transmission of signals: A . physical phenomena that influence the propagation analog source & of electromagnetic channel decoding . no statistical description of those effects in terms digital of modulated signals

filtering, filtering, amplification amplification Noise

Antennas Propagation Time and Frequency Phenomena Selective Radio Channel

2 12.11.2018 Chapter 2: Propagation Fundamentals Institute of Engineering and Electronics Propagation Phenomena

zR zT path N

receiver QTi path i QRi yT xR y Ti yRi xT path 1 yR

reflection: scattering: free space - plane wave reflection - rough surface scattering propagation: - Fresnel coefficients - volume scattering - line of sight - no multipath diffraction: refraction in the troposphere: - knife edge diffraction - not considered

In general leads to at the receiver site

3 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics The Received Signal

Signal fading Fading is a deviation of the that a signal experiences over certain propagation media.

It may vary with time, position Frequency

and/or frequency Time

Classification of fading: . large-scale fading (gradual change in local average of signal level) . small-scale fading (rapid variations

large-scale fading due to random multipath signals) small-scale fading

4 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Propagation Models

Propagation models (PM) are being used to predict: . average signal strength at a given distance from the transmitter . variability of the signal strength in close spatial proximity to a particular location

Severe multipath conditions in PM can be divided into: urban areas (small-scale fading) . large-scale models (mean signal strength for large transmitter receiver separation) . small-scale models (rapid fluctuations of the received signal over very short travel distances)

5 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Large-Scale Propagation

Free Space Propagation

6 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Free Space Propagation

T R x x Assumptions: Pt Pr . unobstructed line of sight (LOS) Gt Gr . no multipath propagation r no (influence of) ground

Received power: Power density at Rx site: effective area:

Friis free space equation:

7 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Received Power and

Using:

i i

Assumptions: . matched receiving antenna . conjugate complex of the receiver

Path loss:

Isotropic path loss (no antenna gains):

8 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Polarization

Orientation of Field Vectors and Reference Planes

9 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Polarization of the EM Waves

Every elliptically polarized EM wave can be decomposed into a horizontal and a vertical component.

Elliptical Circular Linear

10 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Polarization: II, T , V or H?

Plane of incidence: formed by the normal vector to the reflecting surface and Poynting vector of the incidence wave

EII or EV

E T or EH

Polarization (E-field vector) with Polarization (E-field vector) with respect to the plane of incidence: respect to the earth coordinates: . parallel (II) . vertical (V)

. perpendicular ( )T . horizontal (H)

11 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Reflection and Transmission

Dielectric Boundary

12 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Snell’s Law of Reflection

. surface large compared to the wave length θi θr 1 . smooth surface (otherwise scattering) . three angles: - incidence 2 - reflection - transmission / refraction θt

. Relation between angles through Fermat’s principle (principle of least time): - “the rays of (EM-waves) traverse the path of stationary optical length” . This results in* Snell’s laws: - “ratio of the sines of the angles of incidence and refraction is equivalent to the opposite ratio of the indices of refraction” - “the incidence and reflection angles are equal and they are in the same plane”

sin(i ) n2  nx   r,x  r,x i r sin(t ) n1 *full derivation in Arthur Schuster: “An Introduction to the Theory of ”

13 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Which Part is Transmitted / Reflected?

Derivation procedure: . Definition of the strength of the incident wave . Reflected and transmitted field strengths . Faraday’s law of induction . Boundary conditions at the border between two dielectric media . Decomposition of the incident waves on parallel and normal components

14 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Fresnel Reflection & Transmission Coefficients

parallel

perpendicular

where:

Fresnel coefficients are frequency dependent and in general complex

15 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Brewster‘s Angle (I)

Angle, where no reflection occurs is Brewster’s Angle: . exists only for parallel (II / V) polarization . calculation by comparing the reflection coefficient to zero . calculation by using “physical limitations”

16 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Brewster‘s Angle (II)

Air (less dense) Glass (dense)

17 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics

Brewster‘s Angle (III) phasein degree

18 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Brewster‘s Angle (IV)

Operation principle of Brewster window: . used for windows in optical or quasi optical systems . window with normal incidence  reflection loses at window . window tilted at Brewster’s angle  no reflection loses at window

Microwave gyrotron Brewster window

19 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Total Internal Reflection (I)

When does the total internal reflection appears? ni sini  nt sint  t 90 . a ray must strike the medium’s boundary

at an angle larger than the critical angle  nt  c  arcsin  . calculation by comparing the    ni  transmission angle to 90 degree critical angle exists only for nt < ni

Increasing the incidence angle Total reflection of light in PMMA

20 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Total Internal Reflection (II)

Operation principle of rain sensors: . IR-beam projected on the glass-air interface at a specific angle . total inner reflection in dry conditions . partial transmission to the second medium if windshield is wet . reduced receive power triggers the sensor

Rain sensor in the rear view mirror

21 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Visualization Parallel Pol – E-Field

Parallel Pol – Air to Glass Parallel Pol – Glass to Air

22 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Visualization Perpendicular Pol – E-Field

Perpendicular Pol – Air to Glass Perpendicular Pol – Glass to Air

23 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Reflection and (no) Transmission

Perfect Electric Conductor (PEC)

24 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Orthogonal PEC Reflection

Boundary conditions:

Etan  Etan,i  Etan,r  0

Hnorm  Hnorm,i  Hnorm,r  0 reflected wave incident wave

Ey Ey SR S SR

Hx Hx H HxR E xR EyR yR

y

z

x

25 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics PEC Reflection, Orthogonal Polarization H incident reflected wave Ey wave Hxi H i S S

Plane of incidence Eyi ai Ey

Hzi H Hzr

Eyr PEC reflector

PEC reflection: Hxr Hr

x

. RII = +1 y T z . R = -1 (to ensure E = 0) tan ai  ar

26 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics PEC Reflection: Applications

Reflection in the direction of incidence: calibration with metallic: . dihedral . trihedral ()

Buoy with dihedral

Radar image with corner reflectors

Satellite radar calibration

27 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Two-Ray Propagation Model

28 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Geometry

T

d1 R

zT

zR d2 air (휺풓 = ퟏ) j j r ground (휺 ) 풓 d

Two-Ray model is based on and predicts large-scale fading

29 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Assumptions

Assumptions in two-ray model: . ground is PEC

. d >> zT,zR

d

Observations:

2 2 . the received power PR oscillates like a sin or cos with distance

. the minimum value of PR is 0

. the maximum value of PR is 4 · PR,freespace (+ 6 dB)

30 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Large Distances

Conditions:

. d >> k0zTzR . cos2x  1 . sin2x  x2

Observations: . parallel pol: 20 dB / decade, perpendicular pol: 40 dB / decade . perpendicular pol: independent on frequency

. perpendicular pol: antenna height gain (double zT or zR  quadruple PR)

31 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Breakpoint

Definition: The breakpoint is the distance where the argument of the sin2 and cos2 terms equals 0.5

1

0.5

Beyond the 0 1 breakpoint there are no oscillations!

0.5

0 0 0.5 1 1.5 2 2.5

32 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Polarization Dependence

perpendicular polarization parallel polarization

1/d2 1/d2 6 dB 6 dB

dependent on frequency 1/d2 6 dB 6 dB

1/d4 independent on frequency

33 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Frequency Dependence

f = 900 MHz f = 4 GHz

dbreakpoint

dbreakpoint

distances of notches >> l

34 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Path Loss Prediction

80dB 200m height z vertical (parallel)

polarization

path path loss (above ground) (above 50m

0m 130dB 0m range coordinate r (distance from transmitter) 2000m

80dB 200m

horizontal (perpendicular) height z

polarization

path path loss (above ground) (above 50m

0m 130dB 0m range coordinate r (distance from transmitter) 2000m

35 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Diffraction

Diffraction on Absorbing Half-Plates

36 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Geometry

z secondary spherical waves

z = H rT rR H>0

y x d d transmitter T R receiver

. obstacle: semi-infinite, infinitely thin, absorbing plate . calculate behavior behind the plate: Huygens’ principle . wave propagation behind the plate: sum of secondary waves

37 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Model

Assumptions in knife edge model: . cylindrical waves (2D problem)

. Tx and Rx at same height

. |H| << dT,dR

Fresnel Integrals Field-strength relative to free space (no obstacle):

2 2 E 1  1   1     C( )    S( ) E H  2  2   2 

2  1 1    H    l  dT dR 

38 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Electric Field (I)

shadow region

- 6 dB

lit region

2  1 1    H    l  dT dR 

39 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Electric Field (II)

shadow region

- 6 dB

lit region

 0 if   0.78 dB E  6.9  20log  0.1   0.1 2 1     E H    if   0.78

40 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Frequency Dependence (I)

• field strength normalized to free space level • isotropic Tx antenna • semi-infinite, absorbing plate • f = 1 GHz, 3 GHz, 10 GHz

diffraction loss increases with frequency  f for  1

41 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Knife Edge Diffraction: Frequency Dependence (II)

SINGLE KNIFE EDGE DIFFRACTION , FREQUENCY DEPENDENCE shadow / lit region

-6 dB

f  ∞

transmitter height = obstacle height distance transmitter to knife edge = 1000m distance knife edge to receiver = 100m

42 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Fresnel Ellipsoids

Nth is bounded by an ellipsoid, where

the Tx-Rx-path is N half longer than dFN  dT  dR  N l 2

the direct Tx-Rx-path dT + dR between Tx and Rx

rF1 Tx Rx dT dR

1st Fresnel ellipsoid Nth Fresnel ellipsoid

Radius of Nth Fresnel ellipsoid

43 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics When to Neglect the Knife Edge Diffraction?

Relate Fresnel radius RFN with diffraction parameter :

-1

2

If the knife edge does not extend into 1st Fresnel zone, then the error compared to free space propagation is less than 1.1 dB:

If the knife edge does not extend into the 1st Fresnel zone, then knife edge diffraction can be neglected

44 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Fresnel Ellipsoids: Example

Tx Rx

dT dR

RF1

dT+dR+l0/2

45 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Scattering

Scattering of Incident Energy on Rough Surfaces

46 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Different Types of Scattering

point scattering distributed scattering

Simple targets (plate, sphere, rough surface scattering volume scattering cylinder, etc.)

47 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics From to Incoherent Scattering

specular reflection coherent scattering diffuse scattering

Roughness criteria: Roughness paremeter: s : RMS height l h i s Rayleigh: s  0 L: correlation length h 8cosi L l Fraunhofer: 0 s h  sh 32cosi 

48 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals  Institute of Radio Frequency Engineering and Electronics Multipath Propagation

Combination of all Wave Propagation Effects

49 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Propagation Phenomena

refraction reflection zR zT path N diffraction

transmitter receiver QTi path i QRi yT xR y Ti yRi xT path 1 yR scattering

reflection: scattering: free space - plane wave reflection - rough surface scattering propagation: - Fresnel coefficients - volume scattering - line of sight - no multipath diffraction: refraction in the troposphere: - knife edge diffraction - not considered

In general multipath propagation leads to fading at the receiver site

50 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics Path Loss Prediction over Natural Terrain

70 dB 80 m

• f = 435 MHz

height path path loss 16.4 m

0 m • Tx height = 16.4 m 150 dB 0 km distance 7.95 km • vertical polarization 80 dB 80 m

height • f = 1900 MHz path path loss

16.4 m

0 m 160 dB 0 km distance 7.95 km

51 12.11.2018 Chapter 2: Radio Wave Propagation Fundamentals Institute of Radio Frequency Engineering and Electronics