Lecture 4

Antennas, dB, and Introduction to Radio

Propagation
+ 2

Overview

n Quickly review some concepts that we make use of repeatedly

in this class
n You may have seen these things in other classes

n Primarily a refresher
n Not intended to be exhaustive or complete
n Some concepts are simplified to just meet the needs of this class

n Generation, transmission and reception of signals

n Modeled as a linear time invariant system with signals as inputs
and outputs
n Wireless systems and the “radio channel” are also often modeled
as LTI systems
+ 3

Simplified model of a digital

communication system
Focus of next few lectures

Source Channel
Source Modulator
Encoder Encoder

Radio Channel
Source Channel Demod
Destination
Decoder Decoder -ulator
+ 4

Components of the digital

communication system
n Source
n Produces a finite alphabet for transmission
n Examples: Quantized voice samples, ASCII alphabets

n Source coder
n Removes the redundancies and efficiently encodes the alphabet
n Example: In English, you may encode the alphabet “e” with fewer bits than you would “q”

n Channel encoder
n Adds redundant bits to the source bits to recover from any error that the channel may
introduce

n Modulator
n Converts the encoded bits into a signal suitable for transmission over the channel

n Channel
n Carries the signal, but will usually distort it
+ 5

Communication Link
n Transmitter (Tx)
n Signal is transmitted at power Pt

n Receiver (Rx)
n Signal is received at power Pr

n Transmission medium or channel

Tx Rx
Channel
d

x(t) y(t)

∝ Pt ∝ Pr
time time
⌧ = d/c
+ 6

Classifications of Transmission Media

(the channel)
n Transmission Medium
n Physical path between transmitter and receiver

n Guided Media
n Waves are guided along a solid medium
n Example:
n Copper twisted pair, copper coaxial cable, optical fiber

n Unguided Media
n Provides means of transmission but does not guide
electromagnetic signals
n Usually referred to as wireless transmission
n Example: Atmosphere, outer space (free space)
+ 7

Unguided Media

n Transmission and reception are achieved usually by means of

an antenna
n Antennas
n Transducers that allow voltage and current waveforms flowing on a
wire to be converted into electromagnetic waves that propagate in
free space
n Capture electromagnetic waves propagating in air and convert
them into voltage or current waveforms in a wire

n Configurations for wireless transmission

n Directional
n Omnidirectional
+ 8

dB vs absolute power

n Power (signal strength) is expressed in dB for ease of

calculation (all relative quantities)
n dBm: reference to 1 mW
Show in
n dBW: reference to 1 W R and
Matlab
n Example: 100 mW = 20 dBm = -10 dBW
n 10 log10 (100 mW / 1 mW) = 20 dBm
n 10 log10 (100 mW / 1 W) = -10 dBW

n In general dBm value = 30 + dBW value

n Other relative values are simply expressed in dB
+ 9

Examples of using Decibels

n Example 1:Express 2 W in dBm and dBW

n dBm: 10 log10 (2 W / 1 mW) = 10 log10(2000) = 33
dBm
n dBW: 10 log10 (2 W / 1 W) = 10 log10(2) = 3 dBW

n Example 2: The transmit power is 2 W, the RSS is 0.12

W. What is the loss in dB?
n Loss = Transmit power – RSS = 33 dBm – 20.8 dBm
= 12.2 dB
n Or Loss = 3 dBW – (–9.2 dBW) = 12.2 dB

n The loss in Example 2 is usually called the “path loss”

RSS = Received Signal Strength

+ 10

Some notes

n 1 bel = 10 decibels
n Hence the multiplication by 10

n If voltages are given instead of power values, it is

common to assume a 1 W load resistance
n The dB value is calculated as 20 log10(voltage)

n Path loss
n Loss in signal strength between transmitter and
receiver
n Primarily due to distance (hence “path”), but loss in
signal strength also due to other reasons
+ 11

Antennas

n What is an antenna?
n A transducer for converting guided signals in a transmission line or
waveguide into electromagnetic radiation in an unbounded medium or
vice versa
n Conversion should be as efficient as possible
n Match the impedance of the transmission line to that of the
unbounded medium
n Prevent unwanted reflections back to the load
n Focus radiation in the direction required

n Needs change in the velocity of charges carried in the antenna for

radiation to occur
n Antenna material, shape and size impact the radiation and impedance
n The dimension of an antenna is measured in units of the wavelength l of
the carrier
+ 12

What can be an antenna?

n Any conductor or dielectric can serve as the transducer

n The properties may make it inefficient and thus unsuitable
for the application
n Needs careful design of the structure of the antenna

Thin Dipole Biconical Dipole Loop Parabolic Microstrip Horn

Reflector Antenna

Show Pringle’s cantenna

+ 13

Radiation Sources and Antenna

Types
n Radiation Sources n Antenna Types
n Currents n Passive Antennas
n Aperture fields
n Most common
n Current sources n Active (Smart) Antennas
n Example: Loops, dipoles n More expensive
n Time varying current creates an n Possibly widespread in the
electromagnetic field that is future
radiated

n Aperture sources
n Example: Horn antenna
n Fields across the aperture serve as
the source of the radiation
+ 14

The Near and Far Fields l=

wavelength

n There are two distinct regions of electric and magnetic fields around
an antenna
n The near field is called the Fresnel region
n Close to the antenna (around one l)
n The far field is called the Fraunhofer region
n Far away from the antenna (several l’s away)

n The radiation in the far field is similar to plane wave propagation

n This is usually the region of interest for most applications
n Allows us to simplify the characteristics of the antenna

n The boundary between the near and far fields is an arbitrary sphere
of radius Rff = 2d2/l
n d is the physical dimension of the antenna
n Diameter of the smallest sphere that completely encloses the antenna
+ 15

Example of Far Field Calculation

n What isthe far field Far Field

of an antenna for a Near Field

1000 MHz carrier if Reactive

the antenna is a half d

fields

wavelength dipole?
R
n d = l/2
n Rff = 2(l/2)2/ l = l/2
n l = c/f = 3 x 108/1000 x 106 = 0.3
m Radiating fields
n Rff = 0.15 m
+ 16

Basics of Antennas (I)

n Radiation pattern – G(q,j)

n Also called antenna pattern
n Directional function of the relative distribution of power or
intensity in the far field
n Three dimensional plot of the relative strength as a function of
the spherical co-ordinates j and q

n The radiation pattern is independent of distance

n It is relative!

n Typically, it is shown as two 2-D plots

n q-direction (also called elevation plane)
n j-direction (also called azimuth plane)
+ 17

Example of Antenna Pattern

polar plot
x-y rectangular plot
90 1
120 60
0.8
1
0.6
0.9
0.8 q direction 150
0.4
30

0.7
0.6
0.2
q direction
n
i 0.5 180
a 0
g
0.4
0.3
0.2
0.1 210 330
0
0 50 100 150 200 250 300 350 400
angle in degrees
240 300
270
+ 18

More on Antenna Patterns

n The antenna patterns are usually normalized to the

maximum gain Gmax
n The gain is often expressed in dB in such a case

n In the previous example

j
n The pattern is the same for all values of
n In many cases, there may be a change with j in which
case the azimuthal variation also needs to be shown
+ 19

Directivity

n Directivity
n Describes the antenna pattern of a lossless antenna
n Indicates how much gain is there due to the directionality
n D = maximum radiation intensity/average radiation intensity

Gmax
D=
1
4π ∫∫π G (θ , ϕ )dΩ
4
Solid Angle
sinq dq dj
+ 20

Isotropic Antenna

nRadiation propagates equally in all

directions
n“Ideal” – does not exist
nWhat is the directivity of the isotropic
antenna?
Gmax 4π
Diso = 2π π
= π =1
Gmax
4π
∫ ∫ sinθdθdϕ 2π ∫ sinθdθ
0 0 0
+ 21

Radiation lobes

3 dB Beamwidth
n Ideal antenna
Ideal
Antenna n Gain = 1 over a certain
angle
3 dB n Gain = 0 over the rest of
the directions

Main n Real antenna

lobe
n Radiates power in
Side
lobe unwanted directions
n Has one or more main
Back lobes and many sidelobes
lobe
n Specified “beamwidth”
+ 22

Radiation Lobes (II)

n Antenna Beamwidth
n The angle of coverage where the radiated energy is 3
dB down from the peak of the beam (half-power)
n By narrowing the beamwidth we can increase the gain
and create sectors at the same time
n Front-to-Back Ratio
n The ratio of the power in the main lobe to the power
in the lobe created at the back of the antenna
n Ratio should be as large as possible
n Front to back ratio of a dipole is 0 dB!
+ 23

Example: Beamwidth and Directivity

n Compute the 3 dB beamwidth and directivity of an antenna

that has the pattern defined by the following equation:

#cos 2 θ , if 0 ≤ θ ≤ π/2
G (θ , ϕ ) = "
! 0, elsewhere

n Note that this antenna pattern is independent of the azimuth

n Set G(q,j) = 0.5 to find the 3 dB beamwidth (solve for q)
n You can find the directivity by integration
n The answer is D = 6
+ 24

Antenna Gain
n The “gain” of an antenna in a given direction is the ratio of the power density produced by it in
that direction divided by the power density that would be produced by a reference antenna in
the same direction

n Two types of reference antennas are generally used

n Isotropic antenna: gain is given in dBi
n Half-wave dipole antenna: gain is given in dBd

n Manufacturers often use dBi in their marketing

n To show a slightly higher gain J 0 dBi
n dBi = dBd + 2.15 dB

0 dBd

Other
Dipole
Isotropic 5 dBd = 7.15 dBi
+ 25

Basics of Antennas (II)

n Reciprocity
n An antenna can be used both for transmission and
reception
n It performs equally well for both tasks
n The radiation pattern is identical for transmission and
reception
n Exceptions: Solid state antennas

n Impedance
n It is important to match the impedance of the
antenna to that of the transmission line feeding it
+ 26

Omnidirectional Antennas

n Omnidirectional antenna
n Radiation pattern is constant in the azimuth plane
n Half-wave dipoles and quarter-wave monopoles with a
ground plane are good approximations
n Typically made from some type of collinear array of
half-wave dipoles
n Radiation pattern is in the shape of a donut

n At l/2, impedance matching occurs with the 2

transmission line
+ 27

Effective Area

n Characterizes the ability of an antenna to

n Capture energy from an incident wave and convert it into an
intercepted power
n Also called effective aperture and receiving cross-section

n It is not dependent on the physical area of the antenna

although that could affect it

n You can show that the effective area is given by

n Ae = l2D/4p for any antenna (D = directivity)
n Assumes matched impedance
n What is it for an isotropic antenna? (remember – free space loss)
+ 28

Importance of antennas

n Capacity of the system can be increased

n Co-channel interference can be
reduced with directional antennas Rx1

n Multipath effects can be reduced Tx

n If a highly directional antenna is used
for both transmission and reception, Rx2
the number and spread of multipath
components are reduced n Three sector antenna for a cellular
system with two orders of receive
n Diversity gains are possible diversity
n There are two receiving elements per
n Using antenna elements that are
sector and one transmitting element
spaced apart, spatial diversity gains
are achieved

n MIMO – Multiple Input Multiple Output

and smart antennas
+ 29

Antenna Examples

Grid Reflector
Panel Array of Antenna
Monopole dipoles
Omnidirectional for sectored cell
+ 30

Antenna Location

nTrend is to co-locate cells from

multiple companies due to cost
of cell site land/tower
n American Tower
n Crowncastle
+ 31

The Radio Channel

n The radio channel is different

n Extremely harsh environment compared to “wired” or
guided media
n Channel is time variant
n Movement of people
n Switching off and on of interference
n Movement of mobile terminals
n Sensitivity to a variety of other factors
n “Fading” and “Multipath”

n Need a framework that characterizes the radio channel

n Common to approximate it as an LTI system
+ 32

What is Radio Propagation?

n How is a radio signal transformed from the time it leaves a

transmitter to the time it reaches the receiver
n What is the “radio channel”?

n Important for the design, operation and analysis of wireless

networks
n Where should base stations be placed?
n What transmit powers should be used?
n What radio channels need be assigned to a cell?
n How are handoff decision algorithms affected…?
+ 33

Propagation Mechanisms (1)

n EM radiation propagates as various waves depending on wavelength

and distance
n Ground (surface) wave travels close to ground level
n Dominant for low frequencies (30 kHz - 3 MHz)
n Scatters off terrain and buildings

n Tropospheric waves propagate in lower atmosphere and refract back

to ground level
n Amount of refraction increases with frequency, causes significant
annoyance above 30 MHz

n Ionospheric waves can be reflected between upper atmosphere and

ground to propagate thousands of miles
n Effected by sunspot activity, cause signal distortion
+ 34

Propagation Mechanisms (2)

n For a high frequency signal (> 500 MHz)
n An electromagnetic wave can be modeled as a “ray”

n Basic mechanisms
n Transmission (propagation through a medium)
n Scattering (small objects less than wavelength)
n Reflection (objects much larger than wavelength)
n Waves may be reflected by stationary or moving objects
n Diffraction at the edges
+ 35

Reflection and Transmission

n Electromagnetic “ray” impinges on object larger than the wavelength l

n It bounces off the object
n Examples:
n Walls, buildings, ground

n Signal is attenuated by a reflection factor

n Attenuation depends on
n Nature of material
n Frequency of the carrier
n Angle of incidence
n Nature of the surface

n Usually transmission through an object leads to larger losses (absorption)

than reflection
n Multiple reflections can result in a weak signal
+ 36

Oxygen absorption at 60 GHz

n Signals are attenuated (fade) over distance depending on

frequency and weather conditions

f = 60 GHz In oxygen
with rain
In oxygen
Loss in dB

In vacuum

log (distance) For illustration only, not to scale

+ 37

Diffraction

n The radio signal is incident upon the edge of a sharp object

n Example: Wall, roof edge, door

n Each such object becomes a secondary source

n Losses are much larger than with reflection or transmission

n Important in micro-cells for non-line of sight transmission

n Propagation into shadowed regions

n Not significant in indoor areas because of large losses

+ 38

Scattering

n Caused by irregular objects comparable in size to the

wavelength
n These objects scatter rays in all directions

n Each scatterer acts as a source

n Signal propagates in all directions
n Large losses in signal strength
n Insignificant except when the transceiver is in very cluttered
environments

n Examples of scatterers
n Foliage, furniture, lampposts, vehicles
+ 39

Multipath Propagation

n Multipath
n Receiver gets combined radio waves from different
directions with different path delays
n Received signal is very dependent on location -
different phase relationships can cause signal
fading and delay spread
n Causes time variation and inter-symbol
interference in digital systems
n Causes “burst errors”
n Limits maximum symbol rate
+ 40

Time Variation of Signals

nA moving receiver can experience a positive

or negative Doppler shift in received signal,
depending on direction of movement
n Results in widening frequency spectrum
n Rapid fluctuations of signal envelope
Fading
Signal envelope in dB

0
10

−1
10

−2
10

time
−3
10
0 10 20 30 40 50 60 70 80 90 100
+ 41

Time Dispersion and ISI

n Suppose we transmit a single narrow pulse

n Assume there are three paths
n What do we receive?

n What happens if we send two narrow pulses?

Initial Tx
pulse

Received signal
+ 42

First possibility

Write Maxwell’s equations

Solve Maxwell’s equations
• Difficult if not impossible
• Details?
• Approximations may help
• FDTD
• Ray tracing
+ 43

Second possibility

Simplify!
Measurements
Macroscopic characterization
Empirical models
“how signals are affected
vis-à-vis some parameters”
+ 44

Summary

n Several paths from Tx to Rx

n Different delays, phases and
amplitudes
n Add motion – makes it very
complicated
TX
n Very difficult to look at all of the
effects in a composite way
Transmission Diffraction n Use empirical models
Scattering n Use statistical models
n Breakdown phenomena into
Reflection
different categories

RX
+ 45

Radio channel characterization

n Radio propagation is modeled as a random

phenomenon
n Measurements followed by statistical modeling
n Signal strength measurements
n RMS delay spread measurements
n Use spread spectrum or linear FM

n Measurements to fine tune simulations and

simulations followed by statistical modeling
n Ray tracing: Approximate the radio propagation by
means of geometrical optics
+ 46

Classified based on site/application

specificity
n Propagation Conditions n Frequency dependence
n Indoor
n Commercial
n 700, 900 MHz : Cellular
n Office n 1.8, 1.9 GHz : PCS
n Residential
n 2.4 GHz : WLANs, BT, Cordless
n Tunnel
n Outdoor to Indoor n 5 GHz : WLANs, RF tags, MMDS
n Outdoor n 10 GHz : MMDS
n Urban
n 30 GHz : LMDS
n Rural
n Suburban
n Forest/Jungle
n Mountainous
n Open areas/Free space
n Over Water

LMDS: Local multipoint distribution service

MMDS: Multichannel multipoint distribution system
+ 47

Communications Issues in Radio

Propagation
n Coverage
n How far does the signal propagate over a given terrain at a
particular frequency?
n Power or received signal strength (RSS)

n Performance
n Bit error rate
n Statistics of fading – amplitudes and durations
n Data rate (capacity)
n Multipath structure
n MIMO

n Some issues are predominant for certain applications

+ 48

Coverage

n How far does the signal propagate over a given terrain

at a given frequency?
n Same as link budget (in a sense)

n Determines
n Transmit power required to provide service in a given area
n Interference from other transmitters
n Number of base stations or access points that are required

n Parameters of importance
n Path loss
n Shadow fading
+ 49

Signal propagation ranges

n Transmission range
n Communication possible
n Low error rate

n Detection range
n Detection of the signal
sender
possible
n No reliable communication
possible transmission

distance
n Interference range detection
n Signal may not be
detected interference
n Signal adds to the
background noise
+ 50

Rate of Channel Fluctuations

n What are the changes in the channel? How fast are these
changes? How do they influence performance?
n Determines
n Performance of the communication system
n Outage, probability of error
n Receiver design
n Coding, diversity etc.
n Power requirements

n Parameters of importance
n Fluctuation characteristics
n Fade rate, fade duration and Doppler spectrum
+ 51

Data Rate Support

n Whatis the maximum data rate that can be

supported by the channel? What limits it?
n Determines
n Capacity of the system
n Complexity of the receiver
n Application support

n Parameters of importance
n Multipath delay spread and coherence bandwidth
n Fading characteristics of the multipath components
+ 52

Radio Propagation
Characterization
Fading
Channels

Small Scale
Large Scale Fading
Fading

Path Loss
Time Variation Time Dispersion
Shadow Fading

Amplitude fluctuations
Multipath Delay Spread
Distribution of amplitudes
Coverage Rate of change of amplitude
Coherence Bandwidth
Intersymbol Interference
“Doppler Spectrum”

Receiver Design (coding) Receiver Design, Performance

Performance (BER) Maximum Data Rates
+ 53

Summary
Large Scale Fading
−100
Histogram of Deviations is Shadow Fading

−105
Power in dB

−110

Linear Fit of RSS in dB to log(distance)

Slope is the distance-power gradient
−115

−120

Small Scale Fading

−125 Histogram of Deviations is Multipath Fading
Fourier Transform of Deviations is Doppler Spectrum

−130
2.4
10 Distance
10
2.5 from Base
10 Station in Logarithmic
2.6
10
2.7 Scale
10
2.8
10
2.9
+ 54

The Free Space Loss

n Assumption
n Transmitter and receiver are in free space
n No obstructing objects in between
n The earth is at an infinite distance!

n The transmitted power is Pt, and the received power is Pr

n The path loss is Lp = Pt (dB) – Pr (dB)
n Isotropic antennas
n Antennas radiate and receive equally in all directions with unit gain

d
+ 55

The Free Space Model

n The relationship between Pt and Pr is given by

Pr = Pt l2/(4pd)2
n The wavelength of the carrier is l = c/f

n In dB
Pr (dBm)= Pt (dBm) - 21.98 + 20 log10(l) – 20 log10(d)

Lp(d) = Pt – Pr = 21.98 – 20 log10(l) + 20 log10(d)

= L0 + 20 log10(d)
n L0 is called the path loss at the first meter (put d = 1)
n We say there is a 20 dB per decade loss in signal strength
+ 56

A simple explanation of free space

loss
nIsotropic transmit antenna: Radiates signal
equally in all directions

n Assume a point source

n At a distance d from the transmitter, the
area of the sphere enclosing the Tx is: A =
4pd2
n The “power density” on this sphere is: Pt/
4pd2

n Isotropic receive antenna: Captures power

equal to the density times the area of the
antenna
n Ideal area of antenna is
Aant = l2/4p

n The received power is:

Pr = Pt/ 4pd2 ´ l2/4p = Pt l2/(4pd)2
+ 57

Isotropic and Real Antennas

n Isotropic antennas are “ideal” and cannot be achieved in

practice
n Useful as a theoretical benchmark
n Real antennas have gains in different directions
n Suppose the gain of the transmit antenna in the direction of
interest is Gt and that of the receive antenna is Gr
n The free space relation is:
Pr = Pt Gt Gr l2/(4pd)2
n The quantity Pt Gt is called the effective isotropic radiated
power (EIRP)
n This is the transmit power that a transmitter should use
were it having an isotropic antenna
+ 58

Summary: Free space loss

n Transmit power Pt and received power Pr

n Wavelength of the RF carrier l = c/f

n Over a distance d the relationship between Pt and Pr is given by:

Pt l2
Pr =
(4p ) 2 d 2
n where d is in meters

In dB, we have:

Pr (dBm)= Pt (dBm) - 21.98 + 20 log10 (l) – 20 log10 (d)

Path Loss = Lp = Pt – Pr = 21.98 - 20log10(l) + 20log10 (d)

+ 59

Example

nThe transmit power of a wireless

communication system is 2 W. If the
propagation is similar to free space, what
is the received power at a frequency of 1
GHz at a distance of 1 km? Assume
isotropic transmit and receive antennas.
nWhat do we know?
+ 60

Next Week

nImpact of frequency
nImpact of distance
nOther path-loss models