402-Line of Sight Radio Link 2up

Line of sight radio comms linkA.J.Wilkinson, UCT EEE3086F Signals and Systems II402 Page 1 May 13, 2013

EEE3086FSignals and Systems II

2013

A J Wilkinson

[email protected]

http://www.ee.uct.ac.zaDepartment of Electrical Engineering

University of Cape Town


4 Line-of-sight Radio Communications Link

1. Line-of-sight radio link (received power)2. Thermal radiation and radiometer3. Noise in receivers4. Sky noise5. Link budget calculations for line of sight radio link

(SNR calculations).6. Frequency band names used for communications

and radar7. Radio wave propagation

Contents


4.1 Line-of-sight radio link (received power)

A.J.Wilkinson, UCT Line of sight radio comms link EEE3086F Signals and Systems II402 Page 4 May 13, 2013

Line-of-sight Radio Link

S o

N o

=Po

12π

∫−∞

∞S N0ω dω

P t

RF

Carrier ωc

Signal P r

S i

N i

S o

N oInputsignal

Outputsignal

We need to be able to calculate the Signal-to-Noise Ratio S/N at the output.

Output noise PSD

Signalpower

Noisepower

Output signal power

DemodulatorModulator


In order to calculate the SNR at the output of a demodulator, we must first know the SNR at its input.(the propagation of signal and noise though the demodulator is tackled for various modulation schemes later in the course)

The signal power at the input to the demodulator depends on the power level Pr received by the antenna.

The total noise power is comprised of two components being: 1) the noise generated by the receiver circuit. 2) noise received by the antenna.


Calculation of Received Power

If transmitter radiates Pt watts, how much power Pr does the receiver antenna receive?

To answer this, we need to understand how radio antennas work.

Antennas serve both to radiate electromagnetic signals, and also to receive such signals.

A transmitting antenna is sometimes designed to concentrate radiated power in a particular direction.

TransmitterPt

Receiver

Antenna Antenna

Pr

d [m]


Antennas as Radiators

Consider an isotropic radiator (one that radiates in all directions) radiating Pt Watts.

The signal travels as an electromagnetic wave at the speed of light (3E8 m/s).

At a distance d, the power Pt is spread uniformly over the surface area of a sphere of radius d.

Power density at a distance d from the source is watts/m2.P t

4 π d 2

dPt

radiated


Antenna Gain

A physical antenna concentrates power into a directed beam. This effect is modeled by the antenna gain pattern in spherical co-ord’s. Received power density is:

Total received power in watts:

where is the effective captive area of receiver antenna in [m2].

G θ ,φ

Pt

4π d 2⋅G t [W /m2]

Pr=P t

4π d 2⋅G t⋅Aeff

Aeff


Antenna Gain

An isotropic antenna has a gain G = 1 in all directions.

A directional antenna will have G > 1 in some desired direction.

The gain G is the factor by which the power density (in a particular direction) is increased, compared to an isotropic radiator. The gain is sometimes expressed in dB relative to isotropic gain. i.e. 10 log (G/1) dBi. (the subscript “i” is sometimes included to remind us that the gain is defined as relative to an istropic radiator)

A directional aperture-type antenna has a beamwidth and gain determined by the dimensions of the aperture. (e.g. DSTV dish antenna)

Vertically orientated wire antennas like the /2 dipole antenna (G=1.6)

and the /4 monopole antenna (G=3.2) radiate uniformly in the horizontal plain.


Aperture Antennas have Directional Beams

Parabolic Dish Antenna D

For directional beam antennas, the beamwidth depends on the diameter D of the radiating aperture, relative to the wavelength of the radiation. An approximate formula for predicting the beamwidth in radians is:(this formula is useful for /D < 0.5, or beamwidths less than about 30 deg; a more accurate formula is sin(θ/DNote that sin(θθ for small angles) .

e.g. At 10 GHz, =0.03 m.A parabolic dish antenna with D=1m aperture, has beamwidth θ /D = 0.03 rad. = 1.8 deg.

G()

Horn Antenna

D θ≈λ /D rad

θ≈λ /D rad


Gain of a Narrow Conical Beam

The gain of an aperture antenna is related to the beam dimension, which is related to the physical size (area of the aperture).

For a conical beam, the gain (assuming no losses in the antenna) is the ratio of the footprint area to the surface area of a sphere:

G t≈4π d 2

π (d θ / 2)2 =

16

θ2

d

A 1.0 deg beam (0.0175 rad) has a gain of about 16/(0.0175)^2 =52000

For a narrow conical beam of beamwidth θrad,

G t=4π d 2

A fp

A fp≈π (d θ /2)2

A fp

A fp


Gain of a Narrow Rectangular Beam

G t=4π d 2

A fp

≈4π d2

(d θ )(d φ)=

4πθφ

For an ideal “rectangular beam”with a rectangular footprint θ

φ

θ is vertical beamwidth in radiansφ is horizontal beamwidth in radiansAfp is footprint area at distance d (as projected onto the surface of a sphere of radius d)

A fp

A fp≈(dθ )(d φ)

d


Gain of a rectangular radiating aperture

Antenna gain can be related to the area At of the radiating aperture.

Substitute radiating aperture dimensions:

G t≈4πθφ

≈4π

( λ/ D2 )( λ /D1 )=

4π D1 D2

λ2 =4 Aπ t

λ2

G t≈4 Aπ t

λ2

Radiating aperture's area

wavelength

D1

Front view

At

θ

φ

D1

D2

D2


In practice, the effective aperture area is slightly less than the physical aperture area.

Typically Aeff ≈0 .6A physical Aeff =Gλ2

4π

Example: For a 10 GHz dish antenna of diameter 1m calculate:1) physical area: 2) effective area: 3) gain: 4) the approximate beamwidth:

A=π 0 . 5 2=0 .79 m2

Aeff ≈0 . 79×0 .6=0 .48 m2

λ=c/ f =0.03 m

G=4π 0.480.032 ≈7000

θ≈λ /D=0.03 rad=1.7deg


Common Wire Antennas: /2 Dipole

/2 Dipole antenna has a peak gain

The subscript “i” in “dBi” is sometimes used to refer to the fact that the gain is “relative to an isotropic radiator”.

By symmetry, gain is uniform in the horizontal plane (for vertical orientation of the wire antenna)

/2

Dipoleantenna

G=1.64 =2.14 dB or dB i

Cross sectionview G()

3-D view ofradiation patternG(θ).

At 100 MHz, /2=1.5m

G()

Reference: http://en.wikipedia.org/wiki/Dipole_antenna


/4 Monopole Antenna

/4

Monopoleantenna

Ground plane

Freq. /4100 kHz 750 m

1 MHz 75 m

10 MHz 7.5 m

100 MHz 75 cm

1 GHz 7.5 cm

10 GHz 7.5 mm

Monopolelength

G()

G=3 . 28 5. 14 dBi

Max Gain is twice Dipole

Cross section view G()


Coil Antennas

In the Medium Wave band (500 kHz -> 1600 kHz), a resonant monopole wire antenna is too large for portable receivers. A quarter wavelength at 500 kHz is

/4 = (3E8/5E5)/4 = 600/4 = 150 metres.

Medium Wave radios usually use a more compact coil antenna comprising about 100 turns wound on a ferrite core.

The coil is sensitive to the magnetic field component in the electromagnetic wave, and must be orientated correctly such that the radiated magnetic flux lines thread the coil as illustrated.

BChanging magneticflux dψ/dt inducesa voltage across terminals of coil antenna.


Antennas as Receivers

An antenna can function as either a transmitter or a receiver.

All antennas have an effective capture area (for a wave arriving at a particular angle).

For aperture antennas, the effective capture is less than the physical area, typically

From antenna theory, the gain and effective aperture are related by

Aeff ≈0 .6A physical

Aeff =Gλ2

4π

Even wire antennas can have an effective capture area. E.g. at 100 MHz, =3m. A dipole with a gain G=1.6 has an effective area of 1.2m2.


Calculating received power

TransmitterPt Receiver

Antenna Antenna

Pr

Aeff =G r λ2

4π

Pr=Pt

4π d 2⋅G t⋅Aeff

where

Pr=P t

4π d 2⋅G t⋅G r λ2

4π=

P t G t G r

4π d /λ 2

GtGr

d

Received power:

Substitutinggives:


Example: Calculating received power

A TV station radiates a 10 Watt TV signal centred on 500 MHz using a monopole antenna. A home TV receiver located 10 km away receives the signal using a directional Yagi antenna with a gain of 20. Calculate the receiver power in watts.

Aeff =Gr λ2

4π=

20 0 .6 2

4π=0 .57 m2

λ=cf=

3×108

500×106 =0 . 6 m

Pr=P t

4π d 2⋅G t⋅Aeff = 104π100002⋅3 .28⋅0 .57=15×10−9 W

Wavelength

Effectivecapture area

Receivedpower

(NB this calculation ignores attenuation due to rain/fog and signal reduction which may result from destructive interference from multipath reflections)


4.2 Thermal Radiationand

The Microwave Radiometer


Antenna pointing down towards earth

A receiving antenna mounted on a satellite points down to earth.

The antenna “sees” the warm earth, which radiates thermal noise.

The received noise power is

Receiving Antenna

P N=e k T Earth B+(some reflected radiation)

T Earth≈300 K

( = 27 celsius)PN

(maybe e=0.8 is realistic for soil)

WarmEarth

beam

e is the emissivity factor of the surface (0<= e <=1)


Power Spectral Density of the Noise Captured by Antenna

The antenna aiming at a warm, radiating surface captures some of the radiated power.

The voltage signal observed on the terminals of the antenna is a stationary Gaussian random process, that can be characterized by a power spectral density function.

The physical power captured is characterized by

S (ω)=e(ω)k T

2

T is a physical temperature of the radiating surface in kelvin.

e is the emissivity factor of the surface (0<= e <=1))constantsBoltzmann'(1038.1 23k

NOTE : T kelvin=273+T celsius


As long as the footprint falls entirely on the warm body (a,b below), the power received by the antenna is independent of distance to the object.

This may seem odd, because power density from a point source decreases inversely proportional to (distance)2; however in this case, the antenna ‘sees’ more surface area if it is moved further away.The two effects cancel, and the end result is the received power is independent of distance (as long as the beam footprint does not exceed the size of the body as in c below).

a b cPN


Microwave Radiometer

A radiometer is a sensitive instrument for measuring thermal radiation in RF and microwave bands.

Output voltage proportional to input powerwhere ekTB is the power received by antenna from the warm object of temperature T

Kelvin with emissivity factor 0≤e≤1 (a property of the material),

kTeB is the receiver circuit’s equivalent noise referred to the input.

vo

LPF Diode Power Detector

BPF Amp Pin

Antenna

T

0≤e ≤1

Pin=ekTBkT e B

Note: there is also a contribution from noise that is reflected by the surface (not modeled here)



How does it work?

The input signal is translated down in frequency, amplified, filtered and then fed into a power detector.

(you will need to study the concept of heterodyning covered later notes to understand this)

BI F=1GHz 35GHz

B=2BI F= 2GHz

Received PSD S(ω)=kT/2BPF

ω

heterodyne



Two sidebands on either side of the oscillator are mixed down to the bandpass filter.

The power detector converts the bandlimited white noise signal at the output of the BPF to a voltage proportional to the total noise power.

Radiometers are used for:Mapping the Earth form satellites,Mapping the galaxy (astronomers).


4.3 Noise in radio receivers


Noise in receivers

Radio receivers are constructed using passive components (R,L,C) and semiconductors (transistors, diodes).

Resistors and semiconductors generate noise.

Models have been developed to characterize both individual components (e.g. resistor noise and transistor noise), as well as entire modules.

The standard approach to characterizing a module, is to model the noise that it creates as an equivalent additive noise source referred to its input. In reality, this noise is generated within the module, and can be observed at its output.


Amplifier Noise

22 tvo(t)

SR INP POUT

LR

DrivingSource

Resistiveload

vo(t)

Noisy waveform observed at the output created by the amplifier (bandlimited by the bandwidth of the amplifier)


Amplifier noise model

We can draw the following linear system model

Output Noise Power

H (ω)

S i (ω)

S o(ω)=GA(ω)S i(ω)

N o=1

2π ∫−∞

∞

S o(ω )dω=2 S o(ω0)B=2 S i(ω0)G A B

G A(ω)=∣V 0 (ω )∣

2/R

∣V i (ω )∣2/ R

=∣H (ω)∣2

Equivalent noise bandwidth

Power gain

Bandwidth B


Equivalent Noise Temperature Te

The power spectral density referred to the input is usually specified in terms of a parameter known as the “equivalent noise temperature” (Te) of the amplifier (or module). Note: Te is not a physical temperature.

Te is a function of frequency, but can be approximated as a constant over a narrow bandwidth centred on frequency

The noise power spectral density can be obtained from it.

Within a bandwidth B, the equivalent noise at the input to the amplifier is:

The noise power from the output is

N o=1

2π ∫−∞

∞

S o(ω)dω=2 S o(ω0) B=2 S i(ω0)G A B=2n=kT e Bn GA

Equivalent noise bandwidth

GA(ω0)=∣H (ω0)2∣

S i (ω)=k T e(ω)

2

N i=1

2π ∫−∞

∞

S i(ω)dω=2 S i (ω0)B=k T e Bn

ω0


Equivalent Noise Temperature Te

Module

N i=k T e Bn

N o=k T s Bn GA+k T e Bn G AN s=k T s Bn

Power Gain GA

Bandwidth BN

Noise generated by module(referred to its input)

N o=k (T s+T e) Bn G A

Noise from the source


4.4 Sky noise(noise received by an antenna)


Sky Noise

A physical antenna receives noise from the environment.

There are several sources: thermal radiation from earth (if antenna points downwards) plus any radiation

reflected by the surface of the earth towards the antenna. radiation from stars (if antenna points upwards) radiation from lightning atmosphere (i.e. water vapor) radiates

The noise can be described by its power spectral density function, which can be used for noise power calculations.

The sky noise density is described by its “equivalent noise temperature” Tsky. Within a narrow bandwidth B, Tsky is approximately a constant, and the noise power received by an antenna is equal to kTskyB.


Sky Noise

PN=12π

∫−ω0−2 Bπ /2

−ω02 Bπ /2

Sn ω dω12π

∫ω

0−2 Bπ /2

ω02 Bπ /2

Sn ω dω

PN≈12π

2 BπkT sky

2×2=kT sky B

PSD of noise

-ω0 ω0ω

B (Hz)

S n (ω )=kT sky( ω )

2

Sn ω Radio receiver operates with bandwidth of B Hz, centred on ω0

The PSD is related to the sky noise temperature by:

Noise powercaptured byantenna:

T sky is the valueat the centre of the band.


Sky noise

The sky noise contributions from various sources have been measured and are available as plots as a function of frequency.

The designer of a radio link can look up the sky noise temperature at a particular frequency from the graph.

Contributions from uncorrelated sources are added. In some cases, the level of noise is a function of the time of

day (day/night), and also the pointing direction of the antenna. Usually, one would work with the worst case values, when

designing a link.


Sky Noise Temperatures vs frequency

(Reference: F. G. Stremler Introduction to Communications Systems, 2nd Ed.) (from lightning storms)

(from stars)

(in the atmosphere)


Effect of Atmosphere on Sky Noise

A horizontally pointing antenna (see “5 deg elevation” curve on graph) looks through more atmosphere than a vertically pointing antenna (see “90 deg elevation”), as is illustrated below.

Thus the sky noise is higher for the 5 deg case.

5 deg elevation (almost horizontal)

Atmosphere containing watervapour, oxygen etc.

90 deg elevation (vertical)

Earth


Sky Noise

A receiver operates on a centre frequency ω0, and is bandlimited to B Hz.

Obtain Ts k y from graph at ω=ω0

Add contributions from uncorrelated sources.

In some instances, the noise temperature at a particular frequency may vary between a minimum and maximum value (e.g. Galactic noise). In this case it makes sense to assume the worst case, and use the maximum value.

Receiver Amplifier bandwidth B at

centre freq ω0

PN=kT sky BSky noise power receiver within band is:

where k = 1.38×10E-23 Boltzmann’s constant


Example: Using Sky noise graph

At 1 GHz, for an antenna aimed almost horizontally (close to 5 deg elevation),

At 100 MHz (e.g. FM radio), galactic noise dominates:

At 10 MHz, atmospheric noise dominates:

T sky=T galacticT water vapor /O2≈9020=110 K

T sky=T galactic≈20 000 K

T sky=T atmT galactic≈9×1072×106

≈9×107 K


4.5 Line of sight radio communications link. (SNR calculations)


Line-of-sight Radio Link

S x

N x

=Px

12π

∫−∞

∞S Nx ω dω

ModulatorP t

RF

Carrier ωc

Signal P r

S x

N x

S o

N oInputsignal

Outputsignal

How do we calculate the Signal-to-Noise Ratio S/N at point X, at the input to the demodulator?

noise PSD

Signalpower

Noisepower

signal power

Demodulator

X


Refer Quantities to Input

To work out SNR at the input to the demodulator, it is usually easier to refer all quantities to the input of the receiver. i.e. terminals of the receiving antenna.

Additionally, we assume that the receiver chain has an approximately ‘rectangular’ passband of bandwidth B hertz. The receiver power gain is Grec.

If the passband is not perfectly rectangular, then it is assumed that the equivalent noise bandwidth Bn is known for the purposes of noise calculations.


Refer Quantities to Input

S x

N x

=P r G rec

N inpG rec

≈Pr

2 S N0ωc B=

P r

kT sky BkT e B

Noise PSDat receiverinput

Bandwidth(or equivalentnoise bandwidth)

Ouputsignalpower

Outputnoisepower

To work out SNR at the input to the demodulator, it is usually easier to refer all quantities to the input of the receiver. i.e. to the terminals of the receiving antenna.

Receiver gain Gr e c

(amplifier chain)

Receiver power

Receivernoisereferredto input.

Sky noisereceived byantenna.


Typical engineering design questions that arise:What is the SNR for a given Pt ,Gt ,Gr , d and frequency?

What is the maximum range possible to achieve a specified SNR?Given d, Pt and the required SNR, how much antenna gain is required

for Gt and Gr?

Etc.

The above questions can be answered using the formulas derived for line-of-sight radio link. One usually has to solve for a particular parameter of interest.


Example: Satellite Downlink

A geostationary satellite is one that rotates at the same rate as the earth in the equatorial plane, and hence appears stationary in the sky.

Question: Calculate the amount of transmitter power that must be radiated by the

satellite to achieve a SNR of 14dB at a receiver on the earth. (as a ratio, SNR=10( 14 / 10 )=25.1),for the case of a satellite downlink with the following parameters:

f0 = 2 GHz (λ=0.15 m) B = 1 MHz, (receiver bandwidth) Gt= 6 dB (= 4 as Ratio), Gr=40 dB (= 10000 as ratio) Tr e c = 220 K (receiver noise temperature) d = 37750 km (calculated from the geometry.)


Geostationary satellite geometry

h=36000 km

Gt

Gr

d =37750 km

RE≈6400km

N

Satellite

EARTH

Period 24 hours

Geo-stationary satellite is positioned 36000 km above the equator and rotates with same period as the earth being 24 hours. Satellite appears stationary in the sky to an observer on earth – useful for DSTV and other applications.

53◦


Solution

Pr=P t G t Gr

4 dπ / λ 2

N=kT sky BkT rec B=1 .38×10−23 15220 106

=3. 2×10−15 W

SNR=Pr

Nwhere

P t=SNR⋅N 4π d /λ 2

G t Gr

=25.1×3 .2×10−15

×1 .0×1019

4×10000=20 W

Solving for Pt we get:

SNR referred to receiver input:

Noise: (estimate skynoise temp 15K ≈ 6K (atm at 53deg)+8K (galactic)at 2 GHzfrom graph)

SNR=P t G t Gr

N 4 dπ / λ 2


(Reference: F. G. Stremler Introduction to Communications Systems, 2nd Ed.) (from lightning storms)

(from stars)

(in the atmosphere)

T sky=T galacticT water vapor /O2

T galactic≈8 K

T water vapor /O2≈6 K


4.6 Frequency Bands

The following two tables list the band designations commonly used in communications and radar. The names chosen area bit silly!

Engineers and users of the RF & Microwave spectrum use this terminology for describing frequency bands.E.g. a radar engineer would refer to a radar operating at 10 GHzas “an X-band radar”. Terrestrial TV antennas operate in “the VHF and UHF bands”.


Broadcast Frequency Bands

Frequency Designations

ELF Extremely low frequency 30-300 Hz

VF Voice frequency 300-3000 Hz

VLF Very low frequency 3-30 kHz

LF Low frequency 30-300 kHz

MF Medium frequency 300-3000 kHz

HF High frequency 3-30 MHz

VHF Very high frequency 30-300 MHz

UHF Ultra high frequency 300-3000 MHz

SHF Super high frequency 3-30 GHz

EHF Extremely high frequency 30-300 GHz


RADAR Frequency Bands

Band Frequency

HF 3-30 MHz

VHF 30-300 MHz

UHF 300-3000 MHz

L 1-2 GHz

S 2-4 GHz

C 4-8 GHz

X 8-12 GHz

K1 12-18 GHz

K 18-27 GHz

K2 27-40 GHz

V 40-75 GHz

W 75-110 GHz

millimeter 110-300 GHz


4.7 Radio Wave Propagation


Radio Wave Propagation Propagation

In a vacuum, radio waves travel in straight lines. In the atmosphere radio waves can be bent by changes in the refractive index. The refractive index decreases gradually with altitude, causing bending of radio waves

towards the earth, enabling horizontally launched waves to travel beyond the visual horizon.

In addition, layers of charged particles or ‘ions’ (created by ionising radiation from the sun) exist and collectively are called the “ionosphere” (between about 50 km and 420 km). Different layers exist at different heights, and are given special names: D, E, F1 and F2 (see illustration).

Waves radiated by antennas can be classed into two categories:1. Ground (surface) waves that travel below the ionosphere and are affected by currents induced in the earth. (waves over water travel much further than over land)2. Sky waves are launched up at an angle greater than to the horizon. In the absence of atmospheric refraction, these would be lost into space (as is the case for VHF [>30MHz] and higher frequencies).As illustrated in the sketch, sky waves can be refracted down again to enable communication over very long distances (thousands of km around the globe). Multiple hops can occur with the earth and ionosphere forming a “waveguide”.


Refraction in the Ionosphere

Radio waves can travel 10’s or thousands of km around the earth as a result of refraction effects.

Below is shown an illustration of refraction of a ray. Several hops are possible.

E

F2 (night)

Earth

Refraction

Layers of charged particles

Sky wave

72-88 km

320 km

144-190 km

105-120 km

2nd hop

Line of sight

F1 (daytime)

D (daytime)


Multipath Effect on Signal

The total signal received is the sum of that from the direct line of sight, plus reflections from the ground and other objects (walls, trees etc.) called ‘multipath reflections’.

These can add destructively and reduce signal strength or distort the waveform.

Large fluctuations can be observed (>10:1), which should be considered in designing a link.

(reflection coeff is usually negative – causing signal inversion or 180 deg phase shift)

Tx Rx


EEE3086FSignals and Systems II

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