Texas Instruments | Range Measurements in an Open Field Environment (Rev. B) | Application notes | Texas Instruments Range Measurements in an Open Field Environment (Rev. B) Application notes

Texas Instruments Range Measurements in an Open Field Environment (Rev. B) Application notes
Application Report
SWRA169B – January 2008 – Revised June 2018
Range Measurements in an Open Field Environment
Design Note DN018
ABSTRACT
Range is one of the most important parameters of any radio system. Data rate, output power, receiver
sensitivity, antennas, and the intended operation environment all influence the practical range of the radio
link.
1
2
3
4
5
6
Contents
Introduction ...................................................................................................................
Abbreviations .................................................................................................................
Path Loss and Propagation Theory .......................................................................................
3.1
Friis Equation ........................................................................................................
3.2
Link Budget ..........................................................................................................
3.3
Ground Reflection (2-Ray) Model.................................................................................
3.4
Noise .................................................................................................................
Validation Tests ..............................................................................................................
4.1
Friis Equation for Free Space .....................................................................................
4.2
Friis Equation With Ground Reflection ...........................................................................
Summary ......................................................................................................................
References ...................................................................................................................
2
2
2
2
3
3
5
6
6
7
9
9
List of Figures
1
Transmission With Ground ................................................................................................. 3
2
Difference in Transmission Loss Due to Polarization ................................................................... 4
3
Multi-Path Fading ............................................................................................................ 5
4
Measured and Simulated Signal Strengths
5
Gravel Football Pitch in the Town of Finstadbru ......................................................................... 9
..............................................................................
8
Trademarks
SmartRF is a trademark of Texas Instruments.
All other trademarks are the property of their respective owners.
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1
Introduction
1
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Introduction
Range is one of the most important parameters of any radio system. Data rate, output power, receiver
sensitivity, antennas, and the intended operation environment all influence the practical range of the radio
link.
An open field is one of the simplest and most commonly used environments to do RF range tests.
However here there are important effects to consider, and failing to address these often results in the test
results being misinterpreted. This application report addresses non-ideal effects to consider when doing
open field range measurements.
In this application report, the term "open field" means a large open area without any interfering radio
sources (for example, a football field).
2
Abbreviations
EB: Evaluation board (SmartRF™04)
EM: Evaluation module
HW: Hardware (for example, the PCB or components)
LPW: Low-power wireless
PER: Packet error rate
SNR: Signal-to-noise ratio
TI: Texas Instruments
3
Path Loss and Propagation Theory
Communication is achieved through the transmission of signal energy from one location to another. The
received signal energy must be sufficient to distinguish the wanted signal from the always present noise.
This relationship is described as the required signal to noise ratio (S/N). The necessary SNR for a radio
link is sometimes specified in receiver data sheets. More commonly the sensitivity is specified. This is the
absolute signal level (S). When sensitivity is used, one assumes that only thermal noise is present and
that the device is operated at room temperature. This chapter addresses the theory used to determine the
range for radio systems in open and free-space environments.
3.1
Friis Equation
Range in radio communication is generally described by Friis equation (see Equation 1). This equation
describes the dependency between distance, frequency (wavelength), antenna gain, and power.
PR = PT
G T GR l 2
(4 p )2 dn
n=2
where
•
•
•
•
•
•
•
2
PR = Power available from receiving antenna
PT = Power supplied to the transmitting antenna
GR = Gain in receiving antenna
GT = Gain in transmitting antenna
λ = wavelength, where λ = c/f, c = speed of light, f = frequency
d = Distance
c = Speed of light in vacuum 299.972458×106 m/s
Range Measurements in an Open Field Environment
(1)
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Path Loss and Propagation Theory
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3.1.1
Using the Friis Equation
Equation 2 shows an example of using the Friis equation. In free space, the path loss is 80.2 dB over a
100-m distance when operating at 2.445 MHz.
In more typical applications, higher attenuation is expected, because an open field is one of the simplest
environments.
PR = PT
3.2
G T GR l 2
(4 p )2 dn
æ 3 × 10 8
1×1× ç
ç 2445 × 10 6
è
= 1 mW ×
(4 p )2 × 100 2
ö
÷÷
ø
2
= 9.532 × 10 -12 = -80.2 dBm
(2)
Link Budget
The Friis equation is often referred to as the link budget. The difference between the received signal
power, PR, and the sensitivity of the receiver is referred to as the link margin. In a realistic link budget
additional loss has to be added to the losses predicted by Friis equation. This application report addresses
some of these losses in an open field environment. Range is the distance at which the link is operating
with a signal level equal to the receiver sensitivity level. In digital radio systems sensitivity is often defined
as the input signal level where PER exceeds 1%.
3.3
Ground Reflection (2-Ray) Model
In a typical radio link transmission waves are reflected and obstructed by all objects illuminated by the
transmitter antenna. Calculating range in this realistic environment is a complex task requiring huge
computing resources. Many environments include some mobile objects, adding to the complexity of the
problem. Most range measurements are performed in large open spaces without any obstructions, moving
objects, or interfering radio sources. This is primarily done to get consistent measurements. The Friis
equation requires free space to be valid (see Section 3.1). Hand held equipment generally operates close
to ground. This implies that ground influence has to be considered to do valid range calculations.
Figure 1 shows the situation with an infinite, perfectly flat ground plane and no other objects obstructing
the signal. The total received energy can then be modeled as the vector sum of the direct transmitted
wave and one ground reflected wave.
Transmit antenna GT
Direct transmission
Receive antenna GR
H1
H2
Reflected transmission
qi
qr
εr
d
Reflection law: qi = qr
Figure 1. Transmission With Ground
The two waves are added constructively or destructively depending on their phase difference at the
receiver. The magnitude and phase of the direct transmitted wave varies with distance traveled. The
magnitude of the reflected wave depends on total traveled distance and the reflection coefficient (Γ)
relating the wave before and after reflection.
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Path Loss and Propagation Theory
3.3.1
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Reflection Coefficient
Whenever an incident radio signal hits a junction between different dielectric media, a portion of the
energy is reflected, while the remaining energy is passed through the junction. The portion reflected
depend upon signal polarization, incident angle, and the different dielectrics (εr, μr, and σ). Assuming that
both substances have equal permeability μr = 1 and that one dielectric is free space, Equation 3 and
Equation 4 are the Fresnel reflection coefficients for the vertical and horizontal polarized signals,
respectively. [1]
GV =
Gh =
(er – j60 sl )sin qi –
er – j60 sl – cos 2 (qi )
(er – j60 sl )sin qi +
er – j60 sl – cos 2 (qi )
sin qi –
er – j60 sl – cos 2 (qi )
sin qi +
er – j60 sl – cos 2 (qi )
(3)
(4)
The equations require some electrical data for the soil in the test environment. Reference [1] includes a
table that lists εr and σ for some typical soil conditions. εr = 18 and σ = 0 is used for all of the calculations
in this application report.
For systems in which H1 and H2 are low compared to d, Equation 3 and Equation 4 can be simplified to Γv
= Γh = −1. This simplification assumes that with low incident angle all of the energy is reflected. The phase
change of the reflected wave is significant to the transmission budget (see Figure 2).
Friis equation compared to Ground model
H1 = H2 = 1.15 m, er = 18, freq = 2445 MHz
-20
Friis
V
H
-30
Power (dBm)
-40
-50
-60
-70
-80
-90
-100
0
20
40
60
80
100
120
Distance (m)
140
160
180
200
Figure 2. Difference in Transmission Loss Due to Polarization
Figure 2 shows the influence of polarization and ground in open field measurements. The values are
calculated using the Matlab function in Section 4.2. The figure indicates a large difference between the
Friis equation for free space and the expected performance when ground influence is included. Figure 2
also indicates that horizontal polarization (H) is more susceptible to multi-path fading than the vertical
polarized signal (V). At long distances, the signal level including ground is considerably lower than
predicted by the Friis equation. Finally, observe that vertically polarized signals have higher energy at long
distance when compared to horizontally polarized signals.
NOTE: Many applications have strong cross-polarized components, making it difficult to separate
between the polarizations. In this case, the actual signal level is often between the vertical
and horizontal levels calculated as previously shown.
4
Range Measurements in an Open Field Environment
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Figure 3 shows calculated values for a 2445-MHz horizontally polarized signal. The Friis equation for free
space and the 500-kBaud sensitivity level is included in the figure for comparison. To measure the
effective open field range for the CC2500 at this data rate, the typical process would be to start the EB
PER test and then increase the distance between the two radio units.
The figure indicates that communication would be lost at approximately 35 m. Clearly the range potential
is far greater. To identify this unused potential, the two units have to be separated by more than 39 m to
regain communication. The location of this blind spot will vary with frequency, ground electrical
characteristics and antenna elevation. It is however important to be aware of this during measurement to
identify if the test has reached a local blind spot or the final range of the equipment. The difference
between the level predicted by the Friis equation and the receiver sensitivity is often called the fade
margin.
Ground model horizontal polarization
H1 = H2 = 1.15 m, er = 18, freq = 2445 MHz
-20
Friis
H-Polarization
Sensitivity level (CC2500 at 500 kbps)
-30
Power (dBm)
-40
-50
-60
-70
-80
-90
0
50
100
150
Distance (m)
Figure 3. Multi-Path Fading
3.4
Noise
Noise is another important parameter when considering range. Noise can be categorized by its source.
Thermal noise is noise generated by all objects due to its molecular thermal activities. Other radio traffic
may be considered another form of noise. The noise from other electrical equipment is inherently difficult
to describe in mathematical or statistical models. Equation 5 describes thermal noise.
nn =
4hfBR
hf
e kT
»
4kTBR
[Vrms ]
–1
(5)
Temperature, effective noise bandwidth, and impedance determine the total thermal noise. At room
temperature (300K, 27°C) this equation is often approximated by –174 dBm + 10log10(B), describing the
situation with a perfect load match.
3.4.1
Thermal Noise
The CC2500 with 500 kBaud and BW = 812.5 kHz (recommended values) gives a room temperature
noise floor at −174 dBm + 59.1 dBm = −114.9 dBm. The sensitivity is specified to be −83 dBm resulting in
an SNR of 31.9 dB. An SNR of 31.9 dB is more than the demodulator requires, clearly indicating the
potential range extension using an external LNA. (CC2500 has a simulated typical noise figure of
approximately 16 dB).
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Validation Tests
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Thermal noise is not a problem during range measurements. It should however be verified that the area
used is free from other noise sources on the same frequency band. This could be done using a spectrumanalyzer (maximum hold) to look for noise sources before performing the test. This check should
preferably be repeated at regular intervals during the test. Selecting a test area with low probability of
interference is generally recommended. A picture of the test area used in the model validation tests can
be seen in Section 4.2.2.
4
Validation Tests
4.1
Friis Equation for Free Space
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
friis_equation(Gt,Gr,f,n,d);
This function is based on the theory in application report SWRA046
This function calculates the propagation loss.
path_loss_indoor =Gt·Gr·(C/(4·pi·f))^2·(1/d)^n
Gt: Gain in transmitter antenna [dB]
Gr: Gain in receiving antenna [dB]
f: Carrier frequency [Hz]
d: distance in meter [m]
n: path loss exponent (Se table below)
Location
free space
Retail store
Grocery store
Office, hard partitions
Office, soft partitions
Metalworking factory, line of sight
Metalworking factory, obstructed line of sight
Constants:
c = 299.972458e6;
n
2.0
2.2
1.8
3.0
2.6
1.6
3.3
Standard Deviation
8.7
5.7
7.0
14.1
5,8
6.8
Speed of light in vacuum [m/s]
function out=friis_equation(Gt,Gr,f,n,d);
c = 299.972458e6;
% Speed of light in vacuum [m/s]
out = (Gt + Gr + 20*log10(c/(4*pi*f)) − n*10*log10(d));
6
Range Measurements in an Open Field Environment
% Loss in [dB]
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Validation Tests
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4.2
%
%
%
%
%
%
%
%
%
%
Friis Equation With Ground Reflection
friis_equation_with_ground_presence(h1,h2,d,freq,er,pol)
This function calculate the loss of a radio link with ground presence
h1:
Transmitting antenna elevation above ground.
h2:
Receiving antenna elevation above ground.
d:
Distance between the two antennas (projected onto ground plane)
er:
Relative permittivity of ground.
pol: Polarization of signal 'H'=horizontal, 'V'=vertical
freq: Signal frequency in Hz
Transmitting and receiving antenna assumed ideal isotropic G=0dB
**********************************************************************
function retvar=friis_equation_with_ground_presence(h1,h2,d,freq,er,pol)
c=299.972458e6;
Gr=1;
Gt=1;
Pt=1e-3;
lambda=c/freq;
%
%
%
%
Speed of light in vaccum [m/s]
Antenna Gain receiving antenna.
Antenna Gain transmitting antenna.
Energy to the transmitting antenna [Watt]
% m
phi=atan((h1+h2)./d);
% phi incident angle to ground
direct_wave=sqrt(abs(h1-h2)^2+d.^2); % Distance, traveled direct wave
refl_wave=sqrt(d.^2+(h1+h2)^2);
% Distance, traveled reflected wave
if (pol=='H') % horizontal polarization reflection coefficient
gamma=(sin(phi)-sqrt(er-cos(phi).^2))./(sin(phi)+sqrt(er-cos(phi).^2));
else
if (pol=='V')% vertical polarization reflection coefficient
gamma=(er.*sin(phi)-sqrt(er-cos(phi).^2))./(er.*sin(phi)+sqrt(er-cos(phi).^2));
else
error([pol,' is not an valid polarization']);
end %if
end %if
length_diff=refl_wave-direct_wave;
cos_phase_diff=cos(length_diff.*2*pi/lambda).*sign(gamma);
Direct_energy=Pt*Gt*Gr*lambda^2./((4*pi*direct_wave).^2); reflected_energy=Pt*Gt*Gr*lambda^2./
((4*pi*refl_wave).^2).*abs(gamma);
Total_received_energy=Direct_energy+cos_phase_diff.*reflected_energy;
Total_received_energy_dBm=10*log10(Total_received_energy*1e3); retvar=Total_received_energy_dBm;
%end function
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Validation Tests
4.2.1
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Validating the Ground Reflection Model
Figure 4 shows a comparison between the CC2500 operated in a SmartRF04EB and the Matlab ground
reflection model. The measurements have been performed on a football field (se Figure 5). Dots are
measurements and lines represent calculated values.
A fixed correction level has been added to the calculated values to get an overall better match to the
measured values. This correction value represents the difference between the ideal isotropic antenna and
the efficiency of the CC2500EMK Evaluation Module and the SmartRF Studio EB. The plotted values are
the values measured.
The measured signal energy was higher for the horizontal polarized signal. This is explained by the
directivity of a horizontally oriented quarter-wave antenna. When the same antenna is vertically oriented,
the energy is radiated in all directions, reducing its effective gain in the direction of the receiver.
0
-20
Power (dBm)
-40
-60
-80
31 cm
115 cm
-100
7 cm
-120
0
10
20
30
40
50
60
70
80
90
100
Distance (m)
NOTE: Signal strengths with transmitter 7 cm, 31 cm, and 115 cm above ground.
Figure 4. Measured and Simulated Signal Strengths
4.2.2
Open Test Field
A rural environment significantly reduces the probability of 2.4-GHz interference. Figure 5 shows the test
area where the Matlab ground model was validated.
The EB is mounted on a plastic pole to minimize the influence of the mount on the measurement results.
The iron light towers showed no significant influence on measurements; they where sufficiently far away to
allow the direct and ground reflected signals to be the only significant contributors to the total received
power.
The presence of a person had significant influence on the measurement. Measurements at each distance
were made with nobody present.
8
Range Measurements in an Open Field Environment
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Summary
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Figure 5. Gravel Football Pitch in the Town of Finstadbru
5
Summary
This application report addresses the influence of the ground during range measurements.
It has been shown that multi-path fading can generate confusion during measurements if you are unaware
of the phenomenon. Ground presence has also been shown to generate more rapid signal degradation
than predicted by Friis equation for free space. Ground reduces the effective range.
Vertical polarization was shown to be less susceptible to ground reflection fading and range degradation
than horizontal polarization. For hand held equipment polarization is generally not controllable and this
observation has minor importance.
Finally it has been emphasized that other radio traffic influences range measurements and should be
controlled or monitored throughout the measurements. For example, make sure that nearby Bluetooth
transmitters are off during measurement. Coexistence with other equipment is generally not implemented
in test software for range measurements.
6
References
1. Radar Technology Encyclopedia, David K. Barton, Sergey A. Leonov, 1997 Artech House Inc.
Boston/London, ISBN 0-89006-893-3
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Revision History
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Revision History
NOTE: Page numbers for previous revisions may differ from page numbers in the current version.
Changes from April 5, 2008 to June 21, 2018 .................................................................................................................. Page
•
10
Changes to document format and editorial updates throughout document
Revision History
.......................................................
1
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