Summer 2019 CATALYST Research Project – Bits over the Air
Module 4: Spectrum and Spectrogram of Signals
© 2019 Christoph Studer ([email protected]); Version 0.3
The main goal of this module is to learn how to analyze the frequency components of sampled audiosignals in MATLAB. First, you will learn that sampled signals can be represented in the so-called frequencydomain. Second, you will see that one can simultaneously analyze the time-frequency properties ofsignals using a so-called spectrogram. Both of these tools will be useful in designing and understandingwireless communication systems. Remember: Whenever you are stuck, have questions, or are interestedin learning more details about a specific aspect, please feel free to ask us—we are here to help!!
6 Frequency-Domain Representation of Signals
So far, you have learned how to sample signals and how to visualize such signals as a function of time,which is called the time-domain representation of signals. In this module, you will learn that one can useMATLAB to represent signals also in the frequency domain. The frequency-domain representation revealswhich frequencies are present and how strong they are in a given signal. As you will see, communicationsystems transmit information over a given frequency (or a frequency band, which is a set of neighboringfrequencies). We will illustrate this important concept by analyzing the spectrum of a range of audiosignals. The frequency-domain representation is another way of looking at signals, in which they are viewedas a function of frequency (and not of time). In addition to this, you will also learn that it is often useful tovisualize both the time and frequency domains of the same signal; this can be accomplished by visualizingso-called spectrograms that show which frequencies are present in a signal at what time instant. You haveprobably seen such spectrograms before as they are very similar to these well-known “frequency analyzers”in 80s or 90s boomboxes—one of the goals is to understand what they actually show.
6.1 The Spectrum of a Signal
Let us first inspect the spectrum of a very simple signal: a sine function at 440 Hz. Instead of usingMATLAB functions to generate such a sine wave, we can also load one from the examples folder. Use thefollowing command
[y,FS] = load_audio('examples/sine-440Hz.wav');
to load a 5 second 440 Hz sine wave that was sampled at fs = 44, 100 Hz. Now, as in the previous module,plot the time-domain representation of this signal. Simply use
plot_signal(y,FS)
to look at the sample waveform in the time domain—you may have to zoom in to see the actual sine wave.To listen to this waveform, type
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Summer 2019 CATALYST Research Project – Bits over the Air
play_audio(y,FS,OutID);
In case you forgot the output ID of your sound card, re-run the command get_audio_info. For thisspecific signal, we know that it only contains a single frequency at 440 Hz. It is interesting to note thatevery possible signal can be represented as a superposition of one or many sine and cosine waves atdifferent frequencies.
Assume for a moment that you have a continuous signal that is represented as a function f (t) wherethe time t is in the interval from 0 to 1 second. One of the central results in signal processing is that everypossible such function can be represented as an infinite series (or sum) of sine and cosine waves at differentfrequencies:
f (t) =a0
2+
∞
∑n=1
(an cos(2πnt) + bn sin(2πnt)) . (4)
Here, the so-called Fourier coefficients (named after Jean-Baptiste Joseph Fourier, the inventor of thisimportant result) an and bn with n ∈ {0, 1, 2, . . .} characterize which frequency is represented how strong inthe function f (t). If you are not familiar with infinite series or the summation formula ∑, do not worry—itis not important to understand the mathematics behind this (you would learn this anyway in one of thefirst years while studying Electrical and Computer Engineering). If you are interested, feel free to ask ushow the coefficients an and bn can be calculated.
What is more important is to understand the intuition behind all this. Figure 8 provides an example. Onthe left figure, you can see a time-domain signal (think about it as an arbitrary function f (t) for t ∈ [0, 1]).On the right figure, we plot the amplitude of the coefficients an and bn for n = 1, 2, . . . , 8. This figure showswhich frequencies are present and how strong they are. You can see, for example, that at frequency indexn = 2 we have an = bn = 1/3. This means that the frequency with index n = 2 contains both a sine andcosine component which both have an amplitude of 1/3. While the concept of frequency index is a bitabstract (and we will not go into more details here), one can also visualize the frequency componentsdirectly in Hz but then we need to know with which frequency we sampled the signal of interest. Hence,we will do that on our 440 Hz sine waveform that we stored in the variable y.
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Figure 8: Example of a time-domain signal and its frequency spectrum. The frequency spectrum showswhich frequencies are present in a time-domain signal and how strong these frequencies are.
To gain some more intuition, it is interesting to show the same signal as above but by not using alleight frequencies. Figure 9 shows what happens if we sum only one frequency, two frequencies, three
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frequencies, etc. You can see that by superpositioning more and more sinusoids, we can approximate thefunction of interest. Mathematically speaking, we are taking the Fourier series in Equation (4) and do notsum to infinity but rather sum to 1, and then to 2, and then to 3, etc. Since the signal in Figure 8 containedonly 8 different frequencies, we can perfectly approximate this signal with a superposition of 8 sinusoids;this is what is shown in the last figure of Figure 9.
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Figure 9: Adding more and more sinusoids at different frequencies can approximate any function.
While the mathematics behind all this can be quite complicated, we can use MATLAB to do the hardwork for us. Run the following MATLAB command:
plot_spectrum(y,FS);
You should see a new plot that shows the frequency in Hz on the x-axis and the magnitude on the y-axis;this is the frequency-domain representation of the signal stored in the vector y. As expected, only onefrequency is present: 440 Hz. You can zoom in to confirm this fact. Note that all the other frequencies arevery close to zero. This spectrum plot implies that the signal in the frequency domain consists almostexclusively of a single frequency at 440 Hz. Furthermore, you can see that the range of frequencies goesfrom 0 Hz to 22,050 Hz, which is the highest frequency you can represent when sampling a signal atfs = 44, 100 Hz. Remember that such plots show the spectrum of a sampled signal.1
Activity 14: Visualize the spectrum of other signals
The folder examples contains other signals. Plot the spectrum of the wav-file sine-880Hz.wav.Can you see which frequencies are present in that signal? Also try the signal sine-1760Hz.wav.Note that it is always a good idea to listen to the waveform as well, to develop intuition.
Also plot the spectrum of the wav-file noise-white.wav. Then, try noise-pink.wav andnoise-brown.wav. What do you observe? Do these signals all contain the same frequencies?
1In case you are wondering how such plots are generated, the main technique is called the fast Fourier transform (FFT). Thistransform takes in any sampled signal and computes its spectrum. The FFT is probably the most widely used algorithm on thisplanet. Every cell-phone and laptop computes thousands of FFTs per second when transmitting data wirelessly!
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Summer 2019 CATALYST Research Project – Bits over the Air
6.2 The Spectrogram of a Signal
While analyzing the spectrum of signals is interesting and extremely important in the design of wirelesscommunication systems, it has one key limitation. To illustrate this limitation, load the following waveform
[y,FS] = load_audio('examples/chirp-100Hz-to-10000Hz.wav');
and listen to it. This wav-file contains a sinusoid that continuously changes its frequency from 100 Hz to10,000 Hz over time, starting with the low frequency and progressing to higher frequencies over 5 seconds.Such signals are called “chirps” and can be used to measure communication channels (or measure theacoustics of a given room). Now, plot the spectrum of this signal by typing:
plot_spectrum(y,FS);
As you will see, this audio signal contains frequencies from about 100 Hz to 10, 000 Hz as the filenamesuggests. While the spectrum shows that these frequencies are present during the 5 second duration ofthe signal, it does not show that the frequencies actually change over time. Put simply, the spectrum tellsyou which frequencies are present but does not tell you anything about its evolution over time. Hence, itwould be great to have a tool that visualizes both frequency and time—the spectrogram does exactly this!
Figure 10: Example spectrogram of a 5 second chirp signal that sweeps a single sine wave from 100 Hz to10, 000 Hz. Spectrograms show what frequency components are present at what time instant.
Let us first look at a spectrogram before we explain how they are generated. In MATLAB, simplyexecute the following command (which was provided in the zip-file you downloaded)
plot_spectrogram(y,FS);
to plot the spectrogram of the chirp signal that is stored in the variable y. You should see a figure that lookslike the one in Figure 10. The x-axis shows the time in seconds; the y-axis shows the frequency componentsranging from 0 Hz to fs/2 Hz. The colors encode the power (or intensity) measured in something thatis called decibels (dB, for short). (You can ask one of us if you are interested in learning more about
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decibels, but basically it refers to the signal’s magnitudes measured on a logarithmic scale.) Brighter colorsindicate that certain frequencies are more strongly represented; darker colors imply certain frequencies areabsent; think of these as the magnitudes of the the Fourier coefficients an and bn. As you can see, there isa single frequency that starts at around 100 Hz and linearly increases towards 10, 000 Hz. In words, thespectrogram shows at what time which frequencies are contained in the signal.
Figure 11 illustrates the principle of spectrogram computation. The left side shows that one takesthe entire sampled signal and divides it into smaller blocks. For each smaller block, one computes thespectrum (this is called a short-time spectrum). One then generates a two-dimensional figure (as inFigure 10) where the columns correspond to a spectrum per block. The right side shows a typical spectrumanalyzer computer plug-in. These plug-ins (inspired by 80s and 90s boomboxes) simply visualize thefrequency spectrum for a small set of frequencies for separate blocks of the audio signal. Most of the time,the visualization is in sync with the audio signal, which allows one to see which frequencies are present atwhat time. The spectrogram as in Figure 10 is a static version of exactly the same idea.
(a) Principle of spectrogram calculation. (b) Typical spectrum analyzer.
Figure 11: Basics of spectrogram calculation. The signal is divided into small blocks for which the spectrumis calculated. Spectrum analyzer plug-ins (frequency equalizers) visualize the spectrogram over time.
Activity 15: Visualize the spectrogram of other signals
The folder examples contains a wide range of signals, including music and test sounds. Plot thespectrogram of these files and see whether you can observe in the spectrogram what you hear.
Activity 16: What is the highest frequency you can hear?
Visualize the spectrogram of the signal in the file chirp-100Hz-to-22050Hz.wav, which containsa chirp that goes to very high frequencies. Can you hear all frequencies up to 22, 050 Hz? Atwhat frequency can you not hear the signal anymore? Design an experiment to identify thefrequency that you cannot hear anymore. To this end, synthetically generate different sinewaves at different frequencies and play them back—you have learned in previous modules howto do that! At one point you should not be able to hear them anymore... What is that frequency?Important: Please be very cautious when playing test signals at high frequencies. Do not turnup the volume if you cannot hear a signal anymore! Note that even if you cannot hear signalsat high frequencies, they are still present and reaching your ears. Also, maybe some otherpeople in the room can hear them—also, dogs can hear them (that is how dog-whistles work).
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Summer 2019 CATALYST Research Project – Bits over the Air
6.3 Why is the Spectrum of a Signal Important?
The concept of frequencies and spectrum is central in the design of wireless communication systems.Different communication systems typically operate at different frequencies. For example, FM (shortfor frequency-modulation) radio uses frequencies in the electromagnetic spectrum from about 88 MHz(mega-Hertz, which stands for 1, 000, 000 Hz) to 108 MHz. Wireless LAN (also known as Wi-Fi or WLan)typically operates at frequencies of about 2.4 GHz (giga-Hertz, which stands for 1, 000, 000, 000 Hz) or evenhigher (e.g., 5 GHz). Many other communications standards for consumer electronics, such as Bluethooth(which are used for wireless headphones), also operate at around 2.4 GHz. All these communicationsystems (and many other systems used for television, emergency radio, defense, satellite communication,astronomy, weather radar, etc.) are operating simultaneously and they are occupying different frequencies.The are sharing the frequency spectrum.
THIS CHART WAS CREATED BY DELMON C. MORRISONJUNE 1, 2011
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AMAT
EUR
SATE
LLIT
EAM
ATEU
R
LAN
D M
OBIL
E
FIX
ED
F
IXE
D M
OBIL
E
F
IXE
D
AMAT
EUR
MOB
ILE
exce
pt a
eron
autic
al m
obile
(R)
AMAT
EUR
F
IXE
DBROA
DCAS
TING
MAR
ITIM
E M
OBIL
E
MOBILEexcept aeronautical
mobile
300
325
335
405
415
435
495
505
510
525
535
1605
16
15
1705
18
00
1900
20
00
2065
21
07
2170
21
73.5
2190
.5 21
94
2495
25
05
2850
30
00
30 MHz 300 MHz
FIXE
DM
OBIL
E
LAND
MOB
ILE
MOB
ILE
MOB
ILE
MOB
ILE
LAND
MOB
ILE
LAND
MOB
ILE
FIXE
D
FIXE
D
FIXE
D
FIXE
D
FIXE
D
FIXE
D
LAND
MOB
ILE LA
ND M
OBIL
ERa
dio a
stron
omy
FIXE
DM
OBIL
EFI
XED
MOB
ILE
LAND
MOB
ILE
MOB
ILE
FIXE
D
FIXE
DLA
ND M
OBIL
E
LAND
MOB
ILE
FIXE
DM
OBIL
E
LAND
MOB
ILE
FIXE
DM
OBIL
E
AMATEUR BROADCASTING(TELEVISION )
FIXE
DM
OBIL
E
RADIO
ASTRO
NOMY M
OBIL
EFI
XED
AERO
NAUT
ICAL
RAD
IONA
VIGA
TION
MOB
ILE
MOB
ILE
FIXE
DFI
XED
BROADCASTING(TELEVISION)
BROADCASTING(FM RADIO)
AERONAUTICALRADIONAVIGATION
AERO
NAUT
ICAL
MOB
ILE
(R)
AERO
NAUT
ICAL
MOB
ILE
(R)
AERON
AUTIC
AL MO
BILE
AERON
AUTIC
AL MO
BILE
AERON
AUTIC
AL MO
BILE (R
)AER
ONAU
TICAL
MOBIL
E (R)
MOBIL
E-SAT
ELLIT
E(sp
ace-t
o-Eart
h)
MOBIL
E-SAT
ELLIT
E(sp
ace-t
o-Eart
h)
Mobile
-satel
lite(sp
ace-t
o-Eart
h)
Mobile
-satel
lite(sp
ace-t
o-Eart
h)
SPAC
E RES
EARC
H(sp
ace-t
o-Eart
h)SP
ACE R
ESEA
RCH
(spac
e-to-E
arth)
SPAC
E RES
EARC
H(sp
ace-t
o-Eart
h)SP
ACE R
ESEA
RCH
(spac
e-to-E
arth)
SPAC
E OPE
RATIO
N(sp
ace-t
o-Eart
h)SP
ACE O
PERA
TION
(spac
e-to-E
arth)
SPAC
E OPE
RATIO
N(sp
ace-t
o-Eart
h)SP
ACE O
PERA
TION
(spac
e-to-E
arth)
MET.
SATE
LLITE
(spac
e-to-E
arth)
MET.
SATE
LLITE
(spac
e-to-E
arth)
MET.
SATE
LLITE
(spac
e-to-E
arth)
MET.
SATE
LLITE
(spac
e-to-E
arth)
FIXE
DM
OBIL
EAM
ATEU
R- S
ATEL
LITE
AMAT
EUR
AMAT
EUR
FIXE
DM
OBIL
E
MOBIL
E-SAT
ELLIT
E(Ea
rth-to
-spac
e)
FIXE
DM
OBIL
EFI
XED
LAND
MOB
ILE
FIXE
D LA
ND M
OBILE
RA
DIO
NAV
IGAT
ION
-S
ATE
LLIT
E
MAR
ITIME
MOB
ILE
MAR
ITIME
MOB
ILE M
ARITI
ME M
OBILE
MOB
ILE
exce
pt a
eron
autic
al m
obile
FIXE
D LA
ND M
OBILE
MAR
ITIME
MOB
ILE
MOB
ILE
exce
pt a
eron
autic
al m
obile
MAR
ITIME
MOB
ILE (A
IS)
MOB
ILE
exce
pt a
eron
autic
al m
obile
FIXE
D
FIXE
DLa
nd m
obile
FIXE
DM
OBIL
E FIXE
DM
OBIL
E ex
cept
ae
rona
utica
l mob
ile
Mob
ileFI
XED
MOB
ILE
exce
pt a
eron
autic
al m
obile
FIXED
MOBILE
LAND
MOB
ILE
MAR
ITIM
E M
OBIL
E (d
istre
ss, u
rgen
cy, s
afet
y and
callin
g)
MAR
ITIME
MOB
ILE (A
IS)
MOB
ILE
exc
ept a
eron
autic
al m
obile
FIXE
D
Amate
ur
AERO
NAUT
ICAL
MOB
ILE
(R)
MOBIL
E-SAT
ELLIT
E(Ea
rth-to
-spac
e)
BROADCASTING(TELEVISION)
FIXE
DAM
ATEU
R
Land m
obile
Fixe
d
30.0
30.56
32
.0 33
.0 34
.0 35
.0 36
.0 37
.0 37
.5 38
.0 38
.25
39.0
40.0
42.0
43.69
46
.6 47
.0 49
.6 50
.0 54
.0 72
.0 73
.0 74
.6 74
.8 75
.2 75
.4 76
.0 88
.0 10
8.0
117.9
75
121.9
375
123.0
875
123.5
875
128.8
125
132.0
125
136.0
13
7.0
137.0
25
137.1
75
137.8
25
138.0
14
4.0
146.0
14
8.0
149.9
15
0.05
150.8
15
2.855
15
4.0
156.2
475
156.7
625
156.8
375
157.0
375
157.1
875
157.4
5 16
1.575
16
1.625
16
1.775
16
1.962
5 16
1.987
5 16
2.012
5 16
3.037
5 17
3.2
173.4
17
4.0
216.0
21
7.0
219.0
22
0.0
222.0
22
5.0
300.0
FIXE
D
Fixe
dLan
d mobil
e
LAND
MOB
ILE
LAND
MOB
ILE
300.0
32
8.6
335.4
39
9.9
400.0
5 40
0.15
401.0
40
2.0
403.0
40
6.0
406.1
41
0.0
420.0
45
0.0
454.0
45
5.0
456.0
46
0.0
462.5
375
462.7
375
467.5
375
467.7
375
470.0
51
2.0
608.0
61
4.0
698.0
76
3.0
775.0
79
3.0
805.0
80
6.0
809.0
84
9.0
851.0
85
4.0
894.0
89
6.0
901.0
90
2.0
928.0
92
9.0
930.0
93
1.0
932.0
93
5.0
940.0
94
1.0
944.0
96
0.0
1164
.0 12
15.0
1240
.0 13
00.0
1350
.0 13
90.0
1392
.0 13
95.0
1400
.0 14
27.0
1429
.5 14
30.0
1432
.0 14
35.0
1525
.0 15
59.0
1610
.0 16
10.6
1613
.8 16
26.5
1660
.0 16
60.5
1668
.4 16
70.0
1675
.0 16
95.0
1710
.0 17
61.0
1780
.0 18
50.0
2000
.0 20
20.0
2025
.0 21
10.0
2180
.0 22
00.0
2290
.0 23
00.0
2305
.0 23
10.0
2320
.0 23
45.0
2360
.0 23
90.0
2395
.0 24
17.0
2450
.0 24
83.5
2495
.0 25
00.0
2655
.0 26
90.0
2700
.0 29
00.0
3000
.0
300 MHz
AERO
NAUT
ICAL
RAD
IONA
VIGA
TION
FIXE
DM
OBIL
E
RAD
IONA
VIGA
TION
SATE
LLITE
MOBI
LE S
ATEL
LITE
(Eart
h-to-s
pace
)
STAN
DARD
FRE
QUEC
Y AN
D TI
ME S
IGNA
L - S
ATEL
LITE
(400
.1 MH
z)ME
T. AIDS
(Radio
sonde
)MO
BILE
SAT
(S-E)
SPAC
E RES
.(S-
E)Sp
ace Op
n. (S
-E)ME
T. SAT
.(S-
E)
MET. A
IDS(Ra
dioson
de)
SPAC
E OPN
. (S
-E)ME
T-SAT
. (E
-S)EA
RTH
EXPL
SAT. (
E-S)
Earth
Expl S
at(E-
S)
Earth
Expl S
at(E-
S)EA
RTH
EXPL
SA
T. (E-S
)ME
T-SAT
. (E
-S)ME
T. AIDS
(Radio
sonde
)
Met-S
atellite
(E-S)
Met-S
atellite
(E-S)
MET
EORO
LOGI
CAL A
IDS
(RAD
IOSO
NDE)
MOB
ILE
SATE
LLIT
E (E
arth
-to-s
pace
)RA
DIO
ASTR
ONOM
YFI
XED
MOB
ILE
FIXE
DM
OBIL
ESP
ACE
RES
EARC
H (s
pace
-to-sp
ace)
RADI
OLOC
ATIO
NAm
ateu
r
LAND
MOB
ILE
FIXE
DLA
ND M
OBIL
ELA
ND M
OBIL
EFI
XED
LAND
MOB
ILE
MeteorologicalSatellite
(space-to-Earth)
LAND
MOB
ILEFI
XED
LAND
MOB
ILE
FIXE
D LA
ND M
OBILE
LAND
MOB
ILE
LAND
MOB
ILEFI
XED
BROADCASTING(TELEVISION)
FIXEDBROADCASTING
(TELEVISION)
LAN
D M
OB
ILE
(med
ical
tele
met
ry a
ndm
edic
al te
leco
mm
and)
RADI
O AS
TRON
OMY
BROADCASTING(TELEVISION)
BRO
ADCA
STIN
G(T
ELEV
ISIO
N)M
OBIL
E
FIXE
DM
OBIL
E
FIXE
DM
OBIL
E
FIXE
DM
OBIL
E
FIXE
DM
OBIL
E
LAND
MOB
ILE
FIXE
DLA
ND M
OBIL
EAE
RONA
UTIC
AL M
OBILE
LA
ND M
OBIL
E
AERO
NAUT
ICAL
MOB
ILE
FIXE
DLA
ND M
OBIL
E
FIXE
DLA
ND M
OBIL
EFI
XED
MOB
ILE
RADI
OLOC
ATIO
N
FIXE
DFI
XED
LAND
MOB
ILE
FIXE
DM
OBIL
EFI
XED
LAND
MOB
ILE
FIXE
DFI
XED
LAND
MOB
ILE
FIXE
DM
OBIL
EFI
XED
FIXE
D AERONAUTICALRADIONAVIGATION
RADI
ONAV
IGAT
ION-
SATE
LLIT
E(s
pace
-to-E
arth
)(spa
ce-to
-spa
ce)
EARTHEXPLORATION-
SATELLITE(active)
RADIO-LOCATION
RADI
ONAV
IGAT
ION-
SATE
LLIT
E(s
pace
-to-E
arth
)(s
pace
-to-s
pace
)
SPACERESEARCH
(active)
Space research(active)
Earthexploration-
satellite (active)
RADIO-LOCATION
SPACERESEARCH
(active)
AERONAUTICALRADIO -
NAVIGATION
Amateur
AERO
NAUT
ICAL
RAD
IONA
VIGA
TION
FIXE
DM
OBIL
E RA
DIOL
OCAT
ION
FIXE
DM
OBIL
E **
Fixe
d-sa
tellit
e (E
arth
-to-s
pace
)
FIXE
DM
OBIL
E **
LAND
MOB
ILE
(med
ical te
lemet
ry a
nd m
edica
l telec
omm
and)
SPAC
E RES
EARC
H(pa
ssive)
RADI
O AS
TRON
OMY
EART
H EXP
LORA
TION -
SATE
LLITE
(passi
ve)
LAND
MOB
ILE
(telem
etry
and
telec
omm
and)
LAND
MOB
ILE
(med
ical te
lemet
ry a
nd
med
ical te
lecom
man
d
Fixe
d-sa
tellit
e(s
pace
-to-E
arth
)FI
XED
(telem
etry
and
telec
omm
and)
LAND
MOB
ILE
(telem
etry
& te
lecom
man
d)
FIXE
DM
OBIL
E **
MOB
ILE
(aer
onau
tical
telem
etry
)
MOBIL
E SAT
ELLIT
E (sp
ace-t
o-Eart
h)
AERO
NAUT
ICAL
RADI
ONAV
IGAT
ION-
SATE
LLIT
E(s
pace
-to-E
arth
)(spa
ce-to
-spa
ce)
MOBIL
E SAT
ELLIT
E(E
arth-t
o-spa
ce)
RADI
ODET
ERMI
NATIO
N-SA
TELL
ITE (E
arth-t
o-spa
ce)
MOBIL
E SAT
ELLIT
E(E
arth-t
o-spa
ce)
RADI
ODET
ERMI
NATIO
N-SA
TELL
ITE (E
arth-t
o-spa
ce)
RADI
O AS
TRON
OMY
MOBIL
E SAT
ELLIT
E(E
arth-t
o-spa
ce)
RADI
ODET
ERMI
NATIO
N-SA
TELL
ITE (E
arth-t
o-spa
ce)
Mobil
e-sate
llite(sp
ace-t
o-Eart
h) MOBIL
E SAT
ELLIT
E(Ea
rth-to
-spac
e)
MOBIL
E SAT
ELLIT
E(E
arth-t
o-spa
ce)
RADI
O AS
TRON
OMY
RADI
O AS
TRON
OMY
FIXE
DM
OBIL
E **
METE
OROL
OGIC
AL AI
DS(ra
dioso
nde)
MET
EORO
LOGI
CAL
SATE
LLIT
E (s
pace
-to-E
arth
)
MET
EORO
LOGI
CAL
SATE
LLIT
E (s
pace
-to-E
arth
)
FIXE
D
MOB
ILE
FIXE
DM
OBIL
E SP
ACE
OPER
ATIO
N (E
arth
-to-s
pace
)
FIXE
DM
OBIL
E
MOBIL
E SAT
ELLIT
E (Ea
rth-to
-spac
e)FI
XED
MOB
ILE
SPAC
E RES
EARC
H (pa
ssive)
RADI
O AS
TRON
OMY
METE
OROL
OGIC
AL AI
DS(ra
dioso
nde)
SPACERESEARCH
(Earth-to-space)(space-to-space)
EARTHEXPLORATION-
SATELLITE(Earth-to-space)(space-to-space)
FIXED
MOBILE
SPAC
E OPE
RATIO
N(E
arth-t
o-spa
ce)
(spac
e-to-s
pace
)
MOB
ILE
FIXE
D
SPACERESEARCH
(space-to-Earth)(space-to-space)
EARTHEXPLORATION-
SATELLITE(space-to-Earth)(space-to-space)
SPACEOPERATION
(space-to-Earth)(space-to-space)
MOBILE(ling of sight only
including aeronauticaltelemetry, but excludingflight testing of manned
aircraft)
FIXED (line of sight only)
FIXE
DSP
ACE R
ESEA
RCH
(spac
e-to-E
arth)
(deep
spac
e)M
OBIL
E**
Amat
eur
FIXE
DM
OBIL
E**
Amat
eur
RADI
OLOC
ATIO
N
RADI
OLOC
ATIO
NM
OBIL
EFI
XED
Radio
-loc
ation
Mob
ileFi
xed
BROA
DCAS
TING
- SA
TELL
ITE
Fixe
dRa
dioloc
ation
Fixe
dM
obile
Radio
-loc
ation
BROA
DCAS
TING
SATE
LLIT
EFI
XED
MOB
ILE
RADI
OLOC
ATIO
N
RADI
OLOC
ATI
ON
MOB
ILE
MOB
ILE
AMAT
EUR
AMAT
EUR
Radio
locat
ionM
OBIL
EFI
XED
Fixe
d
Amat
eur
Radio
locat
ionMO
BILE S
ATEL
LITE
(spac
e-to-E
arth)
RADI
ODET
ERMI
NATIO
N-SA
TELL
ITE (s
pace
-to-E
arth)
MOBIL
E SAT
ELLIT
E(sp
ace-t
o-Eart
h)RA
DIOD
ETER
MINA
TION-
SATE
LLITE
(spa
ce-to
-Eart
h)FI
XED
MOB
ILE*
*
MOB
ILE*
*FI
XED
Earth exploration-satellite
(passive)
Space research(passive)
Radioastronomy
MOBILE**
FIXEDEARTH
EXPLORATION-SATELLITE
(passive)
RADIOASTRONOMY
SPAC
E RES
EARC
H(pa
ssive
)
AERO
NAUT
ICAL
RADI
ONAV
IGAT
ION
MET
EORO
LOGI
CAL
AIDS
Ra
dioloc
ation
Radiolocation
RADIOLOCATION
MARITIMERADIO-
NAVIGATION
MOB
ILE
FIXE
D
BROA
DCAS
TING
BROA
DCAS
TING
Radio
locati
on
Fixe
d(te
lemet
ry)
FIXE
D (te
lemet
ry a
ndte
lecom
man
d)LA
ND M
OBIL
E (t
elem
etry
& te
lecom
man
d)
AERO
NAUT
ICAL
RADI
ONAV
IGAT
ION
AERO
NAUT
ICAL
RADI
ONAV
IGAT
ION
AERO
NAUT
ICAL
RADI
ONAV
IGAT
ION
AERO
NAUT
ICAL
RADI
ONAV
IGAT
ION
AERO
NAUT
ICAL
RADI
ONAV
IGAT
ION
Space research(active)
Earthexploration-
satellite (active)
EARTHEXPLORATION-
SATELLITE(active)
Fixe
d
FIXE
D FIXE
DM
OBIL
E
ISM – 24.125 ± 0.125 ISM – 5.8 ± .075 GHz3GHz
Radio
locat
ionAm
ateu
r
AERO
NAUT
ICAL
RADI
ONAV
IGAT
ION
(grou
nd ba
sed)
RADI
OLOC
ATIO
NRa
dioloc
ation
FIXED
-SAT
ELLIT
E (s
pace
-to-E
arth)
Radio
locati
on
FIXED
AERO
NAUT
ICAL
RAD
IONA
VIGA
TION M
OBIL
E
FIXE
DM
OBIL
E
RADI
O AS
TRON
OMY
Spac
e Res
earch
(pas
sive)
RADI
OLOC
ATIO
N
RADI
OLOC
ATIO
N
RADI
OLOC
ATIO
NMETE
OROL
OGIC
AL
AIDS
Amat
eur
FIXED SP
ACE
RESE
ARCH
(dee
p spa
ce)(E
arth-
to-sp
ace)
Fixed
FIXED
-SAT
ELLIT
E (sp
ace-t
o-Eart
h)
AERO
NAUT
ICAL
RAD
IONA
VIGA
TION
RADI
OLOC
ATIO
NRa
dioloc
ation
MAR
ITIM
E RA
DION
AVIG
ATIO
N
RADI
ONAV
IGAT
ION
Amat
eur
FIXE
D
RADI
O AS
TRON
OMY
BROA
DCAS
TING
-SAT
ELLI
TE
Fixed
Mobil
e Fixed
Mobil
eFI
XED
MOBI
LE
SPAC
E RE
SEAR
CH(pa
ssive
)RA
DIO
ASTR
ONOM
YEA
RTH
EXPL
ORAT
ION
-SA
TELL
ITE (p
assiv
e)
FIXE
D
FIXE
DMO
BILE
FIXED
-SAT
ELLIT
E (s
pace
-to-E
arth)
FIXED
MOBILE MOBI
LE
AERO
NAUT
ICAL
RAD
IONA
VIGA
TION
Standard frequencyand time signal
satellite(Earth-to-space)
FIXED
FIXE
DM
OBIL
E** FIXE
DM
OBIL
E**
FIXE
D SA
TELL
ITE
(Ear
th-to-
spac
e)
Amat
eur
MOBI
LE
BROA
DCAS
TING
-SAT
ELLIT
E
FIXE
D-SA
TELL
ITE
(spac
e-to-
Earth
)
MOBI
LE
FIXE
DMO
BILE
INTE
R-SA
TELL
ITE
AMAT
EUR
AMAT
EUR-
SATE
LLIT
E
Radio
-loc
ation
Amat
eur
RADI
O-LO
CATI
ON
FIXE
DIN
TER-
SATE
LLITE
RADI
ONAV
IGAT
ION
RADIO
LOCA
TION-S
ATEL
LITE (
Earth
-to-sp
ace)
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
MOBI
LE-S
ATEL
LITE
(Ear
th-to-
spac
e)MOBILE
INTE
R-SA
TELL
ITE
30 GHz
Earthexploration-
satellite(active)
Space resea
rch(activ
e)RA
DIOL
OCAT
ION
RADI
OLOC
ATIO
NAE
RONA
UTIC
ALRA
DION
AVIG
ATIO
N(gr
ound
base
d)
FIXED-SATELLITE(space-to-Earth)
FIXE
D
RADI
ONAV
IGAT
ION-
SATE
LLITE
(Eart
h-to-s
pace
)AE
RONA
UTIC
AL R
ADIO
NAVI
GATI
ON
AERO
NAUT
ICAL
RAD
IONA
VIGA
TION
RADI
ONAV
IGAT
ION-
SATE
LLITE
(sp
ace-t
o-Eart
h)(sp
ace-t
o-spa
ce)
AERO
NAUT
ICAL
RADI
ONAV
IGAT
ION
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
Earthexploration-
satellite (active)
Space research
Radiolocation
EARTHEXPLORATION-
SATELLITE(active)
SPACE RESEARCH(active)
RADI
OLOC
ATIO
N
Earthexploration-
satellite (active)
Radiolocation
Space research(active)
EARTHEXPLORATION-
SATELLITE(active)
SPACE RESEARCH(active)
RADI
OLOC
ATIO
N
Radiolocation
Space research(active)
EARTHEXPLORATION-
SATELLITE(active)
SPACE RESEARCH(active)
RADIOLOCATION
AERONAUTICAL
RADIONAVIGATION
Earthexploration-
satellite (active)
RadiolocationSpace research
(active)
EARTHEXPLORATION-
SATELLITE(active)
SPACE RESEARCH(active)
RADIOLOCATION
RADIONAVIGATION
Earthexploration-
satellite (active)
Space research(active)
EARTHEXPLORATION-
SATELLITE(active)
SPACE RESEARCH(active)
MARI
TIME
RADI
ONAV
IGAT
ION
RADI
OLOC
ATIO
N
MARI
TIME
RAD
IONA
VIGA
TION
RADI
OLOC
ATIO
NMA
RITI
ME
RA
DION
AVIG
ATIO
N
Amat
eur
RADI
OLOC
ATIO
N
MOBI
LEFI
XED-
SATE
LLIT
E (E
arth-
to-sp
ace)
FIXED
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)FIX
EDFI
XED-
SATE
LLIT
E (E
arth-
to-sp
ace)
(spac
e-to-
Earth
)
FIXED
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)(sp
ace-
to-Ea
rth)
MOBI
LE
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)MO
BILE
FIXED
MOBI
LEFIX
EDFIX
EDFIX
EDSP
ACE
RESE
ARCH
(Ear
th-to-
spac
e)
FIXED
MOBI
LE-S
ATEL
LITE
(spac
e-to-E
arth) FI
XED
Mobil
e-sate
llite (
spac
e-to-E
arth)
FIXED
-SAT
ELLIT
E (sp
ace-t
o-Eart
h)
FIXE
DMo
bile-s
atellit
e (sp
ace-t
o-Eart
h)ME
TEOR
OLOG
ICAL
SAT
ELLIT
E (sp
ace-t
o-Eart
h)FIX
ED-S
ATEL
LITE (
spac
e-to-E
arth)
FIXE
DMo
bile-s
atellit
e (sp
ace-t
o-Eart
h)FIX
ED-S
ATEL
LITE (
spac
e-to-E
arth)
FIXED
-SAT
ELLIT
E (Ea
rth-to
-spac
e)MO
BILE
-SAT
ELLIT
E (E
arth-t
o-spa
ce)
Fixed
FIXE
DMo
bile-s
atellit
e(E
arth-t
o-spa
ce)
(no ai
rborne
)
FIXED
SATE
LLITE
(Eart
h-to-s
pace
)EA
RTH
EXPL
ORAT
ION-
SATE
LLITE
(spa
ce-to
-Eart
h)Mo
bile-s
atellit
e(E
arth-t
o-spa
ce)
(no ai
rborne
)FI
XED
EART
H EX
PLOR
ATIO
N-
SATE
LLITE
(spac
e-to-E
arth)
FIXED
-SAT
ELLIT
E (E
arth-t
o-spa
ce)
METE
OROL
OGIC
AL-
SAT
ELLIT
E (s
pace
-to-E
arth)
FIXE
DMo
bile-s
atellit
e(E
arth-t
o-spa
ce)
(no ai
rborne
)
FIXED
-SAT
ELLIT
E (E
arth-t
o-spa
ce)
EART
H EX
PLOR
ATIO
N-SA
TELL
ITE (s
pace
-to-E
arth)
Spac
e res
earch
(dee
p spa
ce)(s
pace
-to-E
arth)
SPAC
E RE
SEAR
CH (d
eep s
pace
)(spa
ce-to
-Ear
th)FI
XED
SPAC
E RE
SEAR
CH (s
pace
-to-E
arth)
FIXE
D Earthexploration -
satellite (active)
Radio-location
Space research (active)
EARTHEXPLORATION-
SATELLITE (active)
RADIO-
LOCATION
SPACERESEARCH
(active)
Radio
locat
ionRA
DIOL
OCAT
ION
Radio
locat
ionRa
dioloc
ation
Radio
locat
ionMe
teoro
logica
l Aids
Earthexploration -
satellite (active)
Radio-location
Space research (active)
EARTHEXPLORATION
SATELLITE (active)
RADIO-
LOCATION
SPACERESEARCH
(active)
Radio
locat
ionRa
dioloc
ation
Amat
eur-s
atell
iteAm
ateu
rRa
dioloc
ation
RADI
OLOC
ATIO
N
RADI
OLOC
ATIO
N
FIXE
DEA
RTH
EXPL
ORAT
ION-
SATE
LLITE
(pas
sive)
SPAC
E RE
SEAR
CH (p
assiv
e)
EART
H EX
PLOR
ATIO
N-SA
TELL
ITE (p
assiv
e)SP
ACE
RESE
ARCH
(pas
sive) FIX
ED-S
ATEL
LITE (
spac
e-to-E
arth)
FIXE
D FIXED
-SAT
ELLIT
E (sp
ace-t
o-Eart
h)
FIXE
D FIXE
DFI
XED-
SATE
LLIT
E (E
arth-
to-sp
ace)
Space research (active)
EARTHEXPLORATION -
SATELLITE (active)
SPACERESEARCH
(active)
Aerona
tuical
Radiona
vigation
EARTHEXPLORATION
SATELLITE (active)
RADIO -LOCATION
SPACE
RESEARCH
Radio-location
Space research
RADIO - LOCATION
Space research
FIXED-SATELLITE
(Earth-to-space)
Space research
Radio - location
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)Mo
bile-s
atellit
e (Ea
rth-to
-spac
e)Sp
ace
rese
arch
Mobil
e-sate
llite (
spac
e-to-E
arth)
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
Mobil
e-sate
llite
(Eart
h-to-s
pace
) Spac
e res
earch
MOBI
LESP
ACE
RESE
ARCH
Fixed
FIXE
DSP
ACE
RESE
ARCH
Mobil
e
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)AE
RONA
UTIC
AL
RADI
ONAV
IGAT
ION
AERO
NAUT
ICAL
RAD
IONA
VIGA
TION
RADI
OLOC
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NSp
ace r
esea
rch (d
eep s
pace
)(Ear
th-to-
spac
e)RA
DIOL
OCAT
ION
RADI
OLOC
ATIO
NEARTH
EXPLORATION- SATELLITE
(active)
RADIO-LOCATION
SPACERESEARCH
(active)
Earthexploration-
satellite (active)
Radio-location
Space research (active)
Radio
locat
ion
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
FIXE
DFI
XED-
SATE
LLIT
E (sp
ace-
to-Ea
rth)
SPAC
E RE
SEAR
CH(pa
ssive
)EA
RTH
EXPL
ORAT
ION
-SA
TELL
ITE (p
assiv
e)FI
XED-
SATE
LLIT
E (sp
ace-
to-Ea
rth)
FIXE
D-SA
TELL
ITE
(spac
e-to-
Earth
)MO
BILE
-SAT
ELLIT
E (sp
ace-t
o-Eart
h)Standardfrequency
andtime signal
satellite(space-to-
Earth)
FIXE
D-SA
TELL
ITE
(spac
e-to-
Earth
)
MOBI
LE-S
ATEL
LITE
(spac
e-to-E
arth)
FIXED
EART
H EX
PLOR
ATIO
N -
SATE
LLITE
(pas
sive)
SPAC
E RE
SEAR
CH(pa
ssive
)
FIXE
DMO
BILE
**
EARTHEXPLORATION-
SATELLITE (passive)
MOBILE**
FIXED
SPAC
ERE
SEAR
CH(pa
ssive
)RA
DIO
ASTR
ONOM
Y
MOBI
LEFI
XED
FIXE
DMO
BILE
FIXE
DMO
BILE
EART
H EX
PLOR
ATIO
N -
SATE
LLITE
- (pa
ssive
)SP
ACE
RESE
ARCH
(pass
ive)
RADI
OAS
TRON
OMY
Earthexploration -
satellite (active)
RADI
ONAV
IGAT
ION
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)FI
XED
Standard frequency and time signal satellite
(Earth-to-space)
FIXE
D
FIXED
EARTHEXPLORATION -
SATELLITE(space-to-Earth)
SPACERESEARCH
(space-to-Earth)
MOBILE
INTER-SATELLITE
Inter-
satel
liteFI
XED
INTE
R-SA
TELL
ITE
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
RADI
OLOC
ATIO
NMA
RITI
MERA
DION
AVIG
ATIO
N
AERO
NAUT
ICAL
RAD
IONA
VIGA
TION
INTE
R-SA
TELL
ITE
Inter-satellite
Earthexploration -
satellite (active)
FIXE
DFIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
FIXED
Spac
e res
earch
Radio
locat
ionRa
dioloc
ation
Radio
locat
ion
RADI
OLOC
ATIO
N
RADI
OLOC
ATIO
N
Earthexploration-
satellite (active)
3.0
3.1
3.3
3.5
3.6
3.65
3.7
4.2
4.4
4.5
4.8
4.94
4.99
5.0
5.01
5.03
5.15
5.25
5.255
5.3
5 5.4
6 5.4
7 5.5
7 5.6
5.6
5 5.8
3 5.8
5 5.9
25
6.425
6.5
25
6.7
6.875
7.0
25
7.075
7.1
25
7.145
7.1
9 7.2
35
7.25
7.3
7.45
7.55
7.75
7.85
7.9
8.025
8.1
75
8.215
8.4
8.4
5 8.5
8.5
5 8.6
5 9.0
9.2
9.3
9.5
9.8
10
.0 10
.45
10.5
10.55
10
.6 10
.68
10.7
11.7
12.2
12.7
13.25
13
.4 13
.75
14.0
14.2
14.4
14.5
14.71
45
14.8
15.13
65
15.35
15
.4 15
.43
15.63
15
.7 16
.6 17
.1 17
.2 17
.3 17
.7 17
.8 18
.3 18
.6 18
.8 19
.3 19
.7 20
.2 21
.2 21
.4 22
.0 22
.21
22.5
22.55
23
.55
23.6
24.0
24.05
24
.25
24.45
24
.65
24.75
25
.05
25.25
25
.5 27
.0 27
.5 29
.5 30
.0
MOBI
LE
FIXE
D-SA
TELL
ITE
(spac
e-to-
Earth
)
FIXE
D-SA
TELL
ITE
(spac
e-to-
Earth
)
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
Earthexploration -
satellite (active)
Amat
eur-s
atell
ite(s
pace
-to-E
arth
)
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
FIXE
D -
SATE
LLIT
E(E
arth-
to-sp
ace)
MOBI
LE -
SATE
LLIT
E(E
arth-
to-sp
ace)
Standard Frequency and
Time SignalSatellite
(space-to-Earth)
FIXE
DMO
BILE
RADI
OAS
TRON
OMY
SPAC
ERE
SEAR
CH
(pas
sive)
EART
HEX
PLOR
ATIO
N -
SATT
ELLIT
E (p
assiv
e)
RADI
ONAV
IGAT
ION
INTE
R-SA
TELL
ITE
RADI
ONAV
IGAT
ION
Radio
locat
ion
FIXE
D
FIXE
D
MOBI
LE
MobileFixed
BROA
DCAS
TING
MOBI
LE
SPAC
E RE
SEAR
CH
(pass
ive)
EART
H EX
PLOR
ATIO
N-SA
TELL
ITE (p
assiv
e)
SPAC
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SEAR
CH (p
assiv
e)EA
RTH
EXPL
ORAT
ION-
SATE
LLIT
E (p
assiv
e)
EART
H EX
PLOR
ATIO
N-SA
TELL
ITE
(pas
sive)
SPAC
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SEAR
CH(p
assiv
e)
MOBILE
FIXED
MOBILESATELLITE(space-to-
Earth)
MOBI
LE-
SATE
LLIT
ERA
DIO
NAVI
GATI
ONRA
DIO
NAVI
GATIO
N-SA
TELL
ITE
FIXED-SATELLITE(space-to-
Earth)
AMAT
EUR
AMAT
EUR-
SATE
LLIT
E
SPACERESEARCH
(passive)
RADIOASTRONOMY
EARTH EXPLORATION-
SATELLITE(passive)
MOBI
LEFI
XED
RADI
O-LO
CATI
ON
INTE
R-SA
TELL
ITE RADIO-
NAVIGATION
RADIO-NAVIGATION-
SATELLITE
AMAT
EUR
AMAT
EUR
- SAT
ELLI
TE
RADI
OLO
CATI
ON
EART
HEX
PLOR
ATIO
N-
SATE
LLIT
E (p
assiv
e)SP
ACE
RESE
ARCH
(pas
sive)SP
ACE
RESE
ARCH
(pas
sive)
RADI
OAS
TRON
OMY
MOBI
LEFI
XED
RADI
OAS
TRON
OMY
INTE
R-SA
TELL
ITE
RADI
ONAV
IGAT
ION
RADI
ONAV
IGAT
ION-
SATE
LLIT
E
SPACERESEARCH
(Passive)
RADI
OAS
TRON
OMY
EARTHEXPLORATION-
SATELLITE(Passive)
MOBI
LEFI
XED
MOBI
LEFI
XED
MOBILE
FIXED
FIXED-SATELLITE
(space-to-Earth)
RADI
OLOC
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NAM
ATEU
RAM
ATEU
R-SA
TELL
ITE
Amat
eur
Amat
eur-s
atell
ite
EART
H EX
PLOR
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N-
SATE
LLIT
E (p
assiv
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MOBI
LE
SPAC
E RE
SEAR
CH(d
eep
spac
e) (s
pace
-to-E
arth)
MOBI
LE
MOBILE
SATELLITE
(space-to-Earth)
SPACE
RESEARCH
(Earth-to-space)
FIXED-SATELLITE
(space-to-Earth)
BROA
DCAS
TING
-SA
TELL
ITE
INTE
R- S
ATEL
LITE
EART
H EX
PLOR
ATIO
N-SA
TELL
ITE
(pas
sive)
SPAC
E RE
SEAR
CH
(pass
ive)
FIXE
DMO
BILE
**
SPAC
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SEAR
CH(p
assiv
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EART
HEX
PLOR
ATIO
N-SA
TELL
ITE
(pas
sive)
RADI
ONAV
IGAT
ION
RADI
O-LO
CATI
ONSP
ACE
RESE
ARCH
(dee
p sp
ace)
(Ear
th-to-
spac
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dio-
locat
ion
Spac
e res
earch
(dee
p sp
ace)
(Ear
th-to-
spac
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Radio
locat
ionRA
DIOL
OCAT
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EART
H
EXPL
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-
SATT
ELLIT
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RADIOLOCATION
SPACERESEARCH
(active)
Earth
explo
ratio
n -sa
ttellit
e (ac
tive)
Radiolocation
Spaceresearch (active)
EART
H EX
PLOR
ATIO
N -
SATE
LLIT
E(p
assiv
e)FI
XED
MOBI
LESP
ACE
RESE
ARCH
(p
assiv
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FIXE
DMO
BILE
FIXE
D-SA
TELL
ITE
(spa
ce-to
-Ear
th)
EART
H E
XPLO
RATI
ONSA
TELL
ITE
(Ear
th-to-
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Earth
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ration
satel
lite(sp
ace-t
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h)
FIXED-SATELLITE(space-to-Earth)
FIXEDMOBILE
BROA
DCAS
TING
-SA
TELL
ITE
BROA
DCAS
TING
FIXED
- SA
TELL
ITE(sp
ace-t
o-Eart
h)
FIXE
DMO
BILE
BROA
DCAS
TING
BROA
DCAS
TING
SAT
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FIXE
DMO
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**FIX
ED-S
ATEL
LITE
(Eart
h-to-s
pace
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DIO
ASTR
ONOM
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FIXED
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E (Ea
rth-to
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BILE
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arth-
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MOBI
LEMO
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E (E
arth-
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MOBI
LE-S
ATEL
LITE
(Ear
th-to-
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BILE
FIXE
D
FIXE
DMO
BILE
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
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FIXE
DMO
BILE
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
MOBI
LE-S
ATEL
LITE
(Ear
th-to-
spac
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FIXED
MOBILE
FIXE
D-SA
TELL
ITE
(Ear
th-to-
spac
e)
EART
H EX
PLOR
ATIO
N-SA
TELL
ITE
(pas
sive)
SPAC
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SEAR
CH (p
assiv
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INTE
R- S
ATEL
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INTE
R- S
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LITE
EART
H EX
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N-SA
TELL
ITE
(pas
sive)
SPAC
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SEAR
CH (p
assiv
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FIXED
MOBILE
EART
H EX
PLOR
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N-SA
TELL
ITE
(pas
sive)
SPAC
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SEAR
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TER-
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MOBILE
INTE
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LITE
EART
H EX
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N-SA
TELL
ITE
(pas
sive)
SPAC
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SEAR
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MOBILE
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RADI
O-LO
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INTE
R- S
ATEL
LITE
FIXE
DMO
BILE
INTE
R- S
ATEL
LITE
INTE
R- S
ATEL
LITE
EART
H EX
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N-SA
TELL
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SPAC
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SEAR
CH
FIXE
DMO
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**
INTE
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ATEL
LITE
MOBI
LE
BROA
DCAS
TING
FIXED- SATELLITE(space-to-
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Spaceresearch
(space-to-Earth)
MOBILE
Amat
eur
RADI
OAS
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RADI
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33.4
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36.0
37.0
37.5
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81.0
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92.0
94.0
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231.5
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30GHz 300 GHz
Amateur
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Amateur
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RADIOASTRONOMY
RADIO
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ISM - 6.78 ± .015 MHz ISM - 13.560 ± .007 MHz ISM - 27.12 ± .163 MHz
ISM - 40.68 ± .02 MHz
3 GHzISM - 915.0± .13 MHz ISM - 2450.0± .50 MHz
3 GHz
ISM - 122.5± 0.500 GHz
This chart is a graphic single-point-in-time portrayal of the Table of Frequency Allocations used by the FCC and NTIA. As such, it may not completely reflect all aspects, i.e. footnotes and recent changes made to the Table of Frequency Allocations. Therefore, for complete information, users should consult the Table to determine the current status of U.S. allocations.
For sale by the Superintendent of Documents, U.S. Government Printing OfficeInternet: bookstore.gpo.gov Phone toll free (866) 512-1800; Washington, DC area (202) 512-1800
Facsimile: (202) 512-2250 Mail: Stop SSOP, Washington, DC 20402-0001
ISM - 61.25± 0.25 GHz ISM - 245.0± 1 GHz
AERONAUTICALMOBILE
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Figure 12: Frequency allocation chart of 2016 in the United States.
Figure 12 shows the United States frequency allocation chart from 2016 in the range of 1 kHz (kilo-Hertz, which stands for 1000 Hz) to 300 GHz. As you can see, nearly all frequencies are occupied bycommunication standards. Hence, when designing a communication system, one has to ensure to onlyoccupy the frequency range allocated for your transmission system. In fact, if you somehow causeinterference with neighboring systems, you will get into legal trouble with the FCC (and you have to payridiculously large fines!). To this end, when designing communication systems, one regularly uses theanalysis tools we have introduced before: the spectrum and the spectrogram.
One of the key goals of almost every communication system is to transmit as many bits per second(this is known as the throughput) as possible through the provided bandwidth. The bandwidth of acommunication system specifies how many contiguous frequencies one can use; a bandwidth of 1 MHzmeans, for example, that one can use the frequency spectrum from 20 MHz to 21 MHz. For this example,
30
Summer 2019 CATALYST Research Project – Bits over the Air
the center frequency would be at 20.5 MHz (which is right in the middle of the two frequencies). Measuringthe amount of bits per second that can be transmitted per bandwidth is known as the spectral efficiency.Engineers who design communication systems are interested in improving spectral efficiency, rather thanachieving the highest possible throughput (also known as the data rate; the throughput is only a measure ofhow many bits per second we can reliably transmit). In contrast, marketing people are mainly interested inadvertising the highest possible throughput—this, however, does not tell you how many frequencies youare occupying (and cannot be used by other communication standards anymore). What most of us do notknow: It is very easy to design communication systems that achieve high throughputs (for example, onecan simply occupy all frequencies and not let anyone else transmit). It is, however, extremely difficult toachieve high throughput while only occupying a tiny fraction of the available frequency spectrum—that’swhy so many engineers are working on the design of wireless communication systems!
Activity 17: Compare spectral efficiencies of real-world communication systems
IEEE 802.11 is the name of many wireless LAN communication standards. If, for example, youare using Wi-Fi on your cell-phone, you are using one of the IEEE 802.11 standards. Since 1997,many wireless LAN standards have been proposed. The following table lists the key designparameter and performance metrics of some of them:
IEEE Standard Year Center Frequency [GHz] Bandwidth [MHz] Data rate [Mbit/s]
802.11g 2003 2.4 20 54802.11n 2009 2.4 40 600802.11ac 2013 5 160 3466.8802.11ay 2020 60 8,000 20,000
IEEE 802.11g, for example, has a spectral efficiency of 54/20 = 2.7 bit/s/Hz (simply take theratio of the data rate and the bandwidth; be careful with the units). Compute the spectralefficiency for the other three standards. What do you observe? Which of these standards isthe most efficient (in terms of spectral efficiency)? Which one achieves the highest data rate?Also, do you have an explanation why more recent standards are operating at higher centerfrequencies (up to 60 GHz for IEEE 802.11ay)? Let us know what you think!
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