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NTIA REPORT 93-298
DIGITAL EMISSION SPECTRUM MODEL
report series U.S. DEPARTMENT OF COMMERCE • National Telecommunications and Information Administration
NTIA Report 93-298
DIGITAL EMISSION SPECTRUM MODEL
David Anderson David Cohen
U.S. DEPARTMENT OF COMMERCE Ronald H. Brown, Secretary
Larry Irving, Assistant Secretary for Communications and Information
SEPTEMBER 1993
ABSTRACT
A computer program was developed to calculate the power spectral density (PSD) and the fractional power containment bandwidth for various digital modulation techniques. The power containment capability was used to provide guidance for determination of necessary bandwidth in support of Annex J of the "NTIA Manual of Regulations and Procedures for Federal Radio Frequency Management." This report documents the models contained in the computer program and illustrates the models with various sample problems. The report also shows the verification of the computer program implementation.
The digital modulation techniques that are presently included in the computer program are:
Phase shift keying (PSK) with non-return-to-zero modulation Quadrature amplitude modulation (OAM). Frequency shift keying (FSK) Minimum shift keying (MSK) Bi-phase shift keying with raised cosine modulation Bi-phase shift keying with Manchester modulation.
KEY WORDS
Bandwidth Digital Modulation Emission Spectrum
Necessary Bandwidth Power Spectral Density
Spectrum Transmitter Spectrum
Ill
TABLE OF CONTENTS
Subsection Page SECTION 1
INTRODUCTION
BACKGROUND . . . . . . . . . . . . . . . . . . . . . • • . . . . . • • . • • . . . . . . . . . . . . . . . . . 1 OBJECTIVE ..•••••.•......•..•••..••••.....•.•• • ......•••••..... , 2 APPROACH ................................................. : . • . • 2
SECTION 2 POWER SPECTRAL DENSITY MODELS
GENERAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Phase Shift Keying (PSK) . . • . . . . . . • . • . . . . . . . • • • • . • . . . • . . . . . . . . . . . . . . . 4 Quadrature Amplituqe Modulation (QAM) . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . 15 Two-level Frequency Shift Keying (FSK) . . . . . . . . . . . . • . . . . . • . . . . . . . . . . . . . . 24 Minimum Shift Keying (MSK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 BPSK with Raised Cosine Modulation .................................. 41 BPSK with Manchester Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
SECTION 3 CONCLUSIONS
CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Figure
2-1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9 2-10 2-11 2-12 2-13 2-14 2-15
UST OF FIGURES Page
Power spectraf density BPSK with NRZ modulation . . . . . . . . . . . . . . . . 7 Power spectral density BPSK with NRZ modulation . . . . . . . . . . . . . . • . 8 Power spectral density BPSK with NRZ modulation . . . . . . . . . . . . . . . . 9 Power spectral density OPSK with NRZ modulation ................ 10 Power spectral density OPSK with NRZ modulation . . . . . . . . . . . . . . • . 11 Power spectral density OPSK with NRZ modulation . . . . . . . . . . . . . . . . 12 Power spectral density 8 PSK with NRZ modulation . . . . . . . . . . . . . . . . 13 Power spectral density 16 PSK with NRZ modulation . . . . . . . . . . . . . . . 14 Power spectral density 4 QAM . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . 16 Power spectral density 16 QAM . . . • . . . . • • . . . • . • . . . . . . . . . . . . . . 17 Power spectral density 64 QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Power spectral density 64 QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Power spectral density 64 QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Power spectral density 25 6 OAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Power spectral density 25 6 OAM . . . . . . . . • . . . . . . . . . . . . . . . . . . . . 22
V
Figure
TABLE OF CONTENTS continued
LIST OF FIGURES continued
Page
2-16 Power spectral density 256 OAM . . . • . . . . • . . . . . . . . . . . . . . . . . . . . 23 2-17 Power spectral density two level FSK .•........................ 31 2-18 Power spectral density two level FSK . • . . • . . . . . . . . . . . . . . . . . . . . . 32 2-19 Power spectral density two level FSK . . . . . • • • . . . . . . . . . . . . . . . . . . 33 2-20 Power spectral density MSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2-21 Power spectral density MSK • • • . . • • . • • • . • • • • . . . . . . . . . . . . . • . • 39 2-22 Power spectral density MSK . • . . . . . • • . • . . • . . . . . . . . . . . . . . . . . . 40 2-23 Power spectral density BPSK with raised cosine modulation .......... 44 2-24 Power spectral density BPSK with raised cosine modulation . . . . . . . . . . 45 2-25 Power spectral density BPSK with raised cosine modulation .......... 47 2-26 Power spectral density BPSK. with Manchester modulation ........... 49 2-27 Power spectral density BPSK with Manchester modulation ... · ........ 54 2-28 Power spectral density BPSK with Manchester modulation . . . . • . . . . . . 55 A-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 A-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
APPENDIX A . . . . . . . . . . . . . . . . . . . . . . . . 59
LIST OF REFERENCES .........•••......... 63
vi
BACKGROUND
SECTION 1 INTRODUCTION
The National Telecommunications and Information Administration (NTIA) is responsible for managing the Federal Government's use of the radio frequency spectrum. NTIA's responsibilities include establishing policies concerning spectrum assignment, allocation and use, and providing various departments and agencies with guidance to ensure that their conduct of telecommunications activities is consistent with these policies.1 In discharging these responsibilities, NTIA assesses spectrum utilization, identifying existing and/or potential compatibility problems among the telecommunications systems that belong to various departments and agencies, provides recommendations for resolving any compatibility conflicts that may exist in the use of the radio frequency spectrum, and recommends changes to promote spectrum efficiency and improve spectrum management procedures.
The Technical Subcommittee (TSC) of the lnterdepartment Radio Advisory Committee (IRAC) is concerned with the technical aspects of the use of the electromagnetic spectrum._ One purpose of the TSC is to develop and recommend new standards and revise existing standards pertinent to the use of the radio spectrum. The TSC was tasked by the IRAC to prepare updated tables of necessary bandwidth formulas for the "NTIA Manual of Regulations and Procedures for Federal Radio Frequency Management." It was determined that formulas for calculating necessary bandwidths are generally available for most analog modulation techniques and that a few formulas for calculating necessary bandwidth for some digital modulation techniques are available. The National Telecommunications and Information Administration (NTIA) agreed to examine the spectral and performance characteristics of certain common digital modulation techniques and develop methodologies for calculating the necessary bandwidth for these modulation types. The results of the NTIA effort are reported in "Necessary Bandwidth and Spectral Properties of Digital Modulation," NTIA Report 84-168. As a result of the analyses documented in NTIA Report 84-168, Annex J of the "NTIA Manual of Regulations and Procedures for Federal Radio Frequency Management" was revised to provide additional guidance for determination of necessary bandwidth. As part of the Report 84-168 study, a computer program was developed to calculate the power spectral density (PSD) and the fractional power containment bandwidth for various digital modulation techniques. The digital modulation techniques that are presently included in the computer program are:
Phase Shift Keying (PSK) with Non-Return-to-Zero (NRZ) Modulation
BPSK QPSK
8 PSK 16 PSK
NTIA, Manual · of Regulations and Procedures for Federal Radio Frequency Management, National Telecommunications and Information Administration, Washington, D.C., Revised May 1992.
Quadrature Amplitude Modulation (OAM}
. 40AM 16 OAM
Two-Level Frequency Shift Keying (FSK} Minimum Shift-Keying (MSK) BPSK with Raised Cosine Modulation BPSK with Manchester Modulation
64 OAM 256 OAM
Since the PSD models are applicable to other spectrum management activities~ NTIA decided to develop the existing computer program into a user-friendly capability that is available on the personal computer (PC). As an initial step in this development, it was decided to verify and document the spectrum models represented in the computer program as these models are not all discussed in NTIA Report 84-168.
OBJECTIVE
The objective of this study was to verify and document with sample problems the models contained in the computer program2 named "Emission Spectrum Model for Digital Signals."
APPROACH
2
To meet the objective of this study, the following approach was taken:
1. The PSD formulations used in the computer program were determined and substantiated by comparison with appropriate references.
2. The PSD models were applied to several sample problems and the results verified through comparison with manual calculations.
This computer program also includes the optional capability to determine the effect of passing the computed emission spectrum through a filter. The filter functions that are available are,
Chebyshev Butterworth Nyquist Boxcar
In addition, the program includes the capability to plot the FCC spectrum mask (FCC Rules and Regulations Section 21. 106) along with the computed spectrum (with or without filtering} to examine comparison with the FCC requirements.
Neither the filter or spectrum mask capabilities were validated by this study and thus these capabilities are not discussed in this report. However, examples of these capabilities are included in Appendix A.
2
SECTION 2 POWER SPECTRAL DENSITY MODELS
GENERAL
In general, the PSD for the digital modulation techniques that were modeled can be represented as:
PSD(fl = a: 'S' (fl
where
thus
S'(f) = shape function
a.' ::; Pr
JS'(f )df
Pr = transmitter power
f = frequency variable
f PSD (f )df = a'f S'(f )df "' Pr
For a specified transmitter power
PSD (f) = "'S' (f)
(2-2)
(2-3)
The computer model that is discussed here uses the formulations of S'(f} and a:' to obtain the required PSD information. The S'(f} formulations that are used to model the various digital modulation techniques are discussed in this section of the report. Sample PSD plots and computations verifying the PSD data are also presented.
3
Phase Shift Keying {PSK)
The computer program models the PSD for PSK wherein a non-return-to-zero (NRZ) modulation signal shifts the carrier phase at the symbol rate between signal states (S) representing dist inct, equally-spaced angular-posit ions. The computer program includes the capability to model
BPSK (Binary PSK) OPSK (Quaternary PSK) 8 PSK
16 PSK
The PSD for M-ary PSK modulation is independent of the number of signal states (S) and is a function of the symbol rate cur.,. It is of the form3
where
S'(f) = [ Sin 1t T• (f-fc )r x T. (f-fc)
T, = M-ary symbol length, T, = T8 (109 2S) T 8 = digital bit length, T 8 = 1 /BR BR = digital bit rate f = frequency variable f c = carrier frequency
(2-4)
The digital bit rate (BR) is the bit rate applied to the modulating process. This bit rate includes bits required for net management, addressing, error correction, etc. In the case of spread spectrum the bit rate would be the psuedo-noise chip rate. This parameter is denoted as modulating bit rate on the various spectrum plots in this report.
Example PSDs for BPSK (S = 2) are shown in Figures 2-1 through 2-3.4
Figure 2-1 is the PSD for a bit rate of 1 MHz and 2 watts transmitter power. Figure 2-2 shows a bit rate of 3 kHz with 300 watts and Figure 3 is a bit rate of 5 MHz and 150 watts. Examination of equation 2-4 shows that S'(f) would have a maximum at (f-() = O where it can be shown that in the limit
3
4
Feher, K., Digital Communications. 1981.
The PSD plots also show a "99% band" value. This is the bandwidth that contains 99% of the transmitter power.
4
S'(O) = 1
and subsequent maxima would occur at
(f-fc) T, = ± 3/2, ± 5/2, ± 7/2, etc.
The minima would occur at ·
(f-fcl T, = ± 1, ± 2, ± 3, etc.
For BPSK where S = 2, T. = T 8 and BR = 1 rr 5, the maxima and minima of Figures 2-1 through 2-3 are at the correct multiples of the bit rate. Equation 2-4 shows the spectral envelope falloff expressed in dB is
20 log 1 n r. (f-fc)
That is, the first maximum would be down 13.5 dB from the maximum at (f-f cl = 0. The second maximum would be down 17.9 dB, the third down 20.8 dB, and the fourth down 23.0 dB. The figures for BPSK show the expected spectral decay. The 3 dB bandwidth for BPSK can be shown to be approximately BR. (A more exact figure would be 0.88 BR.) Figure 2-1 is based on 2.0 watts; the PSD at (f-fc) = 0 should be
10 log 2·0 watts = 3.0 dBW /MHz 1.0 MHz
Figure 2 -2, the maximum PSD is
1 O log 300 watts = 20.0 dBW I kHz . 3 kHz
5
Figure 2-3, the maximum PSD is
10 log 150 watts = 14.7 dBW /MHz 5MHz
The PSDs are shown for OPSK (S =4) in Figures 2-4 through 2-6. For OPSK: S = 4, T
6 = 2/f
8, T
8 = 1 /BR so that the maxima of the PSDs should occur at
The minima should occur at
The spectral fall-off of the PSD maxima should be the same as that of the BPSK case, that is, the first maximum should be down 13.5 dB, relative to the maximum at the carrier frequency. Figure 2-4 is based on 10 watts and for OPSK, the 3 dB bandwidth is approximately 1 /2 BR, thus the PSD at (f-f c> = 0 should be
10 log 10 watts = -6.9 dBW /Hz · 0.5 (100 Hr,
For Figure 2-5, the maximum PSD should be 23.9 dBW/MHz, and for Figure 2-6, it should be 20.0 dBW/kHz.
Similarly, it can be shown that Figure 2-7, an example of 8 PSK (S = 8), is correct and Figure 2-8 for 1 6 PSK (S = 16) is also correct.
Thus, the computer program is developing the PSD for PSK as expected.
6
8PGK Mo ~ilt~~
I 0
I e / "', I I
I \ -10
-20 N :: :c ..... :z SQ
~
..... -30 .... ...,. ::r:: .,... .... ...,.
n (\ (\ (\ (\ I (\.
(\ ( ' I
I \ (\ I
i (n
-40
-50
-60 I
-70
-s -4 -3 -2 -! 8 1 2 3 4 5
( f--f c) NHz ·
Modulating bit rate = 1 .00 mps Power = 2.00 watts 99% band = 15.63 MHz
Figure 2·1. Power spectral density BPSK with NRZ modulation.
7
N :c
"""' ' 3 ll'Q "Q
... ::c ... en
BPSK Ho Filttr 30
I 20 I
JI\
10
n
t ~
0
-10
-20
~ ~ ,r \
~
l . fl I ' • f t ~
I• r ' I\
A ~
' -30
-40
-50
., I I.
r I
-60
-50 -40 -30 -20 -10 e · 10 28 30 40 50
0-fc) kHz
Modulating bit rate = 3.00 kps Power = 300.00 watts 99% band = 46.88 kHz
Figure 2-2. Power spectral density BPSK with NRZ modulation.
8
N :: ;Ji:
' :IC p;i
,::,
..... .....
...... :: ...... .... ...... U)
BPSK Ho Filt~r
10 I \
0 /1, (\
I' {I
- 10
n ~ " (\
1, I'\ {\ '' [\ (\
(\ {\
A (\
-20
I i
-30 l
-40
-50
-60
-50 -40 -30 -20 -10 0 10 20 30 40 50
(,f-fc) NHz
Modulating bit rate = 5.00 mps Power = 150.00 watts 99% band == 78.13 MHz
Figure 2-3. Power spectral density BPSK with NRZ modulation.
9
N :::i::;
' :a:
""" "'C
-. -... :::i::; ,.... ~ ...... V,
QPSK Ho Filter 0
-10 I ~ J \
-20 r /1
-30
-40
{\ n n (\
I I I
I I\ (',
r \11\ r I {\ l'i
(i (1 r
-50 I
-60 I !
-70
-see -400 ·380 -200 ·100 e 10 0 200 300 400 see
(f-fc) Hz
Modulating bit rate = 100.00 bps Power = 10.00 watts 99% band = 937.50 Hz
Figure 24. Power spectral density QPSK with NRZ modulation.
10
40
I QPS K I
IH o Fi 1 er
20
I I \
ft
" e
.... :z: ~ -20 ' ::z: ~
"Q
~ /I "
I f ~ { r r f f
~ ~
~f1M· r ''. ' ~~ I I
p I I 1 H \ ij ,.._ .... "'"' I ::c:
.... (I)
' -40
I !
-60
-80
-15 -10 -5 e 5 10 1S 20
<f-,fc) NHz
Modulating bit rate = 2.00 mps Power = 250.00 watts 99% band = 18.75 MHz
Figure 2-5. Power spectral density QPSK with NRZ modulation.
1 1
N ::c: -' :z ,i:,q
~
-. .... ..... ::z: .... ..... (I)
QPSK Ho Filter 38
28
10
e ~
I 1 I ~
I
-10 I
-20 ~ f, ,,,-,: ··
I -30 I
I
-S0
-80 -60 -40 -20 e 20 40 60 80
(f-ft) kHz
Modulating bit rate == 8.00 kps Power == 400.00 watts 99% band = 75.00 kHz
Figure 2-6. Power spectral density QPSK with NRZ modulation.
12
8 PSK Ho Filter 28
10 l
0 I
-18 ~I
I N
::c a:
' 2 ,za "0
-20 ... ....,. ::c
.... ~ I
U>
-38 ..
-40 I
l -S0
- 60
-tee -00 -60 -49 -2e e 20 48 60 80 100
<-,-,tc) NHz
Modulating bit rate = 10.00 mps Power = 200.00 watts 99% band = 62.50 MHz
Figure 2-7. Power spectral density 8 PSK with NRZ modulation.
13
40
116 P~K I No IFiltL
20
,
0
,
lf , '
' ~ r r ~ ~ (\
r r I
n II ~ fl ~ ~ r ,. ~ . n •
N :c :c -2.0 ' :it P'I
I I ~
...... .... ...... ::i::
.... -40 ...... en
-60
-80 I
· -10 0
-25 -28 -15 -10 -s 0 5 10 15 20 25
< f-f c) NHz
Modulating bit rate = 5.00 mps Power = 300.00 watts 99% band = 23.44 MHz
Figure 2-8. Power spe_ctral density 16 PSK with NRZ modulation.
14
Quadrature Amplitude Modulation (QAM}
The computer program models the PSD for QAM. With OAM, the modulation signal shifts both the carrier phase and amplitude at the symbol rate between distinct signal states {S). The computer program includes the capability to model:
40AM 16 OAM 640AM
256 OAM
The PSD for M-ary QAM5 is modeled using the same formulation as that of PSK (equation 2-4).
An example PSD for 4 OAM (S = 4) is shown in Figure 2-9 for a bit rate of 2 MHz and 250 watts transmitter power. With S =4, Ts = 2fT8 , T8 = 1 /BR so the maxima of the PSD should occur at
The minima should occur at
Examination of Figure 2-9 (BA = 2 MHz) shows the maxima and minima to be as expected. The expected spectral fall-off is as previously stated for PSK (i.e., 13.5 dB, 17 .9 dB, 20.8 dB, 23.0 dB). With a transmitter power of 250 watts, the PSD at {f·fcl = 0 should be 24 dBw/MHz. The spectral fall-off and peak PSD shown in Figure 2-9 are as expected.
Figure 2-10 is an example PSD for 16 QAM (S = 16) for a bit rate of 5 MHz and 300 watts transmitter power. Examination of this PSD shows it is as expected.
Figures 2-11 through 2-13 are example PSDs for 64 QAM (S = 64). These figures show the one·sided spectrum plot that is an output capability of the computer program. Figure 2-11 illustrates a bit rate of 1 MHz and a transmitter power of 1 watt. Figure 2-12 is for a bit rate of 5 MHz and 5 watts of transmitter power; Figure 2·13 represents a 10 MHz bit rate and 10 watts of transmitter power. These spectral plots can also be shown to be correct.
Figures 2-14 through 2·16 are examples of 256 OAM {S = 256). Figure 2-14 is the PSD for a bit rate of 1 MHz and 1 watt transmitter power. Figure 2-15 shows a bit rate of 5 MHz with 5 watts and Figure 2-16 shows a 10 MHz bit rate and 10 watts. These spectral plots are also as expected.
5 Amoroso, F., The Bandwidths of Digital Signals, IEEE Communications Magazine, November 1980.
15
49
I 4 QAl1 I IN O Fi 1 er
, 29
• •
0 II • • r
" I II It
It • ' /t
, n ~ 11 • ~ • It
N :c s: -20 ' :a: I Ql:a
~
.... " :c .... -40 .., (Q
-60
-80
--100
-20 -15 -19 -s 9 18 15 20
<i-fc) NHz
Modulating bit rate = 2.00 mps Power = 250.00 watts 99% band = 18.75 MHz
Figure 2-9. Power spectral density 4 OAM.
16
N ::c: z:; .... ;z .... "'C
.... '"' ::z:: --.... " en
40
I 16 ol11 I Ho,FiltL
20
r
I
0
-20
~ ~ ~ . , ~ I ~ ~ I I ~
f' I ' I
~n I I
-48 I I
-60
,
-80
-100
-2S -20 -15 -10 -5 0 5 10 1S 20 25
Modulating bit rate = 5.00 mps Power == 300.00 watts 99% band == 23.44 MHz
Figure 2-10. Power spectral density 16-0AM.
17
64 QAl1 Ho Filttr 10
\ 0
fl
-10 •
{'I ~
r. -20
~
fl ~ • N :x z::
' -3 0 ::z ~ ~
,... .... ...... :x -40 .....
~ ~ n
" n • • I • " . n ~
M" .... ...... en
-50
-60
-70
-80
• 0 • 5 1.9 1,5 2,0 2.5 3.0 3,5 4.0 4,5 5.0
Cf-fc) 11Hz
Modulating bit rate = 1.00 mps Power = 1 .00 watts 99% band = 3. 13 MHz
Figure 2-11. Power spectral density 64-0AM.
i8
64 Q~N Ho Filttr 10
\
8
"
- 10
r
f ,
-20
N ::c JC
' - 30 :z ""'4 "C
/I
I' n n ~ fl r n , ~
~ ' (', A • f'I •
\ l\~f'I,,
.... :c -40 ... ...,. Cl)
-50
-60
-70
-80
0 5 10 15 20 25
(f-fc> NHz
Modulating bit rate = 5.00 mps Power = 5.00 watts 99% band = 15.63 MHz
Figure 2·12. Power spectral density 64-QAM.
19
.... :::z::: E .... ::s S:Q ,:,
.... ::c .... (,t)
64 QAN Ho Filter 10
\
0
f\
-10
" /1,
i /1,
-20 n f\
~ '
-30
n n " " ' f ~ ~ ' '
n A ' ,
-40
-50
-60
I -70
-80
0 5 10 15 20 25 30 35 40 50
(f-tc) NHz
Modulating bit rate = 10.00 mps Power = 10.00 watts 99% band = 31.25 MHz
Figure 2-13. Power spectral density 64-QAM.
20
256 QAl'I Ho Filter
18
e
)
-10
N % :IC -20 ' :a:
"" "O
..... %
~ -:e en
- ~ t
""l~,,~!!111,,. 111 !!
M~ I I l
-40 I
-58
-60
-5 -~ -3 -2 -1 e 2 3 5
(.f-fc) NHz
Modulating bit rate = 1 .00 mps Power = 1 .00 watts 99% band = 2 .34 MHz
Figure 2-14. Power spectral density 256-QAM.
21
N :z:: :c ... :z .... ~
....... ... '-' :z:: ,... -en
256 QAl1 Ho Filter
10
8
-10
-20 1i l!1 .. 111111
1~111~
-30 ii!! 11111 M~1 ~
~~~~Ml -40 I
-50
-60
-25 -20 -15 -19 -s 0 s 10 15 29 25
(f-fc) '1Hz
Modulating bit rate = 5.00 mps Power= 5.00 watts 99% band = 11.72 MHz
Figure 2-15. Power spectral density 256-0AM.
22
256 QAl1 Ho Filter
10
e
-18
N ::c E - 20 ' :s l'Q "g
;-,. .... ::c
.... -30 <n
I ~~i I
-40
-50
-60
-5e -40 -3e -20 -10 e 10 20 30 40 50
Cf-fc) 11Hz
Modulating bit rate = 10.00 mps Power = 10.00 watts 99% band = 23.44 MH2
Figure 2-16. Power spectral density 256-QAM.
23
Two-Level Frequency Shift Keying (FSK)
The computer program includes the capability to model the PSD for two-level, continuous-phase, frequency-shift keying. The PSD formulation6 is
(2-5)
S'(f) • • 1 • [eos ( 2;:)- Cos (11 -')r [ D -(f-f•) r 1-2 Cos(~) Cos (1t -')• Cos2 (~l
where
D = 1 /2 (difference between mark and space frequencies)
2(f-fc) X = ----'--
The PSD modeled by equation 2-5 is a continuum and is valid if BR and Dare not related such that
(2-6)
If the relation shown in equation 2-6 is true, the PSD for FSK will include two carrier spikes and must be modeled by a formulation that is different than the S'(f) of equation 2-5. The formulation for the other case is not currently included in the computer model. The computer model includes a check of equation 2-6 and prints out a warning
e
SPIKE CONDITION ENCOUNTERED
Pelchat, M.G., The Autocorrelation Function. and Power Spectrum of PCM/FM with Random Binary Modulating Waveforms, IEEE Transactions on Space Electronics and Telemetry, March 1964.
24
if the expression is satisfied. The computer program will not compute S'(f) when the spike condition is encountered.
Figures 2-17 through 2-19 are example PSDs for FSK. Figure 2-17 is for a bit rate of 1 MHz, a transmitter power of 2 watts and a mark/ space frequency difference of 0 .4 MHz. Maxima of S'{f) occur when the term
is a maximum. For a value of D = 0.2 and BR = 1 MHz, the maxima will occur at
Cos 2n (f-fc) = -1
or
(f-fc) = ±1/2, ±3/2, ±5/2, ±7/2,etc.(MHz)
Additional maxima occ·ur when
1 -2 Cos 2n D Cos 1ex + Cos2 (
2n DJ BR BR
is a minimum. For Figure 2-17, this would occur at
(f-fc) = 0, ± 1, ± 2, ± 3, etc. (MHz)
However, the maxima at (f-f c> = ± 1 /2 MHz does not appear as a maximum because for values of I f-f c I < 1 /2 MHz, the term
25
I 0 • _;,_,. >' f
is so large that it causes the S'(f) function to continue to increase as (f-f c> goes from ± 1 /2 to O. A cursory examination of S'(f) might indicate maxima at D = !f·f~I due to the denominator going to zero. However, further examina.tion shows that
Cos 21t D - Cos 1rx BR
also goes to zero at D = lf-fci . It can be shown that S'(f) at D = jf-fcl is
S 1(f) = (_.!!_)2
DBR
Thus, the maxima are expected to occur at
(f-fc) = 0, ± 1, ± 3/2, ± 2, ± 5/2, ± 3, etc. (MHz)
Figure 2-17 shows this effect. The minima of S'(f) would occur when
C 2rcD Co 21t(f-lc )
OS--= S---BR s,,
26
For the example problem, this would occur at
2rr (f-fcl = ±0.4", ±(2rr-0.4n), ±(2n+0.4n), ±(4n-0.4n), etc.
(f-f c:l = ± 0.2, ± 0.8, ± 1.2, ± 1.8, ± 2.2, etc. (MHz.)
When f-f c = ± 0.2, then D = I f-fc I which as previously stated are not true maxima or minima. Thus, the minima occur at
{f-fcl = ± 0.8, ± 1.2, ± 1.8, ± 2.2, etc. (MHz)
Again a cursory examination might indicate a minimum in S'(f) when
1- 2 Cos 21tD Cos 1tX + Cos2 (1tD) BR BR
is a maximum. This would be when
Cos n x = -1
At these values, however, the numerator is a maximum and in fact, the function S'(f) is a maximum. This can be shown through trial calculations of S'(f) .
Thus, the maxima for Figure 2-17 are expected to occur at
(f·fc) = 0, ± l, ± 3/2, ± 2, ± 5/2, ± 3, etc. (MHz)
and minima at
(f-fc) = ± 0.8, ± 1.2, ± 1.8, ± 2.2, etc. {MHz)
which are the values shown in the figure.
The spectral fall-off of the maxima of the PSD for FSK can be computed from
20 log 1 02 - (f-fc )2
27
The fall-off is relative to the value at (f-f0 ) = 0 and for Figure 2-17 is
Relative (f-f0 ) Attenuation
(MHz) (dB)
0 0
1 -27.65
3/2 -34.9
2 -40.0
5/2 -43.9
3 -47.0
7/2 -49.7
This is the fall-off shown in Figure 2-17.
The peak PSD at (f-fc) = 0 can be approximated by
For Figure 2-17,
10 log Transmitter Power 3 dB Spectrum Bandwidth
10 log 2·00 watts = 7 dBW /MHz 0.4 MHz
where the 3 dB bandwidth was estimated from the PSD plot. This peak is in agreement with the value of Figure 2-17 .
Figure 2-18 is the PSD for a 3 kHz bit rate, 300 watts transmitter power and. a mark/space frequency difference of 5 kHz. For these conditions, maxima would be expected at
= 0, ±1.5, ±3, ±4.5, ±6,etc.(kHz)
28
However, because the term
is increasing so rapidly from (f·fc) = 0 to (f-fc) = D, the potential maxima at (f-fc) = ± 1.5 kHz do not occur. Also, the potential maxima at ± 3 kHz and ± 4. 5 kHz are shifted to slightly lower frequencies by the rapid decrease in
[ 0 2 - ~f-fc )2 r
as (Mel increases from D. The maxima at (f-fcl = ± 6 kHz and higher values occur at the expected frequencies. The minima would be expected at
or
C 2rrD Co 21t(f-fc)
OS--= S---BR BR
2rr/3 (f-fc) = ± ll/3, ± 5rr/3, ± 7ll/3, ± 11 rr/3, ± 13rr/3, etc.
(f-fcl = ±0.5, ±2.5, ±3.5, ±5.5, etc. (kHz)
The possible minima at ± 2.5 kHz are really [ f-f c I = D which as previously explained are not minima. The spectral fall-off of the maxima of the PSD is determined by
29
20 log 1 02 - (f-fc )2
For Figure 2-18, the expected fall-off relative to the value at (f-fc) = 0 is
Relative (f-f c) Attenuation (kHz) (dB)
0 0
2.9 +9.2
4.2 -5.2
6 -13.6
7.5 -18.1
The expected peak value of the PSD is
10 log 3oo watts = 21 dBW /kHz 2.4 kHz
The PSD plot shown in Figure 2-18 is as expected.
Figure 2-19 is the PSD for FSK with a 5 MHz bit rate, 150 watts power and a mark/space frequency difference of 3 MHz. Comparisons similar to those of Figure 2-17 and 2-18 show the PSD of Figure 2-19 to be as expected.
30
2 Level FSK No FIiter 20
0 I\ I \
N ::r: I:
-20
' :I /1 A
'° 'U --40
""' 4-w V _. :c
""' 4-V -B0
I' (\ I'
(\ I',
(1 ~ /'1 (\ f (\,
(\, ~ /'1
" (\, I f',
I\ ,, 1 fl
(/)
-80
-100
-10 -8 -6 -4 -2 0 2 4 8 8 10
Cf-fc) MHz
Modulating bit rate .,. 1.00 mps Power "" 2.00 watts Delta "" .40 MHz 99% band • 1.07 MHz
Figure 2~17. Power spectral density two level FSK.
2 Lev•I FSK No FIiter 30
20
\ ( 10
r (\ N 0
I .Y. '\.
-10 3 f A
co 'U
-20 ,..., "f-
u) \J N :c -30 ,...,
'+--
r '1 (I (\
f', f'I r h
I\ " (\ " f',, I 1 ,,
\J
en -40
-50
-B0
-70
-30 -20 -10 0 10 20 30
Cf-fc) kHz
Modulating bit rate = 3.00 kps Power = 300.00 watts Delta = 5.00 kHz 99% band = 9.38 kHz
Figure 2-18. Power spectral density two level FSK.
N :c :c
" :I
'° 1J
,-.. c+, ..._,,
(,J :c (,J ,-.. c+, \J
en
2 Level FSK No FIiter 20 ,r,,, 10
0
I " -10
-20 f n
f " -30
r, " -40
r " ~ I I
-50
/', " /1 r, /1 "
-80
-70
-80
-90
-60 -40 -20 0 20 40 60
(f-fc) MHz
Modulating bit rate = 5,00 mps Power = 150.00 watts Delta "" 3.00 MHz 99% band = 7 .81 MHz
Figure 2-19. Power spectral density two level FSK.
Minimum Shift Keying (MSK)
The capability to model the PSD for minimum shift keying7 is included in the computer program. The PSD formulation is
S'(f) = [Cos 2nTs (f-fc )r 1-16 Tl (f-f0 )2
(2-7)
Figure 20 shows the spectrum for MSK with a bit rate of 1 MHz and 2 watts of transmitter power. A bit rate of 1 MHz results in a bit length of 1 µsec. For these conditions, one would expect possible maxima at
Cos 2 " T 8 (f-f c> = ± 1
(f-fc) = 0, ±1/2, ±1, ±3/2, ±2,etc.(MHz)
However, as explained below there are no minima between O and ± 1 /2 MHz. Thus , ± 1 /2 MHz do not appear as maxima since S' (f) continues to increase from ± 1 /2 MHz to a maximum at (f-f c> = 0. Examination of equation 2-7 might indicate a potential maximum at 1 = 16 T 8 (f-fcl2 because the denominator goes to zero. However, the numerator also goes to zero and application of L' Hospital's Rule will show that S' m = rr2/16 at (f-fc} = 1 /4T 8.
Therefore, maxima would be expected at
(f-f cl = 0, ± 1 , ± 3/2, ± 2, ± 5/2, etc. (MHz)
The actual maxima for small .6.f values (i.e., ± 1 MHz and ± 3/2 MHz) are shifted to slightly lower frequencies. This is caused by the rapid increase of the denominator of S'(f) as at deviates away from 0.
7
Minima values for S'(f} would be expected at
(f-fc) = ± 1 /4, ± 3/4, ± 5/4, ± 7/4, etc. (MHz)
Prabhu, V.K., MSK and Offset QPSK Modulation with Bandlimiting Filters, IEEE Transactions on Aerospace and Electronic Systems, January 1981 .
34
However, as previously stated (f.fc) = ± 1 /4 MHz are not minima. Thus, minima are expected at
(f·fcl = ±3/4, ±5/4, ± 7/4, etc. (MHz)
The PSD at (f-f c) = 0 can be estimated from
10 log Transmitter Power = 10 log 2wstts = 4 9 dBW
3d8 Spectrum Bandwidth 0.65MHz . MHz
The fall-off of the spectra maxima can be determined by considering
For Figure 2-20,
20 log ---1--1-16Tl(t-fc )2
Relative (f •f c) Attenuation
(MHz) (dB)
0 0
1 -23.6
1.5 -30.8
2 -35.9
2.5 -40.0
3 -43.0
4 -48.0
35
Similarly, Figure 2-21 illustrates the PSD for MSK modulation with a bit rate of 3 kHz and 300 watts transmitter power. Using the same consideration as the previous example, one would expect maxima at
(f·fc) = 0, ± 3, ± 9/2, ± 6, ± 15/2, etc. (kHz)
and minima at
(f-f c) = ± 9/4, ± 1 5/4, ± 21 /4, ± 27 /4, etc. (kHz)
Again, the expected maxima at ± 3 kHz are shifted to slightly lower frequencies by the rapid change in the value of the denominator.
The spectral density at (f-f c) = 0 is
10 log SOO = 22.7 dBW 1.6 kHz
and the spectral fall-off should be
Relative (f·fc) Attenuation (kHz) (dB)
0 0
3 -23.6
4.5 -30.8
6 -35.9
7.5 -40.0
9 -43.0
Figure 2-22 is the PSD for MSK with a 5 MHz bit rate and power output of 1 50 watts. For these conditions, maxima are expected at
(f·fc) = 0, ±5, ± 15/2, ± 10, ±25/2, etc., (MHz)
36
and minima at
{f-fc) = ± 15/4, ± 25/4, ± 35/4, ± 45/4, etc. (MHz)
The maxima expected at ± 5 MHz are shifted t o slightly lower frequencies as previously explained.
The spectral density at (f-fc) = 0 should be
10 log 150wstts == 17_0 dBW 3MHz MHz
and the spectral fall-off should be
Relative (f-fc) Attenuation (MHz) (dB)
0 0
5 -23.6
7.5 -30.8
10 -35.9
12.5 -40.0
15 -43 .0
Comparison of the expected PSD values and the computer generated PSD plots for MSK are in agreement.
37
N :i:: :a:
' ::a: IIQ "'O
--~ ....... :i:: ...... ~ ..... U)
"SK H·o Fi 1hr 18
e I ~ I \
-18
•28 r " f'i ~
-38
/1 r,
-48 r, {\,
/', (1
fl, n r 1 -se
-60
-80
'"
-98
-6 -'4 -2 e 2 4 6
<f-fc) NHz
Modulating bit rate = 1 .00 mps Power • 2.00 watts 99% band = 1. 17 MHz
Figure 2-20. Power spectral density MSK.
38
11SK Ho Filhr 30
20 I i\
I \ 10
8 r n N -10 :c
I\ (\
I -' ::z r, ~ -.::::,
-20 .... ..., :c .... '-" (t) -30
I' (\
n f f n
f\ n (\ f'I
-40
-50
-60
-70
-15 -10 -5 0 5 10 15
(f-fc) kHz
Modulating bit rate = 3.00 kps Power = 300.00 watts. 99% band :: 3.52 kHz
Figure 2-21. Power spectral density MSK.
39
NSK Mo Filhr 28
18 ( ~ I
\ e
~ I -18
~ n ... :: -28 E
' ::z "" -0
-- -30 -..., :c ,...
{1 (\
\ I\ I\
I ' I ' n, -..., ~ -40
-50
-68
-78
. -88
-25 -20 -15 -18 -5 e 5 18 15 28 25
Modulating bit rate "'" 5 .00 mps Power = 150.00 watts 99% band = 5.86 MHz
Figure 2~22. Power spectral density MSK.
40
BPSK with Raised Cosine Modulation
This emission spectrum is the result of using a modulating waveform where the amplitude of the modulating signal is shaped to a raised cosine. The modulating signal then bi-phase shift modulates a carrier. The spectrum generated in the computer model should not be confused with the class of signal where the modulated signal is filtered by a filter with a raised-cosine response.
The PSD for BPSK with raised cosine modulation8 is determined using the formulation
Cos n(f-f. )-
[ Tsr 1-[(f-fc ) ~B :
The indeterminate points of the form zero-over-zero occur at
application of L'Hospital's Rule yields
S'(f) = 0.25 when {f-fcl T0 = 1 and
S'(f) = 1.0 when {f-fcl = 0
(2-8)
The PSD for BPSK with raised-cosine modulation is illustrated in Figure 2-23. This is the spectrum for a 1 MHz bit rate and 2 watts transmitter power. The maxima are determined by combining the Sin2 and Cos2 terms in the numerator using Sin 2x = 2 Sin x Cos x. Thus the maxima could occur at
ll(f-fclTs = ±n-/2, ± 3ll/2, ±5rr/2, ±7"/2
For Figure 2-23
(f-fc) = ± 1 /2, ± 3/2, ± 5/2, ± 7 /2, etc.,
8 . Gagliardi, R.M., Satellite Communications, 1984.
41
{MHz)
However, "(f-() T8 = ±rr/2 are not true maxima because the term
1-[(f-f e)T a1 2
becomes relatively small for small values of (f-f c> so that S'(f) continues to increase from the minima at "(f-f c>T 8 = ± TT through the maxima at (f-f c> = 0. The indeterminate value at (f-f c)
= 0 is a maximum. Thus, the maxima would be expected at
(f-fc) = 0, ±5/2, ±7/2, ±9/2, etc. (MHz)
The actual maxima for small t.f values are shifted to slightly lower frequencies. This is caused by the rapid change of the denominator of S'(f) as t.f approaches 0.
The minima could occur at
However, the PSD at TT(f-fe) T6 = 0 is indeterminate and is, in fact, a maximum. At TT(f-fc) T8
= ± "· S'(f) is also indeterminate and is not a minimum with S'(f) = 0.25. Thus, the expected minima, for Figure 2-23, should occur at
(f·fcl = ± 2, ± 3, ±4, ± 5, etc. (MHz)
The PSD at the carrier frequency is
10 log 2.0watts = 1,2 dBW 1.5MHz MHz
42
The expected spectral ~ fall-off of the maxima can be shown to be
Relative (f-f e) Attenuation
(MHz) (dB)
0 0
2.5 -32.4
3.5 -41 .9
4.5 -48.9
Figure 2-24 is c ~he PSD for BPSK with raised cosine modulation with a 3 kHz bit rate and 300 watts of outP' ut power. For these conditions, the maxima are expected at
ll(f-fc)Ti9 = 0, ±Sll/2, ±7"/2, ±9ll/2, ±11ll/2,etc.
(f-fc) = 0, ±15/2, ±21/2, ±27/2, ±33/2, etc. (kHz)
However, the maxima at ± 15/2 kHz are shifted to slightly lower Af values by the rapid change in the denominator.
Minima are expected flt
11(f-fc) Te = ±2rr, ±3ll, ±4", ± 5rr, etc.
(f-fc) = ±6, ±9, ±12, ± 15,etc. (kHz)
The PSD at the carrier frequency is
10 log 300wstts = 18_2 dBW 4.5MHz MHz
43
Raistd COS Ho Filttr 10
e --t--..
V \ -10
-20
I ~
I \ I \
N ·30 ::i: E .... ::a:: i:Q -c,
..... -48 ... :z: -. .... ..... w -50
( I\ (\
t\ (\ I , I \
-60
-70
-80
-90
-s -4 -3 -2 -1 8 2 3 4 s
Modulating bit rate = 1 .00 mps Power = 2.00 watts 99% band = 2.83 MHz
Figure 2-23. Power spectral density BPSK with raised cosine modulation.
44
Rlistd COS Ho Filt,r 20
10
8
I ~ I \
II -18
.... ::c -' -20 2 ~
/1 (\ I ' -0
.,,..._ ... ..... ;c -30 ... en
r~ f \ \ I (\
-40
-50
-60 I
-78
-15 -10 e 5 10 15
(f-fc) kHz
Modulating bit rate == 3.00 kps Power == 300.00 watts 99% band = 8.50 kHz
Figure 2-24. Power spectral density BPSK with raised cosine modulation.
45
The spectral fall-off should be
Relative {f·fe) Attenuation
(kHz) (dB)
0 0
7.5 -32.4
11.5 -41.9
13.5 -48.9
Figure 2-25 is the PSD for BPSK with raised cosine modulation with a 5 MHz bit rate and 1 50 watts. The maxima are expected at
{f-f e> = 0, ± 25/2, ± 35/2, ± 45/2, ± 55/2 etc. (MHz)
The maxima at ± 25/2 MHz are shifted to slightly lower .llf values, as previously explained. The minima are expected at
(f-fe) = ± 10, ± 15, ± 20, ± 25, etc. (MHz)
The PSD at the carrier frequency is
10 log 150watts = 13_1 dBW 7.3MHz MHz
The fall-off should be
Relative (f-fe) Attenuation (MHz) {dB)
0 0
12.5 -32.4
17.5 -41.9
22.5 --48.9
The PSD plots for BPSK with raised-cosine modulation are as expected.
46
N :::c: E ..... ::II:
"" -0
...... ..... '""' :::c:
..... en
R1is1d COS Ho Filttr 20
10 / ~ V \
e
-10
I ~
I \ I 1
-20
-30
-40
f\ A
/' I
/"\ t\
(\ I \ I \
(\ J \
-50
-60
-70
-88
-25 -20 -15 -18 -5 e 5 18 1S 20 25
Cf-fc> NHz
Modulating bit rate = 5.00 mps Power = 150.00 watts 99% band = 14.16 MHz
Figure 2~25. Power spectral density BPSK with raised cosine modulation.
47
BPSK with Manchester Modulation
The capability to model BPSK with Manchester coding as the modulating signal (see reference 8} is also included in the computer program. The PSD formulation is
(2-9)
Sl 4 ,c Ts (f-fc ) n 2
S 1(f) = -----
[ xr. t'·) r
The expression for S'(f) is indeterminate at (f-fc) = 0 and by application of L'Hospital's Rule it can be shown that
S'(f) = O at (f-f cl = 0
Figure 2-26 is the one-sided spectrum for BPSK with Manchester modulation with a 1 MHz bit rate and 2 watts of power. The maxima should occur at
Sin4 n Ts (f-fc ) = 1 or 2
1t T8 (f-fc)
2 = ±1t/2, ±31t/2, ±5-n/2, ±71t/2, etc.
(f-fc) = ±1, ±3, ±5, ±7,etc. (MHz)
48
29
I h. BP K No IFiltL Pl1nc
e
-28
N :: E
' :z
( I\ V ~ I\ V I I\
\ I .... "g
,.. -40 ~
:: ~ ...... en !
I ! !
-60
-80 !
. -100
.e .~ 1.e 1.s 2.e 2.s 3.e 3.5 4.e 4.s s.e
<f-fc> KHz
Modulating bit rate = 1.00 mps Power = 2.00 watts 99% band = 28.13 MHz
Figure 2-26. Power spectral density BPSK with Manchester modulation.
49
All the example PSDs for BPSK with Manchester modulation show the actual maxima at small .O..f values shifted to slightly lower .O.f values. This can be attributed to the rapid change of the denominator for small .O..f values.
The minima should occur at
Sin4 x Ts (f-fc ) = 0 or 2
(f-fc) = 0, ±2, ±4, ±6, ±8, etc. (MHz}
The maximum PSD which occurs at (f-f c) = 1 should be
10 log 2.0wstts = 0_7 dBW 1.7MHz MHz
The spectral fall-off can be determined by evaluating
20 log 2 nT8 (f-fc)
50
which results in
Relative (f·fc) Attenuation
(MHz) (dB)
1 0
3 -9.0
5 -14.0
7 -16.9
9 -19.1
Figure 2-27 is the one-sided spectrum for BPSK with Manchester modulation with a 3 kHz bit rate and 300 watts. The maxima should occur at
and the minima at
7t T8 (f-!0 )
---- = ±n/2, ±3n/2, ±Sn/2, ±7n/2, etc. 2
(f-fc) = ±3, ±9, ±15, ±21,etc. (kHz)
7t T8 (f-fc)
2 "' 0, :ut, ±2n, ±3n, ±4n, etc.
(f-fc) = ±0, ±6, ±12, ±18, ±24, etc. (kHz)
51
The peak PSD value should be
10 log 300wstts = 17_8 dBW 4.9MHz MHz
and the spectral fall-off is expected to follow
Relative (f-fc) Attenuation (kHz) (dB)
3 0
9 -9 .6
15 -14.0
21 -16.9
27 -19.1
Figure 2-28 is another example of PBSK with Manchester modulation. The bit rate is 5 MHz and the transmitter power is 150 watts. The maxima are expected at
(f-fc) = ±5, ±15, ±25, ±35, etc. (MHz)
and the minima are expected at
(f-fc) = 0, ± 10, ± 20, ± 30, ±40, etc. (MHz)
The peak PSD should be
10 log 150wstts = 12,6 dBW 6.3MHz MHz
52
and the spectral fall·off should be
Relative (f·fe) Attenuation
5 MHz OdB
15 -9.6
25 -14.0
35 -16.9
45 -19.1
Thus, the PSD plots for BPSK with Manchester modulation are as expected.
53
Nanch. BPSK Ho Filttr 29
8
( I'\ ~ I ~ \ v-
\ / -29
\ ... : -' 2 -"Q
,.., -40 .... ..... ~ ,.., .... ..... (I)
;. 6 8
-80
-188
e 2 8 18 12 14 16
(f-fc) kHz
Modulating bit rate = 3.00 kps Power = 300.00 watts 99% band = 84.38 kHz
Figure 2~27. Power spectral density BPSK with Manchester modulation.
54
Nanch, BPSK Ho Filt,r 20
8 r I\ ,- r,.....
I
-20
N % E
I ' I .... :a: POI ,:,
-40 "r
%
"r ....,, en
-60
-80
-100
e 5 10 15 20 25
(f-.Pc> NHz
Modulating bit rate == 5.00 mps Power == 150.00 watts 99% band == 140.63 MHz
Figure 2-28. Power spectral density BPSK with Manchester modulation.
55
SECTION 3
CONCLUSION
The power spectral density data developed by the emission spectra computer model have been verified to conform with the theoretical formulations. The computer model is a user-friendly capability that is available for operation on a PC.
\
57
APPENDIX A
The computer program, "Emission Spectrum Model for Digital Signals," contains additional capabilities that were not validated as part of this study. These capabilities include the FCC spectrum mask and various filter options. Several graphs are presented in this Appendix to illustrate these capabilities.
Figure A·1 is a plot of the power spectral density for 16 OAM along with the FCC spectrum mask. The PSD is for power level of one watt and a data rate of 78 Mb/s. The FCC mask is for the 6 GHz band and an authorized bandwidth of 30 MHz.
Figure A-2 is a plot of the PSD of the 16 OAM function of Figure A-1 however the PSD is modified to show the effect of passing the emission spectrum through a filter. The filter used for Figure A·2 was a third order Chebyshev with a 20 MHz bandwidth and 1 dB ripple. The FCC mask for the 6 GHz band with a 30 MHz authorized bandwidth is also shown.
59
0
-20
I - 40 I
i ~ -60 ... i ig
! -80 " ....
i ~-100 :c ~
• C
C. GI
~-120 A,
-140
-160
16 CAM No Fi I ter
/ ~
I \
,,,....._ I\ ('\ J (\ I\ ,,,....._
I ' I ' j 1 /
' I \
I \ ~"'-V /
80 dB FCC mask floor
-80 -60 -40 -20 0 20 40 60 80
(f-fc) MHz
Modulating bit rate ... 78.0 mps Power = 1.00 watts 99% band = 365.63 MHz
FCC Mask for 6 GHz band and 30 MHz authorized bandwidth.
Figure A-1. Power spectrum density with FCC Mask for 16 QAM.
60
0 16 QAM
Ill GI
Ill l'I
• ii!
-50
£ . i - 100
; 3 0 a..
.. ... ~ ~-150 N X -" ,,t
C
(. Ill 3 0 a..
-200
-250
r
Chebyshev
( \
I I \ (' r\ J '-~
~
-80 -60 -40 -20 0 20 40 60 80
(f-fc) MHz
Modulating bit rate = 78.0 mps Power • 1.00 watts 99% band • 21.42 MHz
Chebyshev Filter - 20 MHz bandwidth, 1 dB ripple, 3rd order
FCC Mask for 6 GHz band and 30 MHz authorized bandwidth.
Figure A-2. Filter power spectrum density with FCC Mask for 16 OAM.
61
LIST OF REFERENCES
Amoroso, F., The Bandwidths of Digital Signals, IEEE Communications Magazine, November 1980.
Feher, K., Digital Communications. 1981.
Gagliardi, R.M., Satellite Communications. 1984.
NTIA, Manual of Regulations and Procedures for Federal Radio Frequency Management. National Telecommunications and Information Administration, Washington, D.C., Revised May 1992.
Pelchat, M.G., The Autocorrelation Function, and Power Spectrum of PCM/FM with Random Binary Modulating Waveforms. IEEE Transactions on Space Electronics and Telemetry, March 1964.
Prabhu, V.K., MSK and Offset OPSK Modulation with Bandlimiting Filters, IEEE Transactions on Aerospace and Electronic Systems, January 1981 .
63
' I !
FORM NTIA-29 V.S. DEPARTMENT OF COMMERCE \4-l!Ol NAT1 .• TELECOMMUNICATIONS AND INFORI.AATION ,-OMIHISTR"-TION
BIBLIOGRAPHIC DATA SHEET
1. PUBLICATION NO. 2. Gov·1 Acceuion No. 3. Recipient's Accession No.
NTIA REPORT 93-298 4. TITLE AND SUBTITLE 5. Publication Dale
·Seotember 1993 6. Performing Organization Cocle
DIGITAL EMISSION SPECTRUM MODEL NTIA/OSM/SEAD 7. AUTHOR(S) 9. ProjecVTesk/Work Unit No.
David Anderson and David Cohen 8. PERFORMING ORGANIZATION NAME ANO AOORESS 39013171 National Telecommunications and
Infonnation Administration 10. ContracVGrant No. 179 Admi ra 1 Cochrane Drive Annapolis, Maryland 21401
11. Sponsoring Organization Name and Address 12. Type ol A•port and Period Covered
U.S. Department of Commerce/NTIA Technical 179 Admiral Cochrane Dr ive 13.
Annapolis, Maryland 21401 H. SUPPLEMENT ARY NOTES
1S. ABSTRACT (A 200-word or /.ss /1ctua/ summ1ty ol mosl si9nilic11.nt lnformarion, If document includu • signilicanl bibliog,aphy or literalur• sun-ey. mention it here.}
A computer program was developed to calculate the power spectral density (PSD} and the fractional power containment bandwidth for various digital modulation techniques. The power containment capability was used to provide guidance for determination of necessary bandwidth in support of Annex J of the "N.TIA Manual of Regulations and Procedures for Federal Radio Frequency Management." This report documents the models contained in the computer program and illustrates the models with various sample problems. The report also shows the verification of the computer program implementation.
The digital modulation techniques that are presently included in the computer program are:
Phase shift keying (PSK) with non-return-to-zero modulation Quadrature amplitude modulation 10AM) Frequency shift keying (FSK) Minimum shift keying (MSK) Bi-phase shift keying with raised cosine modulation Bi-phase shift keying with Manchester modulation.
16. Key Words (.A.lphab•lical ord• r , nparat•d by umicolons}
Bandwidth Digital Modulafion Emission Spectrum Necessary Bandwidth Power Spectral Density Spectrum Transmitter Spectrum
17. AVAILABILITY ST A TEMENT 18. Security Cius. ( Thi1 t•port J 20. Number or pages
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