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A Software Simulation Tool for GNSS2 BOC
Signals Analysis
L. Ries, L. Lestarquit, E. ArmengouMiret, CNES, F. Legrand, W. Vigneau, M3Systems
C. Bourga, Alcatel Space Industries, P. Erhard, ESA, JL. Issler, CNES
BIOGRAPHY
Lionel Ries is a Navigation Engineer in the
Radionavigation Departement at CNES (French Space
Agency), since June 2000. He studies GNSS2 signal
including BOC and GPSIIFL5. In addition, he is involved
in experiments on a GNSS2 navigation payload
demonstrator (developed by CNES). He formely worked
for Altran, as consultant (Astrium, Toulouse and Allgon
Stockholm, Sweden). He graduated in 1997 from the
"Ecole Polytechnique de Bruxelles, at Brussels Free
University (Brussels, Belgium), in 1997, and received a
M.S. degree from the "Ecole Nationale Superieure de
l'Aeronautique et de l'Espace" (Supaero, Toulouse,
France).
Laurent Lestarquit is responsible of the GNSS2 navigation
payload demonstrator at CNES. In the RadioNavigation
department, he was involved in this activity with Lionel
Ries and Joel Dantepal. They are also involved in studies
of european spaceborne navigation receivers.
F. Legrand and Willy Vigneau work at the radionavigation
unit of M3Systems, an SMEin the area of Toulouse
(France). M3Systems isclosely involved in various radio
navigation projects (EGNOS, GPS, GNSS2, …).
Ester ArmengouMiret was this year in the
RadioNavigation department, for her endofstudy
internship. She studied the correlation loss budget of
different multiplexing techniques in a Galileo payload in
E2L1E1 band.
Philippe Erhard is a Navigation System Engineer in the
ESA Galileo Project Office. He is coordinating Galileo
Signals Design, Performance and Validation activities, and
is supporting Galileo Receiver Developments. He received
his engineer degree from the E.N.A.C (French Civil
Aviation University) and joined Alcatel Space Industries
Toulouse France where he was involved in previous
GALA and GalileoSat studies. He joined ESA late in
2001, as Galileo Project Signal Expert.
Ch.Bourga graduated from ENSEEIHT (Toulouse, France)
and is involved in the GALILEO project, in the
Engineering Navigation Department of Alcatel Space
Industry.
JeanLuc Issler is head of the RadioNavigation
Department at CNES, whose main task are signal
processing and radionavigation equipments. He is
involved in the development of several GNSS spaceborne
receivers in Europe, as well as studies on the future
European RadioNavigation Programs, like Galileo and the
Pseudolite Network.
ABSTRACT
Several BOC(n,m) signals are planned for future GNSS
systems, with integer reference values of n and m,
including BOC(10,5) for the GPS Mcode, BOC(2,2) for
the baseline open GALILEO signal, flexible BOC(n,m) for
Galileo’s PRS signal and possibly an alternative BOC(a,b)
for GALILEO in the E5 bands (E5a/L5 and E5b). The
values of a and b are released in the paper.
A BOC signal is formed in baseband by the product of
two signal components : first, a non filtered Pseudo
random Noise (PN) code having a chip rate, Rc, and two
possible values : 1 or 1, then a subcarrier, either a non
filtered square signal, or a sine signal, having a frequency,
Rsc, equal or higher than Rc. A BOC(n,m) signal is such
as n = Rsc/Rca and m = Rc/Rca ; n & m are not
necessarily integers. We note Rca the GPS C/A code chip
rate : 1.023 Mcps. The effect of the square subcarrier is to
split the main lobe of the PN code spectrum into two lobes
centered at +/ Rsc from the central frequency. The BOC
expansion ratio, a, is defined by a = n/m. When n & m are
integers and n = m, the associated BOC(n,n) is a
Manchester code.
An AlternativeBOC (ALTBOC) signal is a BOClike
signal having different PN codes in the lower and the
upper main split lobes. AlternativeBOCs allow one signal
service per lobe. If the 2 PN codes of an alternativeBOC
are made identical, the signal becomes a « classical »
BOC. CNES suggested a mean of generating an alternative
BOC, with 4 different codes, while keeping the signal’s
envelope constant.
In order to closely study the BOC signals, in particular
those here above, as well as to provide its partner in the
GALILEO program with valuable expertise, CNES (the
2225
ION GPS 2002, 2427 September 2002, Portland, OR
French Space Agency) has undertaken the development of
software simulation tools of BOC signals, in cooperation
with ESA ( The European Space Agency ). This tool
comprises a highly flexible signal transmitter, capable of
generating any BOC signal (n and m variable, parametric
code length and data rate) and alternative BOC. ( NB :
Internal work about the alternative BOC has also been
performed in CNES, ESA and GAIN ). The tool includes
simulation of payload’s effects (e.g. distorsions). It
includes also the definition of several kinds of receiver
architectures and perturbations like interference, multipath,
and dynamics.
This tool is aimed at studying the acquisition strategies,
the tracking performances in the presence of thermal noise,
interference and multipath. The effect of parameters n and
m on the performances are being investigated, as well as
the impact of alternative BOC both on the receiver’s
architecture and capabilities, but also on the payload.
The tool shows to be is a valuable asset to investigate the
best compromises for defining a good reference receiver
for BOC signal. These reference receivers are then used to
compare the influence of parameters n and m as well as
different scenarii for future GNSS systems.
The paper describes the hypothesis of those simulations
including the nonlinear distorsions model, as well as the
most interesting results and some recommendations on the
E5 band signals.
The results provided in the paper come from ESA and
CNES internal investigations on the AlternativeBOC
Modulation, and from M3System and Alcatel Space
studies on the subject ( BOC and ALTBOC signals ).
INTRODUCTION
Standard Baseband BOC signal
An OC signal (Offset Carrier signal) results from the
modulation of a NRZ PN sequence by a subcarrier. Let
RC/A be the C/A code rate, i.e 1.023 MHz.
A PN sequence with a chip rate Rs = m* RC/A modulated
by a sine subcarrier of frequency Rsc = n* RC/A is defined
as a LOC(n,m).
A PN sequence with a rate Rs = m* RC/A modulated by a
square (NRZ) subcarrier of rate Rsc = n* RC/A is defined as
a BOC(n,m) [ fig 1 ].
The effect of the square subcarrier is to split the main lobe
of the PN code spectrum into two lobes centred at +/ Rsc
from the central frequency. The BOC expansion ratio, a, is
defined by a=n/m. The spreading gain is G=Rc/Rd, where
Rd is the data rate. When n & m are integer and n=m, the
associated BOC(n,n) is a Manchester code.
Re[Sx(f)]
Im [Sx(f)]
f
Rs
R
sc
Rsc
Rs
Fig 1 : BOC signal
A BOC or LOC signal is usually generated in baseband
and then modulates a RF carrier.
ALTERNATIVE BOC
The BOC alternative purpose aims at generating a single
sub carrier signal adopting a source coding similarly to the
one involved in the classical BOC. The process allows
thus to keep the BOC implementation simplicity, and the
possibility to differentiate the lobes
The BOC modulation is a square subcarrier modulation,
))2(sin(*)()( tfsigntsts ss
π
=. The idea is to perform
the same process but multiplying the base band signal by
))2(sin(.))2(cos( tfsignjtfsign ss
ππ
+ following the
following scheme [ fig 2 ].
)sin( 0tw×tw
e0
×
))2(sin(*)()( tfsigntsts ss
π
=
))()(()()( sss fffffSfS +−−⊗≈
δδα
Square sub carrier or BOC Alt ernat e BOC
))
)
2(sin()2(cos(*)()( tfjsigntfsigntsts sss
ππ
+=
))(()()( ss fffSfS −⊗≈
δα
sinusoidal sub carrier sinusoidal sub carrier
Fig 2 : BOC alternative synoptic
Signal generation
notations
symbol Formulation Value
(
MHz
)
f 1.023
FE5 Medium carrier frequency between E5a 1191.795
fa carrier frequency of E5a 1176.42
Fb carrier frequency of E5b 1207.14
fc chip rate of Galileo signals in E5a and
E5b
10*f0
=15.345
Fs frequency offset of E5a or E5b to FE5 15*f0
=15.345
Ts 1/fs
t Time
cr
(
t
)
sign(cos2πfst)
sr
(
t
)
sign(sin2πfst)
er er=cr+j*sr
ca PRN code in E5a (data channel)
cb PRN code in E5b (data channel)
da data flow in E5a
db data flow in E5b
c’a PRN code in E5a (dataless channel)
c’b PRN code in E5b (dataless channel)
2226
ION GPS 2002, 2427 September 2002, Portland, OR
In order to modulate two signals in subcarriers, two
solutions are being investigated :
• modulation by a rectangular signal
• modulation by a sinusoidal signal
modulation by a rectangular signal
A signal can be modulated in subcarriers by multiplying
two symbol flows by conjugate complex exponentials so
as to shift each symbol flow from the centre frequency to
two different bands. Obviously, this modulated signal can
no longer be considered as a signal with constant
envelope.
In order to keep the constant envelope properties, the idea
is to substitute to the true complex exponential by a
rectangular equivalent. The baseband signal will then be
expressed as :
() () () () ()
tertctertctx ba
∗
⋅+⋅=
The spectrum comprises of a main line which is the same
as the line for the ideal complex exponential with the same
frequency Fs, and of minor harmonics spaced every 4*fs.
It is absolutely equivalent to modulate the flow ca+cb by
the waveform cr and to add in quadrature the flow cacb
modulated by the waveform sr, because the base band
signal expression can be arranged as :
() () ()
[]
() () ()
[]
()
tsrtctcjtcrtctctx baba −++=
As cr and sr yield BOC signals, we have two BOC signals
in quadrature, lets determine the values of amplitude for
each channel :
The value of Cr(t) and Sr(t) according to t modulo Ts are
described in the following table [ Tab 1 ]:
t mod Ts ]0;Ts/4[ ]Ts/4;Ts/2[ ]Ts/2;3Ts/4[ ]3Ts/4; Ts[
Cr(t) 1 1 1 +1
Sr(t) 1 1 1 1
Table 1 : Values of Cr and Sr versus time
For a BOC(15,10) signal, we remind that if Tc is the
duration of a chip and Ts the subcarrier period, we have :
Ts=Tc/1.5
Therefore, during the length of a chip, the values of Cr and
Sr cycle 1,5 times through the value of the previous chart
This signal can also be written by the expression :
() {}
4,3,2,12 2∈= ketx jk
π
k defines the « scattered plot » number as below [fig 3] :
1
3
4
2
Fig 3 : Scattered plots of a pilotless ALTBOC signal
Value of x(t) and k according to the value of Ca, Cb, Cr,
and Sr. For Ca and Cb, the number of combination is equal
to 4, when we add Cr and Sr, there is a total number of 16
combinations [ Tab 2 ].
C1(t) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
C2(t) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Cr(t) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Sr(t) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Re[x(t)] = [Ca(t)+Cb(t)]*Cr(t) 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2
Im[x(t)] = [Ca(t)Cb(t)]*Sr(t) 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0
I Re[x(t)] + j*Im[x(t)] I 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
k : scattered plot 2 4 4 2 3 3 1 1 1 1 3 3 4 2 2 4
Table 2 : Possible values of x and k
In that case, we verify that amplitude of I and Q channel is
kept constant, as it is the case in constant enveloppe
modulations
The limitation of the concept lies in the fact that each
signal in Ea and Eb must be a BPSK signal, i.e. with no
pilot channel if the good constant envelope characteristics
are to be kept, because some portions of the baseband
signal will be at null power. Indeed, if the data channels
are on I and the pilot channels are on Q, then the base
band signal can be expressed as :
() () () () ()
[]
() () ()
[]
(){}
() ()
[]
() () () () ()
[]
(){}
tsrtdtctdtctcrtctcj
tsrtctctcrtdtctdtctx
bbaaba
babbaa
−+
′
+
′
+
′
−
′
−+=
This function can take 9 different values :
The following figure [fig 4] show the value of the scattered
plot k according to the values of C1, C’1, C2, C’2, Cr, and
2227
ION GPS 2002, 2427 September 2002, Portland, OR
Sr. There are 16 combinations for the 4 codes alone, and
64 when we add the values Cr and Sr.
() {}
=
=
==
=⋅=
evenkA
oddkA
kforA
with
keAtx
k
k
k
jk
k
4
22
00
8,7,6,5,4,3,2,1,0
4
π
k defines the scattered plot number as below [fig 4] :
0
1
8
7
6
5
4
3
2
+2 +4
+4
2
4
+2
4
2
Fig 4 : Scattered plots for a rectangular modulation
It is clearly seen that the resulting modulation won’t be a
constant envelope modulation. The I and Q channels can
even be at zero at the same time. The non constant
envelope imposes limitation on the HPA, and this solution
is not suitable.
Other ALTBOC modulations
The idea of using a sinusoidal modulating signal instead of
a rectangular one has been also studied, but this variant
still doesn’t provide a signal with a constant envelop.
Another ALTBOC variant, prefered in GALILEO signal
design, allow to generate the E5 signals with a constant
envelop [ 11 ], as shown in next figure [fig 5]. In this case,
the generated signal is a classical 8PSK modulation.
Here, x(t) can take exactly 8 different values :
{}
8,7,6,5,4,3,2,12 4∈⋅ ke jk
π
k defines the scattered plot number as hereafter :
1
8
7
6
5
4
3
2
+22
+2
2
Fig 5 : Scateredplot for the 8PSK ALTBOC
An optimal use of the HPA can be done. The spectrum, the
scattered plot and the autocorrelation function of the
ALTBOC(15,10) are presented hereafter [fig 6 ].
Fig 6 : representations of the ALTBOC(15,10) signal
E5 MODULATION AND PAYLAOD IMPACT
E5 band
The modulation of GALILEO E5 band will be done
according to one of the following schemes:
A. Two QPSK(10) signals will be generated
coherently and transmitted through two separate
wideband channels on E5a and E5b respectively.
The two separate E5a and E5b signals will be
amplified separately and combined in RF through
an OMUX before transmission at the 1176,45
MHz and 1207,14 MHz respective carrier
frequencies.
B. One single wideband signal generated following
the ALTBOC(15,10) 8PSK modulation. This
signal is then amplified through a wideband
amplifier before transmission at the 1191,795
MHz carrier frequency.
The payloadelement diagram in Case A is given on the
following figure.
2228
ION GPS 2002, 2427 September 2002, Portland, OR
X
cos (2π
ππ
πFIb..t)
X
sin (2π
ππ
πFIb..t)
X
+
X
cos (2π
ππ
πFIa..t)
X
sin(2π
ππ
πFIa..t)
X
+
DE5b(t)
CQE5a(t)
HPA
HPA
OMUX
SE5(t)
Up
Conversion
Up
Conversion
E5a(t)
E5b(t)
DE5a(t)
OnBoard
Ref. Code
Generator
OnBoard
Memory
Ranging Codes
Selection
OnBoard
Ref. Code
Generator
OnBoard
Memory
Ranging Codes
Selection
CIE5a(t)
CQE5b(t)
CIE5b(t)
Fig 7 : E5 payloadelement Diagram in case A
The E5 payloadelement diagram in case B is given on the
following figure.
OnBoard
Ref. Code
Generator
OnBoard
Memory
Ranging Codes
Selection
OnBoard
Ref. Code
Generator
OnBoard
Memory
Ranging Codes
Selection
X
X
DE5b
(t)
DE5a
(t)
I
Q
HPA
Up
Conversion
Output
Filter
SE5(t)
e1(t)
e2(t)
e3(t)
e4(t)
CQE5a
(t) =
CIE5a
(t)
CQE5b
(t) =
CIE5b
(t)
ALTBOC 8PSK
Signal generation.
( Several possible
modulation schemes )
Fig 8 : E5 payloadelement diagram in case B
Several modulation schemes are possible to generate a
ALTBOC 8PSK signal. These schemes are under study, to
select the more simple one, which will be a candidate
signal design for GALILEO E5 band.
The generation of two separate QPSK channels is the
present baseline implementation of the GALILEO E5
signals. Its advantage resides in a well known simple
implementation at the signal generator level
However, The main interest of the AltBOC 8PSK
modulation is that it combines the two signals (E5a and
E5b) in a composite constant envelope signal which can
then be injected through a very wideband channel which
can then be exploited in the receivers. These assets make it
worthwhile to investigate on all the aspects related to the
AltBOC modulation, being a candidate for the
implementation of the E5a/E5b GALIEO signals.
The performances of the ALTBOC 8PSK modulation
(multipath and correlation losses) are compared hereafter.
Both full E5 processing and E5a/L5 processing were
considered. The associated results appear in tables 3 and 4.
Table 3. Correlation losses for full E5 processing
Transmitt ed
signal
Reference
signal
Configuration Correlation
losses
LOC(15,10)
filtered in two
24 MHz
bands
LOC(15 ,10) LOC (15,10)
2*24MHz
2 QPSK
!
LOC(15,10)
0.8 dB
ALTBOC
(15,10)
Filtered in
two 24 MHz
LOC(15 ,10)
LOC
(
15,10
)
2*24MHz
ALTBOC
(15,10)
cst_env
1.6 dB
ALTBOC
(15,10)
Filtered in a
single 70
MHz
LOC(15 ,10)
LOC
(
15,10
)
70 MHz
ALTBOC
(15,10)
cst_env
1.2 dB
ALTBOC
(15,10)
filtered in 70
MHz
ALTBOC
(15,10)
ALTBOC
(15,10)
cst env
70 MHz
ALTBOC
(15,10)
cst_env
1.8 dB
Table 4. Correlation losses for full E5 processing
Transmitt ed
signal
Reference
signal Configuration Correlation
losses
QPSK(10)
filtered in
24MHz
QPSK(10) QPSK(10)
24MHz
QPSK(10)
0.8 dB
ALTBOC
(15,10)
filtered in 24
MHz (E5a)
QPSK(10) QPSK(10)
24 MHz
ALTBOC
(15,10)
cst_env
1.8 dB
ALTBOC
(15,10)
filtered in 40
MHz (E5a)
QPSK(10) QPSK(10)
40 MHz
ALTBOC
(15,10)
cst_env
1.4 dB
The baseband generation of combined E5a and E5b signal
presents several advantages:
1: Gain in precision due to the possibility to transmit
many sidelobes.
2: Optimization of use of E5a and E5b : simple/lowcost
receivers can use a single band whereas more complex
receivers can operate in two modes (single band or dual
band ) and thus get advantages in term of performance
3: It allows some flexibility for the service definition,
since a service can be dedicated to one band only while the
second one could in certain conditions use both.
4: Finally, the E5 RF channel is simplified (see
corresponding figure above). Moreover, the insertion losses
of the E5 filter are smaller than with separated bandlimited
E5a and E5b filters. There is also no more isolation
constraints between E5a and E5b filters. The group and
phase delay stabilities are also better. The losses due to the
recombination of the E5a and E5b filters outputs are also
suppressed.
2229
ION GPS 2002, 2427 September 2002, Portland, OR
As illustrations to points 2 and 3, the following figures
show the multipath envelopes simulated by processing the
E5a/L5 signal only with an earlyminuslate discriminator.
The transmitted signal was modulated by an Alternative
BOC signal, or by 2 different QPSK signals. The code
replica was QPSK modulated.
Fig 9: Multipath envelope as a function of the
discriminator spacing. 2 QPSK transmission and E5a/L5
reception in 24 MHz (maximum bandwidth allowed in the
payload).
Fig 10: Multipath envelope as a function of the
discriminator spacing. AlternativeBOC transmission and
E5a/L5 reception in 40 MHz (assumes at least 70 Mhz
transmitted)
These multipath envelopes shows that higher potential
multipath mitigation is allowed by the use of an
Alternative BOC modulation. As a matter, the availability
of a wider bandwidth allows to perform narrower
correlation, which goes to the sense of better multipath
mitigation.
The following figure shows the multipath envelope
obtained by the processing of the whole E5 signal
Alternative BOC modulated. The discriminator is an early
minuslate discriminator of 0.1 chip correlator spacing.
90 MHz Bandwidth
70 MHz Bandwidth
Infinite Bandwidth
70 MHz Bandwidth
90 MHz Bandwidth
Fig. 11: Multipath envelope for the whole processing of
the E5 signal modulated AlternativeBOC. The local
replica is AlternativeBOC modulated.
In the case of an aeronautic receiver having separated E5a,
E5b and L1 filters, to avoid common failure modes in term
of interferences, it might be not mandatory to broadcast
full integrity on E5a, in addition to E5b and L1. Indeed
E5a and E5b represent elements of the same coherent
ALTBOC signal. A pseudorange error at satellite level
would be by construction exactly the same on E5a and
E5b.
While being promising, the Alternative BOC still needs
further investigations, and the following issues in
particular need to be addressed:
 Complexity of the Signal generation implementation
 The promising performances of the Alternative BOC
modulation requires that a wideband filter is implemented
(70 or 90 or 110 MHz). This should be compared to
possibilities to process GPS signals like P code in 80 MHz
[13].
 The Baseband generation of this modulation could lead
to an additional tone in the spectrum domain (20 dBc),
which might be caused by the Local Oscillator leakage.
The potential effects on the carrier frequency acquisition
and tracking will be investigated.
 Performances of the associated Power Amplifiers.
 Noninteger ratio between the resulting carrier frequency
in ALTBOC modulation and the reference clock rate.
 Verification of the tracking performances of the
Alternative BOC modulation.
 Complexity of the associated receiver architecture.
E1L1E2 band
Galileo will provide three signals in the L1 band
(including E1 & E2):
• BOC(2,2) data and pilot channel
• BOC(n,m), with BOC(14,2) and BOC(10,5)
being two possible parameter set, among others
The satellite payload will have to transmit those three
signals. Therefore, it requires an adapted modulation
schemes, if possible featuring a constant envelope.
Three modulation schemes have been identified and
analyzed in terms of HPA requirements, filter and
correlation losses.:
2230
ION GPS 2002, 2427 September 2002, Portland, OR
• Hexaphase,
• Modified Hexaphase (also known as Interplex
modulation),
• QPSK modulation including a time
multiplexing channel for the BOC(2,2)
components.
The two last schemes do provide a constant envelope at the
HPA input.
Hexaphase modulation
The Hexaphase modulation is a QPSK modulation, where
the quadrature component is modulated by the BOC(n,m)
and the inphase component is modulated by the linear
addition of the two BOC(2,2) channels [ fig 12 ].
(
)
)2sin()()(
)2cos()()()()(
t
c
ft
A
Ct
A
d
A
P
t
c
ft
C
C
C
Pt
B
Ct
B
d
B
Pts
π
π
−+=
I
Q
Fig 12 : Scattered plot for Hexaphase modulation
Modified Hexaphase
The Hexaphase modulation can be modified in order to
keep the envelop constant. The Q component’s amplitude
can vary in such a way that, when the I component is null,
the Q amplitude is one [fig 13].
Hexaphase modulation : A, B,
C, D, E, F
Modified Hexaphase modulation : A,
B ’, C, D, E ’, F
B
E
Fig 13 : Modified Hexaphase modulation
This is done by adding a fourth signal, called
intermodulation product, to the three initial BOC.
)sin()sin()()(
1
22)()()(
0
2
)cos()sin()()(
1
22)()()(
0
2)(
t
c
t
s
t
D
CmJ
I
Pt
A
Ct
A
dmJ
Q
P
t
c
t
s
t
C
CmJ
Q
Pt
B
Ct
B
dmJ
I
Pts
ωω
ωω
−−
−
−=
TDMQPSK
As for the two first cases, the quadrature component is
modulated by the BOC(n,m) signal. However, the inphase
component is now modulated by the Time Division
Multiplex of the BOC(2,2) data and pilot channels. This
modulation has intrinsically a constant envelope since it is
a QPSK (the TDM can be seen as a single signal) [fig 14]
TC
Signal A
Signal B
Transmitted
signal
Tm=TC/ 2
A
AA
BB
B
AA
B
B
BA
Fig 14 : Time Division Multiplex
Yet, this modulation is not exactly identical to the L2C
signal of GPSIIF. Indeed, when applied to BOC signal, the
TDM can be perform in two different manners. Either the
components are multiplexed after BOC modulation
(DBM) or before BOC modulation (MSC). The resulting
signals do have quite different properties.
In the case of DBM schemes, it can be shown that the
equivalent signal spectrum is a BPSK(4), while the MSC’s
spectrum is a BOC(4,4) [ fig 15 ]. In order to keep a
BOC(2,2) spectra, TDMMSC multiplexing implies the
generation of two 1 Mcps components, modulated by a 1
Mcps square subcarrier, and sequenced by the time
multiplexing. This multiplexing provides each signal
component with twice more transistions than for a
continuous BOC(1,1) signal.
DBM spectrum : BPSK(4) MSC spectrum : BOC(4,4)
Fig 15 : Time multiplexing of BOC(2,2)
Modulation Analysis and factor of merit
All three modulations were evaluated looking at criteria
like correlation losses, filtering losses, HPA input back
off. For that purpose, the payload was simulated using
COMLIB, a RF library dedicated to payload equipment
analysis, developped by CNES under Matlab.
The payload model is illustrated in figure 16 and 17. Two
types of transistor technologies has been considered for the
HPA ( HFET and PHEMT ). These technologies, widely
spread for telecommunication satellites, worldwide, are
two possible exemples among others. It also has been
shown that a wide band RF filter [fig 17] is mandatory to
avoid too high correlation losses.
2231
ION GPS 2002, 2427 September 2002, Portland, OR
Modulator SSPA
Hexaphase
Interplex
DBM
MSC
HFET
PHEMT
BW=50 MHz
IL=0.12 dB
Fig 16 : simulated payload model
Fig 17 : Filter transfer function (Amplitude)
Simulation results are provided in tables 5, 6, 7 & 8. These
tables provide the HPA Input Back Off ( IBO ). The
presented efficiency concerns the elementary power
modules assembled inside the HPA.
Simulation results : Hexaphase
Table 5. Correlation losses and efficiency of Hexaphase modulation
Signal HPA & IBO
(dB)
C/No losses Efficiency (%)
BOC(2,2) HFET 1.0 2.28 53.73
BOC(14,2) HFET 0.5 2.04 57.5
BOC(2,2) PHEMT 0.0 2.1 59.57
BOC(14,2) PHEMT 0.0 2.03 59.57
Simulation results : Modified Hexaphase
Table 6. Correlation losses and efficiency of Modified Hexaphase
modulation
Signal HPA & IBO
(dB)
C/No losses Efficiency (%)
BOC(2,2) PHEMT &
HFET 0
1.05 58.83
BOC(14,2) PHEMT &
HFET 0
2.42 58.83
BOC(2,2) PHEMT &
HFET 0
0.97 59.57
BOC(10,5) PHEMT &
HFET 0
2.37 59.57
Simulation results : TDMQPSK DBM
Table 7. Correlation losses and efficiency of TDMQPSKDBM
modulation
Signal HPA & IBO
(dB)
C/No losses Efficiency (%)
BOC(2,2) HFET &
PHEMT 0
0.41 59.57
BOC(14,2) HFET &
PHEMT 0
1.93 59.57
BOC(2,2) HFET &
PHEMT 0
0.41 59.57
BOC(10,5) HFET &
PHEMT 0
1.85 59.57
Simulation results : TDMQPSK  MSC
Table 8. Correlation losses and efficiency of TDMQPSKMSC
modulation
Signal HPA & IBO
(dB)
C/No losses Efficiency (%)
BOC(2,2) HFET &
PHEMT 0
0.71 59.57
BOC(14,2) HFET &
PHEMT 0
1.93 59.57
BOC(2,2) HFET &
PHEMT 0
0.72 59.57
BOC(10,5) HFET &
PHEMT 0
1.85 59.57
2232
ION GPS 2002, 2427 September 2002, Portland, OR
Modulation tradeoff
For the Hexaphase modulation, it appears a tradeoff
between the input backoff for the BOC(2,2) and the
BOC(14,2). The BOC(n,m) correlation losses of are not
negligible in the case of Modified Hexaphase, probably
because of the Intermodulation product.
Finally, both Time Multiplexing modulation (TDM
QPSK), the DBM and the MSC, shows the best
performances in term of correlation losses. The choice
between any of those two will rely on interference matters
and refined correlation losses budgets.
In addition, the choice of the transistor technology appears
important for modulations having non constant envelope.
TRACKING PERFORMANCES
Theoretical analysis
In this paper, received signal is assumed to be the sum of a
useful BOC modulated signal with a Gaussian noise that
can be considered as the sum of the receiver thermal noise
with many Gaussian interferences leading to a global noise
unilateral power spectral density (PSD) equal to N0. After
baseband conversion, assuming that the RF filter
bandwidth is infinite and neglecting the double frequency
components (canceled by the predetection filters), signal
can be modeled in complex notation as
() () ( ) () ()
tnjtneTtxtdCty QI
j.... ++−= ∆
φ
(1)
where C is the received power of the signal, d(t) is the
nonreturntozero (NRZ) data signal, T is the transmission
delay from the transmitter to the receiver,
∆φ
is the
difference between local and received carrier phase, nI(t)
and nQ(t) are the Inphase and Quadrate baseband
equivalent noises of the received noise that are assumed to
be Gaussian, independent and with a constant bilateral
PSD equal to N0/2 (well known properties based on Rice
decomposition of white noise), and where finally x(t) is the
BOC signal composed of a pseudorandom noise (PRN)
modulated by a square subcarrier to form a BOC(n,m).
Rca
Rc
m
Rca
Rsc
n== ; (2)
where Rca is the reference GPS C/A code chip rate
(1.023MChips/s).
Code Tracking loop model
Proposed BOC tracking loops are derived from typical
delay lock loops (DLL) used to track classical BPSK
signals. Difference between BPSK and BOC tracking
loops is that local early/prompt/late code replicas are also
modulated by early/prompt/late square subcarriers, so that
DLL works on the main peak of the BOC correlation
function (CF). As an illustration, figure 16 shows
normalized BOC(n,m) with m=n, BOC(n,m) with n=2.m
and BPSK(n) CFs as a function of the delay expressed in
code chip.
Figure 16  Correlation functions of BOC and BPSK
signals
We see on figure 16 that the width of the main CF peak
depends on the ratio between parameters n and m as
Main BOC CF peak width
m
n
4
2
= code chips. (3)
It is clear that the reduction of the width of the main CF
peak due to the coherent subcarrier modulation will result
in more accurate code phase measurements. BOC signal
DLL is shown on figure 16. Lines with full black arrow
represent complex signals and lines with empty arrow
represent real signals. Note that Integrate and Dump (I&D)
filters of the correlation section are complex, which means
that the real one has a total of six I&D filters. I&D filters
are modeled as finite time integrators over the predetection
period Tp (that is usually chosen equal to the bit rate of the
data signal) so that its output at instant k.Tp is given by:
()
()
()
∫
−
=
p
p
Tk
Tk
pDI dttInTkOut
.
.1
&..
(4)
Complex
I&D
Complex
I&D
Complex
I&D
Code
discriminator
Loop filter
E/P/L BOC
generator
y(t)
xE(t)
xP(t)
xL(t)
IE(k)+j.QE(k)
IP(k)+j.QP(k)
IL(k)+j.QL(k)
Ve(k)
Figure 17  BOC Delay Lock Loop
2233
ION GPS 2002, 2427 September 2002, Portland, OR
Expressions of the local signals are:
()
(
)
TtxtxPˆ
−= (5)
()
(
)
cE TTtxtx .
ˆ
δ
+−= (6)
()
(
)
cL TTtxtx .
ˆ
δ
−−= (7)
where T
ˆ is the estimated code delay, Tc is one code chip
duration, and
δ
is the delay between the prompt and
early/late replicas expressed in units of code chips. In
BPSK loops, this spacing can be set from very narrow
value to half of a chip (equivalent to a one chip spacing
between early and late replicas). In the BOC loop shown in
figure 17, as the width of the main correlation peak is
equal to 2Tc/(4m/n) (as shown on figure 16 for m=n, where
m and n are defined in (2)),
δ
can’t be set greater than
Tc/(4m/n).
For more convenience in the rest of the paper, we will
assume that the carrier phase is well estimated by the
phase lock loop (PLL), so that 0
=∆
φ
. The received
signal defined on (1) is then :
() () ( ) () ()
tnjtnTtxtdCty QI ... ++−= (8)
According to (5), (6), (7) and (8), the values of the
correlator outputs of figure 14 are :
() () ()
knRxTdCkI IPpkP +=
ε
. (9)
() ()
knkQ QPP= (10)
() ()()
knTRxTdCkI IEcpkE ++= ..
δε
(10)
() ()
knkQ QEE = (11)
() ()()
knTRxTdCkI ILcpkL +−= ..
δε
(12)
() ()
knkQ QLL = (13)
where Rx(
ε
) is the BOC correlation function as shown on
figure 16, and where
TT ˆ
−=
ε
(14)
is the code synchronization error. The correlation noises
are given by:
() ()
()
()
∫
−
−=
p
p
Tk
Tk
IIP dtTtxtnkn
.
.1
.
ˆ
.
(15)
() ()
()
()
∫
−
−=
p
p
Tk
Tk
QQP dtTtxtnkn
.
.1
.
ˆ
.
(16)
() ()
()
()
∫
−
+−=
p
p
Tk
Tk
cIIE dtTTtxtnkn
.
.1
..
ˆ
.
δ
(17)
() ()
()
()
∫
−
+−=
p
p
Tk
Tk
cQQE dtTTtxtnkn
.
.1
..
ˆ
.
δ
(18)
() ()
()
()
∫
−
−−=
p
p
Tk
Tk
cIIL dtTTtxtnkn
.
.1
..
ˆ
.
δ
(19)
() ()
()
()
∫
−
−−=
p
p
Tk
Tk
cQQL dtTTtxtnkn
.
.1
..
ˆ
.
δ
(20)
The code discrimination function is built from E/P/L
correlation outputs in order to provide synchronization
estimation of code phase. The most common used code
discriminators are:
 the coherent earlyminuslate (EML) given by:
() () ()
kIkIkVe LEEML −= (21)
which needs data demodulation and good carrier phase
estimation;
 the noncoherent earlyminuslate power (EMLp) given
by:
() () ()
(
)
() ()
(
)
kQkIkQkIkVe LLEEEMLp
2222 +−+= (22)
which is totally independent on data modulation and of
carrier phase estimation;
 the noncoherent dotproduct (DP) given by:
() () ()( ) () () ()()()
kQkQkQkIkIkIkVe PLEPLEDP .. −+−= (23)
which is also independent on data modulation and of
carrier phase estimation. Finally, code discriminator
provides an error signal that is filtered by the loop filter in
order to drive and to synchronize the local code phase on
the received one.
Thermal noise on estimated code phase
The method to derive the power of the noise on the
estimated code phase provided by a DLL has been
calculated in [10] for the BPSK case. The same method
2234
ION GPS 2002, 2427 September 2002, Portland, OR
can be applied for the BOC modulation. Estimated code
phase T
ˆcan be predicted using the closed loop linear
model given on figure 18. On this linear model, the
discriminator is modeled by an adder with a gain K that is
the slope of the discrimination function near to the lock
point, around
ε
=0. The numbercontrolled oscillator that
drives the local signal generator is modeled by a integrator
(1/s using the Heaviside operator).
Loop filt er
F(s)
Cod e N CO
1/s
+

T
T
ˆ
K
Ve(
ε
)
Figure 18  Closed loop linear model
Assuming that the error estimation given by the
discriminator is affected by a noise N, then
()
NKVe +=
εε
. (24)
So, estimated code phase T
ˆis given by:
()()()()
+=
+
=K
N
s
sFK
s
sFNVe
T
ε
ε
..
ˆ
(25)
Let’s defined the closed loop transfer function H(s) as
()
()
()
s
sFK
s
sFK
sH .
1
.
+
=
(26)
then
()()()
K
N
sHsHT .1. −−=
ε
(27)
where
ε
in seconds. The noise term on synchronization is
the second term of the right part of (27). The variance of
this noise expressed in squared units of code chip is then
given by
()
()
∫
ℜ
=
=df
TK
fS
fH
T
E
c
N
c
.
.
.)( 2
2
2
2
2
ε
σε
(28)
where
[]
.E denotes the expected value operator and where
()
fSN is the PSD of the noise N at the output of the
discriminator. Generally, the unilateral loop bandwidth BL
defined as
∫
ℜ
=dffHB
L.)(.
2
12
(29)
is sufficiently small as compared with the noise
bandwidth, so that (28) can be approximated by
()
()
22
2
2
.
0..2
c
NL
cTK
SB
T
E=
=
ε
σε
(30)
Noise N is a random process that appears each Tp seconds
at the output of the correlator.
The variance of the error of synchronization expressed in
squared units of chips is finally given by:
()
()
22
2
2
.
0...2
c
NpL
cTK
RTB
T
E=
=
ε
σε
(31)
Now, we can derive the variance of the error for the
common code discriminators.
Coherent DLL : EmL
The expression of the error signal provided by the EML
discriminator is :
() ()()
[]
() ()
knkn
TRxTRxTdCkVe
ILIE
ccpkEML
−+
−−+= ...
δεδε
(32)
The term in bracket is the noiseless or true error signal.
This term allows to derive the gain (or the slope) of the
discriminator. The slope of the EML discriminator close to
the lock point is:
() ()
−
+−
+
−= n
m
T
T
n
m
T
T
TdCK
c
c
c
c
pkEML
4.
1
4.
1...
δεδε
(33)
This expression results in:
n
m
TdCTK pkcEML 8.. −=
(34)
The correlation function of the noise is then equal to:
() () ( )
[]
=
−=
n
m
TN
TRxRxTNR
p
cpN
4
2.
.20..0
0
0
δ
δ
(35)
2235
ION GPS 2002, 2427 September 2002, Portland, OR
Then, inserting (34) and (35) in (31) gives the theoretical
variance of the error of synchronization expressed in
squared units of chips for the BOC EML DLL that is:
n
m
N
C
BL
EML 4
.
0
2
_
δ
σε
=
(36)
Expressed as a function of the chipspacing defined as
δ
.2=∆ , the variance of the BOC EML DLL is:
n
m
N
C
BL
EML 4
.2
.
0
2
_
∆
=
ε
σ
(37)
The 1sigma error is given in meters by:
n
m
N
C
B
Tc L
cmetersEML
4.2
.
..
0
__
∆
=
ε
σ
(38)
Non Coherent DLL : EmL Power
The expression of the error signal provided by the EML
power discriminator is :
() ( ) ( )
[]
() ( ) () ( )
[]
() () () ()
knknknkn
TRxknTRxknTC
TRxTRxTCkVe
QLILQEIE
cILcIEp
ccpEMLp
2222
22
2
.....2
...
−−++
−−++
−−+=
δεδε
δεδε
(39)
The first term in bracket is the true error signal. This term
allows to derive the gain (or the slope) of the
discriminator. The slope of the EML power discriminator
close to the lock point is:
() ()
−
+−
+
−=
22
24.
1
4.
1.. n
m
T
T
n
m
T
T
TCK
c
c
c
c
pEMLp
δεδε
(40)
After calculations, (40) results in:
−−= n
m
n
m
TCTK pcEMLp
δ
41..16... 2
(41)
Noise terms in the error signal of (39) are:
() ( ) () ( )
[]
() () () ()
knknknkn
TRxknTRxknTCN
QLILQEIE
cILcIEpk
2222
.....2
−−++
−−+=
δεδε
(42)
For convenience on calculations, we will assume that the
error is close to the lock point so that 0≈
ε
() ( ) ( )
[]
()
[]
cp
ccpN
TRxTN
TRxTRxNTCR
.21...2
.21.....40
2
22
0
2
0
3
δ
δδ
−+
+=
(43)
Inserting BOC CF values in (43) results in (after
simplifications):
()
+
−= 0
2
041.......320N
n
m
CTTN
n
m
RppN
δδ
(44)
The theoretical variance of the error of synchronization
expressed in squared units of chips for the BOC EML
Power DLL that is (after simplifications):
−
+=
n
m
T
N
C
n
m
N
C
B
p
L
EMLp
δ
δ
σε
41..
1
1
4
.
0
0
2
_
(45)
Expressed as a function of the chipspacing
∆
defined on
(37),we finally have:
∆−
+
∆
=
n
m
T
N
C
n
m
N
C
B
p
L
EMLp
42..
2
1
4
.2
.
0
0
2
_
ε
σ
(46)
The 1sigma error is then given in meters by:
∆−
+
∆
=
n
m
T
N
C
n
m
N
C
B
Tc
p
L
cmetersEML
42..
2
1
4
.2
.
..
0
0
__
ε
σ
(47)
Noncoherent DLL : dotproduct
The same calculations can be performed for the dot
product discriminator defined in (23). Using the same
method than on the two previous case, one can show that:
 The slope of the discriminator is:
n
m
T
T
C
Kp
c
DP .8 2
=
(48)
2236
ION GPS 2002, 2427 September 2002, Portland, OR
 The variance of the discriminator is:
() () ( )
[]
[
]
ppcpN TNTCTRxRxNTR Q....20..0 0
2
0+−=
δ
(49)
which results on
()
+=
p
pN TC
N
NTC
n
m
RQ.
1....
4
.20 0
0
3
δ
(50)
Finally, the theoretical variance of the error of
synchronization expressed in squared units of chips for the
BOC dotproduct DLL that is:
+
∆
=
p
L
DP T
N
C
n
m
N
C
B
.
1
1
4
.2
.
0
0
2
_
ε
σ
(51)
Conclusion
Regarding results from this study concerning BOC signal
tracking and comparing them with common expressions
known for the BPSK case allow us to conclude that they
are related together.
Expressions of tracking errors on BPSK DLL are
0
2
__ .2
.
N
C
BL
EMLBPSK
∆
=
ε
σ
(52)
for the EML DLL,
()
∆−
+
∆
=
2..
2
1
.2
.
00
2
__
p
L
EMLpBPSK T
N
C
N
C
B
ε
σ
(53)
for the EML power, and
+
∆
=
p
L
DPBPSK T
N
C
N
C
B
.
1
1
.2
.
00
2
__
ε
σ
(54)
We see that these expressions are almost identical than the
BOC ones given in (37), (46) and (51), especially for EML
and dotproduct DLLs. For these two types of DLLs, noise
performance of a BOC modulation improves the variance
of the noise by a factor 4m/n so that
n
m
DPBPSK
DPBOC
DPBPSK
DPBOC
4
1
2
__
2
__
2
__
2
__ ==
ε
ε
ε
ε
σ
σ
σ
σ
(55)
For the EML Power DLL, squaring losses seems to be
most important for BOC than for BPSK because
()
∆−<
∆− 242 n
m
(56)
but this effect may be neglected when predetection time is
sufficiently large.
Simulation results
Coherent DLL (EmL)
Boc(2,2) EML Discriminat or – CS=1/10, Tp=1ms, Bdll=2 Hz
Boc(2,2) EML Discriminator – CS=1/3, Tp=1ms, Bdll=2Hz
Noncoherent DLL (dotproduct)
Boc(2,2) DotProduct Discriminator – CS=1/10, Tp=1ms, Bdll=2Hz
2237
ION GPS 2002, 2427 September 2002, Portland, OR
Boc(2,2) DotProduct Discriminator – CS=1/3, Tp=1ms, Bdll=2Hz
CONCLUSIONS
The Alternative BOC, a BOC modulation allowing up to
four signal to be transmitted on the same BOC spectrum
was presented. Preliminary analyses were done on the
impact on payload and the results shown global correlation
losses comparable with those obtained with a twoQPSK
modulation scheme. The Alternative BOC modulation
present better performances in term of measurement errors
such as multipath error, thanks to a wider bandwidth.
Further comparative studies are planed
Examples of modulation schemes for Galileo E1L1E2
band were also presented. Simulations of payload
distortions were performed: the results show an advantage
in Time Division Multiplexing as far as signal correlation
losses are concerned. The results show also the effect of
the HPA transistor technology on performances.
As a conclusion, some performances and capabilities of
the BOC modulations for the tracking operations in
particular, among which the ALTBOC, have been
demonstrated both through theoretical analysis and
simulations.
ACKNOWLEDGEMENT
Acknowledgement is made for the helpful and constructive
cooperation between CNES, ESA and M3Systems, that
lead to the analysis presented here.
The views and concepts expressed herein represent those
of the authors and do not imply any official recognition or
application by any organisation with which the author is
associated.
REFERENCES
[1] “GPS Principles and Applications” [Kaplan.,
1996], E. KAPLAN, , Artech House
[2] “Baseband BOC Modulation”, extract from
Signal Task Force technical note
[3] “A Family of Split Spectrum GPS Civil Signals”,
J. Spilker, et. al. ION GPS ITM 98
[4] “Achievable GPS Multipath Mitigation
Performance Using Dual Civil Frequencies”, L.
Weill, ION GPS NTM 99
[5] “Coherent Adaptive Subcarrier Modulation
(CASM) For GPS Modernization”, P.A. Dafesh,
et. al. NTM 99
[6] “Effective Signal to Noise Ratio Performance
Comparison Of Some GPS Modernization
Signals”, J.K.Holmes, et. al. ION GPS ITM 99
[7] “Time Tracking Performance of GPS Type NRZ
Direct Sequence Signals in the presence of GPS
Modernization Signals” J.K.Holmes, et. al.
[8] “Tracking Algorithm for GPS Offset Carrier
Signals”, P. Fine, et. al. ION GPS NTM 99
[9] “The Offset Carrier Modulation for GPS
Modernization” J. Betz. ION GPS NTM 99
[10] “Code Tracking Loop Performance Including
the Effects of Channel Filtering and Gaussian
Interference”, J.K.Holmes. ION 56th Annual
Meeting. June 2628, 2000.
[11]
[12]
[13]
“GNSS2 Payload : Propagation delays ; possible
architectures”, L. Lestarquit, L. Ries, J. Dantepal,
C.Zanchi, A. Mallet, P. Dumon (CNES), ION GPS
2001
“Status of Galileo Frequency and Signal Design”
G. W. Hein, J. Godet, JL. Issler, JC. Martin, P.
Erhard, R. LucasRodriguez and T. Pratt
“Extending Narrow Correlator technology to
P(Y)code receiers : benefits and issues”. S.
Karels at all. ION GPS.
2238
ION GPS 2002, 2427 September 2002, Portland, OR
APPENDIX : MODULATION LOSSES AT E2/L1/E1
Hexaphase modulation
HFET Amplifier
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
0
,
00 0
,
25 6
,
02 8
,
48 2
,
46 2
,
46 58
,
83
0
,
50 0
,
25 6
,
02 8
,
48 2
,
46 2
,
46 57
,
50
1
,
00 0
,
25 6
,
02 8
,
30 2
,
28 2
,
28 53
,
73
1
,
50 0
,
25 6
,
02 8
,
29 2
,
27 2
,
27 49
,
00
2
,
00 0
,
25 6
,
02 8
,
39 2
,
37 2
,
37 45
,
00
2,50 0,25 6, 02 8,56 2, 54 2,54 41,70
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
0
,
00 0
,
50 3
,
01 5
,
05 2
,
04 2
,
04 58
,
83
0
,
50 0
,
50 3
,
01 5
,
05 2
,
04 2
,
04 57
,
50
1
,
00 0
,
50 3
,
01 5
,
35 2
,
34 2
,
34 53
,
73
1
,
50 0
,
50 3
,
01 5
,
58 2
,
57 2
,
57 49
,
00
2
,
00 0
,
50 3
,
01 5
,
87 2
,
86 2
,
86 45
,
00
2,50 0,50 3, 01 6,18 3, 17 3,17 41,70
BOC(2,2)
BOC(14,2)
PHEMT Amplifier
IBO
(dB)
Signal
Power
Power loss
(dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
0
,
00 0
,
25 6
,
02 8
,
12 2
,
10 2
,
10 59
,
57
0,50 0,25 6,02 8,12 2,10 2
,
10 58
1,00 0,25 6,02 8,12 2,10 2
,
10 56
,
24
1
,
50 0
,
25 6
,
02 8
,
21 2
,
19 2
,
19 54
,
00
2
,
00 0
,
25 6
,
02 8
,
42 2
,
40 2
,
40 51
,
58
2
,
50 0
,
25 6
,
02 8
,
65 2
,
63 2
,
63 49
,
50
3,00 0,25 6,02 8,94 2,92 2,92 46,90
IBO
(dB)
Signal
Power
Power loss
(dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
0
,
00 0
,
50 3
,
01 5
,
04 2
,
03 2
,
03 59
,
57
0
,
50 0
,
50 3
,
01 5
,
28 2
,
27 2
,
27 58
1,00 0,50 3,01 5,51 2,50 2,50 56,24
1
,
50 0
,
50 3
,
01 5
,
81 2
,
80 2
,
80 54
,
00
2
,
00 0
,
50 3
,
01 6
,
13 3
,
12 3
,
12 51
,
58
2
,
50 0
,
50 3
,
01 6
,
50 3
,
49 3
,
49 49
,
50
3,00 0,50 3,01 6,88 3,87 3,87 46,90
BOC(2,2)
BOC(14,2)
Modified Hexaphase modulation
HFET Amplifier
IBO (dB)
Signal
Power
Power loss
(dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0
,
00 0
,
25 6
,
02 7
,
07 1
,
05 1
,
05 58
,
83
BOC(14,2) 0,00 0,5 3,01 5,43 2,42 2,42 58,83
IBO (dB)
Signal
Power
Power loss
(dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0
,
00 0
,
25 6
,
02 6
,
99 0
,
97 0
,
97 58
,
83
BOC(10,5) 0,00 0,5 3,01 5,38 2,37 2,37 58,83
PHEMT Amplifier
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0
,
00 0
,
25 6
,
02 7
,
07 1
,
05 1
,
05 58
,
83
BOC(14,2) 0,00 0,5 3,01 5,43 2,42 2,42 58,83
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0
,
00 0
,
25 6
,
02 7
,
00 0
,
97 0
,
97 59
,
57
BOC(10,5) 0,00 0,5 3,01 5,38 2,37 2,37 59,57
Time Division Multiplex  DBM
HFET
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0
,
00 0
,
53
,
01 9
,
43 6
,
42 0
,
41 58
,
83
BOC(14,2) 0,00 0,5 3, 01 4,94 1,93 1,93 58,83
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0,00 0,5 3,01 9,43 6,42 0,41 58,83
BOC(10,5) 0,00 0,5 3,01 4, 86 1, 85 1,85 58,83
PHEMT
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0,00 0,5 3,01 9,43 6,42 0,41 59,57
BOC(14,2) 0,00 0,5 3,01 4, 94 1, 93 1,93 59,57
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0,00 0,5 3,01 9,43 6,42 0,41 59,57
BOC(10,5) 0,00 0,5 3,01 4, 86 1, 85 1,85 59,57
Time Division Multiplex  MSC
HFET
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0,00 0,5 3,01 9,74 6,73 0,72 58,83
BOC(14,2) 0,00 0,5 3,01 4, 94 1, 93 1,93 58,83
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0,00 0,5 3,01 9,73 6,72 0,71 58,83
BOC(10,5) 0,00 0,5 3,01 4, 86 1, 85 1,85 58,83
PHEMT
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0,00 0,5 3,01 9,74 6,73 0,72 59,57
BOC(14,2) 0,00 0,5 3,01 4, 94 1, 93 1,93 59,57
IBO
(dB)
Signal
Power
Power
loss (dB)
Simu Loss
(dB)
Correlation
loss (dB)
C/No loss
(dB)
Efficiency
(%)
BOC(2,2) 0,00 0,5 3,01 9,73 6,72 0,71 59,57
BOC(10,5) 0,00 0,5 3,01 4, 86 1, 85 1,85 59,57
2239
ION GPS 2002, 2427 September 2002, Portland, OR