# Comparison between Galileo CBOC Candidates  and BOC(1,1) in Terms of Detection Performance

Authors: Fabio Dovis; Letizia Lo Presti; Maurizio Fantino; Paolo Mulassano; Jérémie Godet
Journal: International Journal of Navigation and Observation
 (2008)

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## Abstract

Many scientific activities within the navigation field have been focused on the analysis of innovative modulations for both GPS L1C and Galileo E1 OS, after the 2004 agreement between United States and European Commission on the development of GPS and Galileo. The joint effort by scientists of both parties has been focused on the multiplexed binary offset carrier (MBOC) which is defined on the basis of its spectrum, and in this sense different time waveforms can be selected as possible modulation candidates. The goal of this paper is to present the detection performance of the composite BOC implementation of an MBOC signal in terms of detection and false alarm probabilities. A comparison among the CBOC and BOC(1,1) modulations is also presented to show how the CBOC solution, designed to have excellent tracking performance and multipath rejection capabilities, does not limit the acquisition process.


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## Body

## 1. Introduction

The agreement
reached in 2004 by United States (US) and European Commission (EC) [1] focused on the Galileo and GPS coexistence
clearly stated as central point to the selection of a common signal in
space (SIS) baseline structure that is
the BOC(1,1). In addition, the  same agreement paved the way for common signal
optimization with the goal to provide increased performance as well as
considerable flexibility to receiver manufacturers.Therefore, EC
and US started to analyze possible innovative modulation strategies [2] in the view of Galileo E1 OS optimization and for the
future L1C signals of the new generation GPS satellites.Considering the
recent activities carried out by the Galileo signal task force (STF) jointly to
US experts in the Working Group A, it came out that the multiplexed binary
offset carrier (MBOC) could be a good candidate for both GPS and Galileo
satellites. In fact, on the 26th of July 2007 US and EC announced their
decision to jointly implement the MBOC on the Galileo open service (OS) and the
GPS IIIA civil signal as reported in [3].The MBOC power
spectral density (PSD) is a mixture of BOC(1,1) spectrum and BOC(6,1) spectrum;
then different time waveforms can be combined to produce the MBOC-like spectral
density. The contribution of the BOC(6,1) subcarrier brings in an increased
amount of power on higher frequencies, which leads to signals with narrower
correlation functions and then yielding better performance at the receiver
level.The European
approach to the MBOC implementation consists in adding in time a BOC(1,1) and a
BOC(6,1), defined as composite BOC (CBOC) modulation. At the time of writing, the
US
is likely to choose
a time-multiplexed implementation, named TMBOC. Throughout the paper, the CBOC
features will be described and clarified taking also into account different
implementation options like, for example, the allocation of the power among the
data and pilot channels of the E1 signal.Regardless the
kind of CBOC, such a signal structure allows the receivers to obtain high
performance in terms of multipath rejection and tracking [4, 5]. This is mainly due to a higher transition rate
brought by the BOC(6,1) on top of the BOC(1,1). However, the optimization
process must also consider the signal candidates in terms of their acquisition
performance. It is known that CBOC
signals have sharper correlation functions [4, 5] than the BOC(1,1) solution and this characteristic,
as described in [6, 7], makes the acquisition process more challenging.
In this paper, the acquisition of a CBOC signal in terms of its detection and
false alarm probabilities (more related to the modulation characteristics and less
connected to the acquisition implementation) is investigated and compared to
the performance of the pure BOC(1,1) modulation as well as the detection performance
of a BOC(1,1) legacy receiver acquiring a CBOC signal. In this paper, the mean
acquisition time is not investigated, since it is connected to the detection
rate performance as well as the acquisition solution being implemented, so not
only dependent on the signal modulation itself.The results show
that from the acquisition standpoint, thanks to the 10/11th of power located to a BOC(1,1) in the MBOC
spectrum, the compatibility with the state-of-the-art BOC(1,1) receiver
baseline is assured.Moreover, it is
assumed to use the Galileo acquisition engines presented in [8] which work on a pilot channel with a secondary code,
that further modulates the primary pseudorandom sequences (any kind of BOC or
MBOC).The paper is
organized as follows: Section2 reports the main features of the MBOC approach
while Section 3 presents the correlations properties as well as the possible
CBOC candidates in terms of power allocation. Then, Section 4 is devoted to the
description of the acquisition problem from a theoretical aspect, and Section 5
presents the related simulation results for the CBOCs and BOC(1,1) modulated
signals. Finally, Section 6 draws some conclusions.


## 2. MBOC Definition and Spectrum Characteristics

As reported in [9], the MBOC signal is obtained defining its power
spectral density as a combination of the BOC(1,1) and BOC(6,1) power spectra
(i.e., including both pilot and data channel components). The notation introduced
in [9] is MBOC(6,1,1/11),
where the term (6,1) refers to the BOC(6,1), and the ratio 1/11 represents the power split between the
BOC(1,1) and BOC(6,1) spectrum components as given by(1)GMBOC(f)=1011GBOC(1,1)(f)+111GBOC(6,1)(f), where GBOC(m,n)(f) is the unit-power spectrum density of a
sine-phased BOC modulation as defined in [10].Figure1 shows the comparison among the PSDs of the BOC(1,1)
and the MBOC(6,1,1/11) foreseen for the Galileo E1 signal as well as for the future
GPS L1C. In the picture, it is evident that the increased power at a frequency
shifted about 6 MHz from the central frequency E1, deriving by the presence of
the BOC(6,1) component.Figure 1
Unit power spectral densities comparison
of BOC(1,1) and MBOC(6,1,1/11). (Equivalent baseband representation of the E1
carrier signals.)It is important
to remark that MBOC is defined starting from the power spectrum. In this sense,
many possible time-domain implementations can result with the same
approximation of the defined spectrum.


## 3. CBOC Features

In CBOC
implementations, each ranging code is modulated by a weighted combination of a
BOC(1,1) and a BOC(6,1) subcarriers:(2)sBOC(1,1)(t)={sign[sin(2πtTC)],0≤t≤TC,0,elsewhere,sBOC(6,1)(t)={sign[sin(12πtTC)],0≤t≤TC,0,elsewhere, where TC=1/(1.023⋅106) [second] is the chip duration.The notation
usually reported for the composite BOC signal is CBOC(6,1,γ/ρ), where the parameters γ and ρ are
related to the power splitting between the BOC(1,1) modulated signal and the
BOC(6,1) contribution. However, such a notation does not take into account that
the actual overall signal is obtained by combining data and pilot channels,
then introducing a further degree of freedom. Furthermore, it is not mandatory
that the BOC(6,1) contribution has to be present on both data and pilot channels, opening
additional options to the implementation.Therefore, the
time-domain signal on the E1 data channel can be expressed as(3)sE1tx(t)=xE1,d(t)⋅α[ρ−γρsBOC(1,1)(t)+kdγρsBOC(6,1)(t)], where xE1,d(t) is the product of the navigation message and
the spreading code, and α is the
fraction of power allocated to the data channel. In the same way, the E1 pilot channel
can be expressed as(4)sE1tx(t)=xE1,p(t)⋅β[ρ−γρsBOC(1,1)(t)+kpγρsBOC(6,1)(t)], where xE1,p(t) is the spreading code sequence, and β is the
fraction of power allocated to the pilot channel.The parameterskd and kp can assume the values (0,±1), and they are used to model the presence or not of the BOC(6,1)
subcarrier and its sign in the channels.It is important
to remark that, under the assumption that data and pilot channels use
orthogonal spreading codes, the residual cross-correlation between the spreading sequences
chosen for Galileo can be considered negligible, the overall spectrum on the E1 band is
the summation of the power spectra of the pilot and data channels. Different
combinations of the parametersα, β, kd, kp, γ, and ρ can
be chosen in order to obtain signals, whose power spectral density resembles
the spectral mask defined for the MBOC signal.Table1 shows some possible selection of the parameters
associated to the power split between data and pilot channels.Table 1
Possible options for the MBOC signal implementation by means of CBOC
modulations.
Data channel modulationData channel powerPilot channel modulationPilot channel powerCBOC(6,1,1/11)25%CBOC(6,1,1/11)75%CBOC(6,1,1/11)50%CBOC(6,1,1/11)50%BOC(1,1)25%CBOC(6,1,4/33)75%As already
remarked, it is not always the case that the CBOC is selected for both data and
pilot channels (see third row of Table1). Anyway, the most probable implementation selected
by EC will fall on the CBOC(6,1,1/11) option (and both kd and kp positive) with 50% of power on both channels. This decision is due to the
relatively high data rate on the E1 data channel, which is known also to carry
integrity messages.Regardless the
power splitting, the CBOC in time-domain shows a four-level spreading sequence
as depicted in Figure2, where a CBOC(6,1,1/11) realization with positive
contribution coming from the BOC(6,1) subcarrier has been reported.Figure 2
Example of a CBOC(6,1,1/11) over
an infinite bandwidth (blue line) and shaped with a 12 MHz, 4 pole, Butterworth
filter (red line).The presence of
higher transition rate (due to BOC(6,1) component) creates a sharper
correlation function than the BOC(1,1) baseline. The normalized autocorrelation
functions of the CBOC(6,1,1/11) and CBOC(6,1,4/33) are compared to the BOC(1,1)
correlation in Figure3.Figure 3
Normalized autocorrelation
functions comparison of BOC(1,1), CBOC(6,1,1/11), and CBOC(6,1,4/33) computed over
an infinite bandwidth.The larger is
the contribution of the BOC(6,1) subcarrier (as so theγ over ρ ratio)
in the CBOC implementation, the sharper is the correlation function.This
characteristic will be deeply highlighted in the following sections considering
its impact on the detection performance of the acquisition stage of the
receiver.To better
highlight the sharper CBOC correlation functions, a zoom of Figure3 around the main peak is reported in Figure 4.Figure 4
Zoom of the normalized autocorrelation functions comparison
among BOC(1,1),
CBOC(6,1,1/11), and CBOC(6,1,4/33) computed over an infinite bandwidth.The CBOC
autocorrelation function can be written by means of the BOC(1,1) and BOC(6,1)
autocorrelations and cross-correlations as(5)RCBOC(6,1,γ/ρ)(τ)=ρ−γρRBOC(1,1)(τ)+γρRBOC(6,1)(τ)+2γρργ−1RBOC(1,1)BOC(6,1)(τ), where the term RBOC(1,1)BOC(6,1)(τ) is the cross-correlation term between the
BOC(1,1) and BOC(6,1).The presence of
a cross-correlation factor in (5) results in creating little
differences with respect to the MBOC spectrum as defined in (1). Therefore, on-going studies are in place with the
goal to define implementation strategies to remove such cross factor. Among the
others, the most promising is to alternate BOC(6,1) and BOC(1,1) phases on
adjacent code chips (see as an example [11]).


## 4. Acquisition of the Optimized CBOC Signal

The first operation performed by any GNSS receiver is the signal
acquisition, in charge to understand which satellites are in the line of sight
and to provide the tracking stages with a coarse estimation of the received
code delay and a rough estimation of the Doppler frequency shift.The declaration of the presence or absence of a satellite (determination
of both code delay and Doppler shift) is obtained by evaluating a two-dimensional
matrix called search space. Each item of such a matrix, that is, cell, corresponds
to the value assumed by the bi-dimensional correlation for a specific couple
code delayτ^ and Doppler shift f^d.
This bi-dimensional correlation is also known as cross-ambiguity function.As shown in [8], several are the solutions that can be found in
literature for the signal acquisition: serial search, fast acquisition, and
parallel acquisition in frequency domain, but they just differ in the way the
search space is obtained and equivalent in terms of detection performance.
Other acquisition techniques known with the name of differential acquisition
strategies are nowadays used in GNSS fields [12], but since the mathematical details are different
from the previous mentioned methodologies, they will not be considered in this
paper.Any acquisition technique can be characterized for a givenC/N0 by the false alarm and detection probabilities.
Here, just the false alarm and detection cell probabilities will be considered,
since as discussed in [13] the characteristics of the acquisition engine can
always be related to these fundamental values.Such
probability functions are usually evaluated considering only the peak amplitude
of the correlation function and the presence of noise. Such characterization
does not take into account the fact that, for a given Doppler shift and code
phase error, the correlation generally does not achieve the maximum possible
value. This effect can be modeled as a correlation loss which depends on the
shape of the cross ambiguity function and on its representation in terms of
resolution (i.e., Doppler shift and code delay steps) in the search space [8].In
order to take into account also this effect in the comparison of BOC(1,1) and CBOC(6,1,γ/ρ) functions, the behavior around the
peak in the search space has to be studied.Once
decided the acquisition thresholdVt, the cell false
alarm probability can be easily evaluated as the integral of the tail of the distribution of the
search matrix in a misalignment condition (or equivalently when the signal is
absent). In formula is (see [14])(6)Pfa(Vt)=∫Vt+∞fnaK(x)dx. The
distribution of fnaK(r) can be shown to assume the expression [8]:(7)fnaK(r)=12K(K−1)!σ2KrK−1e−r/2σ2u(r), where, when the
local code spreading sequence has unitary power, and the signal is digitized
respecting the Nyquist criterion, σ2 is equal to (N/2)σn2. N is the number of samples coherently integrated,
and σn2
is the variance of the Gaussian noise affecting the received
signal.Equation (7) holds for the case of noncoherent integration process
applied to a serial or parallel acquisition technique. With this technique, the
detection and decision can be taken over the summation of K correlation outputs before the envelope
operation so to reduce the noise impact and to increase the acquisition detection
rate [8].The probability
density function of the correlator output depends on two variables: the code
displacement errorΔτ=τ−τ^ and the Doppler shift error Δfd=fd−f^d,
respectively. The conditional probability density function to the hypothesis of
a perfect code and Doppler alignment (Δτ=0,Δτ=0) is demonstrated in [8] to assume the expression:(8)faK(r∣Δτ,Δfd=0)=Kασ2(rKα)Ke−(1/2)((r2+Kα2)/σ2)IK−1(rKασ2), where α=CN/2 is a term proportional to the received signal power C.
The corresponding conditional detection probability is then the integral over
the tail of faK(r∣Δτ,Δfd=0) (see [8, 15]), which leads to the expression:(9)Pd∣Δτ,Δfd=0(Vt)=∫Vt/σ+∞faK(x)dx=QK(ασ,Vtσ). Equation (9) involves the kth-order Marcum Q function, QK discussed and defined in [15]. It is remarked how (9) does not still consider the shape of the correlation
function of the signal being acquired.This correlation function can be locally approximated around the peak as
the product of the mono-dimensional correlations along the code delay and
Doppler axes [7, 8], that is(10)R(τ,τ^,fd,f^d)≈RDoppler(fd−f^d)RCode(τ−τ^). It is evident
that in real applications, where a residual error remains in the estimation of
the code phase and Doppler shift, the acquisition does not work using the
maximum possible correlation value. This situation can be modeled as additional
losses or as an impairment, which depends both on the shape of RCode(Δτ) and RDoppler(Δf).The approximation
reported in (10) is extremely important because it makes possible to separate
the effects of the code errors to the one coming from Doppler shift, so to
consider the total loss simply as the product of two single impairments.As far as the
code error loss is concerned, the reduction of the correlation output can be
accounted in a dB amplitude scale as [8](11)αloss|dB=20log|RCode(Δτ)|. A plot of the
code correlation losses for the CBOC(6,1,1/11), CBOC(6,1,4/33), and the
BOC(1,1) is depicted in Figure 5.Figure 5
Performance loss as a function of
the code offset for the BOC(1,1), CBOC(6,1,1/11), and CBOC(6,1,4/33).Similarly to the code correlation loss, the residual Doppler phase error
in the acquisition process produces a reduction of the correlation peak that is
demonstrated, again in [8], to
be equal to(12)βloss|dB=20log10|RDoppler(Δf)|≅20log10|DN[π(fd−f^d)]|. Being DN(x/2)=sin(xN/2)/Nsin(x/2), the Dirichlet kernel function. Remembering
that the term N is the number of samples coherently
integrated, it is clear how the correlation loss βloss depends on the integration time. Figure 6 reports the trend of the Doppler loss when the
integration time goes from T = 4 milliseconds
up to T = 12 millisecondss with 4 milliseconds
of step.Figure 6
Logarithmic Doppler loss.It is necessary to model the probability distribution of the code phase
offset and Doppler shift in order to add up the different losses inside the conditional
detection probability reported in (9). These two realistic hypotheses can be made on the
basis of the functioning of the acquisition engine:(i)
the
resolution used in the acquisition phase is usually of some integer
fraction ±1/L of chip, then the maximum absolute phase
offset Δτ=τ−τ^ can be assumed uniformly distributed between
±1/(2L) chip;(ii)
similarly, the Doppler frequencyΔfd=fd−f^d can be assumed to be uniformly distributed
between zero and half the maximum absolute digital frequency, obtained by normalizing a natural frequency
expressed in Hz with respect to the numerical frequency used to express a
sequence of sample of a digital signal, bin width ±1/(2M),
where M is typically less or equal to N. Furthermore, the
Doppler frequency and code phase errors can be considered independent and
uncorrelated. With all these assumptions, the combined loss simply becomes the
sum (because expressed in dB) of the contributions αloss and βloss.
Thus, according to the
definition of [6, 8], an expected value of the detection
probability, which also accounts for the particular shape of the cross
ambiguity function and the impairments due to the residual code phase and
Doppler errors, can be derived from the conditional detection probability
defined in (9) integrating over the two assumed distribution for Δτ and Δfd:(13)Pd=2N∫−1/2L1/2L∫−1/2M1/2MQk(kασR(f,θ),Vtσ)dfdθ, with R(f,θ)=DN(πf)RCode(θ).Therefore, since
different modulations have differentRCode(θ),
clearly different detection rate must be expected considering what derived in (13).The expected
value of the detection ratePd averages among all the possible code phase and
Doppler offset; the acquisition can deal with, and it can be seen as an
averaged probability even though in the following it will be referred to this
quantity as a normal probability.


## 5. Detection Performance of the CBOC Modulation Candidates

The CBOC candidates
and BOC(1,1) modulations have been compared considering the impairments
addressed in Section4. Both false alarm and detection probabilities have
been obtained by means of Monte Carlo simulations.A classical
acquisition technique not tailored for the new modulation has been considered,
and the false alarm probability as well as the detection rate has been determined
considering an integration period of 4 milliseconds (one Galileo primary code duration).
All the simulated signals (BOC(1,1) and CBOCs) have been sampled at 12 MSamples/s
considering the front end operating under the Nyquist criterion (i.e., 12 MHz
two- sided bandwidth).A common way to express the detection performance of an acquisition
engine is by means of the so-called receiver operative characteristics (ROC) curves,
where the detection probability is reported versus the false alarm probability
at a specific signal to noise ratio. During this performance analysis, aC/N0 of 40 dB·Hz
has been considered to obtain all the ROC curves, where C/N0 here refers to the single channel (pilot or
data component) carrier to noise ratio.In
Figure7, a comparison among the BOC(1,1) modulation and
two different CBOC implementations is depicted. The ROC curves for the three
modulations are reported changing by simulation to simulation and by the code search
resolution starting from a value of half a chip down to an eighth of chip.Figure 7
Receiver operative
characteristic comparison among different CBOC implementations and BOC(1,1) for
different search space spacing atC/N0 of 40 dB·Hz.It is evident
from this comparison that when the code search step is reduced, higher detection
rates can be achieved for the same false alarm probabilities with all the
modulations. These trends can be explained remembering that the larger is the
code phase errorΔτ,
the larger is the correlation loss averaged in (13), and then the lower is the detection rate.The sharper
correlation functions of the CBOC implementations lead to a more relevant code
loss contribution with respect to the BOC(1,1). However, as demonstrated in Figure7, the degradation which stems from the
different code loss among BOC(1,1) and CBOCs can be reduced decreasing the code
phase step, anyway often necessary to guarantee the pull-in phase of the
tracking stages.Another
possibility to address the detection acquisition performance is given by graphs
which depict the
detection probability for a given false alarm probability versus theC/N0, as done in the comparison of Figure 8.Figure 8
Detection probability
versus theC/N0 at a false alarm probability of 10-4. Comparison among
different CBOC implementation for different search space resolution.Here, the BOC(1,1) and CBOCs modulations are compared considering a fixed
false alarm probability of 10-4 varying the C/N0 from a minimum of 30 up to 55 dB·Hz.In this operative scenario,
theC/N0 necessary to acquire the CBOCs with a
detection probability of 0.9 is
reported in Table 2 as well as the degradation with respect to the case
of using a BOC(1,1) modulation.Table 2
Carrier
to noise ratio degradation. Comparison for CBOCs and BOC(1,1) modulations.
ModulationResolution [chip]C/No @ Pd = 0.9 [dB-Hz]Degradation w.r.t BOC(1,1) [dB-Hz]BOC(1,1)0.12541.25—CBOC(6,1,1/11)0.12541.500.25CBOC(6,1,4/33)0.12541.690.44BOC(1,1)0.2542.95—CBOC(6,1,1/11)0.2543.780.83CBOC(6,1,4/33)0.2544.211.26BOC(1,1)0.548.10—CBOC(6,1,1/11)0.548.550.45CBOC(6,1,4/33)0.548.800.7Considering that since MBOC has better self spectral
separation coefficients (SSCs)
than BOC(1,1), the intrasystem interference coming from satellites transmitting
MBOC with a different PRN will
be reduced.In addition, the
SSC between the MBOC and the C/A code is also lower and thus in summary the
intersystem and intrasystem interference is also reduced [16]. Then, the equivalent noise due to interference from
other satellites is around 0.1–0.2 dB lower for MBOC than for BOC(1,1), and the
equivalent C/N0 is expected to be 0.1–0.2 dB-Hz better [16].In addition, the
interplex modulation product with MBOC is around 4 dB lower with CBOC than with
BOC(1,1) and thus the net effect is that at the end, for the same transmitted
power from the satellite, at the ground there is an increase of the received
power of approximately another half a dB.Therefore, the
degradation of the sharper correlation function is mostly compensated in all
the cases by the increased power at the ground and by better SSC, and in some
cases it should
actually outperform the BOC(1,1) at least when code search step is reduced to less or equal to one
quarter of chip.It has not to be
forgotten that one of the aim of the CBOC modulations is to maintain the
interoperability and the compatibility with the existing systems. In fact, the
contribution of the BOC(1,1) in the CBOC definition, (cfr. (3)
and (4)),
still assures a nonzero cross-correlation function among CBOCs and BOC(1,1).Figure9 reports the correlation functions obtained
demodulating a CBOC signal with a local BOC(1,1) code.Figure 9
BOC(1,1) and CBOC
cross-correlation functions comparison computed over an infinite bandwidth and
zoom of correlation peaks.This might be
the working scenario of a BOC(1,1) legacy receiver processing the new optimized
MBOC signal.The
cross-correlation functionsRCBOC(6,1,1/11)BOC(1,1) and RCBOC(6,1,4/33)BOC(1,1) depicted in Figure 9 are practically identical.They are mainly
characterized by a reduction of the peak maximum due to the cross loss given by
the BOC(6,1) term, but the correlation slope and widths are comparable one to
the other.This is the case
of the ROC curves reported in Figure10 where the detection performance of the CBOC(6,1,1/11)
demodulated by a BOC(1,1) replica is reported together with the performance of the standalone
BOC(1,1) and CBOC(6,1,1/11).Figure 10
Receiver operative characteristic comparison, atC/N0 of 40 dB·Hz and different spacing, among the standalone
BOC(1,1), CBOC(6,1,1/11), and the CBOC(6,1,1/11) demodulated with a BOC(1,1)
replica.The comparison
is made considering only a code delay step of 0.25 and 0.125 chip. The
detection probability versus
theC/N0 for a false alarm probability of 10-4 is reported in Figure 11.Figure 11
Detection probability versus theC/N0 at a false alarm probability of 10-4 comparison among standalone BOC(1,1), CBOC(6,1,1/11), and the CBOC(6,1,1/11)
demodulated with a BOC(1,1) replica.It is
interesting to notice how, when the search space has a resolution of 0.25 chip
for the code phase, higher detection probabilities can be obtained by
demodulating the CBOC(6,1,1/11) with a local BOC(1,1) implementation. When the
code step used in the search space is reduced to 0.125 chip, then the solution
to demodulate the CBOC(6,1,1/11) with a local BOC(1,1) does not outperform the
pure CBOC(6,1,1/11) solution.Similar
considerations can be made for the comparison of the CBOC(6,1,4/33) detection performance
which have been reported in Figures12
and 13.Figure 12
Receiver operative characteristic comparison, atC/N0 of 40 dB·Hz and different spacing, among the standalone
BOC(1,1), CBOC(6,1,4/33), and the CBOC(6,1,4/33) demodulated with a BOC(1,1)
replica.Figure 13
Detection probability versus theC/N0 at a false alarm probability of 10-4 comparison among standalone BOC(1,1), CBOC(6,1,4/33), and the CBOC(6,1,4/33)
demodulated with a BOC(1,1) replica.WhenΔτ is reduced, then the maximum peak reduction of RCBOC(6,1,1/11)BOC(1,1) and RCBOC(6,1,4/33)BOC(1,1) plays a more significant role in the total
averaged loss explaining the change of performance outlined in the previous
comments.


## 6.Conclusions

On the basis of
the modernization activities around the future Galileo E1 signals, this paper focuses
on the analysis of the acquisition detection performance of two CBOC solutions,
which are the CBOC(6,1,1/11) and CBOC(6,1,4/33).Such activity, done with an acquisition engine implemented via software,
is a key step for signals comparison considering that the CBOC modulation due
to its sharper correlation function might present some acquisition losses with
respect to the BOC(1,1). Through simulations, it has been proved that, in practical operative conditions
and thanks to the better SSC derived by using an MBOC spectrum and thanks to
the increased power level of the signal at the ground (which results in about
0.7 dB·Hz of
improvement in the equivalent C/N0 seen by the receivers antennas), those
losses can be neglected.Moreover, this
work also shows how the CBOC candidate modulations still assure the compatibility
and interoperability with BOC(1,1) legacy receivers in terms of acquisition.All these
considerations together with the major advantages in terms of better tracking
performance and multipath rejections capabilities clearly justify the
selections of the CBOC as implementation of the agreed MBOC.



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*Source: 793868-2008-04-23.xml*