1

Analysis of the Galileo navigation system

Catarina José Afonso Dias “Departamento de Engenharia Electrotécnica e de Computadores”, DEEC

“Instituto Superior Técnico”, IST Lisbon, Portugal

July 2015

Abstract

The main goal of this article is the study of the Galileo radionavigation system, from the emission of the constellation’s satellite signals to their reception, by the user. Initially, the various existing global radionavigation systems, GNSS, will be presented, with special attention for the American GPS and the European Galileo. A comparison between the number of the visible satellites of the GPS and Galileo systems will be made, during 24 hours, in three different points of the Earth’s surface. In this document the expressions and the multiplexing schemes of each Galileo signal’s modulations will be presented and the respective autocorrelation functions (ACF) and power spectral densities (PSD) are obtained. Finally, the scalar and vectorial architectures of the receiver will be presented, as well as the specific receivers of the AltBOC and MBOC signals, with the scalar architecture being soundly exposed. The NELP and HRC discriminators will be described and presented, and will allow us to study graphically the performance of the multipath mitigation techniques in Galileo signals.

I. INTRODUCTION

The Galileo system is actually in development with the

launching of new satellites. This system aims to be the

European answer to the American GPS and has new types of

signals that allows a bigger precision in the determination of

the receiver’s trajectory, mainly with a higher multipath

robustness.

On 28th March 2015 the Galileo constellation included 8

operational satellites in orbit, with the deployment of 6 more

satellites until the end of the year.

II. GNSS

The concept of GNSS (Global Navigation Satellite System)

consists in global positioning systems with satellites. Each

GNSS has its own satellite constellation and needs to receive

signals from at least 4 satellites to estimate the real position.

Initially, this global system was used only for military purposes

but in 1996 the GPS (American GNSS) became available for

civil users. Besides this, there are systems that only utilized

their countries, which are the RNSS (Regional Navigation

Satellite Systems), as QZSS (Japanese) and IRNSS (Indian).

GPS

This system was developed by DOD of USA with the goal of

offering a navigation system to the army with the capacity of

estimating the position, velocity and time. Later it was used

too by civil users. The GPS satellites transmit in two carriers

modulated in BPSK: L1 (1575.42 MHz) and L2 (1227.6 MHz).

The space segment is constituted by a 32 satellite

constellation in 6 orbits positioned in circular MEO plans.

These orbits cross the equator with an angle of 55º. The first

satellite being launched was Navstar 1 on 22nd February of

1978.

Galileo

Galileo is a navigation satellite system that is being developed

by the EU and ESA and wants to guarantee global positioning

services. However, this system is in development at this

moment and the prevision is to be completely operational in

2020. The advantages of this system is a bigger precision and

security and less problems with multipath and interferences.

The ground control of the system is realized by 2 base

stations, GCS and GMS, located in Funcino (Italy) and Munich

(Germany), respectively. The totally established space

segment of Galileo is a constellation of 30 satellites (27

operational and 3 of substitution), positioned in 3 orbital and

circular MEO plans of 10 satellites with an inclination of 56º

relatively to the equatorial plan. The first satellite launched

was in 28th December of 2005, in which the first Galileo signals

were transmitted on 12 January of 2006.

III. Daily Simulation of the number of GPS and Galileo

satellites

The goal of this chapter is to compare the visibility of Galileo

and GPS satellites, in 3 different points of the Earth’s surface

(latitudes of 0, 40 and 80), in a period of 24 hours, with Matlab.

A. ECEF coordinates

The ECEF coordinates of a centered and fixed system in the Earth are presented in figure 1. The positions of the satellites are determined from the ephemerides that are sent to the receiver in the navigation message, using these coordinates.

Figure 1 - ECEF coordinates system. Source: [1]

2

In order to calculate these coordinates, the equation (1) was used:

[𝑥𝑦𝑧] = [

𝑐𝑜𝑠 𝜃 𝑐𝑜𝑠 Ω − 𝑠𝑖𝑛 𝜃 𝑠𝑖𝑛 Ω 𝑐𝑜𝑠 𝛼𝑐𝑜𝑠 𝜃 𝑠𝑖𝑛 Ω + 𝑠𝑖𝑛 𝜃 𝑐𝑜𝑠 Ω 𝑐𝑜𝑠 𝛼

𝑠𝑖𝑛 𝜃 𝑠𝑖𝑛 𝛼

] (1)

The used parameters are presented in figure 2.

The argument of the latitude at the instant tst if given by:

𝜃 = 𝜈 + 𝜔 (2)

In the equation (2), 𝜔 is the perigee argument and 𝜈 is the true

anomaly, which are related to the equations presented in (3):

𝑠𝑖𝑛 𝜈 =

√1 − 𝑒02 𝑠𝑖𝑛 𝐸

1 − 𝑒0 𝑐𝑜𝑠 𝐸 , 𝑐𝑜𝑠 𝜈 =

𝑐𝑜𝑠 𝐸 − 𝑒0

1 − 𝑒0 𝑐𝑜𝑠 𝐸

(3)

Figure 2 – Detailed scheme of the ECEF coordinates system.

Source: [2]

In order to calculate the true anomaly, we use the values of

the orbital eccentricity, 𝑒0, and the excentric anomaly, E, which

is obtained by the value of the mean anomaly, M (Kepler’s

equation iterative solution):

𝑀 = 𝐸 − 𝑒0 𝑠𝑖𝑛 𝐸 (4)

In equation (4) note that the values of 𝑒0 and M are present

in the Galileo and GPS almanacs. To the calculation of E, we

use the following iterations:

𝐸0 = 𝑀 +

𝑒0 𝑠𝑖𝑛 𝑀

1 − 𝑠𝑖𝑛(𝑀 + 𝑒0) + 𝑠𝑖𝑛 𝑀

(5)

𝐸𝑖 = 𝑀 + 𝑒0 𝑠𝑖𝑛 𝐸𝑖−1, 𝑖 = 1,2, … , 𝑛 (6)

𝐸 = 𝐸𝑛 (7)

The value of the eccentric anomaly has a good approximation

for i=2 and, consequently, we can proceed for the calculation

of the true anomaly because we have all the data that we

need, now.

With the value of the perigee argument and the true anomaly,

we obtain the latitude argument. The orbit’s ray for each

satellite depends on three parameters that we have, and is

given by:

𝑅 = 𝐴 (1 − 𝑒0 𝑐𝑜𝑠 𝐸) (8)

To obtain the value of the Ω, we have the following expression:

Ω = Ω0 + Ω 𝛥𝑡 − Ω𝑒𝑡𝑠𝑡 (9)

In expression (9) we have all the data that we need in the

almanac.

Relatively to the time scales, the receiver times are measured

in relation to the beginning of the GPS week, which is the

midnight from Saturday to Sunday. The reference time of the

ephemeris is 𝑡𝑜𝑒 and 𝑡𝑠𝑡 is the signal’s transmission time, we

obtain 𝛥𝑡 = 𝑡𝑜𝑒 − 𝑡𝑠𝑡. In the next figure we present the relation

of the times referred:

Figure 3 – Time relations. Source: [2]

B. ENU coordinates

The exact location of the satellite coordinates may be

computed in ENU coordinates, obtained from the ECEF

coordinates, as shown in figure 4.

Figure 4 – ENU coordinates referential. Source: [2]

In order to convert the ECEF to ENU coordinates, we apply

the following transformation matrix [3,4]:

[𝑥′

𝑦′

𝑧′] = [

−sin 𝜃𝑢 cos𝜃𝑢 0− sin ∅𝑢 cos𝜃𝑢 − sin ∅𝑢 sin 𝜃𝑢 cos∅𝑢cos∅𝑢 cos𝜃𝑢 cos∅𝑢 sin 𝜃𝑢 sin ∅𝑢

] [

𝑥 − 𝑥𝑢𝑦 − 𝑦𝑢𝑧 − 𝑧𝑢

] (10)

In equation (10) the latitude and longitude of the receiver’s

user in the Earth are given by ∅𝑢 and 𝜃𝑢, respectively. The

values of x, y and z correspond to the ECEF coordinates

previously calculated, and 𝑥𝑢, 𝑦𝑢 and 𝑧𝑢 are the user’s

positions in the Earth, which are fixed.

The choice of the 3 points in the Earth’s surface was based on

varying the latitude to places where this has values of 0, 40

and 80 degrees. The values of ∅𝑢 and 𝜃𝑢 were obtained

directly from the map and to obtain the coordinates 𝑥𝑢, 𝑦𝑢 and

𝑧𝑢 we used two Matlab functions that allows us the direct

calculation of these values. The first used is the following,

where the value of the ECEF coordinates are obtained from

the user’s position in the Earth, with attention to the WGS84

norma:

𝑝 = 𝑙𝑙𝑎2𝑒𝑐𝑒𝑓([𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒, 𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒, 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒],′𝑊𝐺𝑆84′)

The output of the previous function are the x, y and z

coordinates that corresponds to the ECEF coordinates. These

coordinates are used in order to obtain the ENU coordinates,

with the help of the altitude and longitude too:

[𝑥𝑢𝑦𝑢𝑧𝑢] = 𝑒𝑐𝑒𝑓2𝑒𝑛𝑢(𝑥, 𝑦, 𝑧, 𝑙𝑎𝑡𝑖𝑡𝑢𝑑𝑒, 𝑙𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒)

By the previous equation we obtain directly the 𝑥𝑢, 𝑦𝑢 and 𝑧𝑢

coordinates.

C. Simulation of the GPS and Galileo navigation systems,

in 24 hours

In this section we want to simulate the satellite’s behavior

during a day. Therefore, we chose the 12th October 2014, in

the 790th GPS week, because it was a Sunday and 𝑡𝑜𝑒 is 0

because it refers to the seconds of the GPS’s week beginning,

which is in the midnight from Saturday to Sunday. We made

one simulation for each value of latitude (0,40 and 80 degrees)

of Galileo and GPS, and for two mask angles: 15 and 40

degrees. The value of this angle is calculated by the following

expression, in ENU coordinates:

𝑠𝑖𝑛 ∈ =

𝑧′

√(𝑥′)2 + (𝑦′)2 + (𝑧′)2

(11)

With the increase of the mask angle, the number of LoS

satellites will decrease. In table 1 we can conclude about the

3

number of satellites seen in the previous conditions, after all

the simulations done in Matlab. The figures 5 and 6 show the

number of the visible satellites in Lisbon, with a latitude of 40º

(approximately), every 5 minutes.

Visible Satellites

in 24 hours

Latitude (degrees)

α=15º α=40º

GPS Galileo GPS Galileo

Nukak, Colombia

0 14.6 12.6 12.7 10.8

Lisbon, Portugal

40 9.0 7.2 5.4 4.8

Northeast, Greenland

80 11.0 9.8 7.6 7.1

Table 1 - Comparison between the number of visible satellites of GPS and Galileo.

Figure 5 - Number of visible GPS satellites in Lisbon, Portugal, in 24 hours.

Figure 6 - Number of visible Galileo satellites in Lisbon, Portugal, in 24 hours.

As we can conclude, the GPS system is more efficient than

the Galileo because the number of satellites seen from the

same point in the Earth’s surface is always higher in the GPS

case. We can see that, as we expected, the number of visible

satellites is much higher for an elevation angle of 15 degrees

than 40, because there is less space for the satellites in the

second case.

IV. Galileo signals characteristics

The allocation of frequency bands is a complex process

because of the possibility of coexistence of various users and

services in the same frequency interval. ITU is the entity that

regulates the use of the radiofrequency spectrum, such as the

ones used for television, radio, etc. The navigation band for

Galileo and GPS are represented in the figure 5, in purple and

pink, respectively.

Figure 7 - Frequency bands of the GPS and Galileo navigation systems.

The values of the carrier’s frequency and the reference’s

bandwidth of the receiver are presented on table 2. Note that

E5a and E5b together constitute E5:

Signal Carrier

Frequency (MHz)

Reference's Bandwidth of the Receiver

(MHz)

E1 1575.42 24.552

E5 1191.795 51.15

E5a 1176.45 20.46

E5b 1207.14 20.46

E6 1278.75 40.92

Table 2 - Values of the Carrier Frequency and Receiver's Bandwidth

for each Galileo signal.

All the modulations of Galileo signals are presented in figure

8. For the total 4 frequency bands, there are 5 modulations:

Figure 8 - Characteristics of the Galileo signals. Source: [5]

A. E5

This signal is constituted by E5a and E5b signals and is

transmitted in the frequency band between 1164 to 1215 MHz

allocated for RNSS. The multiplexing scheme for E5 signal is

presented in figure 9, with the multiplexing of 2 data channels

and 2 pilot channels, regarding three different services

(OS,CS and SoL):

Figure 9 - Multiplexing Scheme of E5 signal. Source: [7]

4

The four components of E5 signals are:

𝑒𝐸5𝑎−𝐼 comes from the navigation message F/NAV 𝐷𝐸5𝑎−𝐼 modulated with the binary code 𝐶𝐸5𝑎−𝐼

𝑒𝐸5𝑎−𝐼(𝑡)

= ∑ [𝑐𝐸5𝑎−𝐼,|𝑖|𝐿𝐸5𝑎−𝐼 𝑑𝐸5𝑎−𝐼,[𝑖]𝐷𝐶𝐸5𝑎−𝐼 𝑟𝑒𝑐𝑡𝑇𝐶,𝐸5𝑎−𝐼(𝑡

+∞

𝑖=−∞

− 𝑖𝑇𝐶,𝐸5𝑎−𝐼)]

(12)

𝑒𝐸5𝑎−𝑄 it’s a pilot component that comes from the

binary code 𝐶𝐸5𝑎−𝑄

𝑒𝐸5𝑎−𝑄(𝑡) = ∑ [𝑐𝐸5𝑎−𝑄,|𝑖|𝐿𝐸5𝑎−𝑄 𝑟𝑒𝑐𝑡𝑇𝐶,𝐸5𝑎−𝑄(𝑡

+∞

𝑖=−∞

− 𝑖𝑇𝐶,𝐸5𝑎−𝑄)]

(13)

𝑒𝐸5𝑏−𝐼 comes from the navigation message I/NAV 𝐷𝐸5𝑏−𝐼 modulated with the binary code 𝐶𝐸5𝑏−𝐼

𝑒𝐸5𝑏−𝐼(𝑡)

= ∑ [𝑐𝐸5𝑏−𝐼,|𝑖|𝐿𝐸5𝑏−𝐼 𝑑𝐸5𝑏−𝐼,[𝑖]𝐷𝐶𝐸5𝑏−𝐼 𝑟𝑒𝑐𝑡𝑇𝐶,𝐸5𝑏−𝐼(𝑡

+∞

𝑖=−∞

− 𝑖𝑇𝐶,𝐸5𝑏−𝐼)]

(14)

𝑒𝐸5𝑏−𝑄 is a pilot component that comes from the

binary code 𝐶𝐸5𝑏−𝑄

𝑒𝐸5𝑏−𝑄(𝑡) = ∑ [𝑐𝐸5𝑏−𝑄,|𝑖|𝐿𝐸5𝑏−𝑄 𝑟𝑒𝑐𝑡𝑇𝐶,𝐸5𝑏−𝑄

(𝑡

+∞

𝑖=−∞

− 𝑖𝑇𝐶,𝐸5𝑏−𝑄)]

(15)

The resulting signal is given by:

𝑠𝐸5(𝑡) =1

2√2(𝑒𝐸5𝑎−𝐼(𝑡) + 𝑗 𝑒𝐸5𝑎−𝑄(𝑡)) [𝑠𝑐𝐸5−𝑆(𝑡)

− 𝑗 𝑠𝑐𝐸5−𝑆 (𝑡 −𝑇𝑠,𝐸5

4)]

+1

2√2(𝑒𝐸5𝑏−𝐼(𝑡) + 𝑗 𝑒𝐸5𝑏−𝑄(𝑡)) [𝑠𝑐𝐸5−𝑆(𝑡)

− 𝑗 𝑠𝑐𝐸5−𝑆 (𝑡 −𝑇𝑠,𝐸5

4)]

+1

2√2(𝑒5𝑎−𝐼(𝑡) + 𝑒5𝑎−𝑄(𝑡)) [𝑠𝑐𝐸5−𝑃(𝑡)

− 𝑗 𝑠𝑐𝐸5−𝑃 (𝑡 −𝑇𝑠,𝐸5

4)]

+1

2√2(𝑒5𝑏−𝐼(𝑡) + 𝑒5𝑏−𝑄(𝑡)) [𝑠𝑐𝐸5−𝑃(𝑡)

− 𝑗 𝑠𝑐𝐸5−𝑃 (𝑡 −𝑇𝑠,𝐸5

4)]

(16)

The components 𝑒5𝑎−𝐼(𝑡), 𝑒5𝑎−𝑄(𝑡), 𝑒5𝑏−𝐼(𝑡) e 𝑒5𝑏−𝑄(𝑡)

and the parameters 𝑠𝑐𝐸5−𝑃(𝑡) e 𝑠𝑐𝐸5−𝑆(𝑡) are completely

defined in [7].

This modulation is represented by AltBOC(fsp,fc), with 𝑓𝑠𝑝 =

𝑚 ∗ 𝑓𝑟𝑒𝑓 and 𝑓𝑐 = 𝑛 ∗ 𝑓𝑟𝑒𝑓 where 𝑓𝑟𝑒𝑓 = 1.023 𝑀𝐻𝑧, and can be

represented in a simpler way by AltBOC(mn,), with m=15 and

n=10 and is very similar to two BPSK(10) shifted 15MHz for

the right and for the left of the carrier frequency.

The expressions of the power spectral density (PSD) and the

autocorrelation function (ACF) in terms of triangle functions for

this signal is [6,9]:

𝐺𝐴𝑙𝑡𝐵𝑂𝐶(15,10)(𝑓) =𝑇𝑐 cos

2(𝜋𝑓𝑇𝑐)

9 cos (𝜋𝑓𝑇𝑐3)[4 sinc2 (

𝑓𝑇𝑐6)

cos (𝜋𝑓𝑇𝑐3)

− sinc2 (𝑓𝑇𝑐

12) cos (

𝜋𝑓𝑇𝑐

6)]

(18)

𝑅𝐴𝑙𝑡𝐵𝑂𝐶(𝜏) = 8⋀(|𝜏|

𝑇𝐶6⁄) −

16

3⋀(

|𝜏| −𝑇𝐶

3⁄

𝑇𝐶6⁄

)+8

3⋀(

|𝜏| −2𝑇𝐶

3⁄

𝑇𝐶6⁄

)

−1

3⋀(

|𝜏| −𝑇𝐶

12⁄

𝑇𝐶12⁄

) −1

3⋀(

|𝜏| −3𝑇𝐶

12⁄

𝑇𝐶12⁄

)

+1

3⋀(

|𝜏| −5𝑇𝐶

12⁄

𝑇𝐶12⁄

)+1

3⋀(

|𝜏| −7𝑇𝐶

12⁄

𝑇𝐶12⁄

)

−1

3⋀(

|𝜏| −9𝑇𝐶

12⁄

𝑇𝐶12⁄

)−1

3⋀(

|𝜏| −11𝑇𝐶

12⁄

𝑇𝐶12⁄

)

(17)

B. E6

Figure 10 - Multiplexing Scheme of E6 Signal.

The E6 Galileo signal is constituted by BPSK(5) and

BOCcos(10,5) and is transmitted in the frequency band from

1215 to 1300 MHz, interval that belongs to the RNSS [6]. The

multiplexing scheme is presented on figure 10. The

expressions for the data (b) and pilot (C) components are:

𝑒𝐸6−𝐵(𝑡)

= ∑ [𝑐𝐸6−𝐵,|𝑖|𝐿𝐸6−𝐵𝑑𝐸6−𝐵,[𝑖]𝐷𝐶𝐸6−𝐵

𝑟𝑒𝑐𝑡𝑇𝐶,𝐸6−𝐵(𝑡

+∞

𝑖=−∞

− 𝑖𝑇𝐶,𝐸6−𝐵)]

(19)

𝑒𝐸6−𝐶(𝑡) = ∑ [𝑐𝐸6−𝐶,|𝑖|𝐿𝐸6−𝐶

𝑟𝑒𝑐𝑡𝑇𝐶,𝐸6−𝐶(𝑡

+∞

𝑖=−∞

− 𝑖𝑇𝐶,𝐸6−𝐶)]

(20)

The resulting signal is generated with the two components

above and results in:

𝑠𝐸6(𝑡) =

1

√2[𝑒𝐸6−𝐵(𝑡) − 𝑒𝐸6−𝐶(𝑡)]

(21)

The ACF and PSD for the BPSK(5) signal are given by:

𝑅𝐵𝑃𝑆𝐾(5)(𝜏) = ⋀(𝜏

𝑇𝐶5⁄)

(22)

𝐺𝐵𝑃𝑆𝐾(𝑓) = 𝑓𝑐

sin2 (𝜋𝑓𝑓𝑐)

(𝜋𝑓)2

(23)

The ACF and PSD expressions for the BOCcos(10,5) are:

𝑅𝐵𝑂𝐶𝑐𝑜𝑠(10,5)(𝜏)

= ⋀(𝜏

𝑇𝑐8⁄) +∑(−1)𝑘 (1 −

𝑘

4)

3

𝑘=1

⋀(|𝜏| −

𝑘𝑇𝐶4

𝑇𝑐8⁄

)

+1

8∑(−1)𝑘⋀(

|𝜏| −(2𝑘 − 1)𝑇𝐶

8𝑇𝑐8⁄

)

4

𝑘=1

(24)

5

𝐺𝐵𝑂𝐶𝑐𝑜𝑠(10,5)(𝑓) = 4𝑇𝑐sinc2(𝑓𝑇𝑐)

sin4 (𝜋𝑓𝑇𝑐8)

cos2 (𝜋𝑓𝑇𝑐4)

(25)

C. E1

E1 Galileo signal is constituted by BOCcos(15,2.5) and

CBOC(6,1,1/11) and it is transmitted in the band 1559 to 1610

MHz. We can observe the multiplexing scheme in figure 11:

Figure 11 - Multiplexing Scheme of E1 signal. Source: [7]

E1A is a private channel and E1B and E1C corresponds to the

data and pilot components, respectively, and are represented

by:

𝑒𝐸1−𝐴(𝑡) is a private data channel,

𝑒𝐸1−𝐵(𝑡) comes from the binary code 𝐶𝐸1−𝐵 modulated with the binary navigation I/NAV signal 𝐷𝐸1−𝐵, and then modulated with the sub-carriers 𝑠𝑐𝐸1−𝐵,𝑎 and 𝑠𝑐𝐸1−𝐵,𝑏 from BOC(1,1) and BOC(6,1),

respectively,

𝑒𝐸1−𝐵(𝑡) = ∑ [𝑐𝐸1−𝐵,|𝑖|𝐿𝐸1−𝐵

𝐷𝐸1−𝐵,|𝑖|𝐷𝐶𝐸1−𝐵𝑟𝑒𝑐𝑡𝑇𝑐,𝐸1−𝐵(𝑡

∞

𝑖=−∞

− 𝑖𝑇𝑐,𝐸1−𝐵)𝑠𝑖𝑔𝑛[𝑠𝑖𝑛(2𝜋𝑅𝑠,𝐸1−𝐵𝑡)]]

(26)

𝑒𝐸1−𝐶(𝑡) originating from the binary code 𝐶𝐸1−𝐶 including the corresponding secondary code, which is after modulated with the sub-carriers 𝑠𝑐𝐸1−𝐶,𝑎 and

𝑠𝑐𝐸1−𝐶,𝑏 in phase opposition.

𝑒𝐸1−𝐶(𝑡)

= ∑ [𝑐𝐸1−𝐶,|𝑖|𝐿𝐸1−𝐶𝑟𝑒𝑐𝑡𝑇𝑐,𝐸1−𝐶(𝑡

∞

𝑖=−∞

− 𝑖𝑇𝑐,𝐸1−𝐶)𝑠𝑖𝑔𝑛[𝑠𝑖𝑛(2𝜋𝑅𝑠,𝐸1−𝐶𝑡)]]

(27)

Through the binary components 𝑒𝐸1−𝐵(𝑡) and 𝑒𝐸1−𝐶(𝑡) we can achieve the resulting signal E1 with the pilot and data components being modulated in the same carrier, each one with an occupation tax of 50%.

𝑠𝐸1(𝑡) =

1

√2(𝑒𝐸1−𝐵(𝑡) (𝛼 𝑠𝑐𝐸1−𝐵,𝑎(𝑡) + 𝛽 𝑠𝑐𝐸1−𝐵,𝑏(𝑡))

− 𝑒𝐸1−𝐶(𝑡) (𝛼 𝑠𝑐𝐸1−𝐶,𝑎(𝑡)

− 𝛽 𝑠𝑐𝐸1−𝐶,𝑏(𝑡)))

(28)

with 𝑠𝑐𝑋(𝑡) = 𝑠𝑔𝑛 (𝑠𝑖𝑛(2𝜋𝑅𝑠,𝑋𝑡))

𝛼 = √10

11 , 𝛽 = √

1

11

The ACF and PSD for BOCcos(15,2.5) are given by:

𝑅𝐵𝑂𝐶𝑐𝑜𝑠(15,2.5)(𝜏) = ⋀(𝜏

𝑇𝑐24⁄)

+∑(−1)𝑘 (1 −𝑘

12)⋀(

|𝜏| −𝑘𝑇𝐶12

𝑇𝑐24⁄

)

11

𝑘=1

+1

24∑(−1)𝑘⋀(

|𝜏| −(2𝑘 − 1)𝑇𝐶

24𝑇𝑐8⁄

)

12

𝑘=1

(29)

𝐺𝐵𝑂𝐶𝑐𝑜𝑠(15,2.5)(𝑓) = 4𝑇𝑐sinc2(𝑓𝑇𝑐)

sin4 (𝜋𝑓𝑇𝑐24

)

cos2 (𝜋𝑓𝑇𝑐12

)

(30)

For the CBOC(6,1,1/11) signal we obtain the ACF (31,32 and

33) and PSD (34) as:

𝑅𝐶𝐵𝑂𝐶(𝜏) =1

2[𝑅𝑋𝐷(𝜏) + 𝑅𝑋𝑃(𝜏)]

(31)

𝑅𝑋𝐷(𝜏) = 𝑅𝑀𝐵𝑂𝐶(𝜏) + 2

√10

11𝑅12(𝜏)

𝑅𝑋𝑃(𝜏) = 𝑅𝑀𝐵𝑂𝐶(𝜏) − 2√10

11𝑅12(𝜏)

(32)

𝑅12(𝜏)

=

1

12∑[

|𝜏| − (𝑇𝐶12+ 𝑘

𝑇𝐶6)

𝑇𝐶12⁄

] , 0 ≤ |𝜏| ≤ 𝑇𝐶

2

𝑘=0

−1

12∑[

|𝜏| − (7𝑇𝐶12

+ 𝑘𝑇𝐶6)

𝑇𝐶12⁄

] ,𝑇𝐶

2⁄ ≤ |𝜏| ≤ 𝑇𝐶

2

𝑘=0

(33)

𝐺𝐶𝐵𝑂𝐶(6,1,1/11)(𝑓) =10

11𝐺𝐵𝑂𝐶𝑠𝑒𝑛(1,1) +

1

11𝐺𝐵𝑂𝐶𝑠𝑒𝑛(6,1)

=𝑇𝑐

11sinc2(𝑓𝑇𝑐) [10 tan

2 (𝜋𝑓𝑇𝑐

2)

+ tan2 (𝜋𝑓𝑇𝑐

12)]

(34)

D. Supported Services

The services supported by each Galileo signal are:

OS (Open Service) - open service available for all

the users;

SoL (Safety-of-Life service) - open service with

guaranteed precision;

PRS (Public Regulated Service) - restrict access

service;

SAR (Search and Rescue Service) – service to the

detention and localization of emergency signals.

Id OS SoL CS PRS SAR

E5a

E5b

E6A

E6B,C

L6

E1A

E1B,C

Table 3 - Galileo system services.

6

IV. Receiver’s Architecture

Figure 12 - Block Diagram of a GNSS receiver.

The architecture of a GNSS receiver consists of an antenna

that receives the satellite signals, with or without multipath.

After the reception of the signal, it passes through a front end

constituted by amplifiers and filters and, when the signal is

sampled, it is converted into phase and quadrature

components which will be processed in the receiver channel

by the PLL and DLL for a posterior navigation data extraction

and pseudodistances computation. These pseudodistances

will the filtered in the navigation system and will originate a

position, velocity and time (PVT) estimation desired by the

user. It is important to note that the PLL and DLL have a

fundamental role because they allow the tracking of the carrier

signal and the code phase, respectively.

A. Scalar and vector architectures

There are two receiver architectures: scalar and vector, which

are presented in figures 13 and 14, respectively.

Figure 14 – Receiver’s vector architecture.

The main differences between the two architectures are that

the signal tracking in the scalar architecture is done in the

tracking loop and the estimation of the navigation state is

accomplished in the navigator processor, while in the vector

architecture both are done in a single process,

simultaneously. In the scalar architecture, each satellite has

tracking loops dedicated to the signals phase and frequency

estimation and, each time that a satellite is added, new scalar

tracking loops are added to estimate the signal parameters.

What happens in the vector architecture is that the number of

unknowns stands fixed and is continuously available to

explore signals from more than 4 satellites, when this number

becomes available.

B. AltBOC Receivers

It is possible to track the complete E5 AltBOC signal or any

sub-band (E5A or E5b) of this signal. The baseband resulting

signal is correlated with a local generated signal which

depends in the method utilized [9]. In this document are

presented two of the various architectures available for the

tracking of this signal where the first applies for the signal

tracking of the sub-bands E5a or E5b and the second is used

on the signal tracking of the E5 band.

B1. Single-Sideband AltBOC Receiver

The output of the IF section is given by:

𝑟(𝑡) ≈𝐴

2√2[𝑒𝐸5𝑏−𝐼(𝑡)cos((𝑤𝑐 +𝑤𝑠)𝑡)

− 𝑒𝐸5𝑏−𝑄(𝑡)sin((𝑤𝑐 +𝑤𝑠)𝑡)

+ 𝑒𝐸5𝑎−𝐼(𝑡)cos((𝑤𝑐 −𝑤𝑠)𝑡)

− 𝑒𝐸5𝑎−𝑄(𝑡) sin((𝑤𝑐 −𝑤𝑠)𝑡)]

(35)

The phase and quadrature components of the signal are

presented below, after the multiplication of the r(t) by the

components of the NCO carrier, with a lowpass filtering.

𝐼(𝑡) =

𝐴

2√2[𝑒𝐸5𝑏−𝐼(𝑡) cos∅ + 𝑒𝐸5𝑏−𝑄(𝑡) sin ∅]

(36)

𝑄(𝑡) =

𝐴

2√2[−𝑒𝐸5𝑏−𝐼(𝑡) sin ∅ + 𝑒𝐸5𝑏−𝑄(𝑡) cos ∅]

(37)

i. PLL

The PLL correlates I(t) and Q(t) with the locally-generated

code sequence 𝑒𝐸5𝑏−𝑄(𝑡) and the code delay error ϵ, to achieve:

𝑈(ϵ) =

1

𝑇∫ 𝐼(𝑡)𝑇

0

𝑒𝐸5𝑏−𝑄(𝑡 − 𝜖) =𝐴

2√2𝑅𝑐(𝜖)sin (∅)

(38)

𝑉(ϵ) =

1

𝑇∫ 𝑄(𝑡)𝑇

0

𝑒𝐸5𝑏−𝑄(𝑡 − 𝜖) =𝐴

2√2𝑅𝑐(𝜖)cos (∅)

(39)

The output of the 4-quadrant arctangent phase discriminator

is:

∅ = 𝑎𝑟𝑐𝑡𝑎𝑛2 (

𝑈(𝜖)

𝑉(𝜖))

(40)

ii. DLL

We can consider different types of DLLs. For instance, the

response of the Early-Late (EL) discriminator is:

Figure 13 – Receiver’s scalar architecture.

7

𝐷𝐸𝐿(𝜖) = 𝑉 (𝜖 −∆

2) − 𝑉 (𝜖 +

∆

2)

=𝐴

2√2[⋀(

𝜖 −∆2

𝑇𝑐)

− ⋀(𝜖 +

∆2

𝑇𝑐)]cos (∅)

(41)

B2. Double-Sideband AltBOC Receiver

This type of receiver is based on the coherent reception and

the processing of the entire Galileo E5 band and is showed in

[9].

i. PLL

The inphase and quadrature components, after low-pass

filtering, are:

[𝐼(𝑡)𝑄(𝑡)

] = 𝐴 [𝑅𝑒𝑠𝐸5(𝑡) cos(∅) + 𝐼𝑚𝑠𝐸5(𝑡)sin (∅)

−𝑅𝑒𝑠𝐸5(𝑡) sin(∅) + 𝐼𝑚𝑠𝐸5(𝑡)cos (∅)]

(42)

With this, the output of the 4-quadrant arctangent phase

discriminator is:

∅ = −𝑎𝑟𝑐𝑡𝑎𝑛2 (

𝑉(𝜖)

𝑈(𝜖))

(43)

with the locally-generated code delay error being 𝜖 and 𝑉(𝜖)

and 𝑈(𝜖):

𝑈(ϵ) =

1

𝑇∫ [𝐼(𝑡)𝐼(𝑡 − 𝜖) + 𝑄(𝑡)(𝑡 − 𝜖)]𝑇

0

(44)

𝑉(ϵ) =

1

𝑇∫ [𝑄(𝑡)𝐼(𝑡 − 𝜖) + 𝐼(𝑡)(𝑡 − 𝜖)]𝑇

0

(45)

ii. DLL

The response of the EL and NELP discriminators are given by:

𝐷𝐸𝐿(𝜖) = √2𝐴 [⋀(𝜖 −

∆2

𝑇𝑐)𝑅𝑠𝑐 (𝜖 −

∆

2)

− ⋀(𝜖 +

∆2

𝑇𝑐)𝑅𝑠𝑐 (𝜖 +

∆

2)] cos (∅)

(46)

𝐷𝑁𝐸𝐿𝑃(𝜖) = |𝑅𝑋𝐸 |

2− |𝑅𝑋

𝐿 |2

= 2𝐴2 [⋀2(𝜖 −

∆2

𝑇𝑐)𝑅𝑠𝑐

2 (𝜖 −∆

2)

− ⋀2(𝜖 +

∆2

𝑇𝑐)𝑅𝑠𝑐

2 (𝜖 +∆

2)]

(47)

C. MBOC Receiver

MBOC modulation was selected for the E1 Galileo signal and

for the L1C GPS signal.

The E1 signal divides equally the power between the data and

pilot channels, and both uses the CBOC modulation with the

sub-carrier BOC(6,1) which is constituted by a sub-carrier

constituted by the sum of BOC(1,1) and BOC(6,1). The

BOC(6,1) component is added to the BOC(1,1) in phase (‘+’)

for the data channel and in phase-opposition (‘-‘) for the pilot

channel [8].

The major goal of the tracking is to improve the values of the

estimated frequency ∆𝑓𝑖 and the code phase ∆∅𝑖 obtained

during the acquisition process and to track them and to

demodulate the navigation messages.

C1. Classic Tracking

The classic tracking uses the ACF between the local code

replica and the input signal. The classic architecture is

presented in the figure 15 [11,13]:

Figure 15 - Classic CBOC tracking architecture. Source: [10]

In this technique we assume the CBOC replica and the use of

the Early, Prompt and Late correlations. The CBOC tracking

increases the mitigation capability of multipath.

C2. TM61 Tracking

This technique was proposed for the CBOC tracking in [10,12]

and was developed in order to restrict the complexity of the

tracking loop to the minimum possible, decreasing the number

of used correlators. In this context, the TM61 tracking is based

on the utilization of the Early and Late (E and L) correlations

between the input of the CBOC and the local pure replica of

BOC(6,1) and a Prompt (P) correlation between the input of

the CBOC and the pure replica of BOC(1,1) [11].

The TM61 tracking architecture is showed on figure 16:

Figure 16 - TM61 tracking architecture. Source: [10]

V. Multipath Mitigation

The name “multipath” comes from the fact that a satellite

signal might follow a multiple number of propagation paths

until the arrival to the reception antenna [11]. Basically, the

receiver antenna receives the direct signal and/or one or more

reflections from the same signal in structures and in the floor,

as it is represented on figure 17, that shows a direct path and

a reflected signal (multipath).

Figure 17 - Direct path and multipath signals. Source: [14]

8

A. NELP

In figure 18 we have the receiver associated to the NELP

discriminator, where a perfect synchronization of the

frequency is assumed, but with a phase error of θ. In the same

figure, ∆ is the early-space spacing and ∈ is the

synchronization error.

Figure 18 - Receiver structure using NELP. Source: [13]

A1. Performance without multipath

When the signal arrives to the front end of the receiver, the

expression of the receiver input is:

(𝑡) = 𝐴(𝑡) cos(𝑤0𝑡 + 𝜃)

+ 𝑛𝑖(𝑡) cos(𝑤0𝑡) +𝑛𝑖(𝑡) sin(𝑤0𝑡) (48)

In the expression X, the aditive Gaussian noise is 𝑤(𝑡) =

𝑛𝑖(𝑡) cos(𝑤0𝑡) +𝑛𝑖(𝑡) sin(𝑤0𝑡), where 𝑛𝑖(𝑡) and 𝑛𝑞(𝑡) are low-

pass independent Gaussian processes. The phase and

quadrature components are:

𝑖(𝑡) = 𝐴(𝑡) cos𝜃 + 𝑛𝑖(𝑡) (49)

𝑞(𝑡) = 𝐴(𝑡) sin 𝜃 + 𝑛𝑞(𝑡) (50)

The components that enters the discriminator are:

𝐼𝐸 = 𝐴𝑅𝑋 (−

∆

2+∈)cos 𝜃 + 𝑁𝑖,𝐸

(51)

𝑄𝐸 = 𝐴𝑅𝑋 (−

∆

2+∈)cos 𝜃 + 𝑁𝑞,𝐸

(52)

𝐼𝐿 = 𝐴𝑅𝑋 (−

∆

2+∈) cos𝜃 + 𝑁𝑖 ,𝐿

(53)

𝑄𝐿 = 𝐴𝑅𝑋 (−

∆

2+∈)cos 𝜃 + 𝑁𝑞,𝐿

(54)

The normalized NELP discriminator output is:

𝐷𝑁(∈) =

(𝐼𝐸2 + 𝑄𝐸

2) − (𝐼𝐿2 + 𝑄𝐿

2)

(𝐼𝐸2 + 𝑄𝐸

2) + (𝐼𝐿2 + 𝑄𝐿

2)

=𝑅𝑋2 (−

∆2+∈) − 𝑅𝑋

2 (∆2+∈)

𝑅𝑋2 (−

∆2+∈) + 𝑅𝑋

2 (∆2+∈)

(55)

The equilibrium condition for the DLL is 𝐷𝑁(∈) = 0 and the

solution for that condition corresponds to ∈= 0, which means

that the code delay error is null.

A2. Performance with multipath

In the presence of multipath the receiver’s signal is constitute

by the line-of-sight (LoS) signal with amplitude A and for the

reflected signal with amplitude 𝛼𝐴, delay 𝜏 and phase ∅

relatively to the direct signal. The input signal in the receiver

in this case is [13]:

𝑟(𝑡) = 𝐴𝑋(𝑡) cos(𝑤0𝑡 + 𝜃) + 𝛼 𝐴𝑋(𝑡− 𝜏) cos(𝑤0𝑡 + 𝜃 + ∅) + 𝑛𝑖(𝑡) cos(𝑤0𝑡) −𝑛𝑞(𝑡) sin(𝑤0𝑡)

(56)

In the previous expression, 𝛼 varies between 0 and 1

according to the power relation between the secondary and

the direct ray. We consider 𝛼 = 0.5 for the simulations, value

that mens that the secondary ray has quarter of the direct ray

power, in LoS. To obtain the signal components we need to

integrate and the results are:

𝐼𝐸 = 𝐴𝑅𝑋 (−∆

2+∈) cos𝜃 + 𝛼𝐴𝑅𝑋 (−𝜏 −

∆

2+∈) cos(𝜃 + ∅) + 𝑁𝑖,𝐸

(57)

𝑄𝐸 = 𝐴𝑅𝑋 (−∆

2+∈)cos 𝜃

+ 𝛼𝐴𝑅𝑋 (−𝜏 −∆

2+∈) cos(𝜃 + ∅) + 𝑁𝑞,𝐸

(58)

𝐼𝐿 = 𝐴𝑅𝑋 (∆

2+∈) cos𝜃

+ 𝛼𝐴𝑅𝑋 (−𝜏 +∆

2+∈) cos(𝜃 + ∅) + 𝑁𝑖,𝐿

(59)

𝑄𝐿 = 𝐴𝑅𝑋 (∆

2+∈) cos𝜃

+ 𝛼𝐴𝑅𝑋 (−𝜏 +∆

2+∈) cos(𝜃 + ∅) + 𝑁𝑖,𝐿

(60)

The discriminator’s output is calculated:

𝐷(∈, 𝜏, ∅) = 𝐴2𝑅𝑋2 (−

∆

2+∈) + 𝐴2𝛼2𝑅𝑋

2 (−𝜏 −∆

2+∈)

+ 2𝐴2𝛼𝑅𝑋 (−∆

2+∈)𝑅𝑋 (−𝜏 −

∆

2+

∈) cos∅ − 𝐴2𝑅𝑋2 (

∆

2+∈)

− 𝐴2𝛼2𝑅𝑋2 (−𝜏 +

∆

2+∈)

− 2𝐴2𝛼𝑅𝑋 (∆

2+∈)𝑅𝑋 (−𝜏 +

∆

2+

∈) cos∅ + 𝑟𝑢í𝑑𝑜

(61)

The noise is neglected for simplicity. The two situations are:

∅ = 0 → 𝐷(∈, 𝜏, 0) = 0

∅ = 𝜋 → 𝐷(∈, 𝜏, 𝜋) = 0

(62)

With both solutions, which are presented in thesis, the final

solution for the multipath error envelopes is:

𝑅𝑋 (−∆

2+∈) − 𝑅𝑋 (

∆

2+∈)

= ±𝛼 [𝑅𝑋 (−𝜏 −∆

2+∈)

− 𝑅𝑋 (−𝜏 +∆

2+∈)]

(63)

Using the ACF’s of AltBOC(15,10), BOC(1,1), C/A GPS signal

and CBOCpilot(6,1,1/11), we obtain the multipath error

envelopes presented in figure 20.

B. HRC

Let’s consider the HRC discriminator presented in figure 19,

with an (𝑡) input signal and coherent reception (𝜃=0). After

band-pass filtering we have:

(𝑡) = 𝐴(𝑡) cos(𝑤0𝑡)

+ 𝑛𝑖(𝑡) cos(𝑤0𝑡)

+ 𝑛𝑖(𝑡) sin(𝑤0𝑡)

(64)

9

Figure 19 - Receiver structure using HRC. Source: [13]

B1. Performance without multipath

As we can observe in figure 19, there are four correlators

whose responses are:

𝐼𝑉𝐸 = 𝐴𝑅𝑋(−∆+∈) + 𝑁𝑉𝐸 (65)

𝐼𝐸 = 𝐴𝑅𝑋(−

∆

2+∈) + 𝑁𝐸

(66)

𝐼𝐿 = 𝐴𝑅𝑋(

∆

2+∈) + 𝑁𝐿

(67)

𝐼𝑉𝐿 = 𝐴𝑅𝑋(∆+∈) + 𝑁𝑉𝐿 (68)

The discriminator output is given by the expression below:

𝐷(∈) = 2𝐴 [𝑅𝑋 (−

∆

2+∈) − 𝑅𝑋 (

∆

2+∈)]

− 𝐴[𝑅𝑋(−∆+∈) − 𝑅𝑋(∆+∈)]

(69)

B2. Performance with multipath

Consider that the RF input is given by (48) with 𝜃 = 0.

The correlators outputs are:

𝐼𝑉𝐸 = 𝐴𝑅𝑋(−∆+∈) + 𝛼𝐴 cos∅ 𝑅𝑋 (−𝜏 − 2

∆

2+∈) + 𝑁𝑉𝐸

(70)

𝐼𝐸 = 𝐴𝑅𝑋 (−

∆

2+∈) + +𝛼𝐴 cos∅𝑅𝑋 (−𝜏 −

∆

2+∈) + 𝑁𝐸

(71)

𝐼𝐿 = 𝐴𝑅𝑋 (

∆

2+∈) + 𝛼𝐴 cos∅ 𝑅𝑋 (−𝜏 +

∆

2+∈) + 𝑁𝐿

(72)

𝐼𝑉𝐿 = 𝐴𝑅𝑋(∆+∈) + 𝛼𝐴cos ∅𝑅𝑋(−𝜏 + ∆+∈) + 𝑁𝑉𝐿 (73)

If we neglect the contribution of the noise, we obtain the

following discriminator response:

𝐷(∈) = 2𝐴 [𝑅𝑋 (−∆

2+ 𝜖) + 𝛼 cos∅ 𝑅𝑋 (−𝜏 −

∆

2+∈)

− 𝑅𝑋 (∆

2+ 𝜖)

− 𝛼 cos∅ 𝑅𝑋 (−𝜏 +∆

2+∈)]

− 𝐴[𝑅𝑋(−∆+ 𝜖)+ 𝛼 cos∅ 𝑅𝑋(−𝜏 − ∆+∈)− 𝑅𝑋(∆ + 𝜖)

− 𝛼 cos∅ 𝑅𝑋(−𝜏 + ∆+∈)]

(74)

The multipath error envelopes are obtained by the solutions

of equilibrium for ∅ = 0, 𝜋, whose corresponding equations

are:

2 [𝑅𝑋 (−∆

2+ 𝜖) − 𝑅𝑋 (

∆

2+ 𝜖)] + 𝑅𝑋(∆ + 𝜖) − 𝑅𝑋(−∆+ 𝜖)

= ± 2 [−𝑅𝑋 (−𝜏 −∆

2+∈)

+ 𝑅𝑋 (−𝜏 +∆

2+∈)] − 𝑅𝑋(−𝜏 + ∆+∈)

+ 𝑅𝑋(−𝜏 − ∆+∈)

(75)

The sign ‘+’ in the equation (75) corresponds to the

equilibrium solution for ∅ = 0. The multipath error envelopes

for the HRC discriminator corresponds to the modulations

C/A from GPS, BOc(1,1), CBOCpilot(6,1,1/11) and

AltBOC(15,10), which are presented on figure 21, with an

infinite bandwidth.

Figure 20 - Multipath error envelopes for several signals using NELP, with an infinite bandwidth.

Figure 21 - Multipath error envelopes for several signals using HRC,

with infinite bandwidth.

Both curves represented for each modulation of the NELP and

HRC discriminators correspond to the worst situations with

∅ = 0 and ∅ = 𝜋, that is, all the situations are between the two

represented envelopes for each modulation. We can verify

that for both HRC and NELP. The order of the most efficient

modulations is: C/A, BOC(1,1), CBOCpilot and AltBOC. It’s

important to refer that AltBOC has values that are almost null

when compared to the others, for both discriminators. HRC

discriminator is more efficient than NELP because has less

tracking errors on the same secondary ray delay values.

10

VI. Conclusions The radionavigation systems presented in this thesis allows the determination of the position of a receiver with satellites from the corresponding constellation. To achieve a PVT estimation it is necessary to receive information from, at least, 4 satellites. The GPS and Galileo systems were compared through Matlab graphical simulations that represent the number of visible satellites from 3 positions in the Earth’s surface in a complete day, from 0 AM to 12 PM. The GPS system is more efficient than Galileo, as we expected, because the first has 32 satellites while the second has only 27, and this results in a bigger probability of them being in a better position for the information delivery because of the visibility from the Earth’s surface, allowing a better precision. With this, we can conclude, by graphic, that the mean number of visible satellites visualized by GPS system is always bigger than by Galileo, showing that this first system is more efficient. There are 2 band intervals that are simultaneously occupied by the ARNS and RNSS, where the frequency bands from Galileo (E5a, E5b, E6 and E1) and GPS (L5, L2 and L1) are included. The modulations mentioned in Galileo are AltBOC(15,10) for E5a and E5b signals, BPSK(5) and BOCcos(10,5) for E6 signal and BOCcos(15,2.5) and CBOC(6,1,1/11) for E1 signal and we obtained the autocorrelation functions and power spectral densities for all the simulations. The supported services by the Galileo system are 5: OS (open service to all the users), SoL (open service with guaranteed precision with transmission and protection provided by ARNS bands), CS (service available by payment), PRS (restrict access service with governmental control, for security services) and SAR (search and safety service capable of detecting and locating emergency signals in any place of the world). The GNSS receiver consists of an antenna that receives the satellite signal, with or without multipath. This signal passes through a front end constituted by amplifiers and filters and, when the signal is sampled, it is converted in phase and quadrature components that will be processed in each receiver channel by the DLL and PLL for a posterior data navigation extraction and pseudodistances calculation. These pseudodistances will be filtered in the navigation filter and origin the user’s position, velocity and time estimation. We concluded too that there are two receiver architectures: vector and scalar. The main difference between the two architectures is that in the scalar one the signal tracking is done in the tracking loops, independently for each signal and the navigation estimate occurs in the navigation processor, while in the vector architecture both processes are done simultaneously. There are 2 types of AltBOC receivers: single-sideband that processes E5a or E5b and double-sideband that does the reception and processing of the E5 total band of Galileo. The CBOC receivers were studied too. The goals for this modulation are to improve the estimated frequency and code phase values and to simplify the tracking loop complexity to the minimum possible, minimalizing the number of correlators used. The last theme addressed in this document was the multipath error mitigation, namely the performance of two different discriminators, NELP and HRC, in presence of several Galileo signals and the comparison signal C/A. In the presence of multipath, as the number of reflections increase, the signal’s receiver quality will be worse. There are more significant errors for the NELP than for the HRC discriminator, and, in both cases, the increasing efficiency order of the modulations is the same: C/A, BOC(1,1), CBOCpilot(6,1,1/11) and AltBOC(15,10). The values of the AltBOC modulation errors

are much lower than the others, which proves the robustness of this signal (10 times lower). On the other hand, C/A signal has the worst error values, which was expected, because it has the lowest bandwidth. We can conclude for the other modulations that, in the NELP discriminator, the tracking error values are significant until a secondary ray delay of 300 meters in all the modulations except for AltBOC (30 meters). For the HRC discriminator, we have tracking errors with lower values than the ones for NELP, but still with errors until 170 meters of secondary ray delay for BOC(1,1) and until 130 meters for CBOCpilot(6,1,1/11). References [1] http://www.sondasysatelites.blogspot.com, Setembro 2014 [2] P. D. Groves, “Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems", Artech House, Boston, 2008 [3] R. G. Brown and Patrick Y. C. Hwang, “Introduction to Random Signals and Applied Kalman Filtering", 3.rd edition, Wiley, N. York, 1997 [4] P. Misra, P. Enge, “Global Positioning System, Signals, Measurements, and Performance", Ganga-Jamuna, Lincoln, MS, 2004 [5] Ávila-Rodríguez, J., “On Generalized Signal Waveforms for Satellite Navigation”, PhD Thesis, Universität der Bundeswehr München, Munich, Germany, Junho 2008 [6] Fernando M. G. Sousa, Fernando D. Nunes, “New Expressions for the Autocorrelation Function of BOC GNSS Signals”, Navigation, Journal of the Institute of Navigation, vol. 60, no. 1, spring 2013, pp. 1-8. [7] European Space Agency/European GNSS, “Signal in Space Interface Control Document”, 2010 [8] Susmita Bhattacharyya, “Performance and Integrity Analysis of the Vector Tracking Architecture of GNSS Receivers”, Faculty of the Graduate School of the University of Minnesota, PhD Thesis, April 2012 [9] Fernando D. Nunes, “AltBOC Receivers”, internal report, Instituto de Telecomunicações/IST, Março 2015 [10] A. Jovanovic et al, “Analysis and Performance of Tracking Schemes for the Galileo MBOC Signal”, European Navigation Conference – Global Navigation Satellite Systems (ENC-GNSS 2009), Naples, Italy, 2009 [11] O. Julien et al, “Two for One: Tracking Galileo CBOC Signal with TMBOC”, pp. 50-57, Inside GNSS, spring 2007 [12] O. Julien et al, “On Potential CBOC/TMBOC Common Receiver Architectures”, pp. 1530-1542, ION GNSS 2007 [13] F. D. Nunes, “NELP and HRC discriminators”, Instituto de Telecomunicações/IST, 2015 [14] Jason Jones, Pat Fenton, Brian Smith, “Theory and Performance of the Pulse Aperture Correlator”, ION GNSS, September 2005