AltBOC for Dummies or Everything You Want to Know

AltBOC for Dummies or Everything You Always Wanted to Know About AltBOC

Laurent Lestarquit, CNES Géraldine Artaud, CNES Jean-Luc Issler, CNES

BIOGRAPHY Laurent Lestarquit is a navigation signal expert at the CNES Transmission Technique and Signal Processing department (TT). He was a member of the Galileo Signal Task Force (GSTF) and contributed to the definition of the Galileo signal and provided support to the 2004 US-EU agreement of navigation system. He invented the constant envelope 4-code ALT-BOC modulation. Géraldine Artaud is a navigation engineer in the CNES Transmission Techniques department since 2007. She is involved in activities related to GNSS signal analysis, propagation, software receivers and simulations. Jean-Luc Issler is head of the Transmission Techniques and signal processing department of CNES, whose main tasks are signal processing, air interfaces and equipments in Radionavigation, TT&C, propagation and spectrum survey. He is involved in the development of several spaceborne receivers, as well as in studies on GALILEO, including EGNOS and the related evolutions. With DRAST, he represents France in the GALILEO Signal Task Force of the European Commission. He received in 2004 the Astronautic Prize of the AAAF ( French aeronautical and space association ) and in 2008 the EADS Prize of the french Académie des Sciences for his technical work on GALILEO signals and spaceborne GNSS equipments.

ABSTRACT The constant envelope Alt-BOC signal is one of the most exotic GNSS signal ever imagined: it is a complex signal composed of 4 codes multiplexed so as to have constant envelope signal. The main lobes of this signal spans over 50 MHz, meaning receiver desiring to receive the complete signal shall have a bandwidth about thirty times larger than the current basic GPS receivers and implement complex algorithms, quite a challenging task for receiver designers! In fact, Alt-BOC was at first imagined to fulfil a need: be able to generate and multiplex 2 or 4 navigation signal components (each with its own PRN code) on two close frequency bands

taking into account the limitations of the onboard OMUX, and giving it a constant-envelope in order to maximize the amplifier efficiency. Processing the whole signal rather than the 2 separate E5a and E5b signals wasn’t envisioned at first. The idea of receiving the complete Alt-BOC arrived later when theoretical studies showed that the process of this wideband signal would lead to positioning of unprecedented accuracy [1, 2, 3]. This intuition was later confirmed by measurements performed on the real signal broadcasted by GIOVE-A . The understanding of Alt-BOC is challenging, so we propose a step by step approach to apprehend it, beginning with a comprehensive insight of the 2 code Alt-BOC, its characteristics, its properties, the possible variants. Then we’ll move to the 4-codes version. Indeed, the combination of four signals is possible but the resulting signal hasn’t a constant-envelope. The problem was solved by using a “trick” which led to the look-up table defined by CNES [4]. This trick was further put into equation by ESA under the form of a cross product that led to the analytical definition of the signal as defined in the Galileo ICD. An analytical expression quite difficult, but we will show how this expression is to be interpreted. The PSD of this expression is analysed and leads to surprising conclusions. Next we will focus on some reception architectures allowing the reception of the Alt-BOC signal. There are mainly two different approaches. The simplest one consists in independent processing of E5a and E5b as BPSK or QPSK signals. The second consists in coherent Alt-BOC processing of the composite signal for which many method have already been proposed. We will propose a new method for tracking the pilot codes of the Alt-BOC, a method that is using the properties of the 2 code Alt-BOC (which has been noticed in [6]), and using sub-carrier tracking techniques as described in [7] and [8].

INTRODUCTION Alt-BOC is a modulation whose understanding require strong efforts. The mathematical formulation and the equivalent look-up table provided in the GALILEO SIS-ICD are not strait-forward. Written by its inventor,

961ION GNSS 21st. International Technical Meeting of theSatellite Division, 16-19, September 2008, Savannah, GA.

the purpose of this paper, is to help navigation engineers in understanding Alt-BOC or we should say, understanding the numerous Alt-BOC variants, explaining how the constant envelope Alt-BOC was invented, and highlighting its properties. An accurate definition was given in [1] : “ An Alternative-BOC signal is a BOC-like signal having different PN codes in the lower and the upper main split lobes. Alternative-BOCs allow one signal service per lobe.” GALILEO HISTORY & NEED FOR ALT-BOC Let step back in time and into Galileo signal definition history. Alt-BOC appeared for the first time in the year 2000. At that time, the Galileo signal plan was all but settled, the Galileo Signal Task Force (GSTF) group had many issues to cope with. In the year 2000 the Galileo signal plan in what is now the L1 band was quite different from today : there were signal carriers at the E1 and E2 bands, which were bands 4MHz wide and 14 MHz apart from the L1 band for which Galileo had anteriority. Each of these band was to host a navigation signal. This is when a proposal was made to use an alt-BOC signal to transmit 2 independent signal in these two bands using an unique High Power Amplifier (HPA) working at the L1 frequency.

GPS L11575,42 MHz

GalileoE1

GalileoE2

Figure 1 : early Galileo signal plan at L1 Yet, since the signal would be composed of a pilot and data channel on each band, it would have been a 4-code Alt-BOC that would have been needed. Indeed, a 4 code Alt-LOC was studied at the time but was quickly dropped because its envelope wasn’t constant. A constant envelope was researched, so as to allow to use the HPA at saturation, that is with an high efficiency. Furthermore, the Galileo signal plan was changed. In the mean time, in year 2001, CNES discovered that 4-code constant Alt-BOC signal is possible and this is the Alt-BOC that came back with force to be proposed and accepted for the E5a and E5b bands, bands for which the need for an Alt-BOC was even higher due to the low interval between the bands (only 10 MHz between main lobes !)

1176.45 MHz

E5bE5a

1207.14 MHz

51.15 MHz

10.23 MHz

30.69 MHz

1176.45 MHz

E5bE5a

1207.14 MHz

51.15 MHz

10.23 MHz

30.69 MHz

Figure 2 : Galileo frequency plan at E5a and E5b At that time there were 2 proposed architectures to transmit the E5a and E5b signal (figure 3). But in fact the 2 bands were so close that using a single HPA for the 2 frequencies was necessary. If the E5a and E5b were recombined in an OMUX after amplification, the OMUX filtering would have been so close to the desired bands and so sharp that it would generate high propagation delays inside the desired bands, potentially leading to signal distortion and propagation time instability. (Figure 4). Alt-BOC was needed for E5a & E5b. In addition Alt-BOC allows to transmit many sidelobes for use by narrow correlation receivers.

Signal E5a( QPSK)

Signal E5b(QPSK)

OMUX

Signal E5a &Signal E5b(ALT BOC)

Filter

Signal E5a( QPSK)

Signal E5b(QPSK)

OMUX

Signal E5a &Signal E5b(ALT BOC)

Filter

Figure 3 : 2 possible transmission architectures for E5a and E5b bands.

E5bE5a

OMUX Filter

Gro

up d

elay

E5bE5a

OMUX Filter

Gro

up d

elay

Figure 4 : Graph showing the rise of the group delays inside the desired band for the 1st proposed architecture. THE 2-CODES ALT-BOC This is the easiest form of Alt-BOC, yet its properties are worth to be looked at.


First, let’s recall the expression of the BOC sub-carrier with cosine or sine phasing. Actually, this distinction between cosine and sine phasing in a BOC was only realized many years after the BOC was first introduced, the US inventor apparently assumed a sine phasing from the start. BOC subcarrier with cosine phasing :

BOC subcarrier with sine phasing :

Ts/2 Ts 3Ts/2 2Ts

Time plot

Ts/2 Ts 3Ts/2 2Ts

Time plot

Figure 5 : BOC sub-carrier function (In this notation, SC stands for sub-carrier, B for binary) Next, let’s built the Single Side Band (SSB) sub-carriers (SCSSB) and its conjugate(SCSSB*) :

These 2 functions can take 4 values that are shown on the Fresnel plot in Figure 6. A first remarkable properties of these functions is their PSD (Power Spectral Density). They have a single fundamental harmonic located for SC4,SSB at +Fs, and for its complex conjugate at –Fs (See figure 7). These are indeed SSB sub-carriers. The power of each of its harmonics are given in table 1. Notice that for the classical BOC sub-carrier the power are split in half in the positive and negative harmonics PSD

SC4,SSB

SC4,SSB*

SC4,SSB

SC4,SSB*

Figure 6 : Values taken by the SSB sub-carrier function on a Fresnel plot. 4 stands for the number of values taken. Notice also another possible expression for the SSB subcarrier that can be directly derived from fig.6 :

E5bE5a

+Fs-Fs 3Fs 5Fs-3Fs 7Fs 9Fs-7Fs -5Fs-9Fs

SC4,SSBSC4,SSB*

E5bE5a


SC4,SSBSC4,SSB*

Figure 7: SSB subcarrier PSD. Freq -5fs -3fs -fs +fs +3fs +5fs

BOC 1,6 4,5 40,53 40,53 4,5 1,6

0 9,0 0 81,05 0 3,2

3,2 0 81,05 0 9,0 0

Table 1 : PSD table, for each harmonics of the sub-carrier, expressed in % of total power. The 2 code Alt-BOC is defined as :

(6) can be rewritten with the BOC subcarrier expression :

(1)

(2)

(3)

(4)

(5)

( ) ( ) ( ) ( ) ( )tSCtctSCtcts SSBBBSSBBA ,, * ⋅+⋅=E5a E5b

( ) ( ) ( ) ( ) ( )tSCtctSCtcts SSBBBSSBBA ,, * ⋅+⋅=E5a E5b

(6)

(7)

( ) ( )tfsigntSC sB π2sinsin, =

( ) ( ) ( )( )tSCjtSCtSC BBSSB sin,cos,21

,4 +=

( ) ( ) ( )( )tSCjtSCtSC BBSSB sin,cos,21

,4 * −=

SSBSC ,4

*,4 SSBSC

( ) ( ) ( )[ ] ( )( ) ( )[ ] ( )tSCtctcj

tSCtctcts

BAB

BBA

sin,

cos,

−+

+=

( ) ( )tfsigntSC sB π2coscos, =

( )[ ]⎩

⎨⎧

∈=

⋅−

⋅+

44)1(

)(,4

,mod

24

TsiTsi

ijSSB

TstetSC ππ


( ) ( ) ( )[ ] ( ) ( ) ( )[ ] ( )tSCtctcjtSCtctcts BABBBA sin,cos, −++=

« 3 state Code » : (CA + CB)Carrier : In Phase (I)Subcarrier : Cos phasing

« 3 state Code » : (CA - CB)Carrier : In Quadrature (Q)Subcarrier : Sin phasing

( ) ( ) ( )[ ] ( ) ( ) ( )[ ] ( )tSCtctcjtSCtctcts BABBBA sin,cos, −++=

« 3 state Code » : (CA + CB)Carrier : In Phase (I)Subcarrier : Cos phasing

« 3 state Code » : (CA - CB)Carrier : In Quadrature (Q)Subcarrier : Sin phasing

Figure 8 : breakdown of expression (7) Alt-BOC can be viewed as the sum of 2 signals

-201-1

20-11

0-2-1-1

0211

PhasingFresnel plotCA- CBCA+ CBCBCA

-201-1

20-11

0-2-1-1

0211

PhasingFresnel plotCA- CBCA+ CBCBCA

12

34

TsTs/4 Ts/2 3Ts/4

12

34

0

2

1

3

4

4

2

1

3 Table 2 : Values taken by the Alt-BOC modulation as a function of Ca and Cb chip, and time. Expression (7) shows that the 2-code Alt-BOC is the sum of two “3-state codes” (Ca+Cb) and (Cb-Ca) modulating a BOC sub-carrier. Notice that these 2 signals are both in carrier phase quadrature and sub-carrier phase quadrature, and when one of these code values zero the other one doesn’t and vice-versa. The resulting modulation has 4 phase plots and has oscillations at the sub-carrier frequency either along the vertical or the horizontal line, as shown in Table 2 BOC IS Alt-BOC ! It turns out that the standard BOC is a special case of Alt-BOC. If the 2 PN codes of an alternative-BOC are made identical, the signal becomes a « classical » BOC. More precisely, If :

Ca = Cb, then the resulting signal is the cosine BOC, and if :

Ca = - Cb, then the resulting signal is the sine BOC.

It is interesting to notice that there is no such thing as cosine or sine Alt-BOC, as Alt-BOC has both cosine and sine phased signals in it. SUBCARRIER VARIANTS The Alt-BOC is based on a BOC subcarrier. In fact this signal is part of a broader family that we could call “Alt-OC” or Alternate Offset Carrier. Indeed, the carrier doesn’t have to be binary. For example, it could have been possible to base the modulation on pure sine and cosine Subcarrier, that is the Lineary Offset Carrier (LOC) subcarrier :

The resulting SSB “Linear” subcarrier would have been the complex exponential :

(8)

(9)

(10)

( ) ( )tftSC sL π2coscos, =

( ) ( )tftSC sL π2sinsin, =

( ) tfjSSBL

setSC π2, =


The PSD of (10) has a single harmonic at +fs, precisely what we would expect from an ALT-OC SSB sub-carrier. Note that (5) is equivalent to (10) sampled at a rate of 4fs. Expression (7) remains valid with LOC subcarrier. This is only an example, Alt-OC signal could have been derived using 3-state or 4-state or n-state sub-carrier. DIFFERENT CODE RATE A nicety of Alt-BOC is that code rates don’t have to be the same on the lower and on the upper frequencies. It would have been perfectly feasible to have different code rates on E5a and E5b. 4-CODES ALT-BOC There are 2 codes on each frequency, each of which are in phase quadrature, so the baseband expression becomes :

After some computations not detailed here, the resulting modulation constellation is shown in figure 9. This constellation has 9 plots, the “0” plot is possible and correspond to nothing being transmitted. The envelope is clearly not constant so

such a modulation can’t be used with HPA working at saturation.

2

1

2

3

4

5

6

7

8

2

2−

2− 0 2

1

2

3

4

5

6

7

8

2

2−

2− 0

Figure 9 : Modulation constellation for the 4-code Alt-BOC The signal will have oscillations at the sub-carrier frequency, either along the horizontal and vertical axis of the constellation, or along the diagonals. The vertical and horizontal oscillations have higher amplitudes than the diagonal ones. Moreover, they take a zero amplitude half the time.

State 1 or 3

State 5 or 7

Ts/2 Ts 3Ts/2 2Ts

State 2 or 8

State 4 or 6

Ts/2 Ts 3Ts/2 2Ts

2

1

2

3

4

5

6

7

8

2

2−

2− 0 2

1

2

3

4

5

6

7

8

2

2−

2− 0

2

1

2

3

4

5

6

7

8

2

2−

2− 0 2

1

2

3

4

5

6

7

8

2

2−

2− 0

Figure 10 : Oscillating nature of the 4 code Alt-BOC

(11) ( ) ( ) ( )[ ] ( )

( ) ( )[ ] ( )tSCtcjtctSCtcjtcts

SSBBB

SSBAA

,4

,4

'.*'.

⋅++

⋅+=


Ts/2 Ts 3Ts/2 2Ts Ts/2 Ts 3Ts/2 2Ts

2√22

-2

2√2

-2√2 Ts/8-2√2 Figure 11 : How the constant envelope was made MAKING THE ENVELOPPE CONSTANT If you could make the oscillation along the horizontal and vertical axis look like the one along the diagonals, then the envelope would be constant. Well, let’s do it then, and this is how the constant envelope Alt-BOC with 4 codes was invented ! (fig. 11) The modulation now has a constant envelope and presents a 8-PSK constellation (Figure 12) The mathematical formulation found in the Galileo ICD came only later showing that in the process an inter-modulation product was generated. The coordinate of each plot k are given by :

And the modulation can be described using the modulation table that can be found in the Galileo ICD and is shown in table 3 in a graphical way

2

12

3

4

5

6

7

8

2

2−

2−

Figure 12 : resulting 8-PSK constellation

Table 3 : Graphical representation of the ALT-BOC modulation table

{ }8,7,6,5,4,3,2,12 4 ∈⋅ kejkπ

(12)


)(*32 ,8 tSC SSB⋅

( ) ( ) ( )( ) ( ) ( )[ ]

( ) ( )( ) ( ) ( )[ ]

( ) ( )( ) ( ) ( )[ ]

( ) ( )( ) ( ) ( )[ ]422

1

422

1

422

1

422

1

5,5555

5,5555

5,5555

5,55555

EsPEPEQbEIbE

EsPEPEQaEIaE

EsSESEQbEIbE

EsSESEQaEIaEE

Ttscjtsctejte

Ttscjtsctejte

Ttscjtsctejte

Ttscjtsctejtets

−++

+−−+

+−++

+−−+=

−−−−

−−−−

−−−−

−−−−

)(32 ,8 tSC SSB⋅

Desired codes

Inter-modulation product SSB subcarrier function at -3*Fs

)(2 ,8 tSC SSB⋅

SSB subcarrier functions at Fs

)(*2 ,8 tSC SSB⋅

Figure 13 : Interpretation of the Galileo SIS ICD formulas MATHEMATICAL FORMULATION The formulation found in the Galileo SIS ICD was first published in [3]. Figure 13 explains how this formulation is to be understood. We see that in the process of making the envelope constant, an inter-modulation product was generated. Let’s define the SSB “single” and “product” sub-carriers as :

Note that the 12P and 32P factors are there for normalization. 8 stands for the number of states. These 2 sub-carriers can be expressed in a very simple expression similar to (5) :

And the power of each subcarrier is given in table 4 Power exsp. Power Single SC ( )

4221 +=P 85,36 %

Product SC3 ( )4

223 −=P 14,64 %

Table 4 : Amplitude & power of the subcarrier “single” and “product”.

From expression (15) and (16), the Fresnel plot of the “single” and “product” sub-carrier can be easily derived and are shown in figure 14 and 15.

1

23

4

5

6 7

8

Figure 14 : Fresnel plot of the “single” subcarrier, to be compared with figure 6.

1

23

4

5

6 7

8

Figure 15 : Fresnel plot of the “product” subcarrier

(13)

(14)

(15)

(16)

( ) ( )[ ]421)( 5,55

1,8 EsSESESSB Ttscjtsc

PtSC −+= −−

( ) ( )[ ]421)(3 5,55

3,8 EsPEPESSB Ttscjtsc

PtSC −+= −−

( )[ ]⎩

⎨⎧

∈=

⋅−

⋅+

88)1(

)(,8

,mod

48

TsiTsi

ijSSB

TstetSC ππ

( )[ ]⎩

⎨⎧

∈=

⋅−

⋅−

88)1(

)(,8

,mod3 4

38

5

TsiTsi

ijSSB

TstetSC ππ


PSD PROPERTIES These 2 sub-carriers have some remarkable PSD properties that can be guessed from the fresnel plot. The “single” SSB sub-carrier SC8,SSB is a finer approximation of the Linear SSB sub-carrier (expression (10)) that the binary SSB sub-carrier (expression (5)) so you would expect it to have most of its energy in its fundamental harmonic at +fs. The “product” SSC sub-carrier SC38,SSB circle 3 times around the origin of the Fresnel plot in the reverse direction, so you would expect its fundamental harmonic to be at -3fs and it indeed is. In fact, a remarkable property is that the single SSB sub-carrier only has harmonics at +fs, -7fs and +9fs, while the “product” SSB sub-carrier only has harmonics at -3fs and -5fs, as described in table 5 and figure 16. Freq -5fs -3fs -fs +fs +3fs +5fs

0 0 0 94,96 0 0

0 0 94,96 0 0 0

0 61,5 0 0 0 22,2

22,2 0 0 0 61,5 0

Table 5 : PSD table, for each harmonics of the sub-carrier, expressed in % of total power.

E5bE5a


SC8,SSBSC8,SSB*SC38,SSBSC38,SSB*

Figure 16 : Subcarrier PSD And yet another remarkable property is that if we multiply the power of the fundamental harmonic of the single carrier by its relative power in the constant Alt-BOC modulation, we find the exact power of the 2-code Alt-Boc modulation shown in table 1, that is :

0.9496 x 0,8536 = 0,8106 What this all means is :

- Making the envelope constant does not cause any loss of desired signal power in the main lobes.

- The energy that was originally in the harmonic of the BOC sub-carrier is now split between the “single” and “product” sub-carrier (figure 16)

- The inter-modulation product has its main lobe at 3Fs, that is 30 MHz away from E5a and E5b, the cross modulation product will not interfere with the desired signal.

- In fact, when we made the envelope constant, all we did was transform the 3rd and 5th harmonic of the desired signal sub-carrier into inter-modulation product.

- The constant envelope Alt-BOC signal is therefore as good as the non constant envelope Alt-BOC signal

The constant envelope Alt-BOC succeeds completely in doing what it is meant to do, that is providing QPSK modulated codes at +fs and –fs from the center frequency. Of course, if we compare the PSD of the full signal, we see some differences between the constant and non constant envelope Alt-BOC (figure 17) especially for the central secondary lobe and the third harmonic. This might come from complex interaction between the codes and the inter-modulation product. But the same kind of difference can be seen if we compare Alt-BOC with BOC, or BOC sin with BOC cosine. Remarkably, the fundamental harmonic has the same shape in both modulation.

Figure 17 : full signal PSD enveloppe for constant and non constant envelope Alt-BOC (from [11]) ALT-BOC AFTER FILTERING It seems that the transmitted bandwidth at payload will be bellow 90MHz. Therefore, the inter-modulation product at +/-3fs and +/-5Fs is mostly filtered out and the ground user receives only the fundamental harmonic of the sub-carrier, that is an ALT-LOC signal. Furthermore, a ground user using a receiver with from 20 to 40 MHz of bandwidth centred on either E5a or E5b will mostly see a 10 Mchip/s QPSK code. And this is precisely what the user need !

SSBSC ,8

*,8 SSBSC

SSBSC ,83

*3 ,8 SSBSC


-100

-90

-80

-70

-60

-50

-40

-30

-60 -40 -20 0 20 40 60

PO

WE

R (d

Bm

)

Frequency (MHz)

GioveA E5 PSDTheoretical E5 DSP

Figure 18 : signal PSD enveloppe transmitted by Giove A’s NSGU (3 dB bandwidth is 72 MHz) SINGLE LOBE TRACKING This is what Alt-BOC was designed for, as it precisely puts 2 BPSK codes in quadrature at each frequency E5a and E5b. Any classical BPSK or QPSK tracking method can be used at either E5a ans E5b. The first secondary lobe is also transmitted so it can be possible to use a 40 MHz front-end associated with narrow correlation techniques. If tracking both E5a and E5b at the same time on different channel, bear in mind that the observed pseudo-range won’t be the same due to ionospheric delay that is different on E5a and E5b. ALT-BOC PILOT TRACKING We propose an innovative way to track the pilot component of the Alt-BOC. Making abstraction of the data channel, which has orthogonal codes to the pilot channel, the pilot component can be seen as a 2-code Alt-BOC, and therefore will have its properties described earlier. In particular, the desired signal can be expressed in a way similar to (7) :

With ( )tSC cos,4 and ( )tSC sin,4 being the 4 state cosine and sine sub-carrier function defined so that (18) is true.

In fact, expression (17) gives the desired signal in an infinite bandwidth. But if the desired signal is filtered in a bandwidth ranging from 50 Mhz up to 190 Mhz, (the next harmonic of the desired sub-carrier is at +/- 105 MHz), the desired signals

become roughly the Alt-Loc signal expressed in (19) :

This means that this signal can optimally be tracked using an Alt-LOC replica instead of an Alt-BOC replica. Taking advantage of the properties of expression (19) which are mostly the same than for expression (7), we propose a correlator architecture that will isolate the “sum” (CΣ=Ca+Cb) and “delta” (CΔ=Cb-Ca) codes

Σ↓

Σ↓

Σ↓

Σ↓

Σ↓

Σ↓

Σ↓

Σ↓

-

SRF

NCOcode

I

( )θ̂cos

Q

NCOcarrier

( )θ̂sin

( )φ̂cosSC

( )φ̂sinSC

IQ

II( )τ̂ΣC

( )φ̂cosSC

( )φ̂sinSC

QI

QQ

NCOSub-

carrier

( ) )ˆcos()ˆcos(ˆ φθτ ⋅⋅= ΣΣΣ RII

( )τ̂ΣC

( )τ̂ΣC

( )τ̂ΣC

( )τ̂ΔC

( )τ̂ΔC

( )τ̂ΔC

( )τ̂ΔC

( ) )ˆsin()ˆsin(ˆ φθτ ⋅⋅= ΔΔΔ RII

( ) )ˆcos()ˆsin(ˆ φθτ ⋅⋅−= ΔΔΔ RIQ

( ) )ˆsin()ˆcos(ˆ φθτ ⋅⋅= ΣΣΣ RIQ

( ) )ˆcos()ˆsin(ˆ φθτ ⋅⋅= ΣΣΣ RQI

( ) )ˆsin()ˆcos(ˆ φθτ ⋅⋅−= ΔΔΔ RQI

( ) )ˆcos()ˆcos(ˆ φθτ ⋅⋅= ΔΔΔ RQQ

( ) )ˆsin()ˆsin(ˆ φθτ ⋅⋅= ΣΣΣ RQQ

Figure 19 : Correlator architecture Next we do :

Where Raa and Rbb are the auto-correlation functions of the pilot codes, θ is the carrier tracking phase error, φ is the sub-carrier phase error. We obtain trigonometric expression of the carrier and sub-carrier phase tracking error. It is therefore possible to track the carrier and the sub-carrier. The carrier and sub-carrier replica shall optimally be linear sin and cosine functions. A code tracking loop is not required once the code is

(17)

(18)

(19)

(20)

( ) ( ) ( )[ ] ( )( ) ( )[ ] ( )tSCtctcj

tSCtctcts

AB

BA

sin,4

cos,4

−+

+=

( ) ( ) ( )( )tSCjtSCtSC SSB sin,4,cos4,8 +=

( ) ( ) ( )[ ] ( )( ) ( )[ ] ( )tftctcj

tftctcts

sAB

sBA

ππ

2sin2cos

−++=

( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )⎪

⎪⎩

⎪⎪⎨

⎧

⋅⋅+=+=⋅⋅+=−=⋅⋅+=−=⋅⋅+=+=

ΔΣ

ΔΣ

ΔΣ

ΔΣ

)sin(sin2)cos(sin2)sin(cos2)cos(cos2

θφττθφττθφττθφττ

bbaaIQQ

bbaaIQI

bbaaQIQ

bbaaQII

RRIQQRRQIQRRIQIRRQII


acquired, the code NCO can be driven by the sub-carrier loop, as for BOC subcarrier tracking (See [8]). For example we could use the following discriminators (many others are possible).

- for the carrier loop :

- for the sub-carrier loop :

To sum-up, this receiver architecture achieves the tracking of the 2 sub-carriers that are formed in expression (19), quite an original way to track the Alt-BOC signal. IONOSPHERIC DELAY FOR SUBCARRIER TRACKING Just a short word about ionospheric delay. It is easy to show that the sub-carrier will be affected by a group delay (that is same sign as the code), and this delay is equal to :

baSC ff

TECI 3.40=

CONCLUSION To sum up, the constant envelope Alt-BOC fulfills what it was designed for that is provide 2 QPSK navigation signals at E5a and E5b. Fortunately, the transformation of the 4-code Alt-Boc to a constant envelope modulation doesn’t degrade of make any power loss to the desired signal that is in the fundamental harmonic of the subcarrier. The tracking of the Alt-BOC subcarrier of the pilot component is possible and a receiver architecture is proposed. Due to the SPD properties of the desired signal, it is optimal to do the subcarrier tracking with a LOC sub-carrier.

REFERENCES [1] L Ries & al, « A Software Simulation Tool for GNSS2 BOC Signals », ION GPS 2002, September 2002. [2] L Ries & al, « New Investigations on Wideband GNSS2 Signals », GNSS 2003, April 2003. [3] M. Soellner and Ph. Erhard, « Comparison of AWGN Code Tracking Accuracy for Alternative-BOC, Complex-LOC and Complex- BOC Modulation Options in Galileo E5-Band », GNSS 2003, April 2003. [4]. L. Lestarquit, « Method and device for generating a constant envelope navigation signal with four independent codes », US pat n°2006/0038716 A1 published Feb. 23, 2006. [5] N. Martin, H. Guichon, M. Revol, M. Hollreiser, J. De Mateo, « Architecture of the galileo TUS receiver for coherent AltBOC tracking » , 3rd CNES-ESA Workshop on GNSS Signals and Signal Processing, 21 & 22 April 2008 (IAS) Toulouse, France. [6] N. Gerein, «Hardware architecture for processing Galileo alternate binary offset carrier (Altboc) signals », published Jan.20, 2005. [7] N. Martin, V. Leblond “Method for the acquisition of a radio-navigation signal by satellite”, published the 28th October 2004. [8] A. De Latour, T. Grelier, G. Artaud , L. Ries, J-L. Issler, V. Heiries « Subcarrier Tracking Performances of BOC, ALTBOC and MBOC Signals » ION GNSS 2007 , International technical meeting, September 25-28, 2007, Fort Worth, Texas (US). [9]. A. Simsky, JM. Sleewaegen, M. Hollreiser, « Multipath and tracking performance of Galileo ranging signals transmitted by the GIOVEA satellite », First CNES-ESA Workshop on Galileo signals and signal processing, 12 & 13 october 2006, IAS ( Institut Aero Spatial ) Toulouse, France. [10] G. Artaud, G. Menard, L. Ries, J. Dantepal, JL. Issler “ Juzzle Software Receiver ”, Navitec 2006, 11 – 14 december 2006, Noordwijk, the Netherlands. [11] E.Rebeyrol, “Galileo Signal and Payload Optimisation”, Ph. D. Thesis, Oct. 9, 2007.

(21)

(22)

( )θ2sin21

2222 ≈+++

+=

QIQI

QQIIpilotc QQII

IQIQdiscri

( )φ2sin21

22221 ≈

+++

+=

QQII

QIQIsc QIQI

QQIIdiscri


Documents

AltBOC for Dummies or Everything You Want to Know