MBOC Modulation - Revision history

Filipe.Pelica: removed broken link.

2014-09-08T17:37:46Z

removed broken link.

← Older revision		Revision as of 17:37, 8 September 2014
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	== MBOC Tracking Sensitivity ==		== MBOC Tracking Sensitivity ==
	As shown in [O. Julien, 2005] <ref name="OJ_2005"> [O. Julien, 2005] Olivier Julien, Design of Galileo L1F Receiver Tracking Loops, PhD Thesis, Department of Geomatics Engineering, University of Calgary ~~http://www.geomatics.ucalgary.ca/links/GradTheses.html~~ </ref>, we can distinguish two types of tracking sensitivity:		As shown in [O. Julien, 2005] <ref name="OJ_2005"> [O. Julien, 2005] Olivier Julien, Design of Galileo L1F Receiver Tracking Loops, PhD Thesis, Department of Geomatics Engineering, University of Calgary</ref>, we can distinguish two types of tracking sensitivity:

	::* Code Tracking Sensitivity (DLL)		::* Code Tracking Sensitivity (DLL)

Filipe.Pelica: /* MBOC Interference with other GNSSes */

2014-05-26T17:38:58Z

MBOC Interference with other GNSSes

← Older revision		Revision as of 17:38, 26 May 2014
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	== MBOC Interference with other GNSSes ==		== MBOC Interference with other GNSSes ==

	Interoperability and compatibility have been hot issues in the design of Galileo since the beginning. Indeed, as more systems join the select club of countries with their own navigation system, the more important these concepts have become. As we have seen in chapter 2, the global system of systems that GPS, GLONASS, Galileo, the Japanese Quasi Zenith Satellite System (QZSS), the Chinese ~~Compass~~ and the Indian Regional Navigation Satellite System (IRNSS) might become one day makes this chapter of major interest.		Interoperability and compatibility have been hot issues in the design of Galileo since the beginning. Indeed, as more systems join the select club of countries with their own navigation system, the more important these concepts have become. As we have seen in chapter 2, the global system of systems that GPS, GLONASS, Galileo, the Japanese Quasi Zenith Satellite System (QZSS), the Chinese [[BeiDou_General_Introduction\|BeiDou System (BDS)]] and the Indian Regional Navigation Satellite System (IRNSS) might become one day makes this chapter of major interest.

	As defined in, [S. Wallner et al., 2005] <ref name="SW_2005"> [S. Wallner et al., 2005] S. Wallner, G.W. Hein, J.-A. Avila Rodriguez, T. Pany, A. Posfay, Interference Computations Between GPS and Galileo, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref>and [S. Wallner et al., 2006]<ref>[S. Wallner et al., 2006b] S. Wallner, J.-A. Avila-Rodriguez, G.W. Hein, Interference Computations between Several GNSS Systems, ESA Navitec 2006, December 11-13, 2006, Noordwijk, The Netherlands.</ref> and, interoperability refers to the ability of civil U.S. and foreign space-based PNT services to be used together to provide better capabilities compared with those that would be achieved relying solely on one service or signal.		As defined in, [S. Wallner et al., 2005] <ref name="SW_2005"> [S. Wallner et al., 2005] S. Wallner, G.W. Hein, J.-A. Avila Rodriguez, T. Pany, A. Posfay, Interference Computations Between GPS and Galileo, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref>and [S. Wallner et al., 2006]<ref>[S. Wallner et al., 2006b] S. Wallner, J.-A. Avila-Rodriguez, G.W. Hein, Interference Computations between Several GNSS Systems, ESA Navitec 2006, December 11-13, 2006, Noordwijk, The Netherlands.</ref> and, interoperability refers to the ability of civil U.S. and foreign space-based PNT services to be used together to provide better capabilities compared with those that would be achieved relying solely on one service or signal.

Teresa.Ferreira at 11:55, 28 January 2014

2014-01-28T11:55:01Z

← Older revision		Revision as of 11:55, 28 January 2014
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	where represents the modulo operation ~~defined as the remainder of the division of by~~ .		where "mod" represents the modulo operation.

	::{\|		::{\|

Carlos.Lopez at 09:13, 25 November 2011

2011-11-25T09:13:47Z

← Older revision		Revision as of 09:13, 25 November 2011
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	==References==		==References==
	<references/>		<references/>


			== Credits ==
			The information presented in this NAVIPEDIA’s article is an extract of the PhD work performed by Dr. Jose Ángel Ávila Rodríguez in the FAF University of Munich as part of his Doctoral Thesis “On Generalized Signal Waveforms for Satellite Navigation” presented in June 2008, Munich (Germany)


	[[Category:Fundamentals]]		[[Category:Fundamentals]]
	[[Category:GNSS Signals]]		[[Category:GNSS Signals]]

Rui.Pereira at 11:33, 8 November 2011

2011-11-08T11:33:09Z

← Older revision		Revision as of 11:33, 8 November 2011
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	Once we have defined the power spectral density of MBOC, it is the right moment to talk about the implementation. Indeed, different time representations result in the same power spectral density and the Agreement between the EU and the US on MBOC left this freedom to both parties so that each could implement its own solution according to its own conception. Two solutions have been realized to implement MBOC:		Once we have defined the power spectral density of MBOC, it is the right moment to talk about the implementation. Indeed, different time representations result in the same power spectral density and the Agreement between the EU and the US on MBOC left this freedom to both parties so that each could implement its own solution according to its own conception. Two solutions have been realized to implement MBOC:

	::* CBOC: The [[Composite BOC (CBOC)\| Composite BOC]] is the solution adopted by Galileo for the Open Service in [[~~GALIEO~~ Signal Plan\|E1/L1]]. It is an Interplex multiplexing where the sub-carriers [[Binary Offset Carrier (BOC)\|BOC(1,1)]] and [[Binary Offset Carrier (BOC)\|BOC(6,1)]] are added in anti-phase on each channel.		::* CBOC: The [[Composite BOC (CBOC)\| Composite BOC]] is the solution adopted by Galileo for the Open Service in [[GALILEO Signal Plan\|E1/L1]]. It is an Interplex multiplexing where the sub-carriers [[Binary Offset Carrier (BOC)\|BOC(1,1)]] and [[Binary Offset Carrier (BOC)\|BOC(6,1)]] are added in anti-phase on each channel.
	::*TMBOC: The [[Time-Multiplexed BOC (TMBOC)\| Time-Multiplexed BOC]] is the solution adopted by GPS for [[GPS Signal Plan\|L1C]]. It is a binary signal where [[Binary Offset Carrier (BOC) \|BOC(1,1)]] and [[Binary Offset Carrier (BOC)\|BOC(6,1)]] are time-multiplexed according to a pre-established pattern that was optimized to improve the correlation properties of the signal when the effect of the PRN code is taken into account.		::*TMBOC: The [[Time-Multiplexed BOC (TMBOC)\| Time-Multiplexed BOC]] is the solution adopted by GPS for [[GPS Signal Plan\|L1C]]. It is a binary signal where [[Binary Offset Carrier (BOC) \|BOC(1,1)]] and [[Binary Offset Carrier (BOC)\|BOC(6,1)]] are time-multiplexed according to a pre-established pattern that was optimized to improve the correlation properties of the signal when the effect of the PRN code is taken into account.

Carlos.Lopez: /* MBOC Interference with other GNSSes */

2011-11-03T10:36:30Z

MBOC Interference with other GNSSes

← Older revision		Revision as of 10:36, 3 November 2011
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	As defined in, [S. Wallner et al., 2005] <ref name="SW_2005"> [S. Wallner et al., 2005] S. Wallner, G.W. Hein, J.-A. Avila Rodriguez, T. Pany, A. Posfay, Interference Computations Between GPS and Galileo, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref>and [S. Wallner et al., 2006]<ref>[S. Wallner et al., 2006b] S. Wallner, J.-A. Avila-Rodriguez, G.W. Hein, Interference Computations between Several GNSS Systems, ESA Navitec 2006, December 11-13, 2006, Noordwijk, The Netherlands.</ref> and, interoperability refers to the ability of civil U.S. and foreign space-based PNT services to be used together to provide better capabilities compared with those that would be achieved relying solely on one service or signal.		As defined in, [S. Wallner et al., 2005] <ref name="SW_2005"> [S. Wallner et al., 2005] S. Wallner, G.W. Hein, J.-A. Avila Rodriguez, T. Pany, A. Posfay, Interference Computations Between GPS and Galileo, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref>and [S. Wallner et al., 2006]<ref>[S. Wallner et al., 2006b] S. Wallner, J.-A. Avila-Rodriguez, G.W. Hein, Interference Computations between Several GNSS Systems, ESA Navitec 2006, December 11-13, 2006, Noordwijk, The Netherlands.</ref> and, interoperability refers to the ability of civil U.S. and foreign space-based PNT services to be used together to provide better capabilities compared with those that would be achieved relying solely on one service or signal.

	In June 2004, the United States and the European Union signed a historical Agreement on the common use of shared frequencies, setting up a complete methodology to assess the GPS/Galileo radio frequency compatibility. More details on the theoretical framework can be found in[[GNSS Interference Model]]. Based on the mathematical ideas gathered in the work, [S. Wallner et al., 2005] <ref name="SW_2005"/> have carried out simulations with smooth spectra and with real codes. According to the results, the degradation from [[GPS General Introduction\|GPS]] on [[GALILEO General Introduction\|Galileo]] and of Galileo on GPS is lower than 0.25 dB proving thus that both systems can perfectly coexist. Moreover, the introduction of [[QZSS]] will lead to an increase of the intersystem interference in the visibility region of QZSS that will never be higher than 0.07 dB. We show next the degradation values for BOC(1,1) when the analytical model is employed.		In June 2004, the United States and the European Union signed a historical Agreement on the common use of shared frequencies, setting up a complete methodology to assess the GPS/Galileo radio frequency compatibility. More details on the theoretical framework can be found in [[GNSS Interference Model]]. Based on the mathematical ideas gathered in the work, [S. Wallner et al., 2005] <ref name="SW_2005"/> have carried out simulations with smooth spectra and with real codes. According to the results, the degradation from [[GPS General Introduction\|GPS]] on [[GALILEO General Introduction\|Galileo]] and of Galileo on GPS is lower than 0.25 dB proving thus that both systems can perfectly coexist. Moreover, the introduction of [[QZSS]] will lead to an increase of the intersystem interference in the visibility region of QZSS that will never be higher than 0.07 dB. We show next the degradation values for BOC(1,1) when the analytical model is employed.

	::::[[File:MBOC_Fig_13.png\|none\|thumb\|580px\|'''''Figure 13: Maximum <math>C/N_0</math> Degradation due to Intersystem Interference caused by the GPS L1 Signals on Galileo [S. Wallner et al., 2005] <ref name="SW_2005"/> . Minimum: 0.186 dB, mean 0.214 dB and maximum 0.243 dB.]]		::::[[File:MBOC_Fig_13.png\|none\|thumb\|580px\|'''''Figure 13: Maximum <math>C/N_0</math> Degradation due to Intersystem Interference caused by the GPS L1 Signals on Galileo [S. Wallner et al., 2005] <ref name="SW_2005"/> . Minimum: 0.186 dB, mean 0.214 dB and maximum 0.243 dB.]]
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	The mathematical framework of the methodology described in [[GNSS Interference Model]] can be easily expanded to other bands as for example E5-L5 or to other SBAS systems as done in [S. Wallner et al., 2005] <ref name="SW_2005"/> where the results with smooth spectra and real codes were compared. One final comment on the figures above is that the minimum power levels were used for the simulations resulting thus in significantly higher values of interference than those we will observe in a typical scenario. Nonetheless, it must be kept in mind that the purpose of an interference methodology is to assess compatibility in all the cases, and therefore looking at the worst cases is thus of major interest.		The mathematical framework of the methodology described in [[GNSS Interference Model]] can be easily expanded to other bands as for example E5-L5 or to other SBAS systems as done in [S. Wallner et al., 2005] <ref name="SW_2005"/> where the results with smooth spectra and real codes were compared. One final comment on the figures above is that the minimum power levels were used for the simulations resulting thus in significantly higher values of interference than those we will observe in a typical scenario. Nonetheless, it must be kept in mind that the purpose of an interference methodology is to assess compatibility in all the cases, and therefore looking at the worst cases is thus of major interest.


	==References==		==References==

Carlos.Lopez at 10:32, 3 November 2011

2011-11-03T10:32:43Z

Carlos.Lopez at 10:26, 3 November 2011

2011-11-03T10:26:58Z

← Older revision		Revision as of 10:26, 3 November 2011
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	The main drawback from the standard non-coherent integration comes from the fact that the noise is squared. Alternative expressions have been studied in the literature to sort out this problem as explained in [J.-A. Avila-Rodriguez et al., 2005c]<ref>[J.-A. Avila-Rodriguez et al., 2005c] J.-A. Avila-Rodriguez, T. Pany, B. Eissfeller, A theoretical analysis of acquisition algorithms for indoor positioning, 2nd ESA Workshop on Satellite Navigation User Equipment Technologies NAVITEC 2004, 8-10 December, 2004, Noordwijk, The Netherlands.</ref> and [G. Lachapelle, 2004] <ref name="GLP_2004"/>. One of those is the non-coherent differential correlation dc, also known as dot-product correlation, which is based on multiplying consecutive samples. One of its multiple expressions is:		The main drawback from the standard non-coherent integration comes from the fact that the noise is squared. Alternative expressions have been studied in the literature to sort out this problem as explained in [J.-A. Avila-Rodriguez et al., 2005c]<ref>[J.-A. Avila-Rodriguez et al., 2005c] J.-A. Avila-Rodriguez, T. Pany, B. Eissfeller, A theoretical analysis of acquisition algorithms for indoor positioning, 2nd ESA Workshop on Satellite Navigation User Equipment Technologies NAVITEC 2004, 8-10 December, 2004, Noordwijk, The Netherlands.</ref> and [G. Lachapelle, 2004] <ref name="GLP_2004"/>. One of those is the non-coherent differential correlation dc, also known as dot-product correlation, which is based on multiplying consecutive samples. One of its multiple expressions is:

	::[[File: MBOC_Eq_18.png\|none\|~~620px~~]]		::[[File: MBOC_Eq_18.png\|none\|800px]]


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	If perfect normalization is assumed and the loop bandwidth is negligible compared with the bandwidth of the discriminator noise, [J.K. Holmes, 2000]<ref>[J.K. Holmes, 2000] Holmes, J.K., Code Tracking Loop Performance Including the Effect of Channel Filtering and Gaussian Interference, Proceedings of the US Institute of Navigation ION-AM 2000, pp. 382-398, 26-28 June, San Diego, California, USA.</ref> and [O. Julien, 2005]<ref name="OJ_2005"/>: have shown that the DLL estimated code delay tracking error variance with Gaussian noise yields:		If perfect normalization is assumed and the loop bandwidth is negligible compared with the bandwidth of the discriminator noise, [J.K. Holmes, 2000]<ref>[J.K. Holmes, 2000] Holmes, J.K., Code Tracking Loop Performance Including the Effect of Channel Filtering and Gaussian Interference, Proceedings of the US Institute of Navigation ION-AM 2000, pp. 382-398, 26-28 June, San Diego, California, USA.</ref> and [O. Julien, 2005]<ref name="OJ_2005"/>: have shown that the DLL estimated code delay tracking error variance with Gaussian noise yields:

	::[[File: MBOC_Eq_19.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_19.png\|none\|360px]]


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	Additionally, since the noise power spectral density that results from multiplying the incoming signal with the local replica is very wide band, we can approximate the expression above by the following [O. Julien, 2005] <ref name="OJ_2005"/>:		Additionally, since the noise power spectral density that results from multiplying the incoming signal with the local replica is very wide band, we can approximate the expression above by the following [O. Julien, 2005] <ref name="OJ_2005"/>:

	::[[File: MBOC_Eq_20.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_20.png\|none\|380px]]

	where <math>\sigma^2_{D_{disc}}</math> represents the discriminator output standard deviation without normalizing. This expression is very close to that of the PLL, with the difference that the effect of the normalization (through <math>K_{disc}</math>) has been introduced here. This means in other words, that the DLL tracking error is directly dependent upon the discriminator resistance to noise, and thus on the signal structure.		where <math>\sigma^2_{D_{disc}}</math> represents the discriminator output standard deviation without normalizing. This expression is very close to that of the PLL, with the difference that the effect of the normalization (through <math>K_{disc}</math>) has been introduced here. This means in other words, that the DLL tracking error is directly dependent upon the discriminator resistance to noise, and thus on the signal structure.
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	If perfect normalization is assumed again, no frequency uncertainty is considered, a front-end filter with ideal unity gain and receiver bandwidth <math>\beta_r</math> and a code delay error remaining small, the DLL tracking error variance produced by use of an EMLP discriminator is shown to be [O. Julien, 2005] <ref name="OJ_2005"/> and [J.W. Betz and K.R. Kolodziejski, 2000] <ref name="JWB_2000"> [J.W. Betz and K.R. Kolodziejski, 2000] J.W. Betz and K.R. Kolodziejski 2000, Extended Theory of Early-Late Code Tracking for a Bandlimited GPS Receiver, NAVIGATION: Journal of the Institute of Navigation, Vol. 47, No. 3, Fall 2000.</ref>:		If perfect normalization is assumed again, no frequency uncertainty is considered, a front-end filter with ideal unity gain and receiver bandwidth <math>\beta_r</math> and a code delay error remaining small, the DLL tracking error variance produced by use of an EMLP discriminator is shown to be [O. Julien, 2005] <ref name="OJ_2005"/> and [J.W. Betz and K.R. Kolodziejski, 2000] <ref name="JWB_2000"> [J.W. Betz and K.R. Kolodziejski, 2000] J.W. Betz and K.R. Kolodziejski 2000, Extended Theory of Early-Late Code Tracking for a Bandlimited GPS Receiver, NAVIGATION: Journal of the Institute of Navigation, Vol. 47, No. 3, Fall 2000.</ref>:

	::[[File: MBOC_Eq_21.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_21.png\|none\|760px]]

	where <math>\beta_r</math> is the receiver bandwidth and <math>\delta</math>the correlator spacing of the receiver.		where <math>\beta_r</math> is the receiver bandwidth and <math>\delta</math>the correlator spacing of the receiver.
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	Equally, as derived in [O. Julien, 2005] <ref name="OJ_2005"/>, the DLL tracking error variance using a Dot Product (DP) discriminator presents the following expression:		Equally, as derived in [O. Julien, 2005] <ref name="OJ_2005"/>, the DLL tracking error variance using a Dot Product (DP) discriminator presents the following expression:

	::[[File: MBOC_Eq_22.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_22.png\|none\|680px]]

	which simplifies for the case that an infinite receiver bandwidth is assumed, yielding:		which simplifies for the case that an infinite receiver bandwidth is assumed, yielding:

	::[[File: MBOC_Eq_23.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_23.png\|none\|520px]]
	::[[File: MBOC_Eq_24.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_24.png\|none\|380px]]

	where <math>\alpha</math> is the slope of the autocorrelation function around the main peak. The above derived expressions are in consonance with the results obtained in [L. Ries et al., 2003]<ref>[L. Ries et al., 2003] L. Ries, F. Legrand, L. Lestarquit, W. Vigneau, J.L. Issler , Tracking and Multipath Performance Assessments of BOC Signals Using a Bit-Level Signal Processing Simulator, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2003, 9-12 September, 2003, Oregon Convention Center, Portland, Oregon, USA.</ref> and [O. Julien, 2005] <ref name="OJ_2005"/> and confirm the fact that depending on the slope of the autocorrelation function of the signal waveform around the main peak, the tracking performance and achievable sensitivity will be better or worse, as we expected. Indeed, the steeper the autocorrelation function around the main peak is, the better the performance of the signal will be in terms of standard error.		where <math>\alpha</math> is the slope of the autocorrelation function around the main peak. The above derived expressions are in consonance with the results obtained in [L. Ries et al., 2003]<ref>[L. Ries et al., 2003] L. Ries, F. Legrand, L. Lestarquit, W. Vigneau, J.L. Issler , Tracking and Multipath Performance Assessments of BOC Signals Using a Bit-Level Signal Processing Simulator, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2003, 9-12 September, 2003, Oregon Convention Center, Portland, Oregon, USA.</ref> and [O. Julien, 2005] <ref name="OJ_2005"/> and confirm the fact that depending on the slope of the autocorrelation function of the signal waveform around the main peak, the tracking performance and achievable sensitivity will be better or worse, as we expected. Indeed, the steeper the autocorrelation function around the main peak is, the better the performance of the signal will be in terms of standard error.
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	We can see this more clearly if we recall the equations derived in the [[Composite BOC (CBOC)]] implementation of MBOC. Indeed,		We can see this more clearly if we recall the equations derived in the [[Composite BOC (CBOC)]] implementation of MBOC. Indeed,

	::[[File: MBOC_Eq_25.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_25.png\|none\|520px]]


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	Following [P. Ward, 1996]<ref>[P. Ward, 1996] P. Ward, Satellite Signal Acquisition and Tracking in Understanding GPS: Principles and Applications, Artech House Inc.</ref> and [O. Julien, 2005]<ref name="OJ_2005"/> to study the PLL sensitivity, the rule of thumb we will use is to have a 3-sigma of the errors within the linear tracking region, which is in theory <math>\pm \frac{\delta}{2}</math>. This can also be expressed as follows:		Following [P. Ward, 1996]<ref>[P. Ward, 1996] P. Ward, Satellite Signal Acquisition and Tracking in Understanding GPS: Principles and Applications, Artech House Inc.</ref> and [O. Julien, 2005]<ref name="OJ_2005"/> to study the PLL sensitivity, the rule of thumb we will use is to have a 3-sigma of the errors within the linear tracking region, which is in theory <math>\pm \frac{\delta}{2}</math>. This can also be expressed as follows:

	::[[File: MBOC_Eq_26.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_26.png\|none\|180px]]

	It must be noted that actually not all the errors are included in the expression above, and thus the multipath-induced tracking error must be studied separately. The reason for this is that the multipath error does not imply a tracking error in the sense that it would push the tracking loop away from its stability point as explained in detail in [O. Julien, 2005] <ref name="OJ_2005"/>.		It must be noted that actually not all the errors are included in the expression above, and thus the multipath-induced tracking error must be studied separately. The reason for this is that the multipath error does not imply a tracking error in the sense that it would push the tracking loop away from its stability point as explained in detail in [O. Julien, 2005] <ref name="OJ_2005"/>.
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	Recalling now the equations for the tracking error of (23) and (24) above, we can see that (23) can be simplified for the EMLP as follows:		Recalling now the equations for the tracking error of (23) and (24) above, we can see that (23) can be simplified for the EMLP as follows:

	::[[File: MBOC_Eq_27.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_27.png\|none\|320px]]


	where		where

	::[[File: MBOC_Eq_28.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_28.png\|none\|520px]]


	and		and

	::[[File: MBOC_Eq_29.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_29.png\|none\|490px]]


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	with		with

	::[[File: MBOC_Eq_31.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_31.png\|none\|280px]]

	According to this, if we assume as mentioned above that <math>3\sigma_{\delta_{\tau},TH} \le \delta /2</math> for the case of the EMLP discriminator, the EMLP tracking threshold results to be:		According to this, if we assume as mentioned above that <math>3\sigma_{\delta_{\tau},TH} \le \delta /2</math> for the case of the EMLP discriminator, the EMLP tracking threshold results to be:

	::[[File: MBOC_Eq_32.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_32.png\|none\|380px]]


	and for the DP we have equally:		and for the DP we have equally:

	::[[File: MBOC_Eq_33.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_33.png\|none\|380px]]


	Using the expressions above, the tracking thresholds are computed in the next figures as a function of the coherent integration time and the DLL loop bandwidth. For the case of infinite bandwidth the expressions for the standard delay error simplify considerably adopting <math>A_1</math>,<math>A_2</math> and <math>A_3</math> the following values:		Using the expressions above, the tracking thresholds are computed in the next figures as a function of the coherent integration time and the DLL loop bandwidth. For the case of infinite bandwidth the expressions for the standard delay error simplify considerably adopting <math>A_1</math>,<math>A_2</math> and <math>A_3</math> the following values:

	::[[File: MBOC_Eq_34.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_34.png\|none\|240px]]
	::[[File: MBOC_Eq_35.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_35.png\|none\|240px]]
	::[[File: MBOC_Eq_36.png\|none\|~~340px~~]]		::[[File: MBOC_Eq_36.png\|none\|180px]]

Carlos.Lopez at 10:18, 3 November 2011

2011-11-03T10:18:28Z

Show changes

Carlos.Lopez: Created page with "{{Article Infobox2 |Category=Fundamentals |Title={{PAGENAME}} |Authors= J.A Ávila Rodríguez, University FAF Munich, Germany. |Level=Advanced |YearOfPublication=2011 }} == MBOC..."

2011-11-03T09:48:02Z

Created page with "{{Article Infobox2 |Category=Fundamentals |Title={{PAGENAME}} |Authors= J.A Ávila Rodríguez, University FAF Munich, Germany. |Level=Advanced |YearOfPublication=2011 }} == MBOC..."

Show changes

← Older revision		Revision as of 10:32, 3 November 2011
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	::::[[File:MBOC_Fig_2.png\|none\|thumb\|580px\|'''''Figure 2:''''' GPS and Galileo Spectra in E1/L1.]]		::::[[File:MBOC_Fig_2.png\|none\|thumb\|580px\|'''''Figure 2:''''' GPS and Galileo Spectra in E1/L1.]]


	== Implementing MBOC ==		== Implementing MBOC ==
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	Finally, it is important to mention that in the case of [[Composite BOC (CBOC)\| CBOC]], the generation of power presents no limitations since this is achieved by correspondingly modulating the amplitude.		Finally, it is important to mention that in the case of [[Composite BOC (CBOC)\| CBOC]], the generation of power presents no limitations since this is achieved by correspondingly modulating the amplitude.


	== On MBOC and Antisymmetric sequences ==		== On MBOC and Antisymmetric sequences ==
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	\|+align="bottom"\|'' Tables of Distinct Spreading Symbol Sequences for n=2 to 12''		\|+align="bottom"\|'' Tables of Distinct Spreading Symbol Sequences for n=2 to 12''
	\| [[File: MBOC_Table_1.png\|none\|thumb\|400px\|frameless]]		\| [[File: MBOC_Table_1.png\|none\|thumb\|400px\|frameless]]
	\|-
	\| [[File: MBOC_Table_2.png\|none\|thumb\|400px\|frameless]]		\| [[File: MBOC_Table_2.png\|none\|thumb\|400px\|frameless]]
	\|-
	\| [[File: MBOC_Table_3.png\|none\|thumb\|400px\|frameless]]		\| [[File: MBOC_Table_3.png\|none\|thumb\|400px\|frameless]]
	\|-		\|-
	\| [[File: MBOC_Table_4.png\|none\|thumb\|400px\|frameless]]		\| [[File: MBOC_Table_4.png\|none\|thumb\|400px\|frameless]]
	\|-
	\| [[File: MBOC_Table_5.png\|none\|thumb\|400px\|frameless]]		\| [[File: MBOC_Table_5.png\|none\|thumb\|400px\|frameless]]
	\|-
	\| [[File: MBOC_Table_6.png\|none\|thumb\|400px\|frameless]]		\| [[File: MBOC_Table_6.png\|none\|thumb\|400px\|frameless]]
	\|}		\|}
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	From the tables, it can be seen that only tables for , that is , have any entries with zero crosscorrelation with BOC(1,1). For , there is only 1 sequence corresponding to a BOC(2,1) spreading symbol modulation. For , there are 3 permissible sequences, <math>x_3,x_4,x_5</math>. Of these, <math>x_4</math> corresponds to the BOC(4,1) modulation. Finally for , there are 6 possible sequences, <math>x_7,x_{10},x_{13}, x_{17},x_{18}</math> where <math>x_{17}</math> corresponds to BOC(6,1), one of the solutions and indeed the best in terms of performance.		From the tables, it can be seen that only tables for , that is , have any entries with zero crosscorrelation with BOC(1,1). For , there is only 1 sequence corresponding to a BOC(2,1) spreading symbol modulation. For , there are 3 permissible sequences, <math>x_3,x_4,x_5</math>. Of these, <math>x_4</math> corresponds to the BOC(4,1) modulation. Finally for , there are 6 possible sequences, <math>x_7,x_{10},x_{13}, x_{17},x_{18}</math> where <math>x_{17}</math> corresponds to BOC(6,1), one of the solutions and indeed the best in terms of performance.


	== MBOC Tracking Sensitivity ==		== MBOC Tracking Sensitivity ==
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	as also shown in [O. Julien, 2005] <ref name="OJ_2005"/>.		as also shown in [O. Julien, 2005] <ref name="OJ_2005"/>.


	==== Effect of longer integrations on code tracking sensitivity ====		==== Effect of longer integrations on code tracking sensitivity ====
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	In the previous lines we have briefly discussed the most straightforward way of increasing tracking sensitivity by increasing the total integration time. Additionally, there exist other ways of increasing the post-correlation SNR such as increasing the signal power at the satellite. Unfortunately, this would have extremely negative effects on interference with already existing terrestrial systems.		In the previous lines we have briefly discussed the most straightforward way of increasing tracking sensitivity by increasing the total integration time. Additionally, there exist other ways of increasing the post-correlation SNR such as increasing the signal power at the satellite. Unfortunately, this would have extremely negative effects on interference with already existing terrestrial systems.


	==== Signal structure and DLL code tracking error ====		==== Signal structure and DLL code tracking error ====

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	Finally, it is important to note that although MBOC(6,1,1/11) and BOC(1,1) present improved performance with respect to BPSK(1), the tracking region is smaller if we track the whole MBOC. In fact, the linear region around the main peak will be six times narrower.		Finally, it is important to note that although MBOC(6,1,1/11) and BOC(1,1) present improved performance with respect to BPSK(1), the tracking region is smaller if we track the whole MBOC. In fact, the linear region around the main peak will be six times narrower.


	==== Signal structure and DLL sensitivity ====		==== Signal structure and DLL sensitivity ====
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	The figures obtained above extend over very long coherent integrations. In fact, no data channel could in reality reach such values unless external sources were used, what shows clearly the superiority of the pilot channel for these purposes. Indeed, the introduction of pilot channels by Galileo and the modernized GPS can be considered as one of the main contributions to the navigation. Navigation and communication applications require of different needs and the use of pilot signals in GNSS in the future is clear proof of that.		The figures obtained above extend over very long coherent integrations. In fact, no data channel could in reality reach such values unless external sources were used, what shows clearly the superiority of the pilot channel for these purposes. Indeed, the introduction of pilot channels by Galileo and the modernized GPS can be considered as one of the main contributions to the navigation. Navigation and communication applications require of different needs and the use of pilot signals in GNSS in the future is clear proof of that.


	== MBOC Interference with other GNSSes ==		== MBOC Interference with other GNSSes ==
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	The mathematical framework of the methodology described in [[GNSS Interference Model]] can be easily expanded to other bands as for example E5-L5 or to other SBAS systems as done in [S. Wallner et al., 2005] <ref name="SW_2005"/> where the results with smooth spectra and real codes were compared. One final comment on the figures above is that the minimum power levels were used for the simulations resulting thus in significantly higher values of interference than those we will observe in a typical scenario. Nonetheless, it must be kept in mind that the purpose of an interference methodology is to assess compatibility in all the cases, and therefore looking at the worst cases is thus of major interest.		The mathematical framework of the methodology described in [[GNSS Interference Model]] can be easily expanded to other bands as for example E5-L5 or to other SBAS systems as done in [S. Wallner et al., 2005] <ref name="SW_2005"/> where the results with smooth spectra and real codes were compared. One final comment on the figures above is that the minimum power levels were used for the simulations resulting thus in significantly higher values of interference than those we will observe in a typical scenario. Nonetheless, it must be kept in mind that the purpose of an interference methodology is to assess compatibility in all the cases, and therefore looking at the worst cases is thus of major interest.


	==References==		==References==