Correlators - Revision history

Filipe.Pelica: Included editor logo.

2014-09-18T16:33:42Z

Included editor logo.

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Carlos.Lopez at 11:00, 23 February 2012

2012-02-23T11:00:31Z

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Carlos.Lopez at 10:33, 23 February 2012

2012-02-23T10:33:51Z

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	Correlations are the key operation for GNSS receivers to synchronize with the incoming signal, generate GNSS observables, and retrieve the navigation message that will be used to provide a navigation solution later on. The reason is that GNSS signals transmit a ranging code modulated into the carrier, also called Pseudo-Random Noise (PRN) code, which not only spreads the spectrum but also allows retrieving ranging information.		Correlations are the key operation for GNSS receivers to synchronize with the incoming signal, generate GNSS observables, and retrieve the navigation message that will be used to provide a navigation solution later on. The reason is that GNSS signals transmit a ranging code modulated into the carrier, also called Pseudo-Random Noise (PRN) code, which not only spreads the spectrum but also allows retrieving ranging information.

Rui.Pereira: moved Work in Progress:Correlators to Correlators over redirect

2011-05-27T15:51:32Z

moved Work in Progress:Correlators to Correlators over redirect

← Older revision	Revision as of 15:51, 27 May 2011
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Rui.Pereira at 11:32, 11 May 2011

2011-05-11T11:32:31Z

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	Pseudo-Random Noise (PRN) Codes - also called ''ranging'' codes - are a sequence of pulses that are used by GNSS to spread the spectrum of the transmitted signal. For this purpose, several types of codes are used, and some examples are given here (for further information on the codes used by each system, refer to the respective SIS ICDs):		Pseudo-Random Noise (PRN) Codes - also called ''ranging'' codes - are a sequence of pulses that are used by GNSS to spread the spectrum of the transmitted signal. For this purpose, several types of codes are used, and some examples are given here (for further information on the codes used by each system, refer to the respective SIS ICDs):

	* '''GPS''' L1 C/A uses ''Gold'' codes<ref>[[~~wikipedia~~:Gold code]]</ref> that are actually a combination of two maximum length codes<ref>~~http~~:~~//en.wikipedia.org/wiki/Maximum_length_code~~</ref>.		* '''GPS''' L1 C/A uses ''Gold'' codes<ref>[[Wikipedia:Gold code\|Gold code in Wikipedia]]</ref> that are actually a combination of two maximum length codes<ref>[[Wikipedia:Maximum length code\|Maximum length code in Wikipedia]]</ref>.

	* '''GLONASS''' uses only one maximum length code. Since it uses an FDMA approach, low cross-correlation characteristics are not so critical for this system.		* '''GLONASS''' uses only one maximum length code. Since it uses an FDMA approach, low cross-correlation characteristics are not so critical for this system.

	* '''Galileo''' uses ''tiered'' codes, a combination of medium length primary code with a smaller length secondary code. Some of these secondary codes are ''memory'' codes, which are not generated through linear feedback shift registers (LFSR)<ref>[[wikipedia:LFSR]]</ref> like the others: instead, they are stored in the local memory. The advantage of these codes is that they are harder to decode by unauthorized users.		* '''Galileo''' uses ''tiered'' codes, a combination of medium length primary code with a smaller length secondary code. Some of these secondary codes are ''memory'' codes, which are not generated through linear feedback shift registers (LFSR)<ref>[[wikipedia:LFSR\|LFSR in Wikipedia]]</ref> like the others: instead, they are stored in the local memory. The advantage of these codes is that they are harder to decode by unauthorized users.

	[[File:corr_prn.png\|right\|thumb\|250px\|'''''Figure 1:'''''Example of auto-correlation and cross-correlation between GPS PRN1 and GPS PRN17, without noise.]]		[[File:corr_prn.png\|right\|thumb\|250px\|'''''Figure 1:'''''Example of auto-correlation and cross-correlation between GPS PRN1 and GPS PRN17, without noise.]]

Rui.Pereira: moved Correlators to Work in Progress:Correlators

2011-05-11T11:28:11Z

moved Correlators to Work in Progress:Correlators

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Rui.Sarnadas at 10:57, 6 May 2011

2011-05-06T10:57:53Z

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Teresa.Ferreira at 16:51, 5 May 2011

2011-05-05T16:51:56Z

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	Bearing in mind that GNSS receivers aim at tracking the peak of the auto-correlation function using the prompt correlator<ref group="footnotes">Actually GNSS receivers use additional correlators to track the auto-correlation peak, as described [[Multicorrelator\|here]].</ref>. and adjusting its delay to keep high auto-correlation values, it is rather intuitive to infer that narrower autocorrelation peaks potentially yield better accuracies. In fact, a badly formed prompt local replica will lead to a lower correlation output for small variations around the center. As a consequence, it can be inferred that BOC modulations can reach better accuracies, being CBOC the best one, when looking at the GPS and Galileo Open Service signals in the L1 band. When looking at the Power Spectral Density, this can be explained by the wider bandwidths of the BOC signals. The drawback is that the receiver needs wider front ends in order to process the full signal.		Bearing in mind that GNSS receivers aim at tracking the peak of the auto-correlation function using the prompt correlator<ref group="footnotes">Actually GNSS receivers also use additional correlators to track the auto-correlation peak, as described [[Multicorrelator\|here]].</ref>. and adjusting its delay to keep high auto-correlation values, it is rather intuitive to infer that narrower autocorrelation peaks potentially yield better accuracies. In fact, a badly formed prompt local replica will lead to a lower correlation output for small variations around the center. As a consequence, it can be inferred that BOC modulations can reach better accuracies, being CBOC the best one, when looking at the GPS and Galileo Open Service signals in the L1 band. When looking at the Power Spectral Density, this can be explained by the wider bandwidths of the BOC signals. The drawback is that the receiver needs wider front ends in order to process the full signal.


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	Furthermore, BOC modulations present additional side peaks (in Figure 3 for offsets of 0.5 chips). At receiver level, additional processing may be required in order to guarantee that the tracking loops are actually tracking the main peak and not one of the side peaks.		Furthermore, BOC modulations present additional side peaks (in Figure 3 for offsets of 0.5 chips). At receiver level, additional processing may be required in order to guarantee that the tracking loops are actually tracking the main peak and not one of the side peaks.
	Finally, when the lag between the local replica and the incoming signal is higher than 1 chip, the auto-correlation is minimum and only noise will be observed.		Finally, when the lag between the local replica and the incoming signal is higher than 1 chip, the auto-correlation is minimum and only noise will be observed.


			==Notes==
			<references group="footnotes"/>

	==Related articles==		==Related articles==

Teresa.Ferreira: /* Effect of the Modulation on Autocorrelation Function */

2011-05-05T16:50:53Z

Effect of the Modulation on Autocorrelation Function

Teresa.Ferreira: /* Block Diagram */

2011-05-05T16:44:31Z

Block Diagram

← Older revision		Revision as of 16:44, 5 May 2011
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	The local code is generated according to an input “code delay” which indicates the quantity be which the code should be shifted before correlating it with the incoming signal. From the previous definitions, it is clear that when the local replica ~~will be~~ aligned with the incoming signal, the correlation output will be ~~maximal~~.		The local code is generated according to an input “code delay” which indicates the quantity by which the code should be shifted before correlating it with the incoming signal. From the previous definitions, it is clear that when the local replica is aligned with the incoming signal, the correlation output will be maximum.

	Since real life signals are subject to noise and other disturbances, the assessment of the correlation output is solely performed on a single shot. In fact, the receiver uses Integration & Dump (I&D) blocks to integrate the correlation outputs over time. The main objective is to combine the correlations from consecutive PRN codes in order to increase the power of any potential peak and to reduce the inherent noise.		Since real life signals are subject to noise and other disturbances, the assessment of the correlation output is solely performed on a single shot. In fact, the receiver uses Integration & Dump (I&D) blocks to integrate the correlation outputs over time. The main objective is to combine the correlations from consecutive PRN codes in order to increase the power of any potential peak and to reduce the inherent noise.
	GNSS receivers often use a combination between coherent and non-coherent integrations, as further discussed [[Baseband Processing\|here]].		GNSS receivers often use a combination between coherent and non-coherent integrations, as further discussed [[Baseband Processing\|here]].

← Older revision		Revision as of 16:50, 5 May 2011
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	==Effect of the Modulation on Autocorrelation Function==		==Effect of the Modulation on Autocorrelation Function==

	The shape of the auto-correlation function is affected not only by the PRN code characteristics but also by the signal modulation. As an example, Figure 4 presents the normalized auto-correlation functions for:		The shape of the auto-correlation function is affected not only by the PRN code characteristics but also by the signal modulation. As an example, Figure 3 presents the normalized auto-correlation functions for:
	*BPSK(1): used in GPS L1 C/A		*BPSK(1): used in GPS L1 C/A
	*BOC(1,1): used in Galileo E1-B		*BOC(1,1): used in Galileo E1-B
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	Bearing in mind that GNSS receivers aim at tracking the peak of the auto-correlation function using the prompt correlator and adjusting its delay to keep high auto-correlation values, it is rather intuitive to infer that narrower autocorrelation peaks ~~will~~ potentially yield better accuracies. In fact, a badly formed prompt local replica will lead to a lower correlation output for small variations around the center. As a consequence, it can be inferred that BOC modulations can reach better accuracies, being CBOC the best one, when looking at the GPS and Galileo Open Service signals in the L1 band. When looking at the Power Spectral Density, this can be explained by the wider bandwidths of the BOC signals. The drawback is that the receiver needs wider front ends in order to process the full signal.		Bearing in mind that GNSS receivers aim at tracking the peak of the auto-correlation function using the prompt correlator<ref group="footnotes">Actually GNSS receivers use additional correlators to track the auto-correlation peak, as described [[Multicorrelator\|here]].</ref>. and adjusting its delay to keep high auto-correlation values, it is rather intuitive to infer that narrower autocorrelation peaks potentially yield better accuracies. In fact, a badly formed prompt local replica will lead to a lower correlation output for small variations around the center. As a consequence, it can be inferred that BOC modulations can reach better accuracies, being CBOC the best one, when looking at the GPS and Galileo Open Service signals in the L1 band. When looking at the Power Spectral Density, this can be explained by the wider bandwidths of the BOC signals. The drawback is that the receiver needs wider front ends in order to process the full signal.


	The main drivers for including the BOC modulations in GNSS are<ref>“Status of Galileo Frequency and Signal Design”, Guenter W. Hein, Jeremie Godet, Jean-Luc Issler, Jean-Christophe Martin, Philippe Erhard, Rafael Lucas-Rodriguez and Tony Pratt, Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), September 24 - 27, 2002, Oregon Convention Center, Portland, OR</ref>:		The main drivers for including the BOC modulations in GNSS are<ref>“Status of Galileo Frequency and Signal Design”, Guenter W. Hein, Jeremie Godet, Jean-Luc Issler, Jean-Christophe Martin, Philippe Erhard, Rafael Lucas-Rodriguez and Tony Pratt, Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002), September 24 - 27, 2002, Oregon Convention Center, Portland, OR</ref>:
	*To guarantee compatibility while supporting interoperability		*To guarantee compatibility while supporting interoperability among GNSS
	*To provide signals that are more robust in harsh environments such as noise, multipath and interference		*To provide signals that are more robust in harsh environments such as noise, multipath and interference
	*To reduce self-interference		*To reduce self-interference


	Furthermore, BOC modulations present additional side peaks (in Figure 4 for offsets of 0.5 chips). At receiver level, additional processing may be required in order to guarantee that the tracking loops are actually tracking the main peak and not one of the side peaks.		Furthermore, BOC modulations present additional side peaks (in Figure 3 for offsets of 0.5 chips). At receiver level, additional processing may be required in order to guarantee that the tracking loops are actually tracking the main peak and not one of the side peaks.
	Finally, when the lag between the local replica and the incoming signal is higher than 1 chip, the auto-correlation is ~~minimal~~ and only noise will be observed.		Finally, when the lag between the local replica and the incoming signal is higher than 1 chip, the auto-correlation is minimum and only noise will be observed.



	==Related articles==		==Related articles==