Frequency Lock Loop (FLL) - Revision history

Filipe.Pelica: Included editor logo.

2014-09-18T16:36:35Z

Included editor logo.

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James.Curran: /* Principle */

2012-08-30T22:22:27Z

Principle

← Older revision		Revision as of 22:22, 30 August 2012
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	<math>\frac{-1}{2T}< \hat {f}< \frac{1}{2T}\,</math>		<math>\frac{-1}{2T}< \hat {f}< \frac{1}{2T}\,</math>

	Other tracking strategies exist which operate on a different principles, for example, they may directly observe the frequency information via a DFT, or by observing the relative power in correlator values which are computed at various frequency offsets. <ref name="~~kaplan~~">J. C. Juang and Y. H. Chen, “Phase/frequency tracking in a GNSS software receiver,” Selected Topics in Signal Processing, IEEE Journal of, vol. 3, no. 4, pp. 651 –660, August 2009.</ref>		Other tracking strategies exist which operate on a different principles, for example, they may directly observe the frequency information via a DFT, or by observing the relative power in correlator values which are computed at various frequency offsets. <ref name="Juang">J. C. Juang and Y. H. Chen, “Phase/frequency tracking in a GNSS software receiver,” Selected Topics in Signal Processing, IEEE Journal of, vol. 3, no. 4, pp. 651 –660, August 2009.</ref>

	==Discriminators ==		==Discriminators ==

James.Curran: /* Principle */

2012-08-30T22:21:39Z

Principle

← Older revision		Revision as of 22:21, 30 August 2012
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	<math>\frac{-1}{2T}< \hat {f}< \frac{1}{2T}\,</math>		<math>\frac{-1}{2T}< \hat {f}< \frac{1}{2T}\,</math>

	Other tracking strategies exist which operate on a different principles, for example, they may directly observe the frequency information via a DFT, or by observing the relative power in correlator values which are computed at various frequency offsets.		Other tracking strategies exist which operate on a different principles, for example, they may directly observe the frequency information via a DFT, or by observing the relative power in correlator values which are computed at various frequency offsets. <ref name="kaplan">J. C. Juang and Y. H. Chen, “Phase/frequency tracking in a GNSS software receiver,” Selected Topics in Signal Processing, IEEE Journal of, vol. 3, no. 4, pp. 651 –660, August 2009.</ref>

	==Discriminators ==		==Discriminators ==

James.Curran: /* Principle */

2012-08-30T22:20:28Z

Principle

← Older revision		Revision as of 22:20, 30 August 2012
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	'''Frequency Lock Loops (FLL)''' track the Doppler frequency of the incoming signal (with respect to Intermediate Frequency), without necessarily correcting for phase. For that purpose, the FLL uses integrations, filters and Numerical Control Oscillators (NCO) – described [[Tracking Loops\|here]] – as any other typical loop. In this case, the specificity relies on the discriminator used to assess the current frequency error estimated at the receiver.		'''Frequency Lock Loops (FLL)''' track the Doppler frequency of the incoming signal (with respect to Intermediate Frequency), without necessarily correcting for phase. For that purpose, the FLL uses integrations, filters and Numerical Control Oscillators (NCO) – described [[Tracking Loops\|here]] – as any other typical loop. In this case, the specificity relies on the discriminator used to assess the current frequency error estimated at the receiver.

	The principle behind ~~the~~ FLL is to retrieve frequency information, by using the derivative of the phase between two consecutive sets of data (samples). The FLL is expected to work well if the coherent integration time <math>T\,</math> is small, in order to avoid aliasing:		The principle behind most common FLL implementation is to retrieve frequency information, by using the derivative of the phase between two consecutive sets of data (samples). As such, the common FLL is a differential-phase tracking loop. The FLL is expected to work well if the coherent integration time <math>T\,</math> is small, in order to avoid aliasing:


	<math>\frac{-1}{2T}< \hat {f}< \frac{1}{2T}\,</math>		<math>\frac{-1}{2T}< \hat {f}< \frac{1}{2T}\,</math>

			Other tracking strategies exist which operate on a different principles, for example, they may directly observe the frequency information via a DFT, or by observing the relative power in correlator values which are computed at various frequency offsets.

	==Discriminators ==		==Discriminators ==

Carlos.Lopez at 11:01, 23 February 2012

2012-02-23T11:01:00Z

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Carlos.Lopez at 10:34, 23 February 2012

2012-02-23T10:34:23Z

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	Frequency Lock Loops are part of the receiver's signal tracking loops, and aim at tracking the frequency of the incoming GNSS signal. The FLL provides frequency corrections in a continuous loop, generating a frequency error signal.		Frequency Lock Loops are part of the receiver's signal tracking loops, and aim at tracking the frequency of the incoming GNSS signal. The FLL provides frequency corrections in a continuous loop, generating a frequency error signal.

Rui.Pereira: moved Work in Progress:Frequency Lock Loop (FLL) to Frequency Lock Loop (FLL) over redirect

2011-05-27T15:53:53Z

moved Work in Progress:Frequency Lock Loop (FLL) to Frequency Lock Loop (FLL) over redirect

← Older revision	Revision as of 15:53, 27 May 2011
(No difference)

Rui.Pereira: moved Frequency Lock Loop (FLL) to Work in Progress:Frequency Lock Loop (FLL)

2011-05-11T13:38:50Z

moved Frequency Lock Loop (FLL) to Work in Progress:Frequency Lock Loop (FLL)

← Older revision	Revision as of 13:38, 11 May 2011
(No difference)

Rui.Sarnadas at 13:51, 6 May 2011

2011-05-06T13:51:14Z

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			Frequency Lock Loops are part of the receiver's signal tracking loops, and aim at tracking the frequency of the incoming GNSS signal. The FLL provides frequency corrections in a continuous loop, generating a frequency error signal.

			==Principle ==
			'''Frequency Lock Loops (FLL)''' track the Doppler frequency of the incoming signal (with respect to Intermediate Frequency), without necessarily correcting for phase. For that purpose, the FLL uses integrations, filters and Numerical Control Oscillators (NCO) – described [[Tracking Loops\|here]] – as any other typical loop. In this case, the specificity relies on the discriminator used to assess the current frequency error estimated at the receiver.

	~~Frequency Lock Loops are part~~ of the ~~Tracking Loops and aim at tracking the frequency~~ of the ~~incoming GNSS signal~~, ~~providing corrections~~ in ~~a continuous loop.~~		The principle behind the FLL is to retrieve frequency information, by using the derivative of the phase between two consecutive sets of data (samples). The FLL is expected to work well if the coherent integration time <math>T\,</math> is small, in order to avoid aliasing:


	==~~Principle~~ ==		<math>\frac{-1}{2T}< \hat {f}< \frac{1}{2T}\,</math>


			==Discriminators ==

	~~Frequency Lock Loops (FLL) track the Doppler frequency of the incoming signal (with respect to Intermediate Frequency)~~, ~~without necessarily correcting for phase.~~		First, let us define ''cross product'' and ''dot product'', in terms of In-Phase ''I'' and Quadrature ''Q'' components, as:
	~~For that purpose~~, ~~the FLL uses integrations~~, ~~filters and Numerical Control Oscillators (NCO) – described [[Tracking Loops\|here]] –~~ as ~~any other loop.~~
	~~The specificity relies on the discriminator used to assess the current frequency error estimated at the receiver.~~

	~~The principle behind the FLL is to retrieve frequency information by using the derivative of the phase between two consecutive samples.~~

	~~The FLL is expected to work well if the coherent integration time~~, ~~T, is small, in order to avoid aliasing:~~		<math>cross=I_{P1} \times Q_{P2} - I_{P2} \times Q_{P1}\,</math>

	<math>\~~frac~~{-1}{2T}< \~~hat~~ {f}< \~~frac{1}{2T}~~</math>		<math>dot=I_{P1} \times I_{P2} + Q_{P1} \times Q_{P2}\,</math>

	~~==Discriminators ==~~

	~~Defining cross~~ and ~~dot product as:~~		where the indices 1 and 2 refer to samples taken at consecutive time instants, <math>t_1\,</math> and <math>t_2\,</math>.

	<~~math~~>~~cross=I_{P1} \times Q_{P2} - I_{P2} \times Q_{P1}~~</~~math~~>		This way, the most commonly used FLL discriminators are (ordered from lowest to highest computational burden)<ref name="kaplan">Kaplan E.D., Hegarty C.J., "Understanding GPS: Principles and Applications", second edition.</ref>:

	~~<math>dot=I_{P1} \times I_{P2} + Q_{P1} \times Q_{P2}</math>~~

	~~where the indexes 1 and 2 refer to samples taken at consecutive time instants:~~ <math>t_1</math> ~~and <math>t_2</math>.~~		*<math>\frac{cross}{t_2-t_1}\,</math>

			*<math>\frac{cross \times sign(dot)}{t_2-t_1}\,</math>

	~~Then the most commonly used FLL discriminators are (ordered by computational burden)~~ <~~ref name="kaplan"~~>~~Kaplan E.D.~~, ~~Hegarty C.J.,"Understanding GPS: Principles and Applications"~~, ~~second edition~~</~~ref~~>:		*<math>\frac{atan2 (cross, dot)}{t_2-t_1}\,</math>

	*<math>\frac{cross}{t_2-t_1}</math>
	*<math>\frac{cross \times sign(dot)}{t_2-t_1}</math>
	*<math>\frac{ATAN2 (cross, dot)}{t_2-t_1}</math>

	The ~~ATAN2~~ discriminator is optimal although it presents the greatest computational requirements. ~~Finally,~~ the FLL is insensitive to data transitions as long as the consecutive measurements (correlator outputs) refer to the same data bit.		The <math>atan2\,</math> discriminator is optimal, although it presents the greatest computational requirements. Note that the FLL is insensitive to data transitions, as long as the consecutive measurements (correlator outputs) refer to the same data bit.

	==Performance ==		==Performance ==
			The main sources of errors in the FLL are frequency jitter and dynamic stress error<ref name="kaplan"></ref>, which are mostly caused by thermal noise. The FLL thermal noise jitter can be written (in m/s) as:

	~~The main sources of errors in the FLL are frequency jitter and dynamic stress error <ref name="kaplan"></ref>, which are greatly produced by thermal noise.~~
	~~The FLL thermal noise jitter can be written (in m/s) as:~~

	<math>\sigma_{th}=\frac{\lambda}{2 \pi T} \sqrt{\frac{4FB_n}{C/N_0}(1+\frac{1}{TC/N_0})}</math>		<math>\sigma_{th}=\frac{\lambda}{2 \pi T} \sqrt{\frac{4FB_n}{C/N_0}(1+\frac{1}{TC/N_0})}\,</math>

	~~Where~~
	*<math>\lambda</math> is wavelength of the carrier signal [m]
	*<math>B_n</math> is the loop bandwidth [Hz]
	*<math>C/N_0</math> is the carrier to noise ratio [dB-Hz]
	*T is the integration time [s]
	*F=1 at high carrier to noise ration and 2 otherwise

			where:

	~~The performance~~ of the ~~FLL depends mainly on~~ the loop bandwidth ~~and~~ the ~~integration times used~~ to ~~accumulate~~ the ~~correlator outputs~~.		*<math>\lambda\,</math> is the wavelength of the carrier signal [m].
	~~The impact of these parameters is shown in Figure~~ 1, ~~and they are visible mainly for low~~ carrier to noise ~~ratio~~.		*<math>B_n\,</math> is the loop bandwidth [Hz].
			*<math>C/N_0\,</math> is the carrier-to-noise ratio [dB-Hz].
			*<math>T\,</math> is the integration time [s].
			*<math>F\,</math> = 1, at high carrier to noise ration; <math>F\,</math> = 2, otherwise.


			The performance of the FLL depends mainly on the loop bandwidth and the integration times used to accumulate the correlator outputs. The impact of these parameters is shown in Figure 1, and they are visible mainly for low carrier to noise ratio.

	[[File:fll_performance.png\|center\|thumb\|600px\|'''''Figure 1:''''' Impact of loop bandwidth (left) and integration time (right) on the FLL thermal noise jitter performance.]]		[[File:fll_performance.png\|center\|thumb\|600px\|'''''Figure 1:''''' Impact of loop bandwidth (left) and integration time (right) on the FLL thermal noise jitter performance.]]

			These results also illustrate the fact that longer integration times (and lower bandwidths) lead to noise reduction, hence higher performances, as discussed [[Tracking Loops\|here]]. In addition, lower loop noise bandwidths allow coping with higher dynamic environments.
	These results also illustrate the fact that longer integration times (and lower bandwidths) lead to noise reduction ~~and~~ hence higher performances, as discussed [[Tracking Loops\|~~previously~~]].
	In addition, lower loop noise bandwidths allow coping with higher dynamic environments.


	==Related articles==		==Related articles==
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	*[[Phase Lock Loop (PLL)]]		*[[Phase Lock Loop (PLL)]]
	*[[Delay Lock Loop (DLL)]]		*[[Delay Lock Loop (DLL)]]


	==References==		==References==

Teresa.Ferreira: /* Discriminators */

2011-05-05T22:48:44Z

Discriminators

← Older revision		Revision as of 22:48, 5 May 2011
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	*<math>\frac{ATAN2 (cross, dot)}{t_2-t_1}</math>		*<math>\frac{ATAN2 (cross, dot)}{t_2-t_1}</math>

	The ATAN2 discriminator is optimal although it ~~has~~ the ~~greater~~ computational requirements. Finally, the FLL is insensitive to data transitions as long as the consecutive measurements (correlator outputs) refer to the same data bit.		The ATAN2 discriminator is optimal although it presents the greatest computational requirements. Finally, the FLL is insensitive to data transitions as long as the consecutive measurements (correlator outputs) refer to the same data bit.


	==Performance ==		==Performance ==