Generic BCS Signals - Revision history

Carlos.Lopez at 09:11, 25 November 2011

2011-11-25T09:11:53Z

← Older revision		Revision as of 09:11, 25 November 2011
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	In general, in order to understand how the spectrum will look like for a given sequence, we have to be able to understand how every term of the sum above contributes to the total PSD.		In general, in order to understand how the spectrum will look like for a given sequence, we have to be able to understand how every term of the sum above contributes to the total PSD.



			== 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]]

Carlos.Lopez at 11:18, 18 November 2011

2011-11-18T11:18:04Z

← Older revision		Revision as of 11:18, 18 November 2011
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	{{Article Infobox2		{{Article Infobox2
	\|Category=Fundamentals		\|Category=Fundamentals
	~~\|Title={{PAGENAME}}~~		\|Authors=J.A Ávila Rodríguez, University FAF Munich, Germany.
	\|Authors= J.A Ávila Rodríguez, University FAF Munich, Germany.
	\|Level=Advanced		\|Level=Advanced
	\|YearOfPublication=2011		\|YearOfPublication=2011
			\|Title={{PAGENAME}}
	}}		}}
	~~In the previous lines we have studied two~~ particular cases of the BCS modulation~~, namely~~ the BPSK and BOC modulations. Nonetheless~~, the general expression derived at the beginning of the chapter is valid for any BCS vector. For exemplification~~, we show in the next lines how the PSD of a generic BCS could be derived.		Two particular cases of the [[Binary Coded Symbols (BCS)\|BCS modulation]] are the [[Binary Phase Shift Keying Modulation (BPSK) \|BPSK]] and [[Binary Offset Carrier (BOC)\|BOC]] modulations. Nonetheless, we show in the next lines how the [[Autocorrelation & Power Spectral Density\|Power Spectral Density (PSD)]] of a generic BCS could be derived.

	Let us assume a BCS signal with vector s = [+1, +1, -1]. We have thus <math>s_1 = +1 , s_2 = +1 , s_3 = -1</math>. The modulating term of the PSD can be easily calculated as:		Let us assume a BCS signal with vector s = [+1, +1, -1]. We have thus <math>s_1 = +1 , s_2 = +1 , s_3 = -1</math>. The modulating term of the PSD can be easily calculated as:
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	In general, in order to understand how the spectrum will look like for a given sequence, we have to be able to understand how every term of the sum above contributes to the total PSD.		In general, in order to understand how the spectrum will look like for a given sequence, we have to be able to understand how every term of the sum above contributes to the total PSD.



	~~==References==~~
	~~<references/>~~


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

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

2011-09-22T13:57:20Z

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

New page

{{Article Infobox2
|Category=Fundamentals
|Title={{PAGENAME}}
|Authors= J.A Ávila Rodríguez, University FAF Munich, Germany.
|Level=Advanced
|YearOfPublication=2011
}}
In the previous lines we have studied two particular cases of the BCS modulation, namely the BPSK and BOC modulations. Nonetheless, the general expression derived at the beginning of the chapter is valid for any BCS vector. For exemplification, we show in the next lines how the PSD of a generic BCS could be derived.

Let us assume a BCS signal with vector s = [+1, +1, -1]. We have thus <math>s_1 = +1 , s_2 = +1 , s_3 = -1</math>. The modulating term of the PSD can be easily calculated as:

::[[File:GBCS_Eq_1.png|none|700px]]

which can be further simplified to:

::[[File:GBCS_Eq_2.png|none|700px]]

while
::[[File:GBCS_Eq_3.png|none|280px]]

Thus the spectrum of this BCS sequence would adopt the following form:

::[[File:GBCS_Eq_4.png|none|440px]]

In general, in order to understand how the spectrum will look like for a given sequence, we have to be able to understand how every term of the sum above contributes to the total PSD.

==References==
<references/>

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