Binary offset carrier modulation: Difference between revisions

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Binary offset carrier modulation^[1]^[2] (BOC modulation) was developed by John Betz in order to allow interoperability of satellite navigation systems. It is currently used in the US GPS system, Indian IRNSS system and in Galileo^[3] and is a square sub-carrier modulation, where a signal is multiplied by a rectangular sub-carrier of frequency $f_{\text{sc}}$ equal to or greater than the chip rate. Following this sub-carrier multiplication, the spectrum of the signal is divided into two parts, therefore BOC modulation is also known as a split-spectrum modulation. Their major advantages are, that one can shape the spectrum to allow inter-system-compatibility and better theoretically achievable tracking capabilities, due to higher frequencies if downmixed to the complex baseband. On the other hand, a huge variety of different implementations or instantiations was set up, making it difficult to get the whole picture. Early (and sometimes recent) publications dealing with that topic usually do not include matched filters for pulse shaping as well as the concept of complex Gaussian noise - which is very often not treated correctly - to yield a mathematically consistent baseband description, that although complicated looking, models the physics correctly. I.e. if these standards are not treated correctly, theoretical results are not reliable. This is independent of the media and the peer-review and the person, who published it.

Design

The main idea behind BOC modulation is to reduce the interference with BPSK-modulated signals, which have a sinc function shaped spectrum. Therefore, BPSK-modulated signals such as C/A GPS codes have most of their spectral energy concentrated around the carrier frequency, while BOC-modulated signals (used in Galileo system) have low energy around the carrier frequency and two main spectral lobes further away from the carrier (thus the name of split-spectrum).

BOC modulation has several variants: sine BOC (sinBOC), cosine BOC (cosBOC),^[4] alternative BOC (altBOC), multiplexed BOC (MBOC),^[5] double BOC (DBOC)^[4] etc. and some of them have been currently selected for Galileo GNSS signals.^[6]

A BOC waveform is typically denoted via BOC(m, n) or BOC $(f_{\text{sc}},\;f_{\text{c}})$ , where $f_{\text{sc}}$ is the sub-carrier frequency, $f_{\text{c}}$ is the chip frequency, $m=f_{\text{sc}}/f_{\text{ref}}$ , $n=f_{\text{c}}/f_{\text{ref}}$ , and $f_{\text{ref}}=1.023$ Mcps is the reference chip frequency of C/A GPS signal.

A sine BOC(1, 1) modulation is similar to Manchester code; that is, in the digital domain, a '+1' is encoded as a '+1 −1' sequence, and a '0' is encoded as a '−1 +1' sequence. For an arbitrary $N_{\text{BOC}}=2m/n$ modulation order, in sine BOC(m, n) case, a '+1' is encoded as an alternating sequence of '+1 −1 +1 −1 +1 ...', having $N_{\text{BOC}}$ elements, and a '0' (or '−1') is encoded as an alternating '−1 +1 ...' sequence, also having $N_{\text{BOC}}$ elements.

BOC modulation is typically applied on CDMA signals, where each chip of the pseudorandom code is split into BOC sub-intervals, as explained above (i.e., there are $N_{\text{BOC}}$ BOC intervals per chip).

The power spectral density of a BOC-modulated signal depends on the BOC modulation order $N_{\text{BOC}}=2{\frac {f_{\text{sc}}}{f_{\text{c}}}}=2{\frac {m}{n}}$ .^[4]

BOC-modulated signals, by difference with BPSK signals, create the so-called ambiguities in the correlation function. The BOC-modulated signals in GNSS can be processed either with a Full BOC receiver or via various unambiguous approaches.^[7]^[8]

References

^ Betz, J. (January 1999). "The offset carrier modulation for GPS modernization". Proceedings of the 1999 National Technical Meeting of The Institute of Navigation: 639–648.
^ Betz, J. (May 2000). "Overview of the GPS M code signal". The Mitre Corporation.
^ "Galileo Open Service Signal in Space Interface Control Document (OS SIS ICD v1.3)" (PDF). Gallileo Space. Retrieved 14 December 2017.
^ ^a ^b ^c Lohan, Elena Simona; Lakhzouri, Abdelmonaem; Renfors, Markku (7 July 2006). "BOC modulation techniques in satellite navigation systems". Wireless Communications and Mobile Computing. 7 (6). doi:10.1002/wcm.407. Retrieved 14 December 2017.
^ "The MBOC Modulation". Inside GNSS. Archived from the original on 7 February 2009. Retrieved 14 December 2017.
^ Yarlykov, M. S. (2016). "Correlation functions of BOC". Journal of Communications Technology and Electronics. 61 (8): 857–876. doi:10.1134/S1064226916080180. S2CID 114952550.
^ Burian, Adina; Lohan, Elenasimona; Renfors, Markkukalevi (2007). "Efficient Delay Tracking Methods with Sidelobes Cancellation for BOC-Modulated Signals". EURASIP Journal on Wireless Communications and Networking. 2007: 072626. doi:10.1155/2007/72626.
^ Gallardo, Moises Navarro; Granados, Gonzalo Seco; Risueno, Gustavo Lopez; Crisci, Massimo (2013). 2013 International Conference on Localization and GNSS (ICL-GNSS). IEEE. pp. 1–6. doi:10.1109/ICL-GNSS.2013.6577260. ISBN 978-1-4799-0486-0. S2CID 30837429.

[1] Betz, J. (January 1999). "The offset carrier modulation for GPS modernization". Proceedings of the 1999 National Technical Meeting of The Institute of Navigation: 639–648.

[2] Betz, J. (May 2000). "Overview of the GPS M code signal". The Mitre Corporation.

[3] "Galileo Open Service Signal in Space Interface Control Document (OS SIS ICD v1.3)" (PDF). Gallileo Space. Retrieved 14 December 2017.

[Wiley06-4] Lohan, Elena Simona; Lakhzouri, Abdelmonaem; Renfors, Markku (7 July 2006). "BOC modulation techniques in satellite navigation systems". Wireless Communications and Mobile Computing. 7 (6). doi:10.1002/wcm.407. Retrieved 14 December 2017.

[5] "The MBOC Modulation". Inside GNSS. Archived from the original on 7 February 2009. Retrieved 14 December 2017.

[6] Yarlykov, M. S. (2016). "Correlation functions of BOC". Journal of Communications Technology and Electronics. 61 (8): 857–876. doi:10.1134/S1064226916080180. S2CID 114952550.

[7] Burian, Adina; Lohan, Elenasimona; Renfors, Markkukalevi (2007). "Efficient Delay Tracking Methods with Sidelobes Cancellation for BOC-Modulated Signals". EURASIP Journal on Wireless Communications and Networking. 2007: 072626. doi:10.1155/2007/72626.

[8] Gallardo, Moises Navarro; Granados, Gonzalo Seco; Risueno, Gustavo Lopez; Crisci, Massimo (2013). 2013 International Conference on Localization and GNSS (ICL-GNSS). IEEE. pp. 1–6. doi:10.1109/ICL-GNSS.2013.6577260. ISBN 978-1-4799-0486-0. S2CID 30837429.

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-{{Use dmy dates|date=June 2013}}
+{{Use dmy dates|date=December 2023}}
+{{Distinguish|offset binary}}
-'''Binary offset carrier modulation'''<ref>ION-AM99</ref><ref>MITRE00</ref> (BOC modulation) was developed by John Betz, PhD, in order to allow interoperability of satellite navigation systems. It is currently used in the US GPS system, Indian IRNSS system and in [[Galileo (satellite navigation)|Galileo]]<ref>SIS-ICD08</ref> and is a square sub-carrier [[modulation]], where a signal is multiplied by a rectangular [[sub-carrier]] of frequency <math>f_{sc}</math> equal or higher to the [[chip (CDMA)|chip]] rate. Following this [[sub-carrier]] [[multiplication]], the [[spectrum]] of the signal is divided into two parts, therefore BOC modulation is also known as a split-spectrum modulation.
+'''Binary offset carrier modulation'''<ref>{{cite journal|last1=Betz|first1=J.|title=The offset carrier modulation for GPS modernization|journal=Proceedings of the 1999 National Technical Meeting of The Institute of Navigation |date=January 1999|pages=639–648 |url=https://www.ion.org/publications/abstract.cfm?articleID=716}}</ref><ref>{{cite journal|last1=Betz|first1=J.|title=Overview of the GPS M code signal|journal=The Mitre Corporation|url=https://www.mitre.org/publications/technical-papers/overview-of-the-gps-m-code-signal|date=May 2000}}</ref> (BOC modulation) was developed by John Betz in order to allow interoperability of satellite navigation systems. It is currently used in the US GPS system, Indian [[IRNSS]] system and in [[Galileo (satellite navigation)|Galileo]]<ref>{{cite web|title=Galileo Open Service Signal in Space Interface Control Document (OS SIS ICD v1.3)|url=https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo-OS-SIS-ICD.pdf|publisher=Gallileo Space|accessdate=14 December 2017}}</ref> and is a square sub-carrier [[modulation]], where a signal is multiplied by a rectangular [[sub-carrier]] of frequency <math>f_\text{sc}</math> equal to or greater than the [[chip (CDMA)|chip]] rate. Following this [[sub-carrier]] [[multiplication]], the [[spectrum]] of the signal is divided into two parts, therefore BOC modulation is also known as a split-spectrum modulation. Their major advantages are, that one can shape the spectrum to allow inter-system-compatibility and better theoretically achievable tracking capabilities, due to higher frequencies if downmixed to the complex baseband. On the other hand, a huge variety of different implementations or instantiations was set up, making it difficult to get the whole picture. Early (and sometimes recent) publications dealing with that topic usually do not include matched filters for pulse shaping as well as the concept of complex Gaussian noise - which is very often not treated correctly - to yield a mathematically consistent baseband description, that although complicated looking, models the physics correctly. I.e. if these standards are not treated correctly, theoretical results are not reliable. This is independent of the media and the peer-review and the person, who published it.
+==Design==
-The main idea behind BOC modulation is to reduce the interference with [[BPSK]]-modulated signal, which has a [[sinc function]] shaped spectrum. Therefore, BPSK-modulated signals such as C/A [[Global Positioning System|GPS]] codes  have most of their spectral energy concentrated around the [[carrier frequency]], while BOC-modulated signals (used in [[Galileo system]]) have low energy around the carrier frequency and two main spectral lobes further away from the carrier (thus, the name of split-spectrum).
+The main idea behind BOC modulation is to reduce the interference with [[BPSK]]-modulated signals, which have a [[sinc function]] shaped spectrum. Therefore, BPSK-modulated signals such as C/A [[Global Positioning System|GPS]] codes have most of their spectral energy concentrated around the [[carrier frequency]], while BOC-modulated signals (used in [[Galileo system]]) have low energy around the carrier frequency and two main spectral lobes further away from the carrier (thus the name of split-spectrum).
-BOC modulation has several variants: sine BOC (SinBOC),<ref name="ENC-GNSS04">ENC-GNSS04</ref><ref>ION-GPS02</ref> cosine BOC (CosBOC),<ref name="ENC-GNSS04" /><ref>GJU</ref><ref name="Wiley06">Wiley06</ref> Alternative BOC (AltBOC),<ref>Septentrio</ref><ref>GPSJournal07</ref><ref>Margaria08</ref><ref>IEE06</ref> [[multiplexed BOC]] (MBOC),<ref>InsideGNSS07</ref><ref>ION-GNSS07</ref><ref>ION-GNSS07bis</ref><ref>EW07</ref><ref>ESA06</ref> Double BOC (DBOC)<ref name="Wiley06" /> etc. and some of them have been currently selected for  Galileo [[GNSS]] signals.
+BOC modulation has several variants: sine BOC (sinBOC), cosine BOC (cosBOC),<ref name="Wiley06">{{cite journal |last1=Lohan |first1=Elena Simona |last2=Lakhzouri |first2=Abdelmonaem |last3=Renfors |first3=Markku |title=BOC modulation techniques in satellite navigation systems|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/wcm.407 |date=7 July 2006 |journal=Wireless Communications and Mobile Computing |volume=7 |issue=6 |doi=10.1002/wcm.407 |accessdate=14 December 2017}}</ref> alternative BOC (altBOC), [[multiplexed BOC]] (MBOC),<ref>{{cite web|title=The MBOC Modulation|url=http://www.insidegnss.com/node/174|publisher=Inside GNSS|accessdate=14 December 2017|archive-url=https://web.archive.org/web/20090207170636/http://insidegnss.com/node/174|archive-date=7 February 2009|url-status=dead}}</ref> double BOC (DBOC)<ref name="Wiley06" /> etc. and some of them have been currently selected for  Galileo [[GNSS]] signals.<ref>{{cite journal|title=Correlation functions of BOC|journal=Journal of Communications Technology and Electronics|volume=61|issue=8|pages=857–876|doi=10.1134/S1064226916080180|year=2016|last1=Yarlykov|first1=M. S.|s2cid=114952550}}</ref>
-A BOC waveform is typically denoted via BOC(m,n) or BOC<math>(f_{sc}\;,f_c)</math>, where <math>f_{sc}</math> is the sub-carrier frequency, <math>f_c</math> is the chip frequency, <math>m=f_{sc}/f_{ref}</math>,  <math>n=f_{c}/f_{ref}</math>, and <math>f_{ref}=1.023</math> Mcps is the reference chip frequency of C/A [[GPS]] signal.
+A BOC waveform is typically denoted via BOC(m, n) or BOC<math>(f_\text{sc},\; f_\text{c})</math>, where <math>f_\text{sc}</math> is the sub-carrier frequency, <math>f_\text{c}</math> is the chip frequency, <math>m = f_\text{sc}/f_\text{ref}</math>, <math>n = f_\text{c}/f_\text{ref}</math>, and <math>f_\text{ref} = 1.023</math>{{nbsp}}Mcps is the reference chip frequency of C/A [[GPS]] signal.
-A sine BOC(1,1) modulation is similar to [[Manchester code]], that is, in digital domain, a '+1' is encoded as a '+1 −1' sequence, and a '0' is encoded as a '−1 +1' sequence.
-For an arbitrary <math>N_{BOC}=2m/n</math> modulation order, in sine BOC(''m'',''n'') case, a '+1' is encoded as an alternating sequence of '+1 −1 +1 −1 +1 ...', having <math>N_{BOC}</math> elements, and a '0' (or '−1') is encoded as an alternating '−1 +1 ...' sequence, also having <math>N_{BOC}</math> elements.
+A sine BOC(1, 1) modulation is similar to [[Manchester code]]; that is, in the digital domain, a '+1' is encoded as a '+1 −1' sequence, and a '0' is encoded as a '−1 +1' sequence. For an arbitrary <math>N_\text{BOC} = 2m/n</math> modulation order, in sine BOC(''m'', ''n'') case, a '+1' is encoded as an alternating sequence of '+1 −1 +1 −1 +1 ...', having <math>N_\text{BOC}</math> elements, and a '0' (or '−1') is encoded as an alternating '−1 +1 ...' sequence, also having <math>N_\text{BOC}</math> elements.
-BOC modulation is typically applied on [[CDMA]] signals, where each chip of the [[pseudorandom]] code is split into BOC sub-intervals, as explained above (i.e., there are <math>N_{BOC}</math> BOC intervals per chip).
+BOC modulation is typically applied on [[CDMA]] signals, where each chip of the [[pseudorandom]] code is split into BOC sub-intervals, as explained above (i.e., there are <math>N_\text{BOC}</math> BOC intervals per chip).
-The [[Spectral density|power spectral density]] of a BOC-modulated signal depends on the BOC modulation order <math>N_{BOC}=2\frac{f_{sc}}{f_c}=2\frac{m}{n}</math> and its derivation can be found, for example, in.
-<ref name="Wiley06" /><ref>VTC04</ref>
+The [[Spectral density|power spectral density]] of a BOC-modulated signal depends on the BOC modulation order <math>N_\text{BOC} = 2\frac{f_\text{sc}}{f_\text{c}} = 2\frac{m}{n}</math>.<ref name="Wiley06" />
-BOC-modulated signals, by difference with BPSK signals, create the so-called ambiguities in the correlation function. The BOC-modulated signals in GNSS can be processed either with a Full BOC receiver or via various unambiguous approaches, discussed for example in.<ref>Heiries04</ref><ref>Burian07</ref><ref>Navarro2013</ref>
+BOC-modulated signals, by difference with BPSK signals, create the so-called ambiguities in the correlation function. The BOC-modulated signals in GNSS can be processed either with a Full BOC receiver or via various unambiguous approaches.<ref>{{cite journal|title= Efficient Delay Tracking Methods with Sidelobes Cancellation for BOC-Modulated Signals|journal= EURASIP Journal on Wireless Communications and Networking|volume=2007|pages=072626|doi=10.1155/2007/72626|year=2007|last1=Burian|first1=Adina|last2=Lohan|first2=Elenasimona|last3=Renfors|first3=Markkukalevi|doi-access=free}}</ref><ref>{{cite book|publisher=IEEE|doi=10.1109/ICL-GNSS.2013.6577260|title = 2013 International Conference on Localization and GNSS (ICL-GNSS)|pages=1–6|year = 2013|last1 = Gallardo|first1 = Moises Navarro|last2=Granados|first2=Gonzalo Seco|last3=Risueno|first3=Gustavo Lopez|last4=Crisci|first4=Massimo|s2cid=30837429|isbn=978-1-4799-0486-0}}</ref>
-==References==
-{{Reflist|2}}
-{{Refbegin}}
-==Further reading==
+==See also==
+*[[Multiplexed binary offset carrier]]
-{{further reading cleanup|date=June 2014}}
-*Betz J. The offset carrier modulation for GPS modernization. In Proceedings of ION Technical meeting, (Cambridge, Massachusetts) June 1999; 639–648. (ION-AM99)
-*J. Betz, “Design and performance of code tracking for the GPS M code signal,” MITRE, Mclean, Va, USA, September 2000, http://www.mitre.org/work/tech_papers/tech_papers_00/ betz_codetracking/ (MITRE00)
-* Galileo Open Service Signal in Space Interface Control Document https://web.archive.org/web/20090208145704/http://gsa.europa.eu/go/galileo/os-sis-icd/galileo-open-service-signal-in-space-interface-control-document (SIS-ICD08)
-*Hein G, Irsigler M, Rodriguez JA, Pany T. Performance of Galileo L1 signal candidates. In CDROM Proceedings of European Navigation Conference GNSS, May 2004. (ENC-GNSS04)
-* Ries L, Lestarquit L, Armengou-Miret E, et al. A software simulation tool for GNSS2 BOC signals analysis. In Proceedings of ION GPS, (Portland, OR) September 2002; 2225-2239 (ION-GPS02)
-* GJU. Galileo standardisation document for 3GPP. Galileo Joint Undertaking (GJU) webpages, http://www.galileoju.com/page.cfm?voce=s2&idvoce=64&plugIn=1 (GJU)
-*www.septentrio.com/papers/GallileoAltBOC_paperFinal.pdf
-*E. S. Lohan, A. Lakhzouri, and M. Renfors, “Binary-offset-carrier modulation techniques with applications in satellite navigation systems,” Wiley Wireless Communications and Mobile Computing, vol. 7, no. 6, pp. 767–779, 2006, http://www3.interscience.wiley.com/cgi-bin/fulltext/112693999/PDFSTART (Wiley06)
-* Raghavan SH, Holmes JK. Modeling and simulation of mixed modulation formats for improved CDMA bandwidth efficiency. In Proceedings of Vehicular Technology Conference 2004; 6: 4290-4295 (VTC04).
-* D. Margaria, F. Dovis, P. Mulassano, An Innovative Data Demodulation Technique for Galileo AltBOC Receivers, Journal of Global Positioning Systems, Journal of Global Positioning Systems, Vol.6, No.1, pp.&nbsp;89–96, {{ISSN|1446-3156}}, 2007, http://www.gmat.unsw.edu.au/wang/jgps/v6n1/v6n1p10.pdf (GPSJournal07)
-* D. Margaria, F. Dovis, P. Mulassano, Galileo AltBOC Signal Multiresolution Acquisition Strategy, IEEE Aerospace and Electronic Systems Magazine, Vol.23, No.11, pp. 4–10, {{ISSN|0885-8985}}, November 2008. (Margaria08)
-* E. S. Lohan, A. Lakhzouri, M. Renfors, ``Complex Double-Binary-Offset-Carrier modulation for a unitary characterization of Galileo and GPS signals'', IEE Proceedings on Radar, Sonar, and Navigation, vol. 153(5), pp. 403-408, Oct 2006.[IEE06]
-*  Avila-Rodriguez, J.A., Hein, G.W., Wallner, S., Issler, J.L., Ries, L., Lestarquit, L., De Latour, A., Godet, J., Bastide, F., Pratt, T., Owen, J. The MBOC Modulation- A Final Touch for the Galileo Frequency and Signal Plan, http://www.insidegnss.com/node/174 [[Inside GNSS]] (InsideGNSS07)
-*Avila-Rodriguez, J.A., Wallner, S., Hein, G.W., Eissfeller, B., Irsigler, M., Issler, J.L.: A vision on new frequencies, signals and concepts for future GNSS systems, Proceedings of ION GNSS 2007, Fort Worth, Texas, USA, 25–28 September 2007 (ION-GNSS07)
-*Avila-Rodriguez, J.A., Hein, G.W., Wallner, S., Issler, J.L., Ries, L., Lestarquit, L., De Latour, A., Godet, J., Bastide, F., Pratt, T., Owen, J.: The MBOC Modulation: The Final Touch to the Galileo Frequency and Signal Plan, Proceedings of ION GNSS 2007, Fort Worth, Texas, USA, 25–28 September 2007 (ION-GNSS07bis)
-* E.S. Lohan and M. Renfors, ``On the performance of Multiplexed-BOC (MBOC) modulation for future GNSS signals'', in Proc. of European Wireless Conference, Apr 2007, Paris, France.(EW07)
-*Avila-Rodriguez J.A., Wallner S., Hein G.W.: MBOC: The New Optimized Spreading Modulation Recommended for Galileo E1 OS and GPS L1C, ESA Navitec 2006, Noordwijk, The Netherlands, 11-13 Dec. 2006 (ESA06)
-*A. Burian, E.S. Lohan, and M.  Renfors, Efficient Delay Tracking Methods with Sidelobes Cancellation for BOC-Modulated Signals, EURASIP Journal on Wireless Communications and Networking,  Volume 2007 (2007), Article ID 72626, 20 pages (Burian07)
-*V. Heiries, D. Roviras, L. Ries, V. Calmettes, ”Analysis of NonAmbiguous BOC Signal Acquisition performance”, ION GNSS 17th International Technical Meeting of the Satellite Division, 21-24 Sept. 2004, pp. 2611–2622. (Heiries04)
-*M. Navarro Gallardo, G. Seco-Granados, G. López-Risueño, M. Crisci, "Code Smoothing for BOC Ambiguity Mitigation", Proc. International Conference on Localization and GNSS (ICL-GNSS), 2013 (Navarro2013)
-{{Refend}}
-==External links==
+==References==
+{{Reflist}}
-* Binary Offset Carrier (BOC) signal generator in Matlab, https://web.archive.org/web/20100614000658/http://www.mathworks.com/matlabcentral/fileexchange/12829
 {{DEFAULTSORT:Binary Offset Carrier}}