CBCS Modulation - Revision history

Gema.Cueto at 11:46, 20 October 2022

2022-10-20T11:46:08Z

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	where <math>\alpha</math> and <math>\beta</math> indicate the amount of power that is put on BOC(1,1) and on the BCS signal with respect to the total OS power of the signal. Thus, <math>\alpha</math> and <math>\beta</math> fulfil the condition <math>\alpha = \beta = 1</math>. For this same reason, we will use in other parts of the thesis <math>\beta = \rho</math> and <math>\alpha = 1 - \rho</math> instead. Moreover, [s] represents the BCS vector as defined in [[Multilevel Coded Spreading Symbols (MCS)]]. As we saw there, BCS is a generalization of the [[Binary Phase Shift Keying Modulation (BPSK)\|BPSK]] and [[Binary Offset Carrier (BOC)\|BOC]] modulations. In addition, it is important to realize that the CBCS definition intrinsically assumes the use of Interplex to multiplex the signals.		where <math>\alpha</math> and <math>\beta</math> indicate the amount of power that is put on BOC(1,1) and on the BCS signal with respect to the total OS power of the signal. Thus, <math>\alpha</math> and <math>\beta</math> fulfil the condition <math>\alpha + \beta = 1</math>. For this same reason, we will use in other parts of the thesis <math>\beta = \rho</math> and <math>\alpha = 1 - \rho</math> instead. Moreover, [s] represents the BCS vector as defined in [[Multilevel Coded Spreading Symbols (MCS)]]. As we saw there, BCS is a generalization of the [[Binary Phase Shift Keying Modulation (BPSK)\|BPSK]] and [[Binary Offset Carrier (BOC)\|BOC]] modulations. In addition, it is important to realize that the CBCS definition intrinsically assumes the use of Interplex to multiplex the signals.

	The flexibility of the CBCS approach lies in the fact that it could be easily converted into another CBCS by changing the contribution of the BCS part or even choosing different chip rates. In fact, a particular case of the CBCS solution is the pure BCS signal which seems to present the best performance in terms of multipath for selected sequences. Nonetheless, for the EU developers keeping high interoperability with BOC(1,1) receivers was a mandatory from the very beginning and this forced the design to have an important amount of BOC(1,1) in the definition.		The flexibility of the CBCS approach lies in the fact that it could be easily converted into another CBCS by changing the contribution of the BCS part or even choosing different chip rates. In fact, a particular case of the CBCS solution is the pure BCS signal which seems to present the best performance in terms of multipath for selected sequences. Nonetheless, for the EU developers keeping high interoperability with BOC(1,1) receivers was a mandatory from the very beginning and this forced the design to have an important amount of BOC(1,1) in the definition.

Teresa.Ferreira: /* CBCS Positioning Performance */

2012-03-09T12:01:09Z

CBCS Positioning Performance

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	::::[[File:CBCS_Fig_12.png\|none\|thumb\|420px\|'''''Figure 12:''''' Cramér Rao Lower Bound of E1 OS signals. It must be noted that ~~OSA~~ refers to the data channel while <math>OS_B</math> refers to the pilot channel.]]		::::[[File:CBCS_Fig_12.png\|none\|thumb\|420px\|'''''Figure 12:''''' Cramér Rao Lower Bound of E1 OS signals. It must be noted that <math>OS_A</math> refers to the data channel while <math>OS_B</math> refers to the pilot channel.]]


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	Finally, we must underline that the Barankin bound is more accurate than the Cramér Rao lower bound as shown in [R. McAulay and E. Hofstetter, 1971]<ref>[R. McAulay and E. Hofstetter, 1971] R. McAulay and E. Hofstetter, Barankin Bounds on Parameter Estimation, IEEE Transactions on Information Theory, vol. IT-17, number 6, pp. 669-676, 1971.</ref>. In fact, the Barankin bound can be made tighter than the Cramér-Rao bound provided the correct test points are chosen. Moreover, the Barankin bound can be applied in general to more cases than the Cramér Rao bound under the assumption that we have some a priori knowledge on the conditional probability of some particular points. As one can imagine, this information is not always available and justifies the common use of the Cramér Rao lower bound instead.		Finally, we must underline that the Barankin bound is more accurate than the Cramér Rao lower bound as shown in [R. McAulay and E. Hofstetter, 1971]<ref>[R. McAulay and E. Hofstetter, 1971] R. McAulay and E. Hofstetter, Barankin Bounds on Parameter Estimation, IEEE Transactions on Information Theory, vol. IT-17, number 6, pp. 669-676, 1971.</ref>. In fact, the Barankin bound can be made tighter than the Cramér-Rao bound provided the correct test points are chosen. Moreover, the Barankin bound can be applied in general to more cases than the Cramér Rao bound under the assumption that we have some a priori knowledge on the conditional probability of some particular points. As one can imagine, this information is not always available and justifies the common use of the Cramér Rao lower bound instead.


	== CBCS Interference Performance ==		== CBCS Interference Performance ==

Carlos.Lopez at 09:07, 25 November 2011

2011-11-25T09:07:19Z

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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]]

Carlos.Lopez at 11:27, 18 November 2011

2011-11-18T11:27:22Z

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	being  the percentage of power on the BCS component, as we saw above. According to this, we can express the power spectral density of the CBCS([s],1,%) modulation as follows:		being <math>\rho</math> the percentage of power on the BCS component, as we saw above. According to this, we can express the power spectral density of the CBCS([s],1,%) modulation as follows:

	::[[File: CBCS_Eq_16.png\|none\|640px]]		::[[File: CBCS_Eq_16.png\|none\|640px]]
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	with <math>\left (i,j \right ) \in \left \{1,2,\cdots,N \right \} \times \left \{1,2,\cdots,N \right \}</math. Furthermore, the Barankin bound on the covariance </math>Cov[\hat{x}\left(r\right)]</math> for the parameter x based on the measurements r is given by:		with <math>\left (i,j \right ) \in \left \{1,2,\cdots,N \right \} \times \left \{1,2,\cdots,N \right \}</math>. Furthermore, the Barankin bound on the covariance <math>Cov[\hat{x}\left(r\right)]</math> for the parameter x based on the measurements r is given by:

	::[[File: CBCS_Eq_26.png\|none\|320px]]		::[[File: CBCS_Eq_26.png\|none\|320px]]

Carlos.Lopez at 08:31, 16 November 2011

2011-11-16T08:31:34Z

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	\|Title={{PAGENAME}}		\|Title={{PAGENAME}}
	}}		}}
	== Composite Binary Coded Symbols (CBCS) Modulation ~~definition~~ and ~~analysis~~ of ~~performance~~ ==		== Composite Binary Coded Symbols (CBCS) Modulation: Definition and Analysis of Performance ==

	On June 26th, 2004, the United States of America and the European Union signed the Agreement on the promotion, provision and use of Galileo and GPS satellite-based navigation systems and related applications [G.W. Hein et al., 2005]<ref name="GH_2005">[G.W. Hein et al., 2005] G.W. Hein, J.-A. Avila-Rodriguez, L. Ries, L. Lestarquit, J.-L. Issler, J. Godet, A.R. Pratt, Members of the Galileo Signal Task Force of the European Commission: A Candidate for the Galileo L1 OS Optimized Signal, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref>. Among other topics it was decided to adopt a common baseline signal to be transmitted by both the [[GALILEO Signal Plan\|Galileo E1 Open Service (OS)]] and the future [[GPS Signal Plan\|GPS L1 Civil signal (L1C)]] on E1/L1. Although the agreement fixed [[Binary Offset Carrier (BOC)\|BOC(1,1)]] as the baseline for both Galileo E1 OS and the GPS future L1C signals, it left the door open for a possible optimization of that signal considering the overall framework conditions of the agreement.		On June 26th, 2004, the United States of America and the European Union signed the Agreement on the promotion, provision and use of Galileo and GPS satellite-based navigation systems and related applications [G.W. Hein et al., 2005]<ref name="GH_2005">[G.W. Hein et al., 2005] G.W. Hein, J.-A. Avila-Rodriguez, L. Ries, L. Lestarquit, J.-L. Issler, J. Godet, A.R. Pratt, Members of the Galileo Signal Task Force of the European Commission: A Candidate for the Galileo L1 OS Optimized Signal, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref>. Among other topics it was decided to adopt a common baseline signal to be transmitted by both the [[GALILEO Signal Plan\|Galileo E1 Open Service (OS)]] and the future [[GPS Signal Plan\|GPS L1 Civil signal (L1C)]] on E1/L1. Although the agreement fixed [[Binary Offset Carrier (BOC)\|BOC(1,1)]] as the baseline for both Galileo E1 OS and the GPS future L1C signals, it left the door open for a possible optimization of that signal considering the overall framework conditions of the agreement.

Carlos.Lopez at 08:30, 16 November 2011

2011-11-16T08:30:50Z

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	\|Title={{PAGENAME}}		\|Title={{PAGENAME}}
	}}		}}
	== CBCS Modulation definition and analysis of performance ==		== Composite Binary Coded Symbols (CBCS) Modulation definition and analysis of performance ==

	On June 26th, 2004, the United States of America and the European Union signed the Agreement on the promotion, provision and use of Galileo and GPS satellite-based navigation systems and related applications [G.W. Hein et al., 2005]<ref name="GH_2005">[G.W. Hein et al., 2005] G.W. Hein, J.-A. Avila-Rodriguez, L. Ries, L. Lestarquit, J.-L. Issler, J. Godet, A.R. Pratt, Members of the Galileo Signal Task Force of the European Commission: A Candidate for the Galileo L1 OS Optimized Signal, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref>. Among other topics it was decided to adopt a common baseline signal to be transmitted by both the [[GALILEO Signal Plan\|Galileo E1 Open Service (OS)]] and the future [[GPS Signal Plan\|GPS L1 Civil signal (L1C)]] on E1/L1. Although the agreement fixed [[Binary Offset Carrier (BOC)\|BOC(1,1)]] as the baseline for both Galileo E1 OS and the GPS future L1C signals, it left the door open for a possible optimization of that signal considering the overall framework conditions of the agreement.		On June 26th, 2004, the United States of America and the European Union signed the Agreement on the promotion, provision and use of Galileo and GPS satellite-based navigation systems and related applications [G.W. Hein et al., 2005]<ref name="GH_2005">[G.W. Hein et al., 2005] G.W. Hein, J.-A. Avila-Rodriguez, L. Ries, L. Lestarquit, J.-L. Issler, J. Godet, A.R. Pratt, Members of the Galileo Signal Task Force of the European Commission: A Candidate for the Galileo L1 OS Optimized Signal, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref>. Among other topics it was decided to adopt a common baseline signal to be transmitted by both the [[GALILEO Signal Plan\|Galileo E1 Open Service (OS)]] and the future [[GPS Signal Plan\|GPS L1 Civil signal (L1C)]] on E1/L1. Although the agreement fixed [[Binary Offset Carrier (BOC)\|BOC(1,1)]] as the baseline for both Galileo E1 OS and the GPS future L1C signals, it left the door open for a possible optimization of that signal considering the overall framework conditions of the agreement.

Rui.Pereira: /* CBCS Power Spectral Density */

2011-11-08T15:27:11Z

CBCS Power Spectral Density

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	As derived in [[Power Spectral Density of Sine-phased BOC signals]] the power spectral density of BOC(1,1) is shown to be:		As derived in [[Binary_Offset_Carrier_(BOC)#Binary Offset Carrier with sine phasing:\|Power Spectral Density of Sine-phased BOC signals]] the power spectral density of BOC(1,1) is shown to be:

	::[[File: CBCS_Eq_17.png\|none\|500px]]		::[[File: CBCS_Eq_17.png\|none\|500px]]
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	::[[File: CBCS_Eq_21.png\|none\|600px]]		::[[File: CBCS_Eq_21.png\|none\|600px]]
	::[[File: CBCS_Eq_22.png\|none\|600px]]		::[[File: CBCS_Eq_22.png\|none\|600px]]


	== CBCS Positioning Performance ==		== CBCS Positioning Performance ==

Rui.Pereira at 12:40, 8 November 2011

2011-11-08T12:40:13Z

Carlos.Lopez at 13:56, 4 November 2011

2011-11-04T13:56:57Z

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

2011-11-04T12:41:36Z

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

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	As a solution, a new modulation scheme was developed in [L. Ries et al., 2006]<ref>[L. Ries et al., 2006] L. Ries, J.-L. Issler, L. Lestarquit, J.-A. Avila-Rodriguez and G.W. Hein, Spread Spectrum Signal, Patent number WO/2006/075018, International Application No.: PCT/EP2006/050179, Publication date: 20 July 2006</ref> to provide an optimized implementation of the CBCS signals, without the drawbacks described in the preceding lines. The resulting modulation is more efficient than the Modified Hexaphase as it reduces significantly the effect and power of the inter-modulation product.		As a solution, a new modulation scheme was developed in [L. Ries et al., 2006]<ref>[L. Ries et al., 2006] L. Ries, J.-L. Issler, L. Lestarquit, J.-A. Avila-Rodriguez and G.W. Hein, Spread Spectrum Signal, Patent number WO/2006/075018, International Application No.: PCT/EP2006/050179, Publication date: 20 July 2006</ref> to provide an optimized implementation of the CBCS signals, without the drawbacks described in the preceding lines. The resulting modulation is more efficient than the Modified Hexaphase as it reduces significantly the effect and power of the inter-modulation product.

	As shown in [[Power Spectral Density of the CBCS Modulation]], the generic CBCS baseband modulation can be expressed mathematically as follows:		As shown in [[CBCS Modulation#CBCS Power Spectral Density\|Power Spectral Density of the CBCS Modulation]], the generic CBCS baseband modulation can be expressed mathematically as follows:

	::[[File: CBCS_Eq_2.png\|none\|560px]]		::[[File: CBCS_Eq_2.png\|none\|560px]]
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	Indeed, we can clearly recognize that the code that actually modulates the BOC(1,1) signal waveform is the semi-sum of the data and pilot codes. Equally, the semi-difference of the data and pilot codes modulates the BCS sequence. Moreover, these codes are not binary since they can take the values +2, 0 and -2 [P.G. Mattos, 2005]<ref>[P.G. Mattos, 2005] P.G. Mattos, Acquisition of the Galileo OAS L1 b/c Signal for the Mass-Market Receiver, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref>. As shown in [F. Soualle et al., 2005]<ref>[F. Soualle et al., 2005] F. Soualle, M. Soellner, S. Wallner, J.-A. Avila-Rodriguez, G.W. Hein, B. Barnes, A.R. Pratt, L. Ries, J. Winkel, C. Lemenager, P. Erhard: Spreading code selection criteria for the future GNSS Galileo, Proceedings of the European Navigation Conference GNSS 2005, 19 - 22 July 2005, Munich, Germany.</ref> the data and pilot codes were optimized without accounting for the modulation scheme. The consequence of this is that unless the receiver applies a coherent processing of the incoming signal, the codes will show a slight degradation.		Indeed, we can clearly recognize that the code that actually modulates the BOC(1,1) signal waveform is the semi-sum of the data and pilot codes. Equally, the semi-difference of the data and pilot codes modulates the BCS sequence. Moreover, these codes are not binary since they can take the values +2, 0 and -2 [P.G. Mattos, 2005]<ref>[P.G. Mattos, 2005] P.G. Mattos, Acquisition of the Galileo OAS L1 b/c Signal for the Mass-Market Receiver, Proceedings of the International Technical Meeting of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref>. As shown in [F. Soualle et al., 2005]<ref>[F. Soualle et al., 2005] F. Soualle, M. Soellner, S. Wallner, J.-A. Avila-Rodriguez, G.W. Hein, B. Barnes, A.R. Pratt, L. Ries, J. Winkel, C. Lemenager, P. Erhard: Spreading code selection criteria for the future GNSS Galileo, Proceedings of the European Navigation Conference GNSS 2005, 19 - 22 July 2005, Munich, Germany.</ref> the data and pilot codes were optimized without accounting for the modulation scheme. The consequence of this is that unless the receiver applies a coherent processing of the incoming signal, the codes will show a slight degradation.

	Another very important aspect from the CBCS modulation is the power distribution, since this determines in the end the multipath rejection potential of the solutions. As shown in [[Power Spectral Density of the CBCS Modulation]], the following expressions for the data and pilot channels can be derived:		Another very important aspect from the CBCS modulation is the power distribution, since this determines in the end the multipath rejection potential of the solutions. As shown in [[CBCS Modulation#CBCS Power Spectral Density\|Power Spectral Density of the CBCS Modulation]], the following expressions for the data and pilot channels can be derived:

	::[[File: CBCS_Eq_5.png\|none\|500px]]		::[[File: CBCS_Eq_5.png\|none\|500px]]
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	One of the performance figures used to select the CBCS signal was the multipath error. In order to realistically estimate the multipath that the candidate signals could present in real environments, the methodology presented in [G.W. Hein and J.-A. Avila-Rodriguez, 2005] <ref>[G.W. Hein and J.-A. Avila-Rodriguez, 2005] G.W. Hein and J.-A. Avila-Rodriguez, Performance of a Galileo PRS/GPS M-Code Combined Service, Proceedings of the National Technical Meeting of the Institute of Navigation, ION-NTM 2005, January 24-26, 2005 , San Diego, California, USA.</ref> and [M. Irsigler et al., 2005] <ref name="MI_2005">[M. Irsigler et al., 2005] M. Irsigler, J.-A. Avila-Rodriguez, G.W. Hein, Criteria for GNSS Multipath Performance Assessment, Proceedings of the 18th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref> was followed. Furthermore, in order to reduce the computations and given the enormous number of potential signals to assess, a simplified model was employed. Nevertheless, [M. Irsigler et al., 2005] <ref name="MI_2005"/> and [M. Irsigler, 2008] <ref name="MI_2008"> [M. Irsigler, 2008] M. Irsigler, Multipath Propagation, Mitigation and Monitoring in the Light of Galileo and the Modernized GPS, PhD Thesis, University FAF Munich, 2008</ref> have shown that more simplified models also give satisfactory results in the same direction at the expense of generalizing the assumptions and simplifying scenarios.		One of the performance figures used to select the CBCS signal was the multipath error. In order to realistically estimate the multipath that the candidate signals could present in real environments, the methodology presented in [G.W. Hein and J.-A. Avila-Rodriguez, 2005] <ref>[G.W. Hein and J.-A. Avila-Rodriguez, 2005] G.W. Hein and J.-A. Avila-Rodriguez, Performance of a Galileo PRS/GPS M-Code Combined Service, Proceedings of the National Technical Meeting of the Institute of Navigation, ION-NTM 2005, January 24-26, 2005 , San Diego, California, USA.</ref> and [M. Irsigler et al., 2005] <ref name="MI_2005">[M. Irsigler et al., 2005] M. Irsigler, J.-A. Avila-Rodriguez, G.W. Hein, Criteria for GNSS Multipath Performance Assessment, Proceedings of the 18th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION-GNSS 2005, 13-16 September, 2005, Long Beach, California, USA.</ref> was followed. Furthermore, in order to reduce the computations and given the enormous number of potential signals to assess, a simplified model was employed. Nevertheless, [M. Irsigler et al., 2005] <ref name="MI_2005"/> and [M. Irsigler, 2008] <ref name="MI_2008"> [M. Irsigler, 2008] M. Irsigler, Multipath Propagation, Mitigation and Monitoring in the Light of Galileo and the Modernized GPS, PhD Thesis, University FAF Munich, 2008</ref> have shown that more simplified models also give satisfactory results in the same direction at the expense of generalizing the assumptions and simplifying scenarios.

	Another important aspect to note with regards to the CBCS modulation is that the data and pilot channels are in anti-phase and present thus different correlation functions as shown in [[Power Spectral Density of the CBCS Modulation]]. The direct consequence of that is that the data and pilot channels present different performance depending on whether the signal has the BOC(1,1) and BCS in phase or in anti-phase. As we will show in the next pages, the anti-phase signal has got the sharpest ACF and thus better performance. For this reason, this was assigned to the pilot channel.		Another important aspect to note with regards to the CBCS modulation is that the data and pilot channels are in anti-phase and present thus different correlation functions as shown in [[CBCS Modulation#CBCS Power Spectral Density\|Power Spectral Density of the CBCS Modulation]]. The direct consequence of that is that the data and pilot channels present different performance depending on whether the signal has the BOC(1,1) and BCS in phase or in anti-phase. As we will show in the next pages, the anti-phase signal has got the sharpest ACF and thus better performance. For this reason, this was assigned to the pilot channel.

	In the following lines we show the performance of CBCS in terms of multipath using the multipath error envelopes. As we know, its computation relies on the assumptions that the line of sight is always visible, that only one multipath signal is present and that the multipath signal experiences a fixed amplitude attenuation (e.g. coefficient of reflection <math>\alpha = 0.5 </math> in our simulations) with respect to the direct signal. In addition, a static environment is commonly assumed.		In the following lines we show the performance of CBCS in terms of multipath using the multipath error envelopes. As we know, its computation relies on the assumptions that the line of sight is always visible, that only one multipath signal is present and that the multipath signal experiences a fixed amplitude attenuation (e.g. coefficient of reflection <math>\alpha = 0.5 </math> in our simulations) with respect to the direct signal. In addition, a static environment is commonly assumed.
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	::* Wideband interference: The susceptibility to wide band interference is closely linked to the spreading of the PSD: the more the PSD is spread, the higher the robustness will be. Because CBCS features a PSD which is more spread than that of the BOC(1,1) signal, the CBCS was consequently present a higher robustness than BOC(1,1).		::* Wideband interference: The susceptibility to wide band interference is closely linked to the spreading of the PSD: the more the PSD is spread, the higher the robustness will be. Because CBCS features a PSD which is more spread than that of the BOC(1,1) signal, the CBCS was consequently present a higher robustness than BOC(1,1).

	For more details on the mathematical model behind, refer to [[Power Spectral Density of the CBCS Modulation]]. As we will see, also here CBCS was superior to BOC(1,1).		For more details on the mathematical model behind, refer to [[CBCS Modulation#CBCS Power Spectral Density\|Power Spectral Density of the CBCS Modulation]]. As we will see, also here CBCS was superior to BOC(1,1).

	One final aspect to analyze the performance of a signal is the acquisition. A very straightforward strategy to acquire CBCS was presented in [G.W. Hein et al., 2005] <ref name="GH_2005"/>, proving that false acquisition should not represent a big problem. In fact, the only degradation observable with respect to BOC(1,1) would be of less than 1 dB, coming from the correlation losses due to processing with a pure BOC(1,1) receiver.		One final aspect to analyze the performance of a signal is the acquisition. A very straightforward strategy to acquire CBCS was presented in [G.W. Hein et al., 2005] <ref name="GH_2005"/>, proving that false acquisition should not represent a big problem. In fact, the only degradation observable with respect to BOC(1,1) would be of less than 1 dB, coming from the correlation losses due to processing with a pure BOC(1,1) receiver.