Mathematical Model of Non-Coherent-DLL Discriminator Output and Multipath Envelope Error for BOC (α, β) Modulated Signals

Affiliation(s)

Electronics Department, LMSE Laboratory, University of Mohamed El-Bachir El-Ibrahimi, Bordj Bou Arréridj, Algeria.

Electronis Department, LIS Laboratory, University of M’sila, M’sila, Algeria.

Electronics Department, LMSE Laboratory, University of Mohamed El-Bachir El-Ibrahimi, Bordj Bou Arréridj, Algeria.

Electronis Department, LIS Laboratory, University of M’sila, M’sila, Algeria.

ABSTRACT

In this paper we propose the
derivation of the expressions for the non-coherent Delay Locked Loop (DLL)
Discriminator Curve (DC) in the absence and presence of Multipath (MP). Also
derived, are the expressions of MP tracking errors in non-coherent
configuration. The proposed models are valid for all Binary Offset Carrier
(BOC) modulated signals in Global Navigation Satellite Systems (GNSS) such as
Global Positioning System (GPS) and Future Galileo. The non-coherent configuration is used
whenever the phase of the received signal cannot be estimated and thus cannot
be demodulated. Therefore, the signal must be treated in a transposed band by
the non-coherent DLL. The computer implementations show that the proposed
models coincide with the numerical ones.

Cite this paper

Rouabah, K. , Saifeddine, C. , Atia, S. , Flissi, M. and Chikouche, D. (2013) Mathematical Model of Non-Coherent-DLL Discriminator Output and Multipath Envelope Error for BOC (α, β) Modulated Signals.*Positioning*, **4**, 65-79. doi: 10.4236/pos.2013.41008.

Rouabah, K. , Saifeddine, C. , Atia, S. , Flissi, M. and Chikouche, D. (2013) Mathematical Model of Non-Coherent-DLL Discriminator Output and Multipath Envelope Error for BOC (α, β) Modulated Signals.

References

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[2] M. Irsigler and B. Eissfeller, “Comparison of Multipath Mitigation Techniques with Consideration of Future Signal Structures,” Proceedings of the 16th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS/GNSS ’03), Portland, 9-12 September 2003, pp. 2584-2592.

[3] J. W. Betz, “Binary Offset Carrier Modulations for Radionavigation,” Navigation, Journal of the Institute of Navigation, Vol. 48, No. 4, 2001, pp. 227-246.

[4] J. A. Avila-Rodriguez, G. W. Hein, S. Wallner, et al., “The MBOC Modulation: The Final Touch to the Galileo Frequency and Signal Plan,” Proceedings of the 20th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS’07), Fort Worth, 25-28 September 2007, pp. 1515-1529.

[5] G. W. Hein, J. A. Avila-Rodriguez, S. Wallner, et al., “MBOC: The New Optimized Spreading Modulation Recommended for GALILEO L1 OS and GPS L1C,” Proceedings of the IEEE/ION Position, Location, and Navigation Symposium, San Diego, 25-27 April 2006, pp. 883-892.

[6] K. Borre, D. Akos, N. Bertelsen, P. Rinder and S. Jensen, “A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach,” Birkhaauser, Boston, 2007.

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[8] F. Nunes, F. Sousa and J. Leitao, “Gating Functions for Multipath Mitigation in GNSS BOC Signals,” IEEE Transactions on Aerospace and Electronic System, Vol. 43, No. 3, 2007, pp. 951-964. doi:10.1109/TAES.2007.4383585

[9] L. Boccia, G. Amendola and G. Di Massa, “Performance Evaluation of Shorted Annular Patch Antennas for High-Precision GPS Systems,” IET Microwaves, Antennas & Propagation, Vol. 1, No. 2, 2007, pp. 465-471. doi:10.1049/iet-map:20060025

[10] C. C. Counselman, “Multipath-Rejecting GPS Antennas,” Proceedings of the IEEE, Vol. 87, No. 1, 1999, pp. 86-91. doi:10.1109/5.736343

[11] C.-L. Chang and J.-C. Juang, “An Adaptive Multipath Mitigation Filter for GNSS Applications,” EURASIP Journal on Advances in Signal Processing, Vol. 2008, 2008, Article ID: 214815.

[12] G. Seco-Granados, J. A. Fernández-Rubio and C. Fernández-Prades, “ML Estimator and Hybrid Beamformer for Multipath and Interference Mitigation in GNSS Receivers,” IEEE Transactions on Signal Processing, Vol. 53, No. 3, 2005, pp. 1194-1208.

[13] E. S. Lohan, R. Hamila, A. Lakhzouri and M. Renfors, ”Highly Efficient Techniques for Mitigating the Effects of Multipath Propagation in DS-CDMA Delay Estimation,” IEEE Transactions on Wireless Communications, Vol. 4, No. 1, 2005, pp. 149-162.

[14] M. S. Braasch, “Performance Comparison of Multipath Mitigating Receiver Architectures,” Proceedings of the IEEE Aerospace Conference, Vol. 3, 2001, pp. 31309-31315.

[15] Z. Zhang and C. L. Law, “Short-Delay Multipath Mitigation Technique Based on Virtual Multipath,” IEEE Antennas and Wireless Propagation Letters, Vol. 4, No. 1, 2005, pp. 344-348. doi:10.1109/LAWP.2005.857038

[16] S. L. Elena, L. Abdelmonaem and R. Markku, “Feed forward Delay Estimators in Adverse Multipath Propagation for Galileo and Modernized GPS Signals,” Hindawi Vol. 8, 2009, pp. 1434-1435. doi:10.1109/LAWP.2009.2012977

[17] M. Z. H. Bhuiyan, E. S. Lohan and M. Renfors, “Code Tracking Algorithms for Mitigating Multipath Effects in Fading Channels for Satellite-Based Positioning,” EUR-ASIP Journal on Advances in Signal Processing, Vol. 2008, 2008, Article ID 863629, 17 pages.

[18] J. Van Dierendonck, P. Fenton and T. Ford, “Theory and Performance of Narrow Correlator Spacing in a GPS Receiver,” Journal of the Institute of Navigation, Vol. 39, No. 3, 1992, pp. 265-283.

[19] R. Van Nee, J. Siereveld, P. Fenton and B. Townsend, “The Multipath Estimating Delay Lock Loop: Approaching Theoretical Accuracy Limits,” Proceeding of IEEE Position Location and Navigation Symposium, Las Vegas, 11-15 April 1994, pp. 246-251.

[20] K. Rouabah and D. Chikouche, “GPS/Galileo Multipath Detection and Mitigation Using Closed-Form Solutions,” Mathematical Problems in Engineering, Vol. 2009, 2009, Article ID: 106870, 20 pages.

[21] M. Laxton, “Analysis and Simulation of a New Code Tracking Loop for GPS Multipath Mitigation,” M.S. Thesis, Air Force Institute of Technology, Wright-Patterson AFB, 1996.

[22] B. Townsend, D. J. R. van Nee, P. Fenton and K. Van Dierendonck, “Performance Evaluation of the Multipath Estimating Delay Lock Loop,” Proceedings of the National Technical Meeting, Anaheim, 18-20 January 1995, pp. 277-283.

[23] B. Townsend, J. Weibe and A. Jakab, “Results and Analysis of Using the MEDLL Receiver as a Multipath Meter,” Proceedings of ION National Technical Meeting, Anahiem, 26-29 January 2000.

[24] M. Sahmoudi and R. Landry Jr., “Multipath Mitigation Techniques Using Maximum-Likelihood Principle,” Inside GNSS, Vol. 3, No. 8, 2008, pp. 24-29.

[25] M. Sahmoudi and M. G. Amin, “Fast Iterative Maximum-Likelihood Algorithm (FIMLA) for Multipath Mitigation in the Next Generation of GNSS Receivers,” IEEE Transactions on Wireless Communications, Vol. 7, No. 11, 2008, pp. 4362-4374. doi:10.1109/T-WC.2008.070700

[26] O. Julien, C. Macabiau, M. E. Cannon and G. Lachapelle, “ASPeCT: Unambiguous Sine-BOC(n,n) Acquisition/ Tracking Technique for Navigation Applications,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 43, No. 1, 2007, pp. 150-162. doi:10.1109/TAES.2007.357123

[27] A. Burian, E. S. Lohan and M. K. Renfors, “Efficient Delay Tracking Methods with Sidelobes Cancellation for BOC-modulated Signals,” EURASIP Journal on Wireless Communications and Networking, Vol. 2007, 2007, Article ID: 072626. doi:10.1155/2007/72626

[28] Y. Zhou, X. Hu and Z. Tang, “Unambiguous Tracking Technique for Sin-BOC(1,1) and MBOC(6,1,1/11) Signals,” Proceedings of the 2nd International Conference on Future Computer and Communication (ICFCC ’10), 21-24 May 2010, pp. V1188-V1190.

[29] K. Rouabah, M. Flissi, S. Attia and D. Chikouche, “Unambiguous Multipath Mitigation Technique for BOC(n,n) and MBOC-Modulated GNSS Signals,” International Journal of Antennas and Propagation, Vol. 2012, 2012, Article ID: 895390, 13 pages. doi:10.1155/2012/895390

[30] Z. Yao, M. Lu and Z. Feng, “Unambiguous Technique for Multiplexed Binary Offset Carrier Modulated Signals Tracking,” IEEE Signal Processing Letters, Vol. 16, No. 7, 2009, pp. 608-611. doi:10.1109/LSP.2009.2020462

[31] F. Dovis, P. Mulassano and L. Lo Presti, “A Novel Algorithm for the Code Tracking of BOC(n,n) Modulated Signals,” Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS’05), Long Beach, 13-16 September 2005, pp. 152-155.

[32] G. Dempster and J. Wu, “Code Discriminator for Multiplexed Binary Offset Carrier Modulated Signals,” Electronics Letters, Vol. 44, No. 5, 2008, pp. 384-385. doi:10.1049/el:20080138

[33] J. Wu and A. G. Dempster, “Applying a BOC-PRN Discriminator to Cosine Phased BOC(fs,fc) Modulation,” Electronics Letters, Vol. 45, No. 13, 2009, pp. 689-691. doi:10.1049/el.2009.0374

[34] K. Rouabah, D. Chikouche, F. Bouttout, R. Harba and P. Ravier, “GPS/Galileo Multipath Mitigation Using the First Side Peak of Double Delta Correlator,” Wireless Personal Communications, Vol. 60, No. 2, 2010, pp. 321-333. doi:10.1007/s11277-010-9946-2

[35] J. Winkel, “Modeling and Simulating GNSS Signal Structures and Receivers,” University of Federal Armed Forces Munich, Neubiberg, 2003.

[36] F. Nunes, F. Sousa and J. Leitao, “Improving Multipath Mitigation in GPS/Galileo BOC Signals with Gating Functions,” Proceedings of the 61st Annual Meeting of the Institute of Navigation ION-AM 2005, Cambridge, June 2005, pp. 498-507.

[37] B. R. Harris and G. E. Lightsey, “A General Model of Multipath Error for Coherently Tracked BOC Modulated Signals,” IEEE Journal of Selected Topics in Signal Processing, Vol. 3, No. 4, 2009, pp. 682-694. doi:10.1109/JSTSP.2009.2024106

[38] S. Zitouni., K. Rouabah, S. Atia and D. Chikouche, “Comments on ‘A General Model of Multipath Error for Coherently Tracked BOC Modulated Signals’,” Wireless Personal Communications, Springer, 2012, in Press.

[39] M. Braasch, “On the Characterization of Multipath Errors in Satellite-Based Precision Approach and Landing Systems,” Ph.D. Thesis, Ohio University, Athens, 1992.

[1] B. W. Parkinson and J. J. Spilker Jr., “Global Positioning System: Theory and Applications, Vol. I, Progress in Astronautics and Aeronautics,” American Institute of Aeronautics and Astronautics, Washington DC, 1996.

[2] M. Irsigler and B. Eissfeller, “Comparison of Multipath Mitigation Techniques with Consideration of Future Signal Structures,” Proceedings of the 16th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS/GNSS ’03), Portland, 9-12 September 2003, pp. 2584-2592.

[3] J. W. Betz, “Binary Offset Carrier Modulations for Radionavigation,” Navigation, Journal of the Institute of Navigation, Vol. 48, No. 4, 2001, pp. 227-246.

[4] J. A. Avila-Rodriguez, G. W. Hein, S. Wallner, et al., “The MBOC Modulation: The Final Touch to the Galileo Frequency and Signal Plan,” Proceedings of the 20th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS’07), Fort Worth, 25-28 September 2007, pp. 1515-1529.

[5] G. W. Hein, J. A. Avila-Rodriguez, S. Wallner, et al., “MBOC: The New Optimized Spreading Modulation Recommended for GALILEO L1 OS and GPS L1C,” Proceedings of the IEEE/ION Position, Location, and Navigation Symposium, San Diego, 25-27 April 2006, pp. 883-892.

[6] K. Borre, D. Akos, N. Bertelsen, P. Rinder and S. Jensen, “A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach,” Birkhaauser, Boston, 2007.

[7] L. Liu and M. Amin, “Multipath and Precorrelation Filtering Effect on GPS Noncoherent Early-Minus-Late Power Discriminators,” IEEE International Symposium of Signal Processing and Information Technology, Athens, 21 December 2005.

[8] F. Nunes, F. Sousa and J. Leitao, “Gating Functions for Multipath Mitigation in GNSS BOC Signals,” IEEE Transactions on Aerospace and Electronic System, Vol. 43, No. 3, 2007, pp. 951-964. doi:10.1109/TAES.2007.4383585

[9] L. Boccia, G. Amendola and G. Di Massa, “Performance Evaluation of Shorted Annular Patch Antennas for High-Precision GPS Systems,” IET Microwaves, Antennas & Propagation, Vol. 1, No. 2, 2007, pp. 465-471. doi:10.1049/iet-map:20060025

[10] C. C. Counselman, “Multipath-Rejecting GPS Antennas,” Proceedings of the IEEE, Vol. 87, No. 1, 1999, pp. 86-91. doi:10.1109/5.736343

[11] C.-L. Chang and J.-C. Juang, “An Adaptive Multipath Mitigation Filter for GNSS Applications,” EURASIP Journal on Advances in Signal Processing, Vol. 2008, 2008, Article ID: 214815.

[12] G. Seco-Granados, J. A. Fernández-Rubio and C. Fernández-Prades, “ML Estimator and Hybrid Beamformer for Multipath and Interference Mitigation in GNSS Receivers,” IEEE Transactions on Signal Processing, Vol. 53, No. 3, 2005, pp. 1194-1208.

[13] E. S. Lohan, R. Hamila, A. Lakhzouri and M. Renfors, ”Highly Efficient Techniques for Mitigating the Effects of Multipath Propagation in DS-CDMA Delay Estimation,” IEEE Transactions on Wireless Communications, Vol. 4, No. 1, 2005, pp. 149-162.

[14] M. S. Braasch, “Performance Comparison of Multipath Mitigating Receiver Architectures,” Proceedings of the IEEE Aerospace Conference, Vol. 3, 2001, pp. 31309-31315.

[15] Z. Zhang and C. L. Law, “Short-Delay Multipath Mitigation Technique Based on Virtual Multipath,” IEEE Antennas and Wireless Propagation Letters, Vol. 4, No. 1, 2005, pp. 344-348. doi:10.1109/LAWP.2005.857038

[16] S. L. Elena, L. Abdelmonaem and R. Markku, “Feed forward Delay Estimators in Adverse Multipath Propagation for Galileo and Modernized GPS Signals,” Hindawi Vol. 8, 2009, pp. 1434-1435. doi:10.1109/LAWP.2009.2012977

[17] M. Z. H. Bhuiyan, E. S. Lohan and M. Renfors, “Code Tracking Algorithms for Mitigating Multipath Effects in Fading Channels for Satellite-Based Positioning,” EUR-ASIP Journal on Advances in Signal Processing, Vol. 2008, 2008, Article ID 863629, 17 pages.

[18] J. Van Dierendonck, P. Fenton and T. Ford, “Theory and Performance of Narrow Correlator Spacing in a GPS Receiver,” Journal of the Institute of Navigation, Vol. 39, No. 3, 1992, pp. 265-283.

[19] R. Van Nee, J. Siereveld, P. Fenton and B. Townsend, “The Multipath Estimating Delay Lock Loop: Approaching Theoretical Accuracy Limits,” Proceeding of IEEE Position Location and Navigation Symposium, Las Vegas, 11-15 April 1994, pp. 246-251.

[20] K. Rouabah and D. Chikouche, “GPS/Galileo Multipath Detection and Mitigation Using Closed-Form Solutions,” Mathematical Problems in Engineering, Vol. 2009, 2009, Article ID: 106870, 20 pages.

[21] M. Laxton, “Analysis and Simulation of a New Code Tracking Loop for GPS Multipath Mitigation,” M.S. Thesis, Air Force Institute of Technology, Wright-Patterson AFB, 1996.

[22] B. Townsend, D. J. R. van Nee, P. Fenton and K. Van Dierendonck, “Performance Evaluation of the Multipath Estimating Delay Lock Loop,” Proceedings of the National Technical Meeting, Anaheim, 18-20 January 1995, pp. 277-283.

[23] B. Townsend, J. Weibe and A. Jakab, “Results and Analysis of Using the MEDLL Receiver as a Multipath Meter,” Proceedings of ION National Technical Meeting, Anahiem, 26-29 January 2000.

[24] M. Sahmoudi and R. Landry Jr., “Multipath Mitigation Techniques Using Maximum-Likelihood Principle,” Inside GNSS, Vol. 3, No. 8, 2008, pp. 24-29.

[25] M. Sahmoudi and M. G. Amin, “Fast Iterative Maximum-Likelihood Algorithm (FIMLA) for Multipath Mitigation in the Next Generation of GNSS Receivers,” IEEE Transactions on Wireless Communications, Vol. 7, No. 11, 2008, pp. 4362-4374. doi:10.1109/T-WC.2008.070700

[26] O. Julien, C. Macabiau, M. E. Cannon and G. Lachapelle, “ASPeCT: Unambiguous Sine-BOC(n,n) Acquisition/ Tracking Technique for Navigation Applications,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 43, No. 1, 2007, pp. 150-162. doi:10.1109/TAES.2007.357123

[27] A. Burian, E. S. Lohan and M. K. Renfors, “Efficient Delay Tracking Methods with Sidelobes Cancellation for BOC-modulated Signals,” EURASIP Journal on Wireless Communications and Networking, Vol. 2007, 2007, Article ID: 072626. doi:10.1155/2007/72626

[28] Y. Zhou, X. Hu and Z. Tang, “Unambiguous Tracking Technique for Sin-BOC(1,1) and MBOC(6,1,1/11) Signals,” Proceedings of the 2nd International Conference on Future Computer and Communication (ICFCC ’10), 21-24 May 2010, pp. V1188-V1190.

[29] K. Rouabah, M. Flissi, S. Attia and D. Chikouche, “Unambiguous Multipath Mitigation Technique for BOC(n,n) and MBOC-Modulated GNSS Signals,” International Journal of Antennas and Propagation, Vol. 2012, 2012, Article ID: 895390, 13 pages. doi:10.1155/2012/895390

[30] Z. Yao, M. Lu and Z. Feng, “Unambiguous Technique for Multiplexed Binary Offset Carrier Modulated Signals Tracking,” IEEE Signal Processing Letters, Vol. 16, No. 7, 2009, pp. 608-611. doi:10.1109/LSP.2009.2020462

[31] F. Dovis, P. Mulassano and L. Lo Presti, “A Novel Algorithm for the Code Tracking of BOC(n,n) Modulated Signals,” Proceedings of the 18th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS’05), Long Beach, 13-16 September 2005, pp. 152-155.

[32] G. Dempster and J. Wu, “Code Discriminator for Multiplexed Binary Offset Carrier Modulated Signals,” Electronics Letters, Vol. 44, No. 5, 2008, pp. 384-385. doi:10.1049/el:20080138

[33] J. Wu and A. G. Dempster, “Applying a BOC-PRN Discriminator to Cosine Phased BOC(fs,fc) Modulation,” Electronics Letters, Vol. 45, No. 13, 2009, pp. 689-691. doi:10.1049/el.2009.0374

[34] K. Rouabah, D. Chikouche, F. Bouttout, R. Harba and P. Ravier, “GPS/Galileo Multipath Mitigation Using the First Side Peak of Double Delta Correlator,” Wireless Personal Communications, Vol. 60, No. 2, 2010, pp. 321-333. doi:10.1007/s11277-010-9946-2

[35] J. Winkel, “Modeling and Simulating GNSS Signal Structures and Receivers,” University of Federal Armed Forces Munich, Neubiberg, 2003.

[36] F. Nunes, F. Sousa and J. Leitao, “Improving Multipath Mitigation in GPS/Galileo BOC Signals with Gating Functions,” Proceedings of the 61st Annual Meeting of the Institute of Navigation ION-AM 2005, Cambridge, June 2005, pp. 498-507.

[37] B. R. Harris and G. E. Lightsey, “A General Model of Multipath Error for Coherently Tracked BOC Modulated Signals,” IEEE Journal of Selected Topics in Signal Processing, Vol. 3, No. 4, 2009, pp. 682-694. doi:10.1109/JSTSP.2009.2024106

[38] S. Zitouni., K. Rouabah, S. Atia and D. Chikouche, “Comments on ‘A General Model of Multipath Error for Coherently Tracked BOC Modulated Signals’,” Wireless Personal Communications, Springer, 2012, in Press.

[39] M. Braasch, “On the Characterization of Multipath Errors in Satellite-Based Precision Approach and Landing Systems,” Ph.D. Thesis, Ohio University, Athens, 1992.