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  • Research Article
  • Open Access

Second-Order Optimal Array Receivers for Synchronization of BPSK, MSK, and GMSK Signals Corrupted by Noncircular Interferences

EURASIP Journal on Advances in Signal Processing20072007:045605

  • Received: 4 October 2006
  • Accepted: 13 May 2007
  • Published:


The synchronization and/or time acquisition problem in the presence of interferences has been strongly studied these last two decades, mainly to mitigate the multiple access interferences from other users in DS/CDMA systems. Among the available receivers, only some scarce receivers may also be used in other contexts such as F/TDMA systems. However, these receivers assume implicitly or explicitly circular (or proper) interferences and become suboptimal for noncircular (or improper) interferences. Such interferences are characteristic in particular of radio communication networks using either rectilinear (or monodimensional) modulations such as BPSK modulation or modulation becoming quasirectilinear after a preprocessing such as MSK, GMSK, or OQAM modulations. For this reason, the purpose of this paper is to introduce and to analyze the performance of second-optimal array receivers for synchronization and/or time acquisition of BPSK, MSK, and GMSK signals corrupted by noncircular interferences. For given performances and in the presence of rectilinear signal and interferences, the proposed receiver allows a reduction of the number of sensors by a factor at least equal to two.


  • Information Technology
  • Communication Network
  • Radio Communication Network
  • Time Acquisition
  • Quantum Information

Authors’ Affiliations

Thales-Communications, EDS/SPM, 160 Bd Valmy, Colombes, Cedex, 92704, France


  1. Bensley SE, Aazhang B: Subspace-based channel estimation for code division multiple access communication systems. IEEE Transactions on Communications 1996,44(8):1009-1020. 10.1109/26.535441View ArticleGoogle Scholar
  2. Bensley SE, Aazhang B: Maximum-likelihood synchronization of a single user for code-division multiple-access communication systems. IEEE Transactions on Communications 1998,46(3):392-399. 10.1109/26.662645View ArticleGoogle Scholar
  3. Madhow U: Blind adaptive interference suppression for the near-far resistant acquisition and demodulation of direct-sequence CDMA signals. IEEE Transactions on Signal Processing 1997,45(1):124-136. 10.1109/78.552211View ArticleGoogle Scholar
  4. Madhow U: Blind adaptive interference suppression for direct-sequence CDMA. Proceedings of the IEEE 1998,86(10):2049-2069. 10.1109/5.720252View ArticleGoogle Scholar
  5. Mantravadi A, Veeravalli VV: Multiple-access interference-resistant acquisition for band-limited CDMA systems with random sequences. IEEE Journal on Selected Areas in Communications 2000,18(7):1203-1213. 10.1109/49.857920View ArticleGoogle Scholar
  6. Ström EG, Parkvall S, Miller SL, Ottersten BE: Propagation delay estimation in asynchronous direct-sequence code-division multiple access systems. IEEE Transactions on Communications 1996,44(1):84-93. 10.1109/26.476100View ArticleGoogle Scholar
  7. Zheng D, Li J, Miller SL, Ström EG: An efficient code-timing estimator for DS-CDMA signals. IEEE Transactions on Signal Processing 1997,45(1):82-89. 10.1109/78.552207View ArticleGoogle Scholar
  8. Brennan LE, Reed IS: An adaptive array signal processing algorithm for communications. IEEE Transactions on Aerospace and Electronic Systems 1982,18(1):124-130.View ArticleGoogle Scholar
  9. Compton RT Jr.: An adaptive array in a spread-spectrum communication system. Proceedings of the IEEE 1978,66(3):289-298.View ArticleGoogle Scholar
  10. Dlugos DM, Scholtz RA: Acquisition of spread spectrum signals by an adaptive array. IEEE Transactions on Acoustics, Speech, and Signal Processing 1989,37(8):1253-1270. 10.1109/29.31273View ArticleGoogle Scholar
  11. Wang B, Kwon HM: PN code acquisition using smart antenna for spread-spectrum wireless communications—part I. IEEE Transactions on Vehicular Technology 2003,52(1):142-149. 10.1109/TVT.2002.807152View ArticleGoogle Scholar
  12. Winters JH: Spread spectrum in a four-phase communication system employing adaptive antennas. IEEE Transactions on Communications 1982,30(5, part 2):929-936. 10.1109/TCOM.1982.1095539View ArticleGoogle Scholar
  13. Picinbono B: On circularity. IEEE Transactions on Signal Processing 1994,42(12):3473-3482. 10.1109/78.340781View ArticleGoogle Scholar
  14. Neeser FD, Massey JL: Proper complex random processes with applications to information theory. IEEE Transactions on Information Theory 1993,39(4):1293-1302. 10.1109/18.243446MathSciNetView ArticleGoogle Scholar
  15. Sfar S, Letaief KB: Improved group multiuser detection with multiple receive antennas in the presence of improper multi-access interference. IEEE Transactions on Communications 2005,53(4):560-563. 10.1109/TCOMM.2005.844937View ArticleGoogle Scholar
  16. Proakis JG: Digital Communications. 3rd edition. McGraw-Hill, New York, NY, USA; 1995.MATHGoogle Scholar
  17. Chevalier P, Pipon F: New insights into optimal widely linear array receivers for the demodulation of BPSK, MSK, and GMSK signals corrupted by noncircular interferences-application to SAIC. IEEE Transactions on Signal Processing 2006,54(3):870-883.View ArticleGoogle Scholar
  18. Ding Z, Li G: Single-channel blind equalization for GSM cellular systems. IEEE Journal on Selected Areas in Communications 1998,16(8):1493-1505. 10.1109/49.730456View ArticleGoogle Scholar
  19. Trigui H, Slock DTM: Performance bounds for cochannel interference cancellation within the current GSM standard. Signal Processing 2000,80(7):1335-1346. 10.1016/S0165-1684(00)00040-2View ArticleGoogle Scholar
  20. Chevalier P, Pipon F, Delaveau F: Procédé et dispositif de synchronisation de liaisons rectilignes ou quasi-rectilignes en présence d'interférences de même nature. Patent FR.05.01784, February 2005Google Scholar
  21. Picinbono B, Chevalier P: Widely linear estimation with complex data. IEEE Transactions on Signal Processing 1995,43(8):2030-2033. 10.1109/78.403373View ArticleGoogle Scholar
  22. Brown W, Crane R: Conjugate linear filtering. IEEE Transactions on Information Theory 1969,15(4):462-465. 10.1109/TIT.1969.1054330MathSciNetView ArticleGoogle Scholar
  23. Gardner WA: Cyclic Wiener filtering: theory and method. IEEE Transactions on Communications 1993,41(1):151-163. 10.1109/26.212375View ArticleGoogle Scholar
  24. Gardner WA: Cyclostationarity in Communications and Signal Processing. IEEE Press, New York, NY, USA; 1994.MATHGoogle Scholar
  25. Chevalier P: Filtrage d'antenne optimal pour signaux non stationnaires-concepts, performances. Proceedings of the 15th GRETSI Symposium on Signal and Image Processing, September 1995, Juan-Les-Pins, France 233–236.Google Scholar
  26. Chevalier P: Optimal array processing for non stationary signals. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '96), May 1996, Atlanta, Ga, USA 5: 2868–2871.Google Scholar
  27. Ciblat P, Loubaton P, Serpedin E, Giannakis GB: Performance analysis of blind carrier frequency offset estimators for noncircular transmissions through frequency-selective channels. IEEE Transactions on Signal Processing 2002,50(1):130-140. 10.1109/78.972489View ArticleGoogle Scholar
  28. Ciblat P, Serpedin E, Wang Y: On a blind fractionally sampling-based carrier frequency offset estimator for noncircular transmissions. IEEE Signal Processing Letters 2003,10(4):89-92. 10.1109/LSP.2003.809031View ArticleGoogle Scholar
  29. Napolitano A, Tanda M: Doppler-channel blind identification for noncircular transmissions in multiple-access systems. IEEE Transactions on Communications 2004,52(12):2073-2078. 10.1109/TCOMM.2004.838716View ArticleGoogle Scholar
  30. Chevalier P, Pipon F: Optimal array receiver for synchronization of a BPSK signal corrupted by non circular interferences. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '06), May 2006, Toulouse, France 4: 1061–1064.MATHGoogle Scholar
  31. van Trees HL: Detection, Estimation and Modulation Theory—Part I. John Wiley & Sons, New York, NY, USA; 1968.MATHGoogle Scholar
  32. Delaveau F, Pipon F, Lambron O: Smart antennas for interference resolution in cellular networks. Proceedings of the 14th International Wroclaw Symposium and Exhibition on Electromagnetic Compatibility, June 1998, Wroclaw, Poland 264–267.Google Scholar
  33. Picinbono B: Second-order complex random vectors and normal distributions. IEEE Transactions on Signal Processing 1996,44(10):2637-2640. 10.1109/78.539051View ArticleGoogle Scholar
  34. van den Bos A: The multivariate complex normal distribution—a generalization. IEEE Transactions on Information Theory 1995,41(2):537-539. 10.1109/18.370165MathSciNetView ArticleGoogle Scholar
  35. Monzingo RA, Miller TW: Introduction to Adaptive Arrays. John Wiley & Sons, New York, NY, USA; 1980.Google Scholar
  36. Laurent PA: Exact and approximate construction of digital phase modulations by superposition of amplitude modulated pulses (AMP). IEEE Transactions on Communications 1986,34(2):150-160. 10.1109/TCOM.1986.1096504View ArticleGoogle Scholar


© Pascal Chevalier et al. 2007

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