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  • Research Article
  • Open Access
  • Frequency-Shift Zero-Forcing Time-Varying Equalization for Doubly Selective SIMO Channels

    EURASIP Journal on Advances in Signal Processing20062006:047261

    • Received: 1 June 2005
    • Accepted: 30 April 2006
    • Published:


    This paper deals with the problem of designing linear time-varying (LTV) finite-impulse response zero-forcing (ZF) equalizers for time- and frequency-selective (so-called doubly selective) single-input multiple-output (SIMO) channels. Specifically, relying on a basis expansion model (BEM) of the rapidly time-varying channel impulse response, we derive the canonical frequency-domain representation of the minimal norm LTV-ZF equalizer, which allows one to implement it as a parallel bank of linear time-invariant filters having, as input signals, different frequency-shift (FRESH) versions of the received data. Moreover, on the basis of this FRESH representation, we propose a simple and effective low-complexity version of the minimal norm LTV-ZF equalizer and we discuss the relationships between the devised FRESH equalizers and a LTV-ZF equalizer recently proposed in the literature. The performance analysis, carried out by means of computer simulations, shows that the proposed FRESH-LTV-ZF equalizers significantly outperform their competitive alternative.


    • Information Technology
    • Computer Simulation
    • Input Signal
    • Performance Analysis
    • Impulse Response

    Authors’ Affiliations

    Dipartimento di Ingegneria Elettronica e delle Telecomunicazioni, Università degli Studi di Napoli Federico II, via Claudio 21, Napoli, 80125, Italy


    1. Giannakis GB, Tepedelenlioğlu C: Basis expansion models and diversity techniques for blind identification and equalization of time-varying channels. Proceedings of the IEEE 1998, 86(10):1969–1986. 10.1109/5.720248View ArticleGoogle Scholar
    2. Tsatsanis MK, Giannakis GB: Modeling and equalizing of rapidly fading channels. International Journal of Adaptive Control and Signal Processing 1998, 159–176.Google Scholar
    3. Sayeed AM, Aazhang B: Joint multipath-doppler diversity in mobile wireless communications. IEEE Transactions on Communications 1999, 47(1):123–132. 10.1109/26.747819View ArticleGoogle Scholar
    4. Ma X, Giannakis GB: Maximum-diversity transmissions over doubly selective wireless channels. IEEE Transactions on Information Theory 2003, 49(7):1832–1840. 10.1109/TIT.2003.813485MathSciNetView ArticleGoogle Scholar
    5. Leus G, Zhou S, Giannakis GB: Orthogonal multiple access over time- and frequency-selective channels. IEEE Transactions on Information Theory 2003, 49(8):1942–1950. 10.1109/TIT.2003.814477MathSciNetView ArticleGoogle Scholar
    6. Leus G, Barhumi I, Moonen M: Low-complexity serial equalization of doubly-selective channels. In Proceedings of the 6th Baiona Workshop on Signal Processing in Communications, September 2003. Baiona, Spain; 69–74.Google Scholar
    7. Tepedelenlioğlu C, Giannakis GB: Transmitter redundancy for blind estimation and equalization of time- and frequency-selective channels. IEEE Transactions on Signal Processing 2000, 48(7):2029–2043. 10.1109/78.847788View ArticleGoogle Scholar
    8. Jakes WC: Microwave Mobile Channels. John Wiley & Sons, New York, NY, USA; 1974.Google Scholar
    9. Barhumi I, Leus G, Moonen M: Time-varying FIR equalization for doubly selective channels. IEEE Transactions on Wireless Communications 2005, 4(1):202–214.View ArticleGoogle Scholar
    10. Tugnait JK, Luo W: Linear prediction error method for blind identification of periodically time-varying channels. IEEE Transactions on Signal Processing 2002, 50(12):3070–3082. 10.1109/TSP.2002.805493View ArticleGoogle Scholar
    11. Franks L: Polyperiodic linear filtering. In Cyclostationarity in Communications and Signal Processing. Edited by: Gardner WA. IEEE Press, Piscataway, NJ, USA; 1994:240–266.Google Scholar
    12. Ben-Israel A, Greville TNE: Generalized Inverses. Springer, New York, NY, USA; 2002.MATHGoogle Scholar
    13. Bello PA: Characterization of randomly time-variant channels. IEEE Transactions on Communications 1963, 11(4):360–393. 10.1109/TCOM.1963.1088793View ArticleGoogle Scholar
    14. Tugnait JK, Luo W: Blind identification of time-varying channels using multistep linear predictors. IEEE Transactions on Signal Processing 2004, 52(6):1739–1749. 10.1109/TSP.2004.827174View ArticleGoogle Scholar
    15. Luo W, Tugnait JK: Semi-blind time-varying channel estimation using superimposed training. Proceedings of International Conference on Acoustics, Speech, and Signal Processing (ICASSP '04), May 2004, Montreal, Canada 797–800.Google Scholar
    16. Leus G: On the estimation of rapidly time-varying channels. Proceedings of the European Signal Processing Conference, September 2004, Vienna, Austria 120–123.Google Scholar
    17. Proakis JG: Digital Communications. McGraw-Hill, New York, NY, USA; 2001.MATHGoogle Scholar
    18. Tong L, Perreau S: Multichannel blind identification: from subspace to maximum likelihood methods. Proceeedings of the IEEE 1998, 86(10):1951–1968. 10.1109/5.720247View ArticleGoogle Scholar
    19. Horn RA, Johnson CR: Matrix Analysis. Cambridge University Press, Cambridge, UK; 1990.MATHGoogle Scholar
    20. Vescovo R: Inversion of block-circulant matrices and circular array approach. IEEE Transactions on Antennas and Propagation 1997, 45(10):1565–1567. 10.1109/8.633869MathSciNetView ArticleGoogle Scholar
    21. Björck A: Numerical Methods for Least Squares Problems. SIAM, Philadelphia, Pa, USA; 1996.View ArticleGoogle Scholar
    22. Serpedin E, Giannakis GB: A simple proof of a known blind channel identifiability result. IEEE Transactions on Signal Processing 1999, 47(2):591–593. 10.1109/78.740150View ArticleGoogle Scholar
    23. Honig M, Madhow U, Verdù S: Blind adaptive multiuser detection. IEEE Transactions on Information Theory 1995, 41(4):944–960. 10.1109/18.391241View ArticleGoogle Scholar


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