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Multilevel Codes for OFDM-Like Modulation over Underspread Fading Channels
EURASIP Journal on Advances in Signal Processing volume 2006, Article number: 097210 (2006)
We study the problem of modulation and coding for doubly dispersive, that is, time and frequency selective, fading channels. Using the recent result that underspread linear systems are approximately diagonalized by biorthogonal Weyl-Heisenberg bases, we arrive at a canonical formulation of modulation and code design. For coherent reception with maximum-likelihood decoding, we derive the code design criteria as a function of the channel's scattering function. We use ideas from generalized concatenation to design multilevel codes for this canonical channel model. These codes are based on partitioning a constellation carved out from the integer lattice. Utilizing the block fading interpretation of the doubly dispersive channel, we adapt these partitioning techniques to the richness of the channel. We derive an algebraic framework which enables us to partition in arbitrarily large dimensions.
Kozek W: Matched Weyl-Heisenberg expansions of nonstationary environments, M.S. thesis. Vienna University of Technology, Vienna, Austria; March 1997.
Kozek W: Adaptation of Weyl-Heisenberg frames to underspread environments. In Gabor Analysis and Algorithms: Theory and Applications. Edited by: Feichtinger HG, Strohmer T. Birkhäuser, Boston, Mass, USA; 1998:323–352.
Liu K, Kadous T, Sayeed AM: Orthogonal time-frequency signaling over doubly dispersive channels. IEEE Transactions on Information Theory 2004, 50(11):2583–2603. 10.1109/TIT.2004.836931
Giraud X, Boutillon E, Belfiore JC: Algebraic tools to build modulation schemes for fading channels. IEEE Transactions on Information Theory 1997, 43(3):938–952. 10.1109/18.568703
Boutros J, Viterbo E: Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel. IEEE Transactions on Information Theory 1998, 44(4):1453–1467. 10.1109/18.681321
Caire G, Taricco G, Biglieri E: Bit-interleaved coded modulation. IEEE Transactions on Information Theory 1998, 44(3):927–946. 10.1109/18.669123
Ungerboeck G: Channel coding with multilevel/phase signals. IEEE Transactions on Information Theory 1982, 28(1):55–66. 10.1109/TIT.1982.1056454
Zadeh L: Time-varying networks, I. Proceedings of IRE 1961, 49: 1488–1503.
Proakis JG: Digital Communications. 4th edition. McGraw-Hill, New York, NY, USA; 2001. chapter 14
Matz G, Hlawatsch F: Time-frequency transfer function calculus of linear time-varying systems. In Time-Frequency Signal Analysis and Processing. Edited by: Boashash B. Prentice-Hall, Englewood Cliffs, NJ, USA; 2003.
Kozek W, Molisch AF: Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels. IEEE Journal on Selected Areas in Communications 1998, 16(8):1579–1589. 10.1109/49.730463
Leeuwin-Boulle K, Belfiore JC: The cutoff rate of time correlated fading channels. IEEE Transactions on Information Theory 1993, 39(2):612–617. 10.1109/18.212291
Wang Z, Giannakis GB: A simple and general parameterization quantifying performance in fading channels. IEEE Transactions on Communications 2003, 51(8):1389–1398. 10.1109/TCOMM.2003.815053
Biglieri E, Proakis J, Shamai S: Fading channels: information-theoretic and communications aspects. IEEE Transactions on Information Theory 1998, 44(6):2619–2692. 10.1109/18.720551
Siwamogsatham S, Fitz MP: Robust space-time codes for correlated Rayleigh fading channels. IEEE Transactions on Signal Processing 2002, 50(10):2408–2416. 10.1109/TSP.2002.803349
Imai H, Hirakawa S: A new multilevel coding method using error-correcting codes. IEEE Transactions on Information Theory 1977, 23(3):371–377. 10.1109/TIT.1977.1055718
Forney GD Jr., Gallager RG, Lang GR, Longstaff FM, Qureshi SU: Efficient modulation for band-limited channels. IEEE Journal on Selected Areas in Communications 1984, 2(5):632–647. 10.1109/JSAC.1984.1146101
Wachsmann U, Fischer RFH, Huber JB: Multilevel codes: theoretical concepts and practical design rules. IEEE Transactions on Information Theory 1999, 45(5):1361–1391. 10.1109/18.771140
Modestino JW, Mui SY: Convolutional code performance in the rician fading channel. IEEE Transactions on Communications 1976, 24(6):592–606. 10.1109/TCOM.1976.1093351
Royden HL: Real Analysis. 3rd edition. Prentice-Hall, Englewood Cliffs, NJ, USA; 1988. chapter 4
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Mallik, S., Koetter, R. Multilevel Codes for OFDM-Like Modulation over Underspread Fading Channels. EURASIP J. Adv. Signal Process. 2006, 097210 (2006) doi:10.1155/ASP/2006/97210
- Information Technology
- Linear System
- Quantum Information
- Fading Channel
- Canonical Formulation