- Research Article
- Open Access
Optimal Training for Time-Selective Wireless Fading Channels Using Cutoff Rate
EURASIP Journal on Advances in Signal Processing volume 2006, Article number: 047245 (2006)
We consider the optimal allocation of resources—power and bandwidth—between training and data transmissions for single-user time-selective Rayleigh flat-fading channels under the cutoff rate criterion. The transmitter exploits statistical channel state information (CSI) in the form of the channel Doppler spectrum to embed pilot symbols into the transmission stream. At the receiver, instantaneous, though imperfect, CSI is acquired through minimum mean-square estimation of the channel based on some set of pilot observations. We compute the ergodic cutoff rate for this scenario. Assuming estimator-based interleaving and-PSK inputs, we study two special cases in-depth. First, we derive the optimal resource allocation for the Gauss-Markov correlation model. Next, we validate and refine these insights by studying resource allocation for the Jakes model.
Cavers JK: An analysis of pilot symbol assisted modulation for Rayleigh fading channels [Mobile Radio]. IEEE Transactions on Vehicular Technology 1991, 40(4):686–693. 10.1109/25.108378
Tong L, Sadler BM, Dong M: Pilot-assisted wireless transmissions. IEEE Signal Processing Magazine 2004, 21(6):12–25. 10.1109/MSP.2004.1359139
Garcia MJ, Páez-Borrallo JM: Tracking of time misalignments for OFDM systems in multipath fading channels. IEEE Transactions on Consumer Electronics 2002, 48(4):982–989.
Kuo W, Fitz MP: Frequency offset compensation of pilot symbol assisted modulation in frequency flat fading. IEEE Transactions on Communications 1997, 45(11):1412–1416. 10.1109/26.649760
Cai X, Giannakis G: Adaptive PSAM accounting for channel estimation and prediction errors. IEEE Transactions on Wireless Communications 2005, 4(1):246–256.
Dong M, Tong L, Sadler BM: Optimal insertion of pilot symbols for transmissions over time-varying flat fading channels. IEEE Transactions on Signal Processing 2004, 52(5):1403–1418. 10.1109/TSP.2004.826182
Dong X, Xiao L: Symbol error probability of two-dimensional signaling in Ricean fading with imperfect channel estimation. IEEE Transactions on Vehicular Technology 2005, 54(2):538–549. 10.1109/TVT.2004.841537
Hassibi B, Hochwald BM: How much training is needed in multiple-antenna wireless links? IEEE Transactions on Information Theory 2003, 49(4):951–963. 10.1109/TIT.2003.809594
Adireddy S, Tong L, Viswanathan H: Optimal placement of training for frequency-selective block-fading channels. IEEE Transactions on Information Theory 2002, 48(8):2338–2353. 10.1109/TIT.2002.800466
Ma X, Giannakis GB, Ohno S: Optimal training for block transmissions over doubly selective wireless fading channels. IEEE Transactions on Signal Processing 2003, 51(5):1351–1366. 10.1109/TSP.2003.810304
Ohno S, Giannakis GB: Capacity maximizing MMSE-optimal pilots for wireless OFDM over frequency-selective block Rayleigh-fading channels. IEEE Transactions on Information Theory 2004, 50(9):2138–2145. 10.1109/TIT.2004.833365
Baltersee J, Fock G, Meyr H: An information theoretic foundation of synchronized detection. IEEE Transactions on Communications 2001, 49(12):2115–2123. 10.1109/26.974258
Medard M, Abou-Faycal I, Madhow U: Adaptive coded modulation without channel feedback for pilot symbol assisted modulation. Proceedings of the 38th Annual Allerton Conference on Communication, Control and Computing, October 2002, Monticello, Ill, USA
Ohno S, Giannakis G: Average-rate optimal PSAM transmissions over time-selective fading channels. IEEE Transactions on Wireless Communications 2002, 1(4):712–720. 10.1109/TWC.2002.804183
Arikan E: Upper bound on the cutoff rate of sequential decoding. IEEE Transactions on Information Theory 1988, 34(1):55–63. 10.1109/18.2601
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
Jamali S, Le-Ngoc T: Coded-Modulation Techniques for Fading Channels. Kluwer Academic, Dordrecht, The Netherlands; 1994.
Leeuwin-Boulle K, Belfiore JC: Cutoff rate of time correlated fading channels. IEEE Transactions on Information Theory 1993, 39(2):612–617. 10.1109/18.212291
McEliece RJ, Stark WE: Channels with block interference. IEEE Transactions on Information Theory 1984, 30(1):44–53. 10.1109/TIT.1984.1056848
Hero AO, Marzetta TL: Cutoff rate and signal design for the quasi-static Rayleigh-fading space-time channel. IEEE Transactions on Information Theory 2001, 47(6):2400–2416. 10.1109/18.945254
Misra S, Swami A, Tong L: Cutoff rate of the Gauss-Markov channel with adaptive energy allocation. Processing of IEEE Workshop on Signal Processing Advances in Wireless Communications, June 2003, Rome, Italy
Kay S: Fundamentals of Statistical Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.
Massey J: Coding and moulation in digital communications. Proceedings of International Zurich Seminar on Digital Communications, March 1974
Wozencraft JM, Jacobs IM: Principles of Communication Engineering. John Wiley & Sons, New York, NY, USA; 1965.
Proakis J: Digital Communications. McGraw-Hill, New York, NY, USA; 2001.
Wu PH-Y, Duel-Hallen A: Multiuser detectors with disjoint Kalman channel estimators for synchronous CDMA mobile radio channels. IEEE Transactions on Communications 2000, 48(5):752–756. 10.1109/26.843185
Stojanovic M, Proakis JG, Catipovic JA: Analysis of the impact of channel estimation errors on the performance of a decision-feedback equalizer in fading multipath channels. IEEE Transactions on Communications 1995, 43(2):877–886. 10.1109/26.380120
Medard M: The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel. IEEE Transactions on Information Theory 2000, 46(3):933–946. 10.1109/18.841172
Kailath T, Sayed A, Hassibi B: Linear Estimation. Prentice-Hall, Englewood Cliffs, NJ, USA; 2000.
Jakes WC Jr.: Microwave Mobile Communication. John Wiley & Sons, New York, NY, USA; 1974.
Rappaport T: Wireless Communications: Principles & Practice. Prentice-Hall, Upper Saddle River, NJ, USA; 1996.
Baccarelli E: Bounds on the symmetric cutoff rate for QAM transmissions over time-correlated flat-faded channels. IEEE Communications Letters 1998, 2(10):279–281. 10.1109/4234.725223