DocumentCode :
3561406
Title :
Adaptive Training for Correlated Fading Channels With Feedback
Author :
Agarwal, Manish ; Honig, Michael L. ; Ata, Baris
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Northwestern Univ., Evanston, IL, USA
Volume :
58
Issue :
8
fYear :
2012
Firstpage :
5398
Lastpage :
5417
Abstract :
We consider data transmission through a time-selective, correlated (first-order Markov) Rayleigh fading channel subject to an average power constraint. The channel is estimated at the receiver with a pilot signal, and the estimate is fed back to the transmitter. The estimate is used for coherent demodulation, and to adapt the data and pilot powers. We derive the Hamilton--Jacobi--Bellman (HJB) equation for the optimal policy in a continuous-time limit where the channel state evolves as an Ornstein--Uhlenbeck diffusion process, and is estimated by a Kalman filter at the receiver. Finding an explicit solution to the HJB equation, as well as proving that a (twice-differentiable) solution exists, appears to be quite challenging. However, assuming that such a solution does exist, we explicitly determine the optimal pilot and data power control policies. The optimal pilot policy switches between zero and the maximum (peak-constrained) value (“bang-bang” control), and approximates the optimal discrete-time policy at low signal-to-noise ratios (SNRs) (equivalently, large bandwidths). The switching boundary is defined in terms of the system state (estimated channel mean and associated error variance), and can be explicitly computed. Under the optimal policy, the transmitter conserves power by decreasing the training power when the channel is faded, thereby increasing the data rate. Numerical results show a significant increase in achievable rate due to the adaptive training scheme with feedback, relative to constant (nonadaptive) training, which does not require feedback. The gain is more pronounced at relatively low SNRs and with fast fading. Results are further verified through Monte Carlo simulations.
Keywords :
Kalman filters; Monte Carlo methods; Rayleigh channels; channel estimation; data communication; diffusion; feedback; numerical analysis; optimal control; power control; radio transmitters; training; HJB equation; Hamilton-Jacobi-Bellman equation; Kalman filter; Monte Carlo simulations; Ornstein-Uhlenbeck diffusion process; SNR; adaptive training; channel estimation; channel state; coherent demodulation; constant training; continuous-time limit; correlated Rayleigh fading channel; data power control policies; data transmission; optimal discrete-time policy; optimal pilot policy; optimal policy; pilot powers; signal-to-noise ratios; switching boundary; training power; Channel estimation; Coherence; Equations; Fading; Mathematical model; Power control; Training; Adaptive training; Gauss–Markov channel; bang--bang control; channel estimation; diffusion approximation; free boundary problems; limited-rate feedback; variational inequalities; wideband channel;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
Conference_Location :
5/25/2012 12:00:00 AM
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2012.2201345
Filename :
6205382
Link To Document :
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