P. K. , K. =. , ?. .. {0, ?. 1}, . .. {1 et al., ? f ) + q, 3. for any state ? f ), 4. for any state ? q)f , 5. for any state, ? q)(1 ? f ) + f q, p.1

E. V. Belmega, S. Lasaulce, M. Debbah, and A. Hrungnes, A new energy efficiency function for quasi-static MIMO channels, International Wireless Communications and Mobile Computing Conference (IWCMC), 2009.

L. H. Ozarow, S. Shamai, A. D. Shitz-), and . Wyner, Information theoretic considerations for cellular mobile radio, IEEE Transactions on Vehicular Technology, vol.43, issue.2, pp.359-378, 1994.
DOI : 10.1109/25.293655

E. V. Belmega and S. Lasaulce, Energy-efficient precoding for multipleantenna terminals, IEEE. Trans. on Signal Processing, vol.59, issue.1, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00554965

L. Saker and S. E. Elayoubi, Sleep mode implementation issues in green base stations, 21st Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, 2010.
DOI : 10.1109/PIMRC.2010.5671926

G. J. Foschini, Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas, Bell Labs Technical Journal, vol.1, issue.2, pp.41-59, 1996.
DOI : 10.1002/bltj.2015

A. Edelman, Eigenvalues and Condition Numbers of Random Matrices, SIAM Journal on Matrix Analysis and Applications, vol.9, issue.4, 1989.
DOI : 10.1137/0609045

V. Shah, N. B. Mandayam, and D. J. Goodman, Power control for wireless data based on utility and pricing, Ninth IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (Cat. No.98TH8361), pp.427-1432, 1998.
DOI : 10.1109/PIMRC.1998.731433

J. Palicot and C. Roland, On The Use Of Cognitive Radio For Decreasing The Electromagnetic Radiations, URSI 05, XXVIII General Assembly, 2005.

W. Yang, W. Li, Y. Wang, and W. Sun, Energy-Efficient Transmission Schemes in Cooperative Cellular Systems, Globecom, 2010.

Q. Bai and J. A. Nossek, An energy efficient downlink resource allocation strategy for multiuser CP-OFDM and FBMC systems, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00502009

A. L. Moustakas, S. H. Simon, and A. M. Sengupta, MIMO Capacity Through Correlated Channels in the Presence of Correlated Interferers and Noise: A (Not So) Large N Analysis, IEEE Transactions on Information Theory, vol.49, issue.10, pp.10-2545, 2003.
DOI : 10.1109/TIT.2003.817427

C. U. Saraydar, N. B. Mandayam, and D. J. Goodman, Efficient power control via pricing in wireless data networks, IEEE Transactions on Communications, vol.50, issue.2, pp.291-303, 2002.
DOI : 10.1109/26.983324

T. M. Cover and J. A. Thomas, Elements of information theory, 1991.

F. Meshkati, H. V. Poor, S. C. Schwartz, and N. B. Mandayam, An Energy-Efficient Approach to Power Control and Receiver Design in Wireless Data Networks, IEEE Transactions on Communications, vol.53, issue.11, pp.1885-1894, 2005.
DOI : 10.1109/TCOMM.2005.858695

T. L. Marzetta and B. M. Hochwald, Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading, IEEE Transactions on Information Theory, vol.45, issue.1, 1999.
DOI : 10.1109/18.746779

B. Hassibi and B. M. Hochwald, How much training is needed in multiple-antenna wireless links?, IEEE Transactions on Information Theory, vol.49, issue.4, 2003.
DOI : 10.1109/TIT.2003.809594

F. Richter, A. J. Fehske, and G. Fettweis, Energy Efficiency Aspects of Base Station Deployment Strategies for Cellular Networks, 2009 IEEE 70th Vehicular Technology Conference Fall, 2009.
DOI : 10.1109/VETECF.2009.5379031

A. Kammoun, M. Kharouf, W. Hachem, and J. Najim, A Central Limit Theorem for the SINR at the LMMSE Estimator Output for Large-Dimensional Signals, IEEE Transactions on Information Theory, vol.55, issue.11, 2009.
DOI : 10.1109/TIT.2009.2030463

URL : https://hal.archives-ouvertes.fr/hal-00328163

S. Yatawatta, A. P. Petropulu, and C. J. Graff, Energy-Efficient Channel Estimation in MIMO Systems, EURASIP Journal on Wireless Communications and Networking, vol.17, issue.2, pp.2-2, 2006.
DOI : 10.1155/WCN/2006/27694

E. A. Jorswieck and H. Boche, Outage probability in multiple antenna systems, European Transactions on Telecommunications, vol.50, issue.3, 2007.
DOI : 10.1002/ett.1135

E. Telatar, Capacity of Multi-antenna Gaussian Channels, European Transactions on Telecommunications, vol.45, issue.6, pp.585-595, 1999.
DOI : 10.1002/ett.4460100604

I. E. Telatar and R. G. Gallager, Combining queueing theory and information theory for multi-access, Proceedings of 1994 IEEE International Symposium on Information Theory, 1995.
DOI : 10.1109/ISIT.1994.394732

S. Lasaulce and N. Sellami, On the impact of using unreliable data on the bootstrap channel estimation performance, 2003 4th IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2003 (IEEE Cat. No.03EX689), pp.348-352, 2003.
DOI : 10.1109/SPAWC.2003.1318980

V. Rodriguez, An Analytical Foundation for Ressource Management in Wireless Communication, IEEE Proc. of Globecom, pp.898-902, 2003.

V. Varma, M. Debbah, S. Lasaulce, and S. Ayoubi, Optimizing Energy-Efficiency in Slow-Fading MIMO Systems with Imperfect Channel State Information " , submitted to Computer Communications; Special Issue: Wireless Green, 2011.

V. Varma, S. Lasaulce, Y. Hayel, S. Ayoubi, and M. Debbah, Cross- Layer Design for Green Communications: The Case of Power Control

G. Miao, N. Himayat, Y. Li, and A. Swami, Cross-layer optimization for energy-efficient wireless communications: a survey, Wireless Communications and Mobile Computing, vol.54, issue.6, pp.529-542, 2009.
DOI : 10.1002/wcm.698

V. Shah, N. B. Mandayam, and D. J. Goodman, Power control for wireless data based on utility and pricing, Ninth IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (Cat. No.98TH8361), 1998.
DOI : 10.1109/PIMRC.1998.731433

D. J. Goodman and N. Mandayam, Power control for wireless data, IEEE Personal Communications, vol.7, issue.2, pp.48-54, 2000.
DOI : 10.1109/98.839331

D. Fudenberg and J. Tirole, Game Theory, 1991.

S. Lasaulce, M. Debbah, and E. Altman, Methodologies for analyzing equilibria in wireless games, IEEE Signal Processing Magazine, vol.26, issue.5, pp.41-52, 2009.
DOI : 10.1109/MSP.2009.933496

URL : https://hal.archives-ouvertes.fr/hal-00407937

C. U. Saraydar, N. B. Mandayam, and D. J. Goodman, Efficient power control via pricing in wireless data networks, IEEE Transactions on Communications, vol.50, issue.2, pp.291-303, 2002.
DOI : 10.1109/26.983324

S. Lasaulce, Y. Hayel, R. Azouzi, and M. Debbah, Introducing hierarchy in energy games, IEEE Transactions on Wireless Communications, vol.8, issue.7, pp.3833-3843, 2009.
DOI : 10.1109/TWC.2009.081443

URL : https://hal.archives-ouvertes.fr/hal-00446281

F. Meshkati, A. J. Goldsmith, H. V. Poor, and S. C. Schwartz, A gametheoretic approach to energy-efficient modulation in CDMA networks with delay QoS constraints, IEEE J. on Sel. Areas in Comm, vol.25, issue.6, 2007.

F. Meshkati, H. V. Poor, S. C. Schwartz, and R. V. Balan, Energy-efficient resource allocation in wireless networks with quality-of-service constraints, IEEE Transactions on Communications, vol.57, issue.11, pp.3406-3414, 2009.
DOI : 10.1109/TCOMM.2009.11.050638

F. Meshkati, H. V. Poor, and S. C. Schwartz, An Energy-Efficient Approach to Power Control and Receiver Design in Wireless Data Networks, IEEE Transactions on Communications, vol.53, issue.11, pp.1885-1894, 2005.
DOI : 10.1109/TCOMM.2005.858695

G. Bacci and M. Luise, A noncooperative approach to joint rate and power control for infrastructure wireless networks, 2009 International Conference on Game Theory for Networks, 2009.
DOI : 10.1109/GAMENETS.2009.5137380

S. Betz and H. V. Poor, Energy efficiency in multi-hop CDMA networks: a game theoretic analysis, 12th International Conference on Parallel and Distributed Systems, (ICPADS'06), 2006.
DOI : 10.1109/ICPADS.2006.42

G. Bacci, M. Luise, H. V. Poor, and A. M. Tulino, Energy Efficient Power Control in Impulse Radio UWB Wireless Networks, IEEE Journal of Selected Topics in Signal Processing, vol.1, issue.3, pp.508-520, 2007.
DOI : 10.1109/JSTSP.2007.906588

S. Buzzi, H. V. Poor, and D. Saturino, Energy-efficient resource allocation in multiuser MIMO systems: a game-theoretic framework, 2008.

G. Miao, N. Himayat, and G. Li, Energy-efficient link adaptation in frequency-selective channels, IEEE Transactions on Communications, vol.58, issue.2, pp.545-554, 2010.
DOI : 10.1109/TCOMM.2010.02.080587

G. Miao, N. Himayat, G. Y. Li, A. T. Koc, and S. Talwar, Interferenceaware energy-efficient power optimization, IEEE Intl. Conf. on Comm, 2009.

E. V. Belmega, S. Lasaulce, M. Debbah, and A. Hjørungnes, A new energy efficiency measure for quasi-static MIMO channels, Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing Connecting the World Wirelessly, IWCMC '09, 2009.
DOI : 10.1145/1582379.1582485

URL : https://hal.archives-ouvertes.fr/hal-00446968

S. Cui, A. J. Goldsmith, and A. Bahai, Energy-Efficiency of MIMO and Cooperative MIMO Techniques in Sensor Networks, IEEE Journal on Selected Areas in Communications, vol.22, issue.6, pp.1089-1098, 2004.
DOI : 10.1109/JSAC.2004.830916

X. Li, M. Che, and W. Liu, Application of STBC-ecoded cooperative transmissions in wireless sensor networks, IEEE Signal Processing Letters, vol.12, issue.2, 2005.

E. A. Jorswieck and H. Boche, Outage probability in multiple antenna systems, European Transactions on Telecommunications, vol.50, issue.3, pp.217-233, 2006.
DOI : 10.1002/ett.1135

E. V. Belmega and S. Lasaulce, An information-theoretic look at MIMO energy-efficient communications, Proceedings of the 4th International ICST Conference on Performance Evaluation Methodologies and Tools, 2009.
DOI : 10.4108/ICST.VALUETOOLS2009.7497

URL : https://hal.archives-ouvertes.fr/hal-00446961

S. Verdu, Spectral efficiency in the wideband regime, IEEE Transactions on Information Theory, vol.48, issue.6, pp.1319-1343, 2002.
DOI : 10.1109/TIT.2002.1003824

R. W. Wolff, Stochastic Modeling and the Theory of Queues, 1989.