Mathematical Foundations of Cognitive Radios

• Autorzy: Couillet R. , Debbah M.
• Języki publikacji: EN

Abstrakty

EN

Recently, much interest has been directed towards software defined radios and embedded intelligence in telecommunication devices. However, no fundamental basis for cognitive radios has ever been proposed. In this paper, we introduce a fundamental vision of cognitive radios from a physical layer viewpoint. Specifically, our motivation in this work is to embed human-like intelligence in mobile wireless devices, following the three century-old work on Bayesian probability theory, the maximum entropy principle and minimal probability update. This allows us to partially answer such questions as, what are the signal detection capabilities of a wireless device, when facing a situation in which most parameters are missing, how to react and so on. As an introductory example, we will present previous works from the same authors following the cognitive framework, and especially the multi-antenna channel modeling and signal sensing.

Słowa kluczowe

EN

Bayesian inference; cognitive radio; maximum entropy

• Wydawca: Instytut Łączności - Państwowy Instytut Badawczy
• Czasopismo: Journal of Telecommunications and Information Technology
• Rocznik: 2009
• Tom: nr 4
• Strony: 108--117
• Opis fizyczny: Bibliogr. 34 poz., rys.

Twórcy

autor

Couillet R.

autor

Debbah M.

• Alcatel-Lucent Chair, Sup´elec, 3 rue Joliot Curie, 91192 Gif sur Yvette, France,

Bibliografia

• [1] C. Shannon, “A mathematical theory of communications”, Bell Syst. Tech. J., vol. 27, no. 7, pp. 379–423, 1948.
• [2] G. Foschini and M. Gans, “On limits of wireless communications in a fading environment when using multiple antennas”, Wirel. Pers. Commun., vol. 6, no. 3, pp. 311–335, 1998.
• [3] E. Telatar, “Capacity of multi-antenna Gaussian channels”, Eur. Trans. Telecommun., vol. 10, no. 6, pp. 585–595, 1999.
• [4] J. Mitola III and G. Q. Maguire Jr, “Cognitive radio: making software radios more personal”, IEEE Pers. Commun., vol. 6, no. 4, pp. 13–18, 1999.
• [5] S. Haykin, “Cognitive radio: brain-empowered wireless communications”, IEEE J. Selec. Areas in Commun., vol. 23, no. 2, pp. 201–220, 2005.
• [6] A. Ghasemi and E. S. Sousa, “Collaborative spectrum sensing for opportunistic access in fading environments”, in First IEEE Int. Sympo. New Front. Dynam. Spectr. Acc. Netw., Baltimore, USA, 2005, pp. 131–136.
• [7] L. S. Cardoso, M. Kobayashi, Ø. Ryan, and M. Debbah, “Vandermonde frequency division multiplexing for cognitive radio”, in IEEE 9th Worksh. Sig. Proces. Adv. Wirel. Commun., Recife, Brazil, 2008, pp. 421–425.
• [8] C. Shannon, “Programming a computer for playing chess”, Phil. Mag., Ser. 7, vol. 41, no. 314, pp. 256–275, 1950.
• [9] C. Shannon, “Computers and automata”, Proc. IRE, vol. 41, iss. 10, pp. 1234–1241, 1953.
• [10] C. Shannon, “A mind-reading machine”, Bell Laboratories memorandum, 1953 (reprinted in Claude Elwood Shannon Collected Pa- pers. New York: IEEE Press, 1993).
• [11] E. T. Jaynes, Probability Theory: The Logic of Science. Cambridge: Cambridge University Press, June 2003.
• [12] A. Caticha, “Maximum entropy, fluctuations and priors”, in Maximum Entropy and Bayesian Methods in Science and Engineering, Ed. A. Mohammad-Djafari, vol. 568, no. 94, 2001, http://arxiv.org/abs/math-ph/0008017
• [13] A. Caticha, “Lectures on probability, entropy and statistical physics”, 2008, http://arxiv.org//abs/0808.0012 [physics.data-an]
• [14] L. Brillouin, Science and Information Theory. New York: Dover Publ., 1963.
• [15] E. T. Jaynes, “On the rationale of maximum-entropy methods”, Proc. IEEE, vol. 70, no. 9, pp. 939–952, 1982.
• [16] E. T. Jaynes, “Information theory and statistical mechanics”, Phys. Rev., vol. 106, no. 4, pp. 620–630, 1957.
• [17] J. Shore and R. Johnson, “Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy”, IEEE Trans. Inform. Theory, vol. 26, no. 1, pp. 26–37, 1980.
• [18] R. T. Cox, “Of inference and inquiry, an essay in inductive logic”, in Proceedings 1978 Maximum Entropy Formalism Conference. Cambridge: MIT Press, 1979, pp. 119–167.
• [19] R. T. Cox, “Probability, frequency and reasonable expectation”, Amer. J. Phys., vol. 14, pp. 1–13, 1946.
• [20] K. H. Knuth, A. Caticha, J. L. Center, A. Giffin, and C. C. Rodriguez, “Lattice theory, measures and probability”, in 27th Int. Worksh. Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conf. Proc., Melville, USA, 2007, vol. 954, pp. 23–36.
• [21] H. Marko, “The bidirectional communication theory – a generalization of information theory”, IEEE Trans. Commun., vol. COM-21, no. 12, pp. 1345–1351, 1973.
• [22] J. Massey, “Causality, feedback and directed information”, in Proc. Int. Symp. Inform. Theory Appl., Waikiki, Hawaii, 1990.
• [23] M. Guillaud, M. Debbah, and A. L. Moustakas, “Maximum entropy MIMO wireless channel models”, IEEE Trans. Inform. Theory, Dec. 2006, http://arxiv.org/abs/cs.IT/0612101
• [24] H. Jeffreys, “An invariant form for the prior probability in estimation problems”, Proc. Royal Soc. London, Ser. A, Math. Phys. Sci., vol. 186, no. 1007, pp. 453–461, 1946.
• [25] A. M. Tulino and S. Verd´u, Random Matrix Theory and Wireless Communications. Hanover (USA): Now Publishers, 2004, vol. 1, iss. 1.
• [26] R. Couillet and M. Debbah, “Bayesian inference for multiple antenna cognitive receivers”, IEEE Wirel. Commun. Netwo. Conf., Budapest, Hungary, 2009.
• [27] A. B. Balantekin, “Character expansions, Itzykson-Zuber integrals, and the QCD partition function”, Phys. Rev. D, vol. 62, no. 8, p. 085017, 2000.
• [28] H. Urkowitz, “Energy detection of unknown deterministic signals”, Proc. IEEE, vol. 55, no. 4, pp. 523–531, 1967.
• [29] V. I. Kostylev, “Energy detection of a signal with random amplitude”, in Proc. IEEE Int. Conf. Commun. ICC’02, New York, USA, 2002, pp. 1606–1610.
• [30] Z. Quan, S. Cui, A. H. Sayed, and H. V. Poor, “Spatial-spectral joint detection for wideband spectrum sensing in cognitive radio networks”, in Proc. ICASSP Conf., Las Vegas, USA, 2008.
• [31] R. Couillet and M. Debbah, “A maximum entropy approach to OFDM channel estimation”, in IEEE Sig. Proces. Adv. Wirel. Com- mun. Conf., Perugia, Italy, 2009.
• [32] L. Song, T. Jiang, and Y. Zhang, Orthogonal Frequency Division Multiple Access (OFDMA) to be published by Auerbach Publ., CRC Press, Taylor & Francis Group.
• [33] R. Couillet, A. Ancora and M. Debbah, “Minimal update for OFDM channel estimation” to be submitted.
• [34] C. Y. Tseng and A. Caticha, “Maximum entropy approach to the theory of simple fluids”, 2003, Arxiv preprint cond-mat/0310746.