Random beamforming over quasi-static and fading channels: A deterministic equivalent approach

IEEE Transactions on Information Theory

Volumn 58, Issue 10, 2012, Pages 6392-6425

  Couillet, Romain ^a   Hoydis, Jakob ^b   Debbah, Mérouane ^c  

^a Department of Telecommunications ^*  (France)

^b LUCENT TECHNOLOGIES   (United States)

^c NOKIA RESEARCH CENTER   (United States)

Author keywords

Deterministic equivalent; interference channel; isometric precoding; MIMO MAC; random beamforming

Indexed keywords

DETERMINISTIC EQUIVALENTS; INTERFERENCE CHANNELS; MIMO-MAC; PRECODING; RANDOM BEAMFORMING;

APPROXIMATION ALGORITHMS; BEAMFORMING; COMMUNICATION SYSTEMS; FADING CHANNELS; MIMO SYSTEMS; RANDOM VARIABLES; SPURIOUS SIGNAL NOISE;

SIGNAL INTERFERENCE;

EID: 84866505673     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2012.2201913     Document Type: Article

References (45)

1. S.Wagner, R. Couillet, M. Debbah, and D. T. M. Slock, "Large system analysis of linear precoding in MISO broadcast channels with limited feedback," IEEE Trans. Inf. Theory, vol. 58, no. 7, pp. 4509-4537, Jul. 2012.
2. J. Hoydis, M. Debbah, and M. Kobayashi, "Asymptotic moments for interference mitigation in correlated fading channels," in Proc. IEEE International Symposium on Information Theory (ISIT), Saint Petersburg, Russia, Jun.-Aug. 31-5, 2011 [Online]. Available: http://arxiv.org/abs/1104.4911
3. C. N. Chuah, D. N. C. Tse, J. M. Kahn, and R. A. Valenzuela, "Capacity scaling in MIMO wireless systems under correlated fading," IEEE Trans. Inf. Theory, vol. 48, no. 3, pp. 637-650, Mar. 2002. (Pubitemid 34239793)
4. R. Couillet, M. Debbah, and J. W. Silverstein, "A deterministic equivalent for the analysis of correlated MIMO multiple access channels," IEEE Trans. Inf. Theory, vol. 57, no. 6, pp. 3493-3514, Jun. 2011.
5. W. Hachem, P. Loubaton, and J. Najim, "Deterministic equivalents for certain functionals of large random matrices," Ann. Appl. Probab., vol. 17, no. 3, pp. 875-930, 2007.
6. W. Hachem, P. Loubaton, and J. Najim, "A CLT for information theoretic statistics of Gram random matrices with a given variance profile," Ann. Appl. Probab., vol. 18, no. 6, pp. 2071-2130, Dec. 2008.
7. J. Dumont, W. Hachem, S. Lasaulce, P. Loubaton, and J. Najim, "On the capacity achieving covariance matrix for rician MIMO channels: An asymptotic approach," IEEE Trans. Inf. Theory, vol. 56, no. 3, pp. 1048-1069, Mar. 2010.
8. M. Debbah, W. Hachem, P. Loubaton, and M. de Courville, "MMSE analysis of certain large isometric random precoded systems," IEEE Trans. Inf. Theory, vol. 49, no. 5, pp. 1293-1311, May 2003.
9. W. Hachem, "Simple polynomial MMSE receivers for CDMA transmissions on frequency selective channels," IEEE Trans. Inf. Theory, vol. 50, no. 1, pp. 164-172, Jan. 2004.
10. W. Hachem, An expression for , 2008, to be published.
11. R. Couillet andM. Debbah, Random Matrix Methods forWireless Communications, 1st ed. New York: Cambridge Univ. Press, 2011.
12. M. J. M. Peacock, I. B. Collings, and M. L. Honig, "Asymptotic analysis of LMMSE multiuser receivers for multi-signature multicarrier CDMA in Rayleigh fading," IEEE Trans. Commun., vol. 52, no. 6, pp. 964-972, Jun. 2004.
13. M. J. M. Peacock, I. B. Collings, and M. L. Honig, "Asymptotic spectral efficiency of multiuser multisignature CDMA in frequency-selective channels," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1113-1129, Mar. 2006. (Pubitemid 46444895)
14. R. Couillet and M. Debbah, "Uplink capacity of self-organizing clustered orthogonal CDMA networks in flat fading channels," presented at the IEEE Information Theory Workshop, Taormina, Sicily, 2009.
15. M. J. M. Peacock, I. B. Collings, and M. L. Honig, "Eigenvalue distributions of sums and products of large random matrices via incremental matrix expansions," IEEE Trans. Inf. Theory, vol. 54, no. 5, pp. 2123-2138, May 2008. (Pubitemid 351689552)
16. A. L. Moustakas, "Synchronous MMSE SIR with interference: Diagrams & replicas," in BIRS Workshop on Free Probability, Extensions and Applications, Banff, Canada, Jan. 2008 [Online]. Available: http://temple.birs. ca/08w5076/presentation-Moustakas.pdf
17. I. E. Telatar, "Capacity of multi-antenna Gaussian channels," Eur. Trans. Telecommun., vol. 10, no. 6, pp. 585-595, Feb. 1999.
18. J.Dumont,W. Hachem, P. Loubaton, and J. Najim, "On the asymptotic analysis of mutual information of MIMO Rician correlated channels," presented at the IEEE-EURASIP Int. Symp. Control, Communication, and Signal Processing, Marrakech, Morocco, Mar. 2006.
19. R. S. Blum, J. H. Winters, and N. R. Sollenberger, "On the capacity of cellular systems with MIMO," IEEE Commun. Lett., vol. 6, pp. 242-244, Jun. 2002. (Pubitemid 34916018)
20. R. S. Blum, "MIMO capacity with interference," IEEE J. Sel. Areas Commun., vol. 21, no. 5, pp. 793-801, Jun. 2003.
21. P.Viswanath, D. N. C. Tse, and R. Laroia, "Opportunistic beamforming using dumb antennas," IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1277-1294, Jun. 2002. (Pubitemid 34759845)
22. D. J. Love and R. W. Heath, "Limited feedback unitary precoding for spatial multiplexing systems," IEEE Trans. Inf. Theory, vol. 51, no. 8, pp. 2967-2976, Aug. 2005. (Pubitemid 41158620)
23. J. Lee, J. K. Han, and J. Zhang, "MIMO technologies in 3GPP LTE and LTE-advanced," EURASIP J. Wireless Commun. Netw., vol. 2009, May 2009.
24. K. Huang, J. G. Andrews, and R. W. Heath, "Performance of orthogonal beamforming for SDMAwith limited feedback," IEEE Trans. Veh. Technol., vol. 58, no. 1, pp. 152-164, Jan. 2009.
25. V. A. Mar?enko and L. A. Pastur, "Distribution of eigenvalues for some sets of random matrices," Math USSR-Sbornik, vol. 1, no. 4, pp. 457-483, Apr. 1967.
26. Z. D. Bai and J. W. Silverstein, Spectral Analysis of Large Dimensional Random Matrices, 2nd ed. New York: Springer, 2009.
27. L. A. Pastur and M. Shcherbina, Eigenvalue Distribution of Large Random Matrices. Providence, RI: AMS, 2011, Mathematical Surveys and Monographs, vol. 171.
28. T. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. New York: Wiley, 2006.
29. S. Verdú, Multiuser Detection. New York: Cambridge Univ. Press, 1998.
30. D. Voiculescu, K. J. Dykema, and A. Nica, "Free random variables," in Amer. Math. Soc., 1992.
31. F. Hiai and D. Petz, The Semicircle Law, Free Random Variables and Entropy. Providence, RI: AMS, 2006, Mathematical Surveys and Monographs vol. 77.
32. R. Speicher, C. Vargas, and T. Mai, Free Deterministic Equivalents, Rectangular RandomMatrixModels, and Operator-Valued Free Probability Theory, 2011 [Online]. Available: http://arxiv.org/abs/1110.1237
33. S. Verdu and S. Shamai, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 622-640, Mar. 1999.
34. Z. D. Bai and J. W. Silverstein, "No eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices," Ann. Probab., vol. 26, no. 1, pp. 316-345, Jan. 1998. (Pubitemid 128073876)
35. D. Chizhik, F. Rashid-Farrokhi, J. Ling, and A. Lozano, "Effects of antenna separation on the capacity of BLAST in correlated channels," IEEE Commun. Lett., vol. 4, pp. 337-339, Nov. 2000. (Pubitemid 32138910)
36. K. I. Pedersen, P. E. Mogensen, and B. H. Fleury, "A stochastic model of the temporal and azimuthal dispersion seen at the base station in outdoor propagation environments," IEEE Trans. Inf. Theory, vol. 49, no. 2, pp. 437-437, Mar. 2000.
37. A. L. Moustakas, H. U. Baranger, L. Balents, A. M. Sengupta, and S. H. Simon, "Communication through a diffusive medium: Coherence and capacity," Science, vol. 287, pp. 287-290, 2000. (Pubitemid 30046751)
38. R. D. Yates, "A framework for uplink power control in cellular radio systems," IEEE J. Sel. Areas Commun., vol. 13, no. 7, pp. 1341-1347, 1995.
39. P. Billingsley, Probability andMeasure, 3rd ed. Hoboken, NJ:Wiley, 1995.
40. E. C. Titchmarsh, The Theory of Functions. New York: Oxford Univ. Press, 1939.
41. W. Rudin, Real and Complex Analysis, 3rd ed. New York: McGraw- Hill, 1986.
42. P. Billingsley, Probability andMeasure, 3rd ed. Hoboken, NJ:Wiley, 1995.
43. J.W. Silverstein and Z. D. Bai, "On the empirical distribution of eigenvalues of a class of large dimensional random matrices," J. Multivar. Anal., vol. 54, no. 2, pp. 175-192, 1995.
44. R. A. Horn and C. R. Johnson, Matrix Analysis. New York: Cambridge Univ. Press, 1985.
45. S. Wagner, "MU-MIMO Transmission and Reception Techniques for the Next Generation of Cellular Wireless Standards (LTE-A)," Ph.D. dissertation, EURECOM, Sophia-Antipolis cedex, 2011.