Randomly spread CDMA: Asymptotics via statistical physics

IEEE Transactions on Information Theory

Volumn 51, Issue 6, 2005, Pages 1983-2010

  Guo, Dongning ^a,b   Verdú, Sergio ^a  

^a Princeton University   (United States)

^b Northwestern University   (United States)

Author keywords

Channel capacity; Code division multiple access (CDMA); Free energy; Multiple input multiple output (MIMO) channel; Multiuser detection; Multiuser efficiency; Replica method; Statistical mechanics

Indexed keywords

BANDWIDTH; CHANNEL CAPACITY; CODE DIVISION MULTIPLE ACCESS; DECODING; FADING (RADIO); MATHEMATICAL MODELS; RANDOM PROCESSES; SIGNAL DETECTION; SIGNAL INTERFERENCE; SIGNAL RECEIVERS; SIGNAL TO NOISE RATIO; STATISTICAL MECHANICS;

MULTIPLE INPUT MULTIPLE OUTPUT (MIMO) CHANNEL; MULTIUSER DETECTION; MULTIUSER EFFICIENCY; REPLICA METHOD;

COMMUNICATION CHANNELS (INFORMATION THEORY);

EID: 20544442268     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2005.847700     Document Type: Article

References (68)

1. S. Verdú, Multiuser Detection. Cambridge, U.K.: Cambridge Univ. Press, 1998.
2. S. Verdú, "Minimum probability of error for asynchronous multiple access communication systems," in Proc. IEEE Military Communications Conf., vol. 1, Washington, DC, Nov. 1983, pp. 213-219.
3. S. Verdú, "Optimum Multiuser Signal Detection," Ph.D. dissertation, Dept. Elec. Eng., University of Illinois at Urbana-Champaign, Urbana, IL, 1984. Coordinated Science Lab., Tech. Rep. T-151.
4. S. Verdú, "Minimum probability of error for asynchronous Gaussian multiple-access channels," IEEE Trans. Inf. Theory, vol. IT-32, no. 1, pp. 85-96, Jan. 1986.
5. S. Verdú, "Optimum multiuser asymptotic efficiency," IEEE Trans. Inf. Theory, vol. 34, no. 5, pp. 890-897, Sep. 1986.
6. D. N. C. Tse and S. V. Hanly, "Linear multiuser receivers: Effective interference, effective bandwidth, and user capacity," IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 641-657, Mar. 1999.
7. Y. C. Eldar and A. M. Chan, "On the asymptotic performance of the decorrelator," IEEE Trans. Inf. Theory, vol. 49, no. 9, pp. 2309-2313, Sep. 2003.
8. D. Guo and S. Verdú, "Multiuser detection and statistical mechanics," in Communications, Information, and Network Security, V. Bhargava, H. V. Poor, V. Tarokh, and S. Yoon, Eds. Norwell, MA: Kluwer Academic, 2002, ch. 13, pp. 229-277.
9. D. Guo, S. Verdú, and L. K. Rasmussen, "Asymptotic normality of linear multiuser receiver outputs," IEEE Trans. Inf. Theory, vol. 48, no. 12, pp. 3080-3095, Dec. 2002.
10. S. Verdú and S. Shamai (Shitz), "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inf. Theory, vol. 45, no. 2, pp. 622-640, Mar. 1999.
11. S. Shamai (Shitz) and S. Verdú, "The impact of frequency-flat fading on the spectral efficiency of CDMA," IEEE Trans. Inf. Theory, vol. 47, no. 4, pp. 1302-1327, May 2001.
12. A. M. Tulino and S. Verdú, "Random matrix theory and wireless communications," Foundations Trends Commun. Inf. Theory, vol. 1, pp. 1-182, 2004.
13. Z. D. Bai, "Methodologies in spectral analysis of large dimensional random matrices, a review," Statist. Sinica, vol. 9, pp. 611-677, July 1999.
14. S. Verdú, "Capacity region of Gaussian CDMA channels: The symbol-synchronous case," in Proc. 24th Allerton Conf. Communications, Control and Computing, Monticello, IL, Oct. 1986, pp. 1025-1034.
15. A. J. Grant and P. D. Alexander, "Random sequence multisets for synchronous code-division multiple-access channels," IEEE Trans. Inf. Theory, vol. 44, no. 7, pp. 2832-2836, Nov. 1998.
16. P. B. Rapajic and D. Popescu, "Information capacity of a random signature multiple-input multiple-output channel," IEEE Trans. Commun., vol. 48, no. 8, pp. 1245-1248, Aug. 2000.
17. G. J. Foschini, "Layered space-time architecture for wireless communication in a fading environment when using multiple antennas," Bell Labs. Tech. J., vol. 1, pp. 41-59, 1996.
18. I. E. Telatar, "Capacity of multi-antenna Gaussian channels," Europ. Trans. Telecommun., vol. 10, pp. 585-595, Nov./Dec. 1999.
19. G. J. Rodgers, "Comment: Spectral analysis of random matrices using the replica method," Statist. Sinica, vol. 9, pp. 662-667, 1999.
20. T. Tanaka, "Analysis of bit error probability of direct-sequence CDMA multiuser demodulators," in Advances in Neural Information Processing Systems, T. K. Leen et al., Eds. Cambridge, MA: MIT Press, 2001, vol. 13, pp. 315-321.
21. T. Tanaka, "Average-case analysis of multiuser detectors," in Proc. IEEE Int. Symp. Information Theory, Washington, DC, Jun. 2001, p. 287.
22. T. Tanaka, "Statistical mechanics of CDMA multiuser demodulation," Europhys. Lett., vol. 54, pp. 540-546, 2001.
23. T. Tanaka, "A statistical mechanics approach to large-system analysis of CDMA multiuser detectors," IEEE Trans. Inf. Theory, vol. 48, no. 11, pp. 2888-2910, Nov. 2002.
24. R. R. Müller and W. H. Gerstacker, "On the capacity loss due to separation of detection and decoding," IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1769-1778, Aug. 2004.
25. R. R. Müller, "On channel capacity, uncoded error probability, ML-detection and spin glasses," in Proc. Workshop on Concepts in Information Theory, Breisach, Germany, 2002, pp. 79-81.
26. S. F. Edwards and P. W. Anderson, "Theory of spin glasses," J. Phys. F: Metal Physics, vol. 5, pp. 965-974, 1975.
27. H. Nishimori, Statistical Physics of Spin Glasses and Information Processing: An Introduction, ser. Number 111 in International Series of Monographs on Physics. Oxford, U.K.: Oxford Univ. Press, 2001.
28. N. Sourlas, "Spin-glass models as error-correcting codes," Nature, vol. 339, pp. 693-695, June 1989.
29. Y. Kabashima and D. Saad, "Statistical mechanics of error-correcting codes," Europhys. Lett., vol. 45, pp. 97-103, 1999.
30. A. Montanari, "Turbo codes: The phase transition," Europ. Phys. J. B, vol. 18, pp. 121-136, 2000.
31. T. Murayama, Y. Kabashima, D. Saad, and R. Vicente, "Statistical physics of regular low-density parity-check error-correcting codes," Phys. Rev. E, vol. 62, pp. 1577-1591, 2000.
32. A. Montanari and N. Sourlas, "The statistical mechanics of turbo codes," Europ. Phys. J. B, vol. 18, pp. 107-119, 2000.
33. Y. Kabashima and D. Saad, "Statistical mechanics of low-density parity-check codes," J. Phys. A: Mathematical and General, vol. 37, pp. R1-R43, 2004.
34. 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 Trans. Inf. Theory, vol. 49, no. 10, pp. 2545-2561, Oct. 2003.
35. Y. Kabashima, "A CDMA multiuser detection algorithm on the basis of belief propagation," J. Phys. A: Mathematical and General, vol. 36, pp. 11 111-11 121, 2003.
36. T. Fabricius and O. Winther, "Correcting the bias of subtractive interference cancellation in CDMA: Advanced mean field theory," IEEE Trans. Inf. Theory, submitted for publication.
37. M. Talagrand, "Rigorous results for mean field models for spin glasses," Theor. Comp. Sci., vol. 265, pp. 69-77, Aug. 2001.
38. M. Talagrand, Spin Glasses: A Challenge for Mathematicians. Berlin, Germany: Springer-Verlag, 2003.
39. M. Mezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond. Singapore: World Scientific, 1987.
40. V. Dotsenko, The Theory of Spin Glasses and Neural Networks. Singapore: World Scientific, 1994.
41. D. Guo, S. Shamai (Shitz), and S. Verdú, "Mutual information and minimum mean-square error in Gaussian channels," IEEE Trans. Inf. Theory, vol. 51, no. 4, pp. 1261-1282, Apr. 2005.
42. M. K. Varanasi and T. Guess, "Optimum decision feedback multiuser equalization with successive decoding achieves the total capacity of the Gaussian multiple-access channel," in Proc. Asilomar Conf. Signals, Systems and Computers, Monterey, CA, Nov. 1997, pp. 1405-1409.
43. P. Rapajic, M. Honig, and G. Woodward, "Multiuser decision-feedback detection: Performance bounds and adaptive algorithms," in Proc. IEEE Int. Symp. Information Theory, Cambridge, MA, Aug. 1998, p. 34.
44. S. L. Ariyavisitakul, "Turbo space-time processing to improve wireless channel capacity," IEEE Trans. Commun., vol. 48, no. 8, pp. 1347-1359, Aug. 2000.
45. R. R. Müller, "Multiuser receivers for randomly spread signals: Fundamental limits with and without decision-feedback," IEEE Trans. Inf. Theory, vol. 47, no. 1, pp. 268-283, Jan. 2001.
46. T. Guess and M. K. Varanasi, "An information-theoretic framework for deriving canonical decision-feedback receivers in Gaussian channels," IEEE Trans. Inf. Theory, vol. 51, no. 1, pp. 173-187, Jan. 2005.
47. G. D. Forney, Jr., "Shannon meets Wiener II: On MMSE estimation in successive decoding schemes," in Proc. 42nd Allerton Conf. Commun., Control, and Computing, Monticello, IL, Oct. 2004. Available: [Online] at http://arxiv.org/pdf/cs.IT/0409011.
48. F. Comets, "The martingale method for mean-field disordered systems at high temperature," in Mathematical Aspects of Spin Glasses and Neural Networks, A. Bovier and P. Picco, Eds. Basel, Switzerland: Birkhüuser, 1998, pp. 9-113.
49. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
50. J. Yedidia, W. Freeman, and Y. Weiss, "Generalized belief propagation," in Advances in Neural Information Processing Systems 13. Cambridge, MA: MIT Press, 2001, pp. 689-695.
51. P. Pakzad and V. Anantharam, "Belief propagation and statistical physics," in Proc. Conf. Information Sciences and Systems, Princeton, NJ, Mar. 2002.
52. J. van Mourik, D. Saad, and Y. Kabashima, "Critical noise levels for LPDC decoding," Phys. Rev. E, vol. 66, pp. 026 705:1-026 705:8, 2002.
53. M. Chiang and S. Boyd, "Geometric programming duals of channel capacity and rate distortion," IEEE Trans. Inf. Theory, vol. 50, no. 2, pp. 245-258, Feb. 2004.
54. R. R. Müller, "Random matrices, free probability, and the replica method," in Proc. European Signal Processing Conf., Vienna, Austria, 2004.
55. D. Guo and S. Verdú, "Minimum probability of error of many-user CDMA without power control," in Proc. IEEE Int. Symp. Information Theory, Lausanne, Switzerland, Jun./Jul. 2002, p. 188.
56. D. Guo and S. Verdú, "Replica analysis of CDMA spectral efficiency," in Proc. IEEE Information Theory Workshop, Paris, France, 2003, pp. 22-25.
57. D. Guo, "Gaussian channels: Information, estimation, and multiuser detection," Ph.D. dissertation, Dep. Elec. Eng., Princeton Univ., Princeton, NJ, 2004.
58. R. R. Müller, "Channel capacity and minimum probability of error in large dual antenna array systems with binary modulation," IEEE Trans. Signal Process., vol. 51, no. 11, pp. 2821-2828, Nov. 2003.
59. G. Caire, "Statistical physics and the analysis of exact belief-propagation decoding of CDMA," in Proc. Joint Workshop on Communications and Coding (JWCC), Barolo, Italy, 2002, pp. 30-32.
60. G. Caire, R. R. Müller, and T. Tanaka, "Iterative multiuser joint decoding: Optimal power allocation and low-complexity implementation," IEEE Trans. Inf. Theory, vol. 50, no. 9, pp. 1950-1973, Sep. 2004.
61. T. Tanaka and M. Okada, "Approximate belief propagation, density evolution, and statistical neurodynamics for CDMA multiuser detection," IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 700-706, Feb. 2005.
62. R. S. Ellis, Entropy, Large Deviations, and Statistical Mechanics, ser. A series of comprehensive studies in mathematics. New York: Springer-Verlag, 1985, vol. 271.
63. H. Nishimori and D. Sherrington, "Absence of replica symmetry breaking in a region of the phase diagram of the Ising spin glass," in Amer Inst. Phys. Conf. Proc. 553: Disordered and Complex Systems, 2001, p. 67.
64. J. Hubbard, "Calculation of partition functions," Phys. Rev. Lett., vol. 3, pp. 77-78, 1959.
65. W. Feller, An Introduction to Probability Theory and Its Applications, 2nd ed. New York: Wiley, 1971, vol. II.
66. D. N. C. Tse and S. Verdú, "Optimum asymptotic multiuser efficiency for randomly spread CDMA," IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2718-2722, Nov. 2000.
67. F. Meshkati, D. Guo, H. V. Poor, S. Schwartz, and N. B. Mandayam, "A unified approach to power control for multiuser detectors," in Proc. 2nd Int. Workshop on Signal Processing for Wireless Communications, London, U.K., 2004.
68. C.-K. Wen and K.-K. Wong, "Asymptotic spectral efficiency of spatially correlated MIMO multiple-access channels with arbitrary signaling inputs for joint and separate decoding," in Proc. IEEE Int. Symp. Information Theory, Chicago, IL, Jun./Jul. 2004, p. 282.