Gradient of mutual information in linear vector Gaussian channels

IEEE Transactions on Information Theory

Volumn 52, Issue 1, 2006, Pages 141-154

  Palomar, Daniel P ^a   Verdú, Sergio ^a  

^a Princeton University   (United States)

Author keywords

De Bruijn's identity; Divergence; Gaussian noise; Minimum mean square error (MMSE); Multiple input multiple output (MIMO) channels; Mutual information; Nonlinear estimation; Precoder optimization

Indexed keywords

COMMUNICATION CHANNELS (INFORMATION THEORY); DATA COMMUNICATION SYSTEMS; ESTIMATION; GAUSSIAN NOISE (ELECTRONIC); GRADIENT METHODS; MATRIX ALGEBRA; OPTIMIZATION; VECTORS;

DE BRUIJN'S IDENTITY; MINIMUM MEAN-SQUARE ERROR (MMSE); MULTIPLE-INPUT MULTIPLE-OUTPUT (MIMO) CHANNELS; MUTUAL INFORMATION; NONLINEAR ESTIMATION; PRECODER OPTIMIZATION;

INFORMATION THEORY;

EID: 33144485285     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2005.860424     Document Type: Article

References (30)

1. K. H. Lee and D. P. Petersen, "Optimal linear coding for vector channels," IEEE Trans. Commun., vol. COM-24, no. 12, pp. 1283-1290, Dec. 1976.
2. A. J. Stam, "Some inequalities satisfied by the quantities of information of Fisher and Shannon," Inf. Contr., vol. 2, pp. 101-112, Jun. 1959.
3. T. E. Duncan, "On the calculation of mutual information," SIAM J. Applied Math., vol. 19, pp. 215-220, Jul. 1970.
4. T. T. Kadota, M. Zakai, and J. Ziv, "Mutual information of the white Gaussian channel with and without feedback," IEEE Trans. Inf. Theory, vol. IT-17, no. 4, pp. 368-371, Jul. 1971.
5. J. Ziv and M. Zakai, "Some lower bounds on signal parameter estimation," IEEE Trans. Inf. Theory, vol. IT-15, no. 3, pp. 386-391, May 1969.
6. 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.
7. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993.
8. G. Jöngren, M. Skoglund, and B. Ottersen, "Combining beamforming and orthogonal space-time block coding," IEEE Trans. Inf. Theory, vol. 48, no. 3, pp. 611-627, Mar. 2002.
9. D. P. Palomar, J. M. Cioffi, and M. A. Lagunas, "Joint Tx-Rx beamforming design for multicarrier MIMO channels: A unified framework for convex optimization," IEEE Trans. Signal Process., vol. 51, no. 9, pp. 2381-2401, Sep. 2003.
10. J. Salz, "Digital transmission over cross-coupled linear channels," AT&T Tech. J., vol. 64, no. 6, pp. 1147-1159, Jul.-Aug. 1985.
11. J. Yang and S. Roy, "On joint transmitter and receiver optimization for multiple-input-multiple-output (MIMO) transmission systems," IEEE Trans. Commun., vol. 42, no. 12, pp. 3221-3231, Dec. 1994.
12. A. Scaglione, G. B. Giannakis, and S. Barbarossa, "Redundant filterbank precoders and equalizers. Part I: Unification and optimal designs," IEEE Trans. Signal Process., vol. 47, no. 7, pp. 1988-2006, Jul. 1999.
13. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
14. V. V. Prelov and S. Verdú, "Second-order asymptotics of mutual information," IEEE Trans. Inf. Theory, vol. 50, no. 8, pp. 1567-1580, Aug. 2004.
15. J. R. Magnus and H. Neudecker, Matrix Differential Calculus With Applications in Statistics and Econometrics. New York: Wiley, 1999.
16. S. Verdú, "Spectral efficiency in the wideband regime," IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1319-1343, Jun. 2002.
17. N. M. Blachman, "The convolution inequality for entropy powers," IEEE Trans. Inf. Theory, vol. IT-11, no. 2, pp. 267-211, Apr. 1965.
18. M. H. M. Costa, "A new entropy power inequality," IEEE Trans. Inf. Theory, vol. IT-31, no. 6, pp. 751-760, Nov. 1985.
19. A. Dembo, T. M. Cover, and J. A. Thomas, "Information theoretic inequalities," IEEE Trans. Inf. Theory, vol. 37, no. 6, pp. 1501-1518, Nov. 1991.
20. A. Dembo, "Information Inequalities and Uncertainty Principles," Dept. Statistics, Stanford Univ., Stanford, CA, Tech. Rep. 75, Jul. 1990.
21. O. Johnson and Y. Suhov, "Entropy and random vectors," J. Statist. Phys., vol. 104, no. 1-2, pp. 145-165, Jul. 2001.
22. W. Rudin, Principles of Mathematical Analysis, 3rd ed. New York: McGraw-Hill, 1976.
23. H. V. Poor, An Introduction to Signal Detection and Estimation, 2nd ed. New York: Springer-Verlag, 1994.
24. M. S. Pinsker, V. V. Prelov, and S. Verdú, "Sensitivity of channel capacity," IEEE Trans. Inf. Theory, vol. 41, no. 6, pp. 1877-1888, Nov. 1995.
25. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods. Englewood Cliffs, NJ: Prentice-Hall, 1989.
26. D. P. Bertsekas, Nonlinear Programming, 2nd ed. Belmont, MA: Athena Scientific, 1999.
27. S. Haykin, Adaptive Filter Theory, 4th ed. Upper Saddle River, NJ: Prentice-Hall, 2002.
28. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
29. D. H. Brandwood, "A compex gradient operator and its application in adaptive array theory," Proc. Inst. Elec. Eng., vol. 130, no. 1, pp. 11-16, Feb. 1983.
30. P. Billingsley, Probability and Measure, 3rd ed. New York: Wiley, 1995.