New space-time block codes from spectral norm
Autoři:
Carlos A. R. Martins aff001; Mauro Luiz Brandão, Jr. aff002; Eduardo Brandani da Silva aff003
Působiště autorů:
Department of Mathematics, UTFPR, Pato Branco, PR, Brazil
aff001; Department of Electrical Engeneering, State University of Maringá, Maringá, PR 87020-900, Brazil
aff002; DMA - UEM, Avenida Colombo 5790 - Campus Universitário, 87020-900-Maringá-PR, Brazil
aff003
Vyšlo v časopise:
PLoS ONE 14(9)
Kategorie:
Research Article
doi:
https://doi.org/10.1371/journal.pone.0222708
Souhrn
Current research proposes a natural environment for space-time codes and a new design criterion is obtained for space-time block codes in multi-antenna communication channels. The objective of this criterion is to minimize the pairwise error probability of the maximum likelihood decoder, endowed with the matrix spectral norm. The random matrix theory is used and an approximation function for the probability density function for the largest eigenvalue of a Wishart Matrix is obtained.
Klíčová slova:
Eigenvalues – Graphs – Information theory – Probability theory – Block codes – Antennas – Signal decoders – Probability density
Zdroje
1. Shannon C. Mathematical theory of communications. Bell Systems Tech J. 1948;27: 379–423, 623–656. doi: 10.1002/j.1538-7305.1948.tb01338.x
2. Foschini GJ and Gans MJ. On limits of wireless communications in a fading environment when using multiple antennas. Wirel Pers Commun. 1998;6: 311–335. doi: 10.1023/A:1008889222784
3. Telatar IE. Capacity of multi-antenna Gaussian channels. European Trans on Telecomm. 1999;10(6): 585–595. doi: 10.1002/ett.4460100604
4. Tarokh V, Seshadri N and Calderbank AR. Space-time codes for high data rate wireless communication: Performance Criterion and Code Construction. IEEE Trans Inf Theory. 1998;44(2): 744–765. doi: 10.1109/18.661517
5. Alamouti SM. A simple transmit diversity technique for wireless communications. IEEE J Sel Top Comm. 1998;16(8): 1451–1458. doi: 10.1109/49.730453
6. Tarokh V, Jafarkani H and Calderbank AR. Space-time block codes from orthogonal designs. IEEE Trans Inf Theory. 1999;45(5): 1456–1467. doi: 10.1109/18.771146
7. Yuan J, Chen Z and Vucetic B. Performance and design of space-time Coding in fading channels. IEEE Trans Commun. 2003;51(12): 1991–1996. doi: 10.1109/TCOMM.2003.820741
8. Tirkkonen O and Hottinen A. Square-matrix embeddable space-time block codes for complex signal constellations. IEEE Trans Inf Theory. 2002;48(2): 384–395. doi: 10.1109/18.978740
9. Wishart J. The generalized product moment distribution in samples from a normal multivariate population. Biometrika 1928;20A: 32–43. doi: 10.1093/biomet/20A.1-2.32
10. Wigner EP. On the Statistical distribution of the widths and spacings of nuclear resonance levels. Proc Camb Philos Soc. 1951;47: 790–798. doi: 10.1017/S0305004100027237
11. Wigner EP. Characteristic vectors of bordered matrices with infinite dimensions. Ann Math. 1955;62: 548–564. doi: 10.2307/1970079
12. Wigner EP. On the distribution of the roots of certain symmetric matrices. Ann Math. 1958;67: 325–327. doi: 10.2307/1970008
13. Dyson F. A Brownian-motion model for the eigenvalues of a random matrix. J Math Phys. 1962;3: 1191–1198. doi: 10.1063/1.1703862
14. Dyson F. Statistical theory of the energy levels of complex systems, I-III. J Math Phys. 1962;3: 140–156, 157–165, 166–175. doi: 10.1063/1.1703773
15. Dyson F. The threefoldway algebraic structure of symmetry groups and ensembles in quantum mechanics. J Math Phys. 1962;3: 1199–1215. doi: 10.1063/1.1703863
16. Tao T and Vu V. Random Matrices: the distribution of the smallest singular values. Geom Funct Anal. 2010;20: 260–297. doi: 10.1007/s00039-010-0057-8
17. Tao T and Vu V. The Wigner-Dyson-Mehta bulk universality conjecture for Wigner Matrices. Electron J Probab. 2011;16: 2104–2121. doi: 10.1214/EJP.v16-944
18. Tao T and Vu V. Random Matrices: Universality of local eigenvalue statistics. Acta Math. 2011;206: 127–204. doi: 10.1007/s11511-011-0061-3
19. Tao T and Vu V. A Central limit theorem for the determinant of a Wigner matrix. Adv Math. 2012;231(1): 74–101. doi: 10.1016/j.aim.2012.05.006
20. Forrester PJ. Log-gases and random matrices. Princeton. Princeton University Press, 2010.
21. Tulino AM and Verdú S. Random matrix theory and wireless communications. Foundations and Trends in Communications and Information Theory, 2004. doi: 10.1561/0100000001
22. Hsu PL. On the distribution of the roots of certain determinantal equations. Ann Eugen. 1939;9: 250–258. doi: 10.1111/j.1469-1809.1939.tb02212.x
23. Jonsson D. Some limit theorems for the eigenvalue of a sample covariance matrix. J Multivar Anal. 1982;12: 1–38. doi: 10.1016/0047-259X(82)90080-X
24. Marcenko VA and Pastur LA. Distributions of eigenvalues for some sets of random matrices. Math USSR-Sb. 1967;1: 457–483. doi: 10.1070/SM1967v001n04ABEH001994
25. Trotter HF. Eigenvalue distributions of large hermitian matrices Wigner semi-circle law and theorem of Kac, Murdock and Szego. Adv Math.1984;54: 67–82. doi: 10.1016/0001-8708(84)90037-9
26. Wachter KW. The strong limits of random matrix spectra for sample matrices of independent elements. Ann Probab. 1978;6: 1–18. doi: 10.1214/aop/1176995607
27. German S. A limit theorem for the norm of random matrices. Ann Probab. 1980;8: 252–261. doi: 10.1214/aop/1176994775
28. Sugiyama T. On the distribution of the largest root of the covariance matrix. Ann Math Stat. 1967;38, 1148–1151. doi: 10.1214/aoms/1177698783
29. Krishnaiah PR and Cheng TC. On the exact distribution of the smallest roots of the Wishart Matrix using zonal polynomials. Ann Inst Stat Math. 1971;23: 293–295. doi: 10.1007/BF02479230
30. Silverstein JW. The smallest eigenvalue of a large-dimensional Wishart Matrix. Ann Probab. 1985;13: 1364–1368. doi: 10.1214/aop/1176992819
31. Vlok JD. Analytic approximation to the largest eigenvalue distribution of a white Wishart matrix. IET Comm. 2012;6(12): 1804–1811. doi: 10.1049/iet-com.2011.0843
32. Chiani M. Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution. J Multivar Anal. 2014;129: 69–81. doi: 10.1016/j.jmva.2014.04.002
33. Alfano G, Lozano A, Tulino AM and S. Verdú. Mutual information and eigenvalue distribution of MIMO rician channels. International Symposium on Information Theory and its Applications, ISITA, 2004.
34. Chiani M, Win MZ and Zanella A. On the capacity of spatially correlated MIMO Rayleigh fading channels. IEEE Trans Inf Theory. 2003;49(10): 2363–2371. doi: 10.1109/TIT.2003.817437
35. Ahmadi A. A new approach to fast decode quasi-orthogonal space-time block codes. IEEE Trans Wirel Commun. 2015;14(1): 165–176. doi: 10.1109/TWC.2014.2334615
36. Raleigh GG and Cioffi JM. Spatio-temporal coding for wireless communication. IEEE Trans Commun. 1998;46(3): 357–366. doi: 10.1109/26.662641
37. Gesbert D, Kountouris M, Heath RW Jr, Chae C and Chae T. Shifting the MIMO paradigm. IEEE Signal Process Mag. 2007;24(5): 36–46. doi: 10.1109/MSP.2007.904815
38. Caire G and Shamai S. On the achievable throughput of a multi-antenna gaussian broadcast channel. IEEE Trans Inf Theory. 2003;49(7): 1691–1706. doi: 10.1109/TIT.2003.813523
39. Viswanath P and Tse DNC. Sum capacity of a vector gaussian broadcast channel and uplink-downlink duality. IEEE Trans Inf Theory. 2003;49(8): 1912–1921. doi: 10.1109/TIT.2003.814483
40. Vishwanath S, Jindal N and Goldsmith A. Duality, achievable rates, sum-rate capacity of gaussian MIMO broadcast channels. IEEE Trans Inf Theory. 2003;49(10): 658–668. doi: 10.1109/TIT.2003.817421
41. Larsson EG, Tufvesson F, Edfors O and Marzetta TL. Massive MIMO for next generation wireless systems. IEEE Commun Mag. 2014;52(2): 186–195. doi: 10.1109/MCOM.2014.6736761
42. Marzetta TL. How much training is required for multiuser MIMO. Proc. 40th Asilomar Conf. Signals, Syst., Comput., Nov. 2006; 359–363.
43. Marzetta TL. Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Trans Wirel Commun. 2010;9(1): 3590–3600. doi: 10.1109/TWC.2010.092810.091092
44. Rusek F, Persson D, Lau BK, Larsson EG, Marzetta TL, Edfors O, et al. Scaling up MIMO: opportunities and challenges with very large arrays. IEEE Signal Process Mag. 2013;30(1): 40–60. doi: 10.1109/MSP.2011.2178495
45. Björnson E, Hoydis J and Sanguinetti L. Massive MIMO has unlimited capacity. IEEE Trans Wirel Commun. 2018;17(1): 574–590. doi: 10.1109/TWC.2017.2768423
46. Vucetic B and Yuan J. Space-time coding. Wiley, 2003.
47. Horn RA and Johnson CR. Matrix analysis. Cambridge University Press, 1990.
48. Edelman A. Eigenvalues and condition numbers of random matrices. SIAM J Matrix Anal Appl. 1988;9(4): 543–560. doi: 10.1137/0609045
49. Zanella A and Chiani M. The PDF of the Ith largest eigenvalue of central Wishart matrices and its application to the performance analysis of MIMO channels. GLOBECOM, New Orleans, 2008.
50. Zanella A, Chiani M and Win MZ. On the marginal distribution of the eigenvalues of Wishart Matrices. IEEE Trans Commun. 2009;57(4): 1050–1060. doi: 10.1109/TCOMM.2009.04.070143
51. Biglieri E. Coding for wireless channels. Springer, 2005.
52. Jafarkhani H. A quasi-orthogonal space-time block code. IEEE Trans Commun. 2001;49(1): 1–4. doi: 10.1109/26.898239
53. Hughes BL. Optimal space-time constellations from groups. IEEE Trans Inf Theory. 2003;49(2): 401–410. doi: 10.1109/TIT.2002.807283
54. Grover R, Su W and Pados DA. An 8 × 8 quasi-orthogonal STBC form for transmissions over eight or four antennas. IEEE Trans Wirel Commun. 2008;7(12): 4777–4785. doi: 10.1109/T-WC.2008.070791
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