Correlation Matrices Design in the Spatial Multiplexing Systems

Sunil Chinnadurai; Poongundran Selvaprabhu; Abdul Latif Sarker

doi:doi:10.11648/j.dmath.20170201.15

| Peer-Reviewed

Correlation Matrices Design in the Spatial Multiplexing Systems

Sunil Chinnadurai, Poongundran Selvaprabhu, Abdul Latif Sarker

Published in International Journal of Discrete Mathematics (Volume 2, Issue 1)

Received: 13 January 2017 Accepted: 6 February 2017 Published: 24 February 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Channel correlation is closely related to the capacity of the multiple-input multiple-output (MIMO) correlated channel. Indeed, the high correlated channel degrades the system performance and the quality of wireless communication systems in terms of the capacity. Thus, we design an inverse-orthogonal matrix such as Toeplitz-Jacket matrix to design transmit and receive correlation matrices to mitigate the channel correlation of the MIMO systems. The numerical and simulation results are performed for both uncorrelated and correlated channel capacities in the case of single sided fading correlations.

Published in	International Journal of Discrete Mathematics (Volume 2, Issue 1)
DOI	10.11648/j.dmath.20170201.15
Page(s)	20-30
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Transmit and Receive Correlation Matrices, The Correlated MIMO Channel, Inverse-Orthogonal Matrices Toeplitz -Jacket Matrices, The Channel Capacity, The Spatial Correlation

References

[1]	D. Gesbert, M. Shafi, D. S. Shiu, P. J. Smith, A. Naguib, “From theory to practice: An overview of MIMO space-time coded wireless systems,” IEEE J. Sel. Areas Communication. Vol. 21, pp. 681–683, 2003.
[2]	G. J. Foschini, M. J. Gans, “Capacity when using diversity at transmits and receives sites and the Rayleigh-faded matrix channel is unknown at the transmitter,” in Proceeding of the Sixth WINLAB Workshop on Third Generation Wireless Information Network, New Jersey, USA, 1996.
[3]	G. J. Foschini, M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Communication, vol. 6, pp. 311-335, 1998.
[4]	F. Rusek, P. Daniel, B. L. Kiong, L. G. Erik, T. L. Marzetta, O. Edfors, F. Tufvesson, “Scaling up MIMO: Opportunities and challenges with Very Large Arrays,” IEEE Signal Processing Magazine, vol.30, pp. 40-60, 2013.
[5]	E. Telatar, “Capacity of Multi-antenna Gaussian Channels. European Transaction on Telecommunications, vol. 10, pp. 585-595, 1999.
[6]	A. Tulino, M. Lozano, S. Verdu, “Impact of antenna correlation on the capacity of multi antenna channels,” IEEE Transaction on Information Theory, vol. 51, pp. 2491–2509, 2005.
[7]	E. A. Jorswieck, H. Boche, “Channel Capacity and Capacity-Range of Beamforming in MIMO Wireless Systems under Correlated Fading with Covariance Feedback,” IEEE Transaction on Wireless Communication, vol. 3, 1543-1553, 2004.
[8]	C. N. Chuah, D. N. C. Tse, J. M. Kahn, “Capacity scaling in MIMO wireless systems under correlated fading,” IEEE Transaction on Information Theory, vol.48, pp. 637-650, 2002.
[9]	D. Shiu, G. J. Foschini, M. J. Gans, J. M. Kahn, “Fading correlation and its effect on the capacity of multi-element antenna systems,” IEEE Transaction on Communication, vol. 48, pp. 502-513, 2000.
[10]	J. P. Kermoal, L. Schumacher, K. I. Pedersen, P. E. Mogensen, F. Frederik-Sen, “A Stochastic MIMO Radio Channel Model with Experimental Validation,” IEEE Journal on Selected Area in Communications, vol.20, pp. 1211-1226, 2002.
[11]	D. P. McNamara, M. A. Beach, P. N. Fletcher, “Spatial correlation in indoor MIMO channels,” in Proceeding of the 13^th IEEE International Symposium of Personal, Indoor and Mobile Radio Communications, IEEE, Lisbon, Portugal, vol.1, 2002, pp. 290–294.
[12]	K. I. Pedersen, J. B. Andersen, J. P. Kermoal, P. E. Mogensen, “A stochastic multiple-input-multiple-output radio channel model for valuation of space–time coding algorithms,” In Proceeding of the 52^th IEEE Vehicular Technology Conference-Fall, Boston, MA, USA, vol. 2, 2002, pp. 893–897.
[13]	D. Gesbert, H. Bölcskei, D. A. Gore, A. J. Paulraj, “Outdoor MIMO wireless channels: Models and performance prediction,” IEEE Transaction on Communication, vol. 50, pp. 1926–1934, 2002.
[14]	K. Yu, M. Bengtsson, B. Ottersten, D. McNamara, P. Karlsson, M. Beach, “A wideband statistical model for NLOS indoor MIMO channels,” In Proceeding of the IEEE Vehicular Technology Conference-spring, Birmingham, AL., vol. 1, 2002, pp. 370–374.
[15]	M. T. Ivrlac, W. Utschick, J. A. Nossek, “Fading correlations in wireless MIMO communication systems,” IEEE Journal of Selected Areas Communication, vol. 21, pp. 819–828, 2003.
[16]	A. F. Molisch, J. R. Foerster, M. Pendergrass, “Channel models for ultra-wideband personal area networks,” IEEE Wireless Communication, vol.10, pp. 14–21, 2003.
[17]	G. G. Raleigh, M. C. John, “Spatio-Temporal Coding for Wireless Communication,” IEEE Transactions on Communications, vol.46, pp. 357-366 1998.
[18]	D. Chizhik, F. Farrokhi, J. Ling, A. Lozano, “Effect of antenna separation on the capacity of BLAST in correlated channels,” IEEE Communication Letter, vol.4, pp. 337–339, 2000.
[19]	W. C. Y. Lee, Y. S. Yen, “Polarization diversity system for mobile radio,” IEEE Transaction on Communication,” vol.20, pp. 912–923, 1972.
[20]	S. A. Bergmann, H. W. Arnold, “Polarization diversity in portable communications environment,” Electronics Letters, vol. 22, pp. 609–610, 1986.
[21]	R. M. Gray, “Toeplitz and Circulant Matrices: A review,” Foundation and Trends in Communication and Information Theory, vol. 2, pp. 155-239, 2006.
[22]	S. Gilbert, “Essays in Linear Algebra: Toeplitz matrices and Circulant,” Cambridge University Press, UK: 2012, pp. 94–100.
[23]	M. H. Lee, “The Center Weighted Hadamard Transform,” IEEE Transaction on Circuits and Systems, vol. 36, pp. 1247-1249, 1989.
[24]	M. H. Lee, “A New Reverse Jacket Transform based on Hadamard matrix,” IEEE International Symposium on Information Theory, Sorrento, Italy, 25-30 pp. 471, June 2000.
[25]	K. J. Horadam, Hadamard Matrices and Their Applications, Princeton University Press, Princeton: NJ, 2007.
[26]	S. Ferenc, Construction, “Classification and Parametrization of Complex Hadamard Matrices,” PhD Thesis, Central European University, Budapest, Hungary, 2011.
[27]	A. M. Sayeed, “Deconstructing multi antenna fading channels,” IEEE Transaction on Signal Processing, vol. 50, pp. 2563–2579, 2002.
[28]	S. Haykin, Adaptive Filter Theory, Upper Saddle River, NJ: Prentice-Hall, 1991.
[29]	M. H. Lee, “A New Reverse Jacket Transform and Its Fast Algorithm,” IEEE Transaction on circuits and Systems II, vol. 47, pp. 39-47, 2000.
[30]	M. H. Lee, S. Ferenc, “A Note on Inverse-Orthogonal Toeplitz Matrices,” Electronic Journal of Linear of Linear Algebra, vol. 26, pp. 898-904, 2013.
[31]	P. Dit¸˘a, “One method for construction of inverse orthogonal matrices,” Romanian Journal of Physical, vol. 54, pp. 433–440, 2009.
[32]	K. Nomura, “Type II matrices of size five,” Graphs Combin. Vol. 15, pp. 79–92 1999.
[33]	M. H. Lee, X. D. Zhang, X. Jiang, “Fast Parametric Reciprocal-Orthogonal Jacket Transforms,” EURASIP Journal on Advanced in Signal Processing, 2014: doi: 10.1186/1687-6180-2014-149.
[34]	U. Haagerup, Orthogonal maximal abelian *-subalgebras of the n × n matrices and cyclic n-roots. In: S. Doplicher et al. (editors), Operator Algebras and Quantum Field Theory (Rome), MA International Press: Cambridge, 1996, pp. 296–322.
[35]	M, Kolountzakis, M. Matolcsi, “Complex Hadamard matrices and the spectral set conjecture,” Collectanea Mathematica, vol. 57, pp. 281–291, 2006.
[36]	S. Wagner, S. Sesia, D. T. M. Slock, “Unitary beamforming under constant modulus constraint in MIMO broadcast channels,” in proceeding of the 10th IEEE International Workshop on Signal Processing Advances in Wireless Communications, Perugia, Italy, 2009.
[37]	T. M. Cover, A. J. Thomas, Element of Information Theory, John Wiley & Sons, Inc., Publication: 2nd ed., Ch.7, 2006, pp.183-240.
[38]	S. C. Young, J. Kim, W. Y. Yang, C. G. Kang, MIMO-OFDM Wireless Communications with MatLab, John Wiley and Sons (Asia) Pte. Ltd., Ch.9, 2010, pp. 266-280.
[39]	T. H. Hon, “Influence of Antenna Characteristic on MIMO with Compact Monopole Arrays,” IEEE Antenna and Wireless Propagation Letters, vol.8, pp.133-136, 2009.
[40]	J. W. Wallace, A. J. Michael, “Modeling the Indoor MIMO Wireless Channel. IEEE Transaction on Antenna and Propagation,” vol.50, pp. 591-599, 2002.
[41]	T. H. Hon, X. Wang, “Building Antenna Characteristics into Multiple-Input and Multiple-Output Channel Simulation,” International Journal of Electronics, vol. 97, pp.703-7014, 2010.

Cite This Article

Plain Text BibTeX RIS

APA Style

Sunil Chinnadurai, Poongundran Selvaprabhu, Abdul Latif Sarker. (2017). Correlation Matrices Design in the Spatial Multiplexing Systems. International Journal of Discrete Mathematics, 2(1), 20-30. https://doi.org/10.11648/j.dmath.20170201.15

Copy | Download

ACS Style

Sunil Chinnadurai; Poongundran Selvaprabhu; Abdul Latif Sarker. Correlation Matrices Design in the Spatial Multiplexing Systems. Int. J. Discrete Math. 2017, 2(1), 20-30. doi: 10.11648/j.dmath.20170201.15

Copy | Download

AMA Style

Sunil Chinnadurai, Poongundran Selvaprabhu, Abdul Latif Sarker. Correlation Matrices Design in the Spatial Multiplexing Systems. Int J Discrete Math. 2017;2(1):20-30. doi: 10.11648/j.dmath.20170201.15

Copy | Download

@article{10.11648/j.dmath.20170201.15,
  author = {Sunil Chinnadurai and Poongundran Selvaprabhu and Abdul Latif Sarker},
  title = {Correlation Matrices Design in the Spatial Multiplexing Systems},
  journal = {International Journal of Discrete Mathematics},
  volume = {2},
  number = {1},
  pages = {20-30},
  doi = {10.11648/j.dmath.20170201.15},
  url = {https://doi.org/10.11648/j.dmath.20170201.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170201.15},
  abstract = {Channel correlation is closely related to the capacity of the multiple-input multiple-output (MIMO) correlated channel. Indeed, the high correlated channel degrades the system performance and the quality of wireless communication systems in terms of the capacity. Thus, we design an inverse-orthogonal matrix such as Toeplitz-Jacket matrix to design transmit and receive correlation matrices to mitigate the channel correlation of the MIMO systems. The numerical and simulation results are performed for both uncorrelated and correlated channel capacities in the case of single sided fading correlations.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Correlation Matrices Design in the Spatial Multiplexing Systems
AU  - Sunil Chinnadurai
AU  - Poongundran Selvaprabhu
AU  - Abdul Latif Sarker
Y1  - 2017/02/24
PY  - 2017
N1  - https://doi.org/10.11648/j.dmath.20170201.15
DO  - 10.11648/j.dmath.20170201.15
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 20
EP  - 30
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20170201.15
AB  - Channel correlation is closely related to the capacity of the multiple-input multiple-output (MIMO) correlated channel. Indeed, the high correlated channel degrades the system performance and the quality of wireless communication systems in terms of the capacity. Thus, we design an inverse-orthogonal matrix such as Toeplitz-Jacket matrix to design transmit and receive correlation matrices to mitigate the channel correlation of the MIMO systems. The numerical and simulation results are performed for both uncorrelated and correlated channel capacities in the case of single sided fading correlations.
VL  - 2
IS  - 1
ER  -

Copy | Download

Author Information

Sunil Chinnadurai

Department of Electronics Engineering, Chonbuk National University, Jeonju, Republic of Korea
Poongundran Selvaprabhu

Department of Electronics Engineering, Chonbuk National University, Jeonju, Republic of Korea
Abdul Latif Sarker

Department of Electronics Engineering, Chonbuk National University, Jeonju, Republic of Korea

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Sunil Chinnadurai, Poongundran Selvaprabhu, Abdul Latif Sarker. (2017). Correlation Matrices Design in the Spatial Multiplexing Systems. International Journal of Discrete Mathematics, 2(1), 20-30. https://doi.org/10.11648/j.dmath.20170201.15

Copy | Download

ACS Style

Sunil Chinnadurai; Poongundran Selvaprabhu; Abdul Latif Sarker. Correlation Matrices Design in the Spatial Multiplexing Systems. Int. J. Discrete Math. 2017, 2(1), 20-30. doi: 10.11648/j.dmath.20170201.15

Copy | Download

AMA Style

Sunil Chinnadurai, Poongundran Selvaprabhu, Abdul Latif Sarker. Correlation Matrices Design in the Spatial Multiplexing Systems. Int J Discrete Math. 2017;2(1):20-30. doi: 10.11648/j.dmath.20170201.15

Copy | Download

@article{10.11648/j.dmath.20170201.15,
  author = {Sunil Chinnadurai and Poongundran Selvaprabhu and Abdul Latif Sarker},
  title = {Correlation Matrices Design in the Spatial Multiplexing Systems},
  journal = {International Journal of Discrete Mathematics},
  volume = {2},
  number = {1},
  pages = {20-30},
  doi = {10.11648/j.dmath.20170201.15},
  url = {https://doi.org/10.11648/j.dmath.20170201.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170201.15},
  abstract = {Channel correlation is closely related to the capacity of the multiple-input multiple-output (MIMO) correlated channel. Indeed, the high correlated channel degrades the system performance and the quality of wireless communication systems in terms of the capacity. Thus, we design an inverse-orthogonal matrix such as Toeplitz-Jacket matrix to design transmit and receive correlation matrices to mitigate the channel correlation of the MIMO systems. The numerical and simulation results are performed for both uncorrelated and correlated channel capacities in the case of single sided fading correlations.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Correlation Matrices Design in the Spatial Multiplexing Systems
AU  - Sunil Chinnadurai
AU  - Poongundran Selvaprabhu
AU  - Abdul Latif Sarker
Y1  - 2017/02/24
PY  - 2017
N1  - https://doi.org/10.11648/j.dmath.20170201.15
DO  - 10.11648/j.dmath.20170201.15
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 20
EP  - 30
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20170201.15
AB  - Channel correlation is closely related to the capacity of the multiple-input multiple-output (MIMO) correlated channel. Indeed, the high correlated channel degrades the system performance and the quality of wireless communication systems in terms of the capacity. Thus, we design an inverse-orthogonal matrix such as Toeplitz-Jacket matrix to design transmit and receive correlation matrices to mitigate the channel correlation of the MIMO systems. The numerical and simulation results are performed for both uncorrelated and correlated channel capacities in the case of single sided fading correlations.
VL  - 2
IS  - 1
ER  -

Copy | Download