# FIXED POINT SVD COMPUTATION ERROR CHARACTERIZATION AND PERFORMANCE LOSSSES IN MIMO SYSTEMS

### César Benavente-Peces, Andreas Ahrens, José M. Pardo-Martín, Fco. Javier Ortega-González

#### Abstract

This paper is devoted to analyze the error met when computing the singular value decomposition (SVD) of the gain channel matrix in a MIMO communication system and using fixed-point arithmetic for the calculations. The study is focused in the case of the SVD implementation for modulation-mode and power assignment in non-frequency selective MIMO, and M-ary Quadrature Amplitude Modulation (QAM). It is demonstrated that not necessarily all MIMO layers must be activated. The combination of the CORDIC algorithm and look-up tables seems to be a good solution for this task since it can efficiently compute the singular value decomposition. The paper highlights the characterization of computation errors and shows the performance losses produced by the use of approximations in the eigenvalues and eigenvectors calculation, including the effects produced in the power assignment process.

#### References

- Kühn, V., 2006. Wireless Communications over MIMO Channels - Applications to CDMA and Multiple Antenna Systems. Chichester: Wiley.
- Zheng, L. and Tse, D. N. T., 2003. “Diversity and Multiplexing: A Fundamental Tradeoff in MultipleAntenna Channels”, IEEE Transactions on Information Theory, vol. 49, no. 5, pp. 1073-1096, May.
- Ahrens, A. and Lange, C., 2008. “Modulation-Mode and Power Assignment in SVD-equalized MIMO Systems.” Facta Universitatis (Series Electronics and Energetics), vol. 21, no. 2, pp. 167-181, August.
- Benavente-Peces, C., Ahrens, A., Arriero-Encinas, L. and Lange, C., 2008 ”Implementation Analysis of SVD for Modulation-Mode and Power Assignment in MIMO Systems”, 7th IASTED International Conference on Communications Systems and Networks (CSN), Palma de Mallorca ( Spain), 01-03 September.
- Ahrens, A. and Lange, C., 2007. Transmit Power Allocation in SVD Equalized Multicarrier Systems, International Journal of Electronics and Communications (AEÜ), 61 (1), pp 51-61.

#### Paper Citation

#### in Harvard Style

Benavente-Peces C., Ahrens A., M. Pardo-Martín J. and Javier Ortega-González F. (2009). **FIXED POINT SVD COMPUTATION ERROR CHARACTERIZATION AND PERFORMANCE LOSSSES IN MIMO SYSTEMS** . In *Proceedings of the International Conference on Wireless Information Networks and Systems - Volume 1: WINSYS, (ICETE 2009)* ISBN 978-989-674-008-5, pages 91-94. DOI: 10.5220/0002188800910094

#### in Bibtex Style

@conference{winsys09,

author={César Benavente-Peces and Andreas Ahrens and José M. Pardo-Martín and Fco. Javier Ortega-González},

title={FIXED POINT SVD COMPUTATION ERROR CHARACTERIZATION AND PERFORMANCE LOSSSES IN MIMO SYSTEMS},

booktitle={Proceedings of the International Conference on Wireless Information Networks and Systems - Volume 1: WINSYS, (ICETE 2009)},

year={2009},

pages={91-94},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002188800910094},

isbn={978-989-674-008-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Wireless Information Networks and Systems - Volume 1: WINSYS, (ICETE 2009)

TI - FIXED POINT SVD COMPUTATION ERROR CHARACTERIZATION AND PERFORMANCE LOSSSES IN MIMO SYSTEMS

SN - 978-989-674-008-5

AU - Benavente-Peces C.

AU - Ahrens A.

AU - M. Pardo-Martín J.

AU - Javier Ortega-González F.

PY - 2009

SP - 91

EP - 94

DO - 10.5220/0002188800910094