Copula techniques in wireless communications

Abstract

Copula techniques were originally developed as a method for modelling data dependence in financial applications and are proving useful in many other fields. We show how the Copula concept may be exploited to model dependence in wireless communications problems. In particular we consider multipath correlation, with signal fading, in a wireless propagation medium. The Copula approach is also considered for the purpose of separating signals that have become dependent in such propagation scenarios and we investigate methods for Blind Source Separation that provide alternatives to the popular Independent Component Analysis approach. Our approach to the Blind Source Separation problem forms an objective function based on the copula parameter of the dependence structure, then a transformation is sought which inverts the function producing the dependence and which yields an independent copula. This approach has the potential to provide a robust and easily applied technique for isolating wireless communications signals in a wide range of propagation scenarios. References M.-S. Alouini, A. Abdi, and M. Kaveh. Sum of gamma variates and performance of wireless communication systems over Nakagami-fading channels. Vehicular Technology, IEEE Transactions on, 50(6):1471--1480, November 2001. doi:10.1109/25.966578 N. C. Beaulieu and C. Cheng. an efficient procedure for Nakagami-m fading simulation. In Global Telecommunications Conference, 2001. GLOBECOM '01. IEEE, volume 6, pages 3336--3342, November 2001. doi:10.1109/GLOCOM.2001.966304 Ray-Bing Chen, Meihui Guo, Wolfgang Hardle, and Shih-Feng Huang. Independent component analysis via copula techniques. SFB 649 Discussion Papers SFB649DP2008-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany, January 2008. http://ideas.repec.org/p/hum/wpaper/sfb649dp2008-004.html David Christensen. Fast algorithms for the calculation of Kendall's $\tau $. Computational Statistics, 20(1):51--62, March 2005. doi:10.1007/BF02736122 P. Dita. Factorization of unitary matrices. Journal of Physics A: Mathematical and General, 36(11):2781--2789, March 2003. doi:10.1088/0305-4470/36/11/309 A. Hyvarinen. Fast and robust fixed-point algorithms for independent component analysis. Neural Networks, IEEE Transactions on, 10(3):626--634, May 1999. doi:10.1109/72.761722 Jian Ma and Zengqi Sun. Copula component analysis. CoRR, 2007. http://arxiv.org/abs/cs/0703095 Erik G. Miller and John W. Fisher III. ICA using spacings estimates of entropy. Journal of Machine Learning Research, 4:1271--1295, December 2003. http://jmlr.csail.mit.edu/papers/v4/learned-miller03a.html R. B. Nelsen. An introduction to copulas. Springer-Verlag New York, Inc., 1999. doi:10.1007/0-387-28678-0 P. Tichavsky, Z. Koldovsky, and E. Oja. Performance analysis of the FastICA algorithm and Cramer--Rao bounds for linear independent component analysis. IEEE Trans. on Signal Processing, April 2006. doi:10.1109/TSP.2006.870561 M. D. Yacoub, G. Fraidenraich, and J. C. S. Santos Filho. Nakagami-m phase-envelope joint distribution. Electronics Letters, 41(5):259--261, March 2005. doi:10.1049/el:20057014 Q. T. Zhang. A decomposition technique for efficient generation of correlated nakagami fading channels. Selected Areas in Communications, IEEE Journal on, 18(11):2385--2392, November 2000. doi:10.1109/49.895043