# MIMO INSTANTANEOUS BLIND IDENTIFICATION BASED ON THIRD-ORDER CUMULANT

### Xizhong Shen, Dachao Hu, Guang Meng

#### Abstract

This paper presents a new MIMO instantaneous blind identification algorithm based on third-order temporal property. Third-order temporal structure is reformulated in a particular way such that each column of the unknown mixing matrix satisfies a system of nonlinear multivariate homogeneous polynomial equations. The nonlinear system is solved by improved steepest descent method. We construct a general goal of the nonlinear system and convert the nonlinear problem into an optimal problem. The optimal solutions are obtained one by one by adding a penalty item to the general goal, which is Gaussian function characterized with valley-filled feature. Our algorithm allows estimating the mixing matrix for scenarios with 3 sources and 2 sensors, etc. Finally, simulations and comparisons show its effectiveness.

#### References

- Cichocki, A., Amari S I. 2002. Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. New York: Wiley.
- van de Laar J, Moonen M, Sommen P C W., 2008. MIMO Instantaneous Blind Identification Based on SecondOrder Temporal Structure. IEEE Transactions on Signal Processing. Volume 56, Issue 9, Sept., Page(s):4354 - 4364
- Shen Xizhong, Hu Dachao, and Meng Guang., 2009. MIMO Instantaneous Blind Identification Based on Steepest Descent Method. SIGMAP 2009. Accepted
- Richard L. Burden; J. Douglas Faires., 2001. Numerical Analysis. Thomson Learning, Inc., pp: 628-635.
- Byrne, C., 2008. Sequential unconstrained minimization algorithms for constrained optimization, Inverse Problems, Vol. 24, pp. 1-27.
- N. D. Sidiropoulos and R. Bro., 2000. On the uniqueness of multilinear decomposition of N-way arrays. J. Chemometrics, vol. 14, pp. 229-239.
- Horn R A, Johnson C R., 1985. Matrix Analysis, Cambridge University Press.

#### Paper Citation

#### in Harvard Style

Shen X., Hu D. and Meng G. (2010). **MIMO INSTANTANEOUS BLIND IDENTIFICATION BASED ON THIRD-ORDER CUMULANT** . In *Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2010)* ISBN 978-989-674-018-4, pages 127-132. DOI: 10.5220/0002581401270132

#### in Bibtex Style

@conference{biosignals10,

author={Xizhong Shen and Dachao Hu and Guang Meng},

title={MIMO INSTANTANEOUS BLIND IDENTIFICATION BASED ON THIRD-ORDER CUMULANT},

booktitle={Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2010)},

year={2010},

pages={127-132},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002581401270132},

isbn={978-989-674-018-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2010)

TI - MIMO INSTANTANEOUS BLIND IDENTIFICATION BASED ON THIRD-ORDER CUMULANT

SN - 978-989-674-018-4

AU - Shen X.

AU - Hu D.

AU - Meng G.

PY - 2010

SP - 127

EP - 132

DO - 10.5220/0002581401270132