Research Article

# An integral formula for large random rectangular matrices and its application to analysis of linear vector channels

@INPROCEEDINGS{10.4108/ICST.WIOPT2008.3087, author={Yoshiyuki Kabashima}, title={An integral formula for large random rectangular matrices and its application to analysis of linear vector channels}, proceedings={1st International ICST Workshop on Physics Inspired Paradigms for Wireless Communications and Network}, publisher={IEEE}, proceedings_a={PHYSCOMNET}, year={2008}, month={8}, keywords={Communication channels Computational intelligence Decoding Degradation Eigenvalues and eigenfunctions Magnetic analysis Magnetic noise Random variables Symmetric matrices Vectors}, doi={10.4108/ICST.WIOPT2008.3087} }

- Yoshiyuki Kabashima

Year: 2008

An integral formula for large random rectangular matrices and its application to analysis of linear vector channels

PHYSCOMNET

IEEE

DOI: 10.4108/ICST.WIOPT2008.3087

## Abstract

A statistical mechanical framework for analyzing random linear vector channels is presented in a large system limit. The framework is based on the assumptions that the left and right singular value bases of the rectangular channel matrix H are generated independently from uniform distributions over Haar measures and the eigenvalues of HTH asymptotically follow a certain specific distribution. These assumptions make it possible to characterize the communication performance of the channel utilizing an integral formula with respect to H, which is analogous to the one introduced by Marinari et. al. in J. Phys. A 27, 7647 (1994) for large random square (symmetric) matrices. A computationally feasible algorithm for approximately decoding received signals based on the integral formula is also provided.