Noncoherent SIMO pre-log via resolution of singularities


Erwin Riegler, Veniamin I. Morgenshtern, Giuseppe Durisi, Shaowei Lin, Bernd Sturmfels, and Helmut Bölcskei


Proc. of IEEE International Symposium on Information Theory (ISIT), St. Petersburg, Russia, pp. 2020-2024, Aug. 2011.

DOI: 10.1109/ISIT.2011.6033909

[BibTeX, LaTeX, and HTML Reference]


We establish a lower bound on the noncoherent capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel. Our result holds for arbitrary rank Q of the channel correlation matrix, arbitrary block-length L > Q, and arbitrary number of receive antennas R, and includes the result in Morgenshtern et al. (2010) as a special case. It is well known that the capacity pre-log for this channel in the single-input single-output (SISO) case is given by 1−Q/L, where Q/L is the penalty incurred by channel uncertainty. Our result reveals that this penalty can be reduced to 1/L by adding only one receive antenna, provided that L ≥ 2Q − 1 and the channel correlation matrix satisfies mild technical conditions. The main technical tool used to prove our result is Hironaka’s celebrated theorem on resolution of singularities in algebraic geometry.

Download this document:


Copyright Notice: © 2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.