Noncoherent SIMO pre-log via resolution of singularities

Authors

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

Reference

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

DOI: 10.1109/ISIT.2011.6033909

Abstract

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.

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