Capacity Pre-Log of Noncoherent SIMO Channels via Hironaka’s Theorem
Journal article, 2013

We find the capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel in the noncoherent setting. It is well known that for blocklength $L$ and rank of the channel covariance matrix equal to $Q$, the capacity pre-log in the single-input single-output (SISO) case is given by $1-Q/L$. Here, $Q/L$ can be interpreted as the pre-log penalty incurred by channel uncertainty. Our main result reveals that, by adding only one receive antenna, this penalty can be reduced to $1/L$ and can, hence, be made to vanish for the blocklength $L\to\infty$, even if $Q/L$ remains constant as $L\to\infty$. Intuitively, even though the SISO channels between the transmit antenna and the two receive antennas are statistically independent, the transmit signal induces enough statistical dependence between the corresponding receive signals for the second receive antenna to be able to resolve the uncertainty associated with the first receive antenna’s channel and thereby make the overall system appear coherent. The proof of our main theorem is based on a deep result from algebraic geometry known as Hironaka’s Theorem on the Resolution of Singularities.

noncoherent capacity


multiple-antenna channels


Veniamin I. Morgenshtern

Stanford University

Erwin Riegler

Vienna University of Technology

Wei Yang

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Giuseppe Durisi

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

Shaowei Lin

Institute for Infocomm Research, A-Star, Singapore

Bernd Sturmfels

University of California

Helmut Bölcskei

Swiss Federal Institute of Technology in Zürich (ETH)

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 59 7 4213-4229 6475182

Areas of Advance

Information and Communication Technology

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