# Capacity Pre-Log of Noncoherent SIMO Channels via Hironaka’s Theorem Artikel i vetenskaplig tidskrift, 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.

multiple-antenna channels

noncoherent capacity

## Författare

### Veniamin I. Morgenshtern

Stanford University

### Erwin Riegler

Technische Universität Wien

### Wei Yang

Chalmers, Signaler och system, Kommunikation, Antenner och Optiska Nätverk, Kommunikationssystem

### Giuseppe Durisi

Chalmers, Signaler och system, Kommunikation, Antenner och Optiska Nätverk, Kommunikationssystem

### Shaowei Lin

Agency for Science, Technology and Research (A*STAR)

### Bernd Sturmfels

University of California

### Helmut Bölcskei

Eidgenössische Technische Hochschule Zürich (ETH)

#### IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 59 7 4213-4229 6475182

### Styrkeområden

Informations- och kommunikationsteknik

### Ämneskategorier

Telekommunikation

### DOI

10.1109/TIT.2013.2251394

2022-04-14