5 research outputs found
Noncoherent SIMO Pre-Log via Resolution of Singularities
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 \geq 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.Comment: IEEE International Symposium on Information Theory 2011 (ISIT 2011),
Saint Petersburg, Russia, to appea
High-SNR Capacity of Wireless Communication Channels in the Noncoherent Setting: A Primer
This paper, mostly tutorial in nature, deals with the problem of
characterizing the capacity of fading channels in the high signal-to-noise
ratio (SNR) regime. We focus on the practically relevant noncoherent setting,
where neither transmitter nor receiver know the channel realizations, but both
are aware of the channel law. We present, in an intuitive and accessible form,
two tools, first proposed by Lapidoth & Moser (2003), of fundamental importance
to high-SNR capacity analysis: the duality approach and the escape-to-infinity
property of capacity-achieving distributions. Furthermore, we apply these tools
to refine some of the results that appeared previously in the literature and to
simplify the corresponding proofs.Comment: To appear in Int. J. Electron. Commun. (AE\"U), Aug. 201
Capacity Pre-Log of Noncoherent SIMO Channels via Hironaka's Theorem
We find the capacity pre-log of a temporally correlated Rayleigh block-fading
SIMO channel in the noncoherent setting. It is well known that for block-length
L and rank of the channel covariance matrix equal to Q, the capacity pre-log in
the 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 in the large-L limit, even if Q/L remains constant as
L goes to infinity. 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