6 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
Achievability of Nonlinear Degrees of Freedom in Correlatively Changing Fading Channels
A new approach toward the noncoherent communications over the time varying
fading channels is presented. In this approach, the relationship between the
input signal space and the output signal space of a correlatively changing
fading channel is shown to be a nonlinear mapping between manifolds of
different dimensions. Studying this mapping, it is shown that using nonlinear
decoding algorithms for single input-multiple output (SIMO) and multiple input
multiple output (MIMO) systems, extra numbers of degrees of freedom (DOF) are
available. We call them the nonlinear degrees of freedom
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
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 il larger or equal to 2Q - 1 and the channel correlation matrix satisfies mild technical conditions. The main technical tool used to prove our result is Hironaka\u27s celebrated theorem on resolution of singularities in algebraic geometry