8 research outputs found
Asymptotic Mutual Information Statistics of Separately-Correlated Rician Fading MIMO Channels
Precise characterization of the mutual information of MIMO systems is
required to assess the throughput of wireless communication channels in the
presence of Rician fading and spatial correlation. Here, we present an
asymptotic approach allowing to approximate the distribution of the mutual
information as a Gaussian distribution in order to provide both the average
achievable rate and the outage probability. More precisely, the mean and
variance of the mutual information of the separatelycorrelated Rician fading
MIMO channel are derived when the number of transmit and receive antennas grows
asymptotically large and their ratio approaches a finite constant. The
derivation is based on the replica method, an asymptotic technique widely used
in theoretical physics and, more recently, in the performance analysis of
communication (CDMA and MIMO) systems. The replica method allows to analyze
very difficult system cases in a comparatively simple way though some authors
pointed out that its assumptions are not always rigorous. Being aware of this,
we underline the key assumptions made in this setting, quite similar to the
assumptions made in the technical literature using the replica method in their
asymptotic analyses. As far as concerns the convergence of the mutual
information to the Gaussian distribution, it is shown that it holds under some
mild technical conditions, which are tantamount to assuming that the spatial
correlation structure has no asymptotically dominant eigenmodes. The accuracy
of the asymptotic approach is assessed by providing a sizeable number of
numerical results. It is shown that the approximation is very accurate in a
wide variety of system settings even when the number of transmit and receive
antennas is as small as a few units.Comment: - submitted to the IEEE Transactions on Information Theory on Nov.
19, 2006 - revised and submitted to the IEEE Transactions on Information
Theory on Dec. 19, 200
Living at the Edge: A Large Deviations Approach to the Outage MIMO Capacity
Using a large deviations approach we calculate the probability distribution
of the mutual information of MIMO channels in the limit of large antenna
numbers. In contrast to previous methods that only focused at the distribution
close to its mean (thus obtaining an asymptotically Gaussian distribution), we
calculate the full distribution, including its tails which strongly deviate
from the Gaussian behavior near the mean. The resulting distribution
interpolates seamlessly between the Gaussian approximation for rates close
to the ergodic value of the mutual information and the approach of Zheng and
Tse for large signal to noise ratios . This calculation provides us with
a tool to obtain outage probabilities analytically at any point in the parameter space, as long as the number of antennas is not too
small. In addition, this method also yields the probability distribution of
eigenvalues constrained in the subspace where the mutual information per
antenna is fixed to for a given . Quite remarkably, this eigenvalue
density is of the form of the Marcenko-Pastur distribution with square-root
singularities, and it depends on the values of and .Comment: Accepted for publication, IEEE Transactions on Information Theory
(2010). Part of this work appears in the Proc. IEEE Information Theory
Workshop, June 2009, Volos, Greec
A CLT for Information-theoretic statistics of Gram random matrices with a given variance profile
Consider a random matrix where the entries are
given by the
being centered, independent and identically distributed random
variables with unit variance and
being an array of numbers we shall refer to as a variance profile. We study in
this article the fluctuations of the random variable where is the Hermitian adjoint of and is an
additional parameter. We prove that when centered and properly rescaled, this
random variable satisfies a Central Limit Theorem (CLT) and has a Gaussian
limit whose parameters are identified. A complete description of the scaling
parameter is given; in particular it is shown that an additional term appears
in this parameter in the case where the 4 moment of the
's differs from the 4 moment of a Gaussian random
variable. Such a CLT is of interest in the field of wireless communications
On the capacity achieving covariance matrix for Rician MIMO channels: an asymptotic approach
The capacity-achieving input covariance matrices for coherent block-fading
correlated MIMO Rician channels are determined. In this case, no closed-form
expressions for the eigenvectors of the optimum input covariance matrix are
available. An approximation of the average mutual information is evaluated in
this paper in the asymptotic regime where the number of transmit and receive
antennas converge to . New results related to the accuracy of the
corresponding large system approximation are provided. An attractive
optimization algorithm of this approximation is proposed and we establish that
it yields an effective way to compute the capacity achieving covariance matrix
for the average mutual information. Finally, numerical simulation results show
that, even for a moderate number of transmit and receive antennas, the new
approach provides the same results as direct maximization approaches of the
average mutual information, while being much more computationally attractive.Comment: 56 pp. Extended version of the published article in IEEE Inf. Th.
(march 2010) with more proof
Optimum Receiver Design for MIMO Fading Channels
This thesis describes the analytical design and the performance analysis of optimum receivers for Multiple Input - Multiple Output (MIMO) fading channels. In particular, a novel Optimum Receiver for separately-correlated MIMO channels is proposed. This novel pilot-aided receiver is able to process jointly the pilot symbols, transmitted within each time frame as a preamble, and the information symbols and to decode the transmitted data in a single step, avoiding the explicit estimation of the channel matrix. The optimum receiver is designed for the following two scenarios, corresponding to different transmission schemes and channel models: 1) Narrowband Rician fading MIMO channel with spatial separate correlation; 2) MIMO-OFDM Rician fading channel with space and frequency separate correlation. For each system the performance of the optimum receiver is studied in detail under different channel conditions. The optimum receiver is compared with: - the ideal Genie Receiver, knowing perfectly the Channel State Information (CSI) at no cost; - the standard Mismatched Receiver, estimating the CSI in a first step, then using this imperfect estimate in the ideal channel metric. Since the optimum receiver requires the knowledge of the channel parameters for the decoding process, an estimation algorithm is proposed and tested. Moreover, a complexity analysis is carried out and methods for complexity reduction are proposed. Furthermore, the narrowband receiver is tested in realistic conditions using measured channel samples. Finally, a blind version of the receiver is propose