4,582 research outputs found
Quantization Bounds on Grassmann Manifolds and Applications to MIMO Communications
This paper considers the quantization problem on the Grassmann manifold
\mathcal{G}_{n,p}, the set of all p-dimensional planes (through the origin) in
the n-dimensional Euclidean space. The chief result is a closed-form formula
for the volume of a metric ball in the Grassmann manifold when the radius is
sufficiently small. This volume formula holds for Grassmann manifolds with
arbitrary dimension n and p, while previous results pertained only to p=1, or a
fixed p with asymptotically large n. Based on this result, several quantization
bounds are derived for sphere packing and rate distortion tradeoff. We
establish asymptotically equivalent lower and upper bounds for the rate
distortion tradeoff. Since the upper bound is derived by constructing random
codes, this result implies that the random codes are asymptotically optimal.
The above results are also extended to the more general case, in which
\mathcal{G}_{n,q} is quantized through a code in \mathcal{G}_{n,p}, where p and
q are not necessarily the same. Finally, we discuss some applications of the
derived results to multi-antenna communication systems.Comment: 26 pages, 7 figures, submitted to IEEE Transactions on Information
Theory in Aug, 200
Rate Splitting for MIMO Wireless Networks: A Promising PHY-Layer Strategy for LTE Evolution
MIMO processing plays a central part towards the recent increase in spectral
and energy efficiencies of wireless networks. MIMO has grown beyond the
original point-to-point channel and nowadays refers to a diverse range of
centralized and distributed deployments. The fundamental bottleneck towards
enormous spectral and energy efficiency benefits in multiuser MIMO networks
lies in a huge demand for accurate channel state information at the transmitter
(CSIT). This has become increasingly difficult to satisfy due to the increasing
number of antennas and access points in next generation wireless networks
relying on dense heterogeneous networks and transmitters equipped with a large
number of antennas. CSIT inaccuracy results in a multi-user interference
problem that is the primary bottleneck of MIMO wireless networks. Looking
backward, the problem has been to strive to apply techniques designed for
perfect CSIT to scenarios with imperfect CSIT. In this paper, we depart from
this conventional approach and introduce the readers to a promising strategy
based on rate-splitting. Rate-splitting relies on the transmission of common
and private messages and is shown to provide significant benefits in terms of
spectral and energy efficiencies, reliability and CSI feedback overhead
reduction over conventional strategies used in LTE-A and exclusively relying on
private message transmissions. Open problems, impact on standard specifications
and operational challenges are also discussed.Comment: accepted to IEEE Communication Magazine, special issue on LTE
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