5 research outputs found
On Information Rates of the Fading Wyner Cellular Model via the Thouless Formula for the Strip
We apply the theory of random Schr\"odinger operators to the analysis of
multi-users communication channels similar to the Wyner model, that are
characterized by short-range intra-cell broadcasting. With the channel
transfer matrix, is a narrow-band matrix and in many aspects is
similar to a random Schr\"odinger operator. We relate the per-cell sum-rate
capacity of the channel to the integrated density of states of a random
Schr\"odinger operator; the latter is related to the top Lyapunov exponent of a
random sequence of matrices via a version of the Thouless formula. Unlike
related results in classical random matrix theory, limiting results do depend
on the underlying fading distributions. We also derive several bounds on the
limiting per-cell sum-rate capacity, some based on the theory of random
Schr\"odinger operators, and some derived from information theoretical
considerations. Finally, we get explicit results in the high-SNR regime for
some particular cases.Comment: Submitted to IEEE Transactions on Information Theor
Capacity and Power Scaling Laws for Finite Antenna MIMO Amplify-and-Forward Relay Networks
In this paper, we present a novel framework that can be used to study the
capacity and power scaling properties of linear multiple-input multiple-output
(MIMO) antenna amplify-and-forward (AF) relay networks. In
particular, we model these networks as random dynamical systems (RDS) and
calculate their Lyapunov exponents. Our analysis can be applied to systems
with any per-hop channel fading distribution, although in this contribution we
focus on Rayleigh fading. Our main results are twofold: 1) the total transmit
power at the th node will follow a deterministic trajectory through the
network governed by the network's maximum Lyapunov exponent, 2) the capacity of
the th eigenchannel at the th node will follow a deterministic trajectory
through the network governed by the network's th Lyapunov exponent. Before
concluding, we concentrate on some applications of our results. In particular,
we show how the Lyapunov exponents are intimately related to the rate at which
the eigenchannel capacities diverge from each other, and how this relates to
the amplification strategy and number of antennas at each relay. We also use
them to determine the extra cost in power associated with each extra
multiplexed data stream.Comment: 16 pages, 9 figures. Accepted for publication in IEEE Transactions on
Information Theor