816 research outputs found
Channel Capacity Estimation using Free Probability Theory
In many channel measurement applications, one needs to estimate some
characteristics of the channels based on a limited set of measurements. This is
mainly due to the highly time varying characteristics of the channel. In this
contribution, it will be shown how free probability can be used for channel
capacity estimation in MIMO systems. Free probability has already been applied
in various application fields such as digital communications, nuclear physics
and mathematical finance, and has been shown to be an invaluable tool for
describing the asymptotic behaviour of many large-dimensional systems. In
particular, using the concept of free deconvolution, we provide an
asymptotically (w.r.t. the number of observations) unbiased capacity estimator
for MIMO channels impaired with noise called the free probability based
estimator. Another estimator, called the Gaussian matrix mean based estimator,
is also introduced by slightly modifying the free probability based estimator.
This estimator is shown to give unbiased estimation of the moments of the
channel matrix for any number of observations. Also, the estimator has this
property when we extend to MIMO channels with phase off-set and frequency
drift, for which no estimator has been provided so far in the literature. It is
also shown that both the free probability based and the Gaussian matrix mean
based estimator are asymptotically unbiased capacity estimators as the number
of transmit antennas go to infinity, regardless of whether phase off-set and
frequency drift are present. The limitations in the two estimators are also
explained. Simulations are run to assess the performance of the estimators for
a low number of antennas and samples to confirm the usefulness of the
asymptotic results.Comment: Submitted to IEEE Transactions on Signal Processing. 12 pages, 9
figure
A Bayesian Framework for Collaborative Multi-Source Signal Detection
This paper introduces a Bayesian framework to detect multiple signals
embedded in noisy observations from a sensor array. For various states of
knowledge on the communication channel and the noise at the receiving sensors,
a marginalization procedure based on recent tools of finite random matrix
theory, in conjunction with the maximum entropy principle, is used to compute
the hypothesis selection criterion. Quite remarkably, explicit expressions for
the Bayesian detector are derived which enable to decide on the presence of
signal sources in a noisy wireless environment. The proposed Bayesian detector
is shown to outperform the classical power detector when the noise power is
known and provides very good performance for limited knowledge on the noise
power. Simulations corroborate the theoretical results and quantify the gain
achieved using the proposed Bayesian framework.Comment: 15 pages, 9 pictures, Submitted to IEEE Trans. on Signal Processin
Signal Processing in Large Systems: a New Paradigm
For a long time, detection and parameter estimation methods for signal
processing have relied on asymptotic statistics as the number of
observations of a population grows large comparatively to the population size
, i.e. . Modern technological and societal advances now
demand the study of sometimes extremely large populations and simultaneously
require fast signal processing due to accelerated system dynamics. This results
in not-so-large practical ratios , sometimes even smaller than one. A
disruptive change in classical signal processing methods has therefore been
initiated in the past ten years, mostly spurred by the field of large
dimensional random matrix theory. The early works in random matrix theory for
signal processing applications are however scarce and highly technical. This
tutorial provides an accessible methodological introduction to the modern tools
of random matrix theory and to the signal processing methods derived from them,
with an emphasis on simple illustrative examples
Theoretical Foundations of Mobile Flexible Networks
International audienceThe general framework of Mobile Flexible Networks (MFN) is to design dense self-organizing, self-healing and self-energy harvesting secure networks where terminals and base stations interact and self-adapt in an intelligent manner without the need of a central controller or with the right amount of regulation to let the agents in the network exploit fully the degrees of freedom. The design depends mainly on the mobility pattern as in highly mobile envi- ronments, intelligence at the terminal reduces the cost of signalling whereas for fixed (non-mobile) networks, all the intelligence can be put on the network side. One of the big challenges is to find how to optimally split the intelligence between cognitive terminals and cognitive networks. In this paper, we discuss the challenges ahead and provide some research directions to develop the theoretical foundations of these networks
Iterative Deterministic Equivalents for the Performance Analysis of Communication Systems
In this article, we introduce iterative deterministic equivalents as a novel
technique for the performance analysis of communication systems whose channels
are modeled by complex combinations of independent random matrices. This
technique extends the deterministic equivalent approach for the study of
functionals of large random matrices to a broader class of random matrix models
which naturally arise as channel models in wireless communications. We present
two specific applications: First, we consider a multi-hop amplify-and-forward
(AF) MIMO relay channel with noise at each stage and derive deterministic
approximations of the mutual information after the Kth hop. Second, we study a
MIMO multiple access channel (MAC) where the channel between each transmitter
and the receiver is represented by the double-scattering channel model. We
provide deterministic approximations of the mutual information, the
signal-to-interference-plus-noise ratio (SINR) and sum-rate with
minimum-mean-square-error (MMSE) detection and derive the asymptotically
optimal precoding matrices. In both scenarios, the approximations can be
computed by simple and provably converging fixed-point algorithms and are shown
to be almost surely tight in the limit when the number of antennas at each node
grows infinitely large. Simulations suggest that the approximations are
accurate for realistic system dimensions. The technique of iterative
deterministic equivalents can be easily extended to other channel models of
interest and is, therefore, also a new contribution to the field of random
matrix theory.Comment: submitted to the IEEE Transactions on Information Theory, 43 pages, 4
figure
Transmit Power Minimization in Small Cell Networks Under Time Average QoS Constraints
We consider a small cell network (SCN) consisting of N cells, with the small
cell base stations (SCBSs) equipped with Nt \geq 1 antennas each, serving K
single antenna user terminals (UTs) per cell. Under this set up, we address the
following question: given certain time average quality of service (QoS) targets
for the UTs, what is the minimum transmit power expenditure with which they can
be met? Our motivation to consider time average QoS constraint comes from the
fact that modern wireless applications such as file sharing, multi-media etc.
allow some flexibility in terms of their delay tolerance. Time average QoS
constraints can lead to greater transmit power savings as compared to
instantaneous QoS constraints since it provides the flexibility to dynamically
allocate resources over the fading channel states. We formulate the problem as
a stochastic optimization problem whose solution is the design of the downlink
beamforming vectors during each time slot. We solve this problem using the
approach of Lyapunov optimization and characterize the performance of the
proposed algorithm. With this algorithm as the reference, we present two main
contributions that incorporate practical design considerations in SCNs. First,
we analyze the impact of delays incurred in information exchange between the
SCBSs. Second, we impose channel state information (CSI) feedback constraints,
and formulate a joint CSI feedback and beamforming strategy. In both cases, we
provide performance bounds of the algorithm in terms of satisfying the QoS
constraints and the time average power expenditure. Our simulation results show
that solving the problem with time average QoS constraints provide greater
savings in the transmit power as compared to the instantaneous QoS constraints.Comment: in Journal on Selected Areas of Communications (JSAC), 201
Random Beamforming over Correlated Fading Channels
We study a multiple-input multiple-output (MIMO) multiple access channel
(MAC) from several multi-antenna transmitters to a multi-antenna receiver. The
fading channels between the transmitters and the receiver are modeled by random
matrices, composed of independent column vectors with zero mean and different
covariance matrices. Each transmitter is assumed to send multiple data streams
with a random precoding matrix extracted from a Haar-distributed matrix. For
this general channel model, we derive deterministic approximations of the
normalized mutual information, the normalized sum-rate with
minimum-mean-square-error (MMSE) detection and the
signal-to-interference-plus-noise-ratio (SINR) of the MMSE decoder, which
become arbitrarily tight as all system parameters grow infinitely large at the
same speed. In addition, we derive the asymptotically optimal power allocation
under individual or sum-power constraints. Our results allow us to tackle the
problem of optimal stream control in interference channels which would be
intractable in any finite setting. Numerical results corroborate our analysis
and verify its accuracy for realistic system dimensions. Moreover, the
techniques applied in this paper constitute a novel contribution to the field
of large random matrix theory and could be used to study even more involved
channel models.Comment: 35 pages, 5 figure
Random Beamforming over Quasi-Static and Fading Channels: A Deterministic Equivalent Approach
In this work, we study the performance of random isometric precoders over
quasi-static and correlated fading channels. We derive deterministic
approximations of the mutual information and the
signal-to-interference-plus-noise ratio (SINR) at the output of the
minimum-mean-square-error (MMSE) receiver and provide simple provably
converging fixed-point algorithms for their computation. Although these
approximations are only proven exact in the asymptotic regime with infinitely
many antennas at the transmitters and receivers, simulations suggest that they
closely match the performance of small-dimensional systems. We exemplarily
apply our results to the performance analysis of multi-cellular communication
systems, multiple-input multiple-output multiple-access channels (MIMO-MAC),
and MIMO interference channels. The mathematical analysis is based on the
Stieltjes transform method. This enables the derivation of deterministic
equivalents of functionals of large-dimensional random matrices. In contrast to
previous works, our analysis does not rely on arguments from free probability
theory which enables the consideration of random matrix models for which
asymptotic freeness does not hold. Thus, the results of this work are also a
novel contribution to the field of random matrix theory and applicable to a
wide spectrum of practical systems.Comment: to appear in IEEE Transactions on Information Theory, 201
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