2,967 research outputs found
Eigen-Inference for Energy Estimation of Multiple Sources
In this paper, a new method is introduced to blindly estimate the transmit
power of multiple signal sources in multi-antenna fading channels, when the
number of sensing devices and the number of available samples are sufficiently
large compared to the number of sources. Recent advances in the field of large
dimensional random matrix theory are used that result in a simple and
computationally efficient consistent estimator of the power of each source. A
criterion to determine the minimum number of sensors and the minimum number of
samples required to achieve source separation is then introduced. Simulations
are performed that corroborate the theoretical claims and show that the
proposed power estimator largely outperforms alternative power inference
techniques.Comment: to appear in IEEE Trans. on Information Theory, 17 pages, 13 figure
Collaborative Spectrum Sensing Based on Upper Bound on Joint PDF of Exreme Eigenvalues
Detection based on eigenvalues of received signal covariance matrix is currently one of the most effective solution for spectrum sensing problem in cognitive radios. However, the results of these schemes often depend on asymptotic assumptions since the distribution of ratio of extreme eigenvalues is exceptionally mathematically complex to compute in practice. In this paper, a new approach to determine the distribution of ratio of the largest and the smallest eigenvalues is introduced to calculate the decision threshold and sense the spectrum. In this context, we derive a simple and analytically tractable expression for the distribution of the ratio of the largest and the smallest eigenvalues based on upper bound on the joint probability density function (PDF) of the largest and the smallest eigenvalues of the received covariance matrix. The performance analysis of proposed approach is compared with the empirical results. The decision threshold as a function of a given probability of false alarm is calculated to illustrate the effectiveness of the proposed approach
Joint Beamforming and Power Control in Coordinated Multicell: Max-Min Duality, Effective Network and Large System Transition
This paper studies joint beamforming and power control in a coordinated
multicell downlink system that serves multiple users per cell to maximize the
minimum weighted signal-to-interference-plus-noise ratio. The optimal solution
and distributed algorithm with geometrically fast convergence rate are derived
by employing the nonlinear Perron-Frobenius theory and the multicell network
duality. The iterative algorithm, though operating in a distributed manner,
still requires instantaneous power update within the coordinated cluster
through the backhaul. The backhaul information exchange and message passing may
become prohibitive with increasing number of transmit antennas and increasing
number of users. In order to derive asymptotically optimal solution, random
matrix theory is leveraged to design a distributed algorithm that only requires
statistical information. The advantage of our approach is that there is no
instantaneous power update through backhaul. Moreover, by using nonlinear
Perron-Frobenius theory and random matrix theory, an effective primal network
and an effective dual network are proposed to characterize and interpret the
asymptotic solution.Comment: Some typos in the version publised in the IEEE Transactions on
Wireless Communications are correcte
Performance of Statistical Tests for Single Source Detection using Random Matrix Theory
This paper introduces a unified framework for the detection of a source with
a sensor array in the context where the noise variance and the channel between
the source and the sensors are unknown at the receiver. The Generalized Maximum
Likelihood Test is studied and yields the analysis of the ratio between the
maximum eigenvalue of the sampled covariance matrix and its normalized trace.
Using recent results of random matrix theory, a practical way to evaluate the
threshold and the -value of the test is provided in the asymptotic regime
where the number of sensors and the number of observations per sensor
are large but have the same order of magnitude. The theoretical performance of
the test is then analyzed in terms of Receiver Operating Characteristic (ROC)
curve. It is in particular proved that both Type I and Type II error
probabilities converge to zero exponentially as the dimensions increase at the
same rate, and closed-form expressions are provided for the error exponents.
These theoretical results rely on a precise description of the large deviations
of the largest eigenvalue of spiked random matrix models, and establish that
the presented test asymptotically outperforms the popular test based on the
condition number of the sampled covariance matrix.Comment: 45 p. improved presentation; more proofs provide
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
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
Distributed Detection and Estimation in Wireless Sensor Networks
In this article we consider the problems of distributed detection and
estimation in wireless sensor networks. In the first part, we provide a general
framework aimed to show how an efficient design of a sensor network requires a
joint organization of in-network processing and communication. Then, we recall
the basic features of consensus algorithm, which is a basic tool to reach
globally optimal decisions through a distributed approach. The main part of the
paper starts addressing the distributed estimation problem. We show first an
entirely decentralized approach, where observations and estimations are
performed without the intervention of a fusion center. Then, we consider the
case where the estimation is performed at a fusion center, showing how to
allocate quantization bits and transmit powers in the links between the nodes
and the fusion center, in order to accommodate the requirement on the maximum
estimation variance, under a constraint on the global transmit power. We extend
the approach to the detection problem. Also in this case, we consider the
distributed approach, where every node can achieve a globally optimal decision,
and the case where the decision is taken at a central node. In the latter case,
we show how to allocate coding bits and transmit power in order to maximize the
detection probability, under constraints on the false alarm rate and the global
transmit power. Then, we generalize consensus algorithms illustrating a
distributed procedure that converges to the projection of the observation
vector onto a signal subspace. We then address the issue of energy consumption
in sensor networks, thus showing how to optimize the network topology in order
to minimize the energy necessary to achieve a global consensus. Finally, we
address the problem of matching the topology of the network to the graph
describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R.
Chellapa and S. Theodoridis, Eds., Elsevier, 201
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