4,436 research outputs found
Exact distributions of finite random matrices and their applications to spectrum sensing
The exact and simple distributions of finite random matrix theory (FRMT) are critically important for cognitive radio networks (CRNs). In this paper, we unify some existing distributions of the FRMT with the proposed coefficient matrices (vectors) and represent the distributions with the coefficient-based formulations. A coefficient reuse mechanism is studied, i.e., the same coefficient matrices (vectors) can be exploited to formulate different distributions. For instance, the same coefficient matrices can be used by the largest eigenvalue (LE) and the scaled largest eigenvalue (SLE); the same coefficient vectors can be used by the smallest eigenvalue (SE) and the Demmel condition number (DCN). A new and simple cumulative distribution function (CDF) of the DCN is also deduced. In particular, the dimension boundary between the infinite random matrix theory (IRMT) and the FRMT is initially defined. The dimension boundary provides a theoretical way to divide random matrices into infinite random matrices and finite random matrices. The FRMT-based spectrum sensing (SS) schemes are studied for CRNs. The SLE-based scheme can be considered as an asymptotically-optimal SS scheme when the dimension K is larger than two. Moreover, the standard condition number (SCN)-based scheme achieves the same sensing performance as the SLE-based scheme for dual covariance matrix [Formula: see text]. The simulation results verify that the coefficient-based distributions can fit the empirical results very well, and the FRMT-based schemes outperform the IRMT-based schemes and the conventional SS schemes
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
Eigenvalue-Based Spectrum SensingWith Two Receive Antennas
National audience"Le concept de la radio intelligente dĂ©finit deux types dâutilisateurs: les utilisateurs primaires (UP) qui ont accĂšs aux ressources spectrales dâune façon prioritaire et les utilisateurs secondaires (US) qui exploitent les opportunitĂ©s de communication laissĂ©es vacantes parles UPs. Dans ce papier on sâintÂŽeresse au probl`eme de dÂŽetection des ressources spectrales libres en utilisant les distributions du nombre deconditionnement (NDC) de la matrice de covariance des signaux reus par lâUS. Une nouvelle formule mathÂŽematique est proposÂŽee pour ladistribution du NDC dans le cas dâabsence des UPs permettant ainsi de dÂŽevelopper un nouveau algorithme de dÂŽetection. Les rÂŽesultats dessimulations nous permettent de valider la formulation thÂŽeorique et les hypoth`eses de bases.
Spectrum Sharing in Wireless Networks via QoS-Aware Secondary Multicast Beamforming
Secondary spectrum usage has the potential to considerably increase spectrum utilization. In this paper, quality-of-service (QoS)-aware spectrum underlay of a secondary multicast network is considered. A multiantenna secondary access point (AP) is used for multicast (common information) transmission to a number of secondary single-antenna receivers. The idea is that beamforming can be used to steer power towards the secondary receivers while limiting sidelobes that cause interference to primary receivers. Various optimal formulations of beamforming are proposed, motivated by different ldquocohabitationrdquo scenarios, including robust designs that are applicable with inaccurate or limited channel state information at the secondary AP. These formulations are NP-hard computational problems; yet it is shown how convex approximation-based multicast beamforming tools (originally developed without regard to primary interference constraints) can be adapted to work in a spectrum underlay context. Extensive simulation results demonstrate the effectiveness of the proposed approaches and provide insights on the tradeoffs between different design criteria
Spectrum sensing algorithms and software-defined radio implementation for cognitive radio system
The scarcity of spectral resources in wireless communications, due to a fixed frequency allocation policy, is a strong limitation to the increasing demand for higher data rates. However, measurements showed that a large part of frequency channels are underutilized or almost unoccupied. The cognitive radio paradigm arises as a tempting solution to the spectral congestion problem. A cognitive radio must be able to identify transmission opportunities in unused channels and to avoid generating harmful interference with the licensed primary users. Its key enabling technology is the spectrum sensing unit, whose ultimate goal consists in providing an indication whether a primary transmission is taking place in the observed channel. Such indication is determined as the result of a binary hypothesis testing experiment wherein null hypothesis (alternate hypothesis) corresponds to the absence (presence) of the primary signal. The first parts of this thesis describes the spectrum sensing problem and presents some of the best performing detection techniques. Energy Detection and multi-antenna Eigenvalue-Based Detection algorithms are considered. Important aspects are taken into account, like the impact of noise estimation or the effect of primary user traffic. The performance of each detector is assessed in terms of false alarm probability and detection probability. In most experimental research, cognitive radio techniques are deployed in software-defined radio systems, radio transceivers that allow operating parameters (like modulation type, bandwidth, output power, etc.) to be set or altered by software.In the second part of the thesis, we introduce the software-defined radio concept. Then, we focus on the implementation of Energy Detection and Eigenvalue-Based Detection algorithms: first, the used software platform, GNU Radio, is described, secondly, the implementation of a parallel energy detector and a multi-antenna eigenbased detector is illustrated and details on the used methodologies are given. Finally, we present the deployed experimental cognitive testbeds and the used radio peripherals. The obtained algorithmic results along with the software-defined radio implementation may offer a set of tools able to create a realistic cognitive radio system with real-time spectrum sensing capabilities
Distributed Constrained Recursive Nonlinear Least-Squares Estimation: Algorithms and Asymptotics
This paper focuses on the problem of recursive nonlinear least squares
parameter estimation in multi-agent networks, in which the individual agents
observe sequentially over time an independent and identically distributed
(i.i.d.) time-series consisting of a nonlinear function of the true but unknown
parameter corrupted by noise. A distributed recursive estimator of the
\emph{consensus} + \emph{innovations} type, namely , is
proposed, in which the agents update their parameter estimates at each
observation sampling epoch in a collaborative way by simultaneously processing
the latest locally sensed information~(\emph{innovations}) and the parameter
estimates from other agents~(\emph{consensus}) in the local neighborhood
conforming to a pre-specified inter-agent communication topology. Under rather
weak conditions on the connectivity of the inter-agent communication and a
\emph{global observability} criterion, it is shown that at every network agent,
the proposed algorithm leads to consistent parameter estimates. Furthermore,
under standard smoothness assumptions on the local observation functions, the
distributed estimator is shown to yield order-optimal convergence rates, i.e.,
as far as the order of pathwise convergence is concerned, the local parameter
estimates at each agent are as good as the optimal centralized nonlinear least
squares estimator which would require access to all the observations across all
the agents at all times. In order to benchmark the performance of the proposed
distributed estimator with that of the centralized nonlinear
least squares estimator, the asymptotic normality of the estimate sequence is
established and the asymptotic covariance of the distributed estimator is
evaluated. Finally, simulation results are presented which illustrate and
verify the analytical findings.Comment: 28 pages. Initial Submission: Feb. 2016, Revised: July 2016,
Accepted: September 2016, To appear in IEEE Transactions on Signal and
Information Processing over Networks: Special Issue on Inference and Learning
over Network
- âŠ