57 research outputs found
Passive detection of rank-one signals with a multiantenna reference channel
In this work we consider a two-channel passive detection problem, in which there is a surveillance array where the presence/absence of a target signal is to be detected, and a reference array that provides a noise-contaminated version of the target signal. We assume that the transmitted signal is an unknown rank-one signal, and that the noises are uncorrelated between the two channels, but each one having an unknown and arbitrary spatial covariance matrix. We show that the generalized likelihood ratio test (GLRT) for this problem rejects the null hypothesis when the largest canonical correlation of the sample coherence matrix between the surveillance and the reference channels exceeds a threshold. Further, based on recent results from random matrix theory, we provide an approximation for the null distribution of the test statistic.The work of I. SantamarĂa was supported by the Spanish Government through grants PRX14/0028 (Estancias de Movilidad de Profesores, Ministerio de EducaciĂłn) and by project RACHEL (TEC2013-47141-C4-3-R) funded by the Ministerio de EconomĂa y Competitividad (MINECO). The work of L. Scharf and D. Cochran was supported in part by a sub-contract with Matrix Research for research sponsored by the Air Force Research Laboratory under contract FA8650-14-D-1722
Analysis and Design of Multiple-Antenna Cognitive Radios with Multiple Primary User Signals
We consider multiple-antenna signal detection of primary user transmission
signals by a secondary user receiver in cognitive radio networks. The optimal
detector is analyzed for the scenario where the number of primary user signals
is no less than the number of receive antennas at the secondary user. We first
derive exact expressions for the moments of the generalized likelihood ratio
test (GLRT) statistic, yielding approximations for the false alarm and
detection probabilities. We then show that the normalized GLRT statistic
converges in distribution to a Gaussian random variable when the number of
antennas and observations grow large at the same rate. Further, using results
from large random matrix theory, we derive expressions to compute the detection
probability without explicit knowledge of the channel, and then particularize
these expressions for two scenarios of practical interest: 1) a single primary
user sending spatially multiplexed signals, and 2) multiple spatially
distributed primary users. Our analytical results are finally used to obtain
simple design rules for the signal detection threshold.Comment: Revised version (14 pages). Change in titl
Passive detection of correlated subspace signals in two MIMO channels
In this paper, we consider a two-channel multiple-input multiple-output passive detection problem, in which there is a surveillance array and a reference array. The reference array is known to carry a linear combination of broadband noise and a subspace signal of known dimension, but unknown basis. The question is whether the surveillance channel carries a linear combination of broadband noise and a subspace signal of the same dimension, but unknown basis, which is correlated with the subspace signal in the reference channel. We consider a second-order detection problem where these subspace signals are structured by an unknown, but common, p-dimensional random vector of symbols transmitted from sources of opportunity, and then received through unknown M Ă— p matrices at each of the M-element arrays. The noises in each channel have spatial correlation models ranging from arbitrarily correlated to independent with identical variances. We provide a unified framework to derive the generalized likelihood ratio test for these different noise models. In the most general case of arbitrary noise covariance matrices, the test statistic is a monotone function of canonical correlations between the reference and surveillance channels.I. SantamarĂa and J. VĂa have received funding from Ministerio de EconomĂa y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U. under projects TEC2013-47141-C4-3-R (RACHEL), TEC2016-75067-C4-4-R (CARMEN) and TEC2016-81900-REDT (KERMES). The research of Haonan Wang was partially supported by NSF grant DMS-1521746
Spectrum sensing for cognitive radio
In this thesis we will study the generalized likelihood ratio test as a solution
to the spectrum sensing in multiple-input multiple-output environments. The performance
will be analyzed by means of Monte Carlo simulations.El objetivo de este Proyecto Fin de carrera ha sido estudiar una posible soluciĂłn a la radio
cognitiva. Para ello y con ayuda de Matlab, se ha simulado el comportamiento de varios
tipos de detectores diseñados bajo diferentes suposiciones y comparando sus resultados.
Finalmente el detector GLRT es estudiado con más profundidad dado a sus buenas prestaciones.
Por ello, en el capĂtulo final se representarán las curvas ROC de detectores GLRT
derivados bajo diferentes condiciones y aplicados bajo diferentes escenarios para comparar
los resultados obtenidos con cada uno de ellos.IngenierĂa de TelecomunicaciĂł
Source enumeration via Toeplitz matrix completion
This paper addresses the problem of source enumeration by an array of sensors in the presence of noise whose spatial covariance structure is a diagonal matrix with possibly different variances, referred to non-iid noise hereafter, when the sources are uncorrelated. The diagonal terms of the sample covariance matrix are removed and, after applying Toeplitz rectification as a denoising step, the signal covariance matrix is reconstructed by using a low-rank matrix completion method adapted to enforce the Toeplitz structure of the sought solution. The proposed source enumeration criterion is based on the Frobenius norm of the reconstructed signal covariance matrix obtained for increasing rank values. As illustrated by simulation examples, the proposed method performs robustly for both small and large-scale arrays with few snapshots, i.e. small-sample regime.This work was supported by the Ministerio de EconomĂa y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grants TEC2016-75067-C4-4-R (CARMEN), PID2019-104958RB-C43/C41 (ADELE) and BES-2017-080542
Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors
In this paper we study the existence of locally most powerful invariant tests
(LMPIT) for the problem of testing the covariance structure of a set of
Gaussian random vectors. The LMPIT is the optimal test for the case of close
hypotheses, among those satisfying the invariances of the problem, and in
practical scenarios can provide better performance than the typically used
generalized likelihood ratio test (GLRT). The derivation of the LMPIT usually
requires one to find the maximal invariant statistic for the detection problem
and then derive its distribution under both hypotheses, which in general is a
rather involved procedure. As an alternative, Wijsman's theorem provides the
ratio of the maximal invariant densities without even finding an explicit
expression for the maximal invariant. We first consider the problem of testing
whether a set of -dimensional Gaussian random vectors are uncorrelated or
not, and show that the LMPIT is given by the Frobenius norm of the sample
coherence matrix. Second, we study the case in which the vectors under the null
hypothesis are uncorrelated and identically distributed, that is, the
sphericity test for Gaussian vectors, for which we show that the LMPIT is given
by the Frobenius norm of a normalized version of the sample covariance matrix.
Finally, some numerical examples illustrate the performance of the proposed
tests, which provide better results than their GLRT counterparts
LMPIT-inspired Tests for Detecting a Cyclostationary Signal in Noise with Spatio-Temporal Structure
In spectrum sensing for cognitive radio, the presence of a primary user can
be detected by making use of the cyclostationarity property of digital
communication signals. For the general scenario of a cyclostationary signal in
temporally colored and spatially correlated noise, it has previously been shown
that an asymptotic generalized likelihood ratio test (GLRT) and locally most
powerful invariant test (LMPIT) exist. In this paper, we derive detectors for
the presence of a cyclostationary signal in various scenarios with structured
noise. In particular, we consider noise that is temporally white and/or
spatially uncorrelated. Detectors that make use of this additional information
about the noise process have enhanced performance. We have previously derived
GLRTs for these specific scenarios; here, we examine the existence of LMPITs.
We show that these exist only for detecting the presence of a cyclostationary
signal in spatially uncorrelated noise. For white noise, an LMPIT does not
exist. Instead, we propose tests that approximate the LMPIT, and they are shown
to perform well in simulations. Finally, if the noise structure is not known in
advance, we also present hypothesis tests using our framework
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