6,497 research outputs found
Adaptive detection of a signal known only to lie on a line in a known subspace, when primary and secondary data are partially homogeneous
This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence
of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known linear subspace. Furthermore, we consider the partially homogeneous case, for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels. This provides an extension to the framework considered by Bose and Steinhardt. The natural invariances of the detection problem are studied, which leads to the derivation of the maximal invariant. Then, a detector is proposed that proceeds in two steps. First, assuming that the noise covariance matrix is known, the generalized-likelihood ratio test (GLRT) is formulated. Then, the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector. The latter is compared with a similar detector that assumes the steering vector to be known
Random matrix approach in search for weak signals immersed in background noise
We present new, original and alternative method for searching signals coded
in noisy data. The method is based on the properties of random matrix
eigenvalue spectra. First, we describe general ideas and support them with
results of numerical simulations for basic periodic signals immersed in
artificial stochastic noise. Then, the main effort is put to examine the
strength of a new method in investigation of data content taken from the real
astrophysical NAUTILUS detector, searching for the presence of gravitational
waves. Our method discovers some previously unknown problems with data
aggregation in this experiment. We provide also the results of new method
applied to the entire respond signal from ground based detectors in future
experimental activities with reduced background noise level. We indicate good
performance of our method what makes it a positive predictor for further
applications in many areas.Comment: 15 pages, 16 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
Evaluation of bistable systems versus matched filters in detecting bipolar pulse signals
This paper presents a thorough evaluation of a bistable system versus a
matched filter in detecting bipolar pulse signals. The detectability of the
bistable system can be optimized by adding noise, i.e. the stochastic resonance
(SR) phenomenon. This SR effect is also demonstrated by approximate statistical
detection theory of the bistable system and corresponding numerical
simulations. Furthermore, the performance comparison results between the
bistable system and the matched filter show that (a) the bistable system is
more robust than the matched filter in detecting signals with disturbed pulse
rates, and (b) the bistable system approaches the performance of the matched
filter in detecting unknown arrival times of received signals, with an
especially better computational efficiency. These significant results verify
the potential applicability of the bistable system in signal detection field.Comment: 15 pages, 9 figures, MikTex v2.
Max-Min SNR Signal Energy based Spectrum Sensing Algorithms for Cognitive Radio Networks with Noise Variance Uncertainty
This paper proposes novel spectrum sensing algorithms for cognitive radio
networks. By assuming known transmitter pulse shaping filter, synchronous and
asynchronous receiver scenarios have been considered. For each of these
scenarios, the proposed algorithm is explained as follows: First, by
introducing a combiner vector, an over-sampled signal of total duration equal
to the symbol period is combined linearly. Second, for this combined signal,
the Signal-to-Noise ratio (SNR) maximization and minimization problems are
formulated as Rayleigh quotient optimization problems. Third, by using the
solutions of these problems, the ratio of the signal energy corresponding to
the maximum and minimum SNRs are proposed as a test statistics. For this test
statistics, analytical probability of false alarm () and detection ()
expressions are derived for additive white Gaussian noise (AWGN) channel. The
proposed algorithms are robust against noise variance uncertainty. The
generalization of the proposed algorithms for unknown transmitter pulse shaping
filter has also been discussed. Simulation results demonstrate that the
proposed algorithms achieve better than that of the Eigenvalue
decomposition and energy detection algorithms in AWGN and Rayleigh fading
channels with noise variance uncertainty. The proposed algorithms also
guarantee the desired in the presence of adjacent channel
interference signals
A bayesian approach to adaptive detection in nonhomogeneous environments
We consider the adaptive detection of a signal of interest embedded in colored noise, when the environment is nonhomogeneous, i.e., when the training samples used for adaptation do not share the same covariance matrix as the vector under test. A Bayesian framework is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices require a rough knowledge about the environment. This provides a flexible, yet simple, knowledge-aided model where the degree of nonhomogeneity can be tuned through some scalar variables. Within this framework, an approximate generalized likelihood ratio test is formulated. Accordingly, two Bayesian versions of the adaptive matched filter are presented, where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori estimate. Two detectors require generating samples distributed according to the joint posterior distribution of primary and secondary data covariance matrices. This is achieved through the use of a Gibbs sampling strategy. Numerical simulations illustrate the performances of these detectors, and compare them with those of the conventional adaptive matched filter
Estimation of the Number of Sources in Unbalanced Arrays via Information Theoretic Criteria
Estimating the number of sources impinging on an array of sensors is a well
known and well investigated problem. A common approach for solving this problem
is to use an information theoretic criterion, such as Minimum Description
Length (MDL) or the Akaike Information Criterion (AIC). The MDL estimator is
known to be a consistent estimator, robust against deviations from the Gaussian
assumption, and non-robust against deviations from the point source and/or
temporally or spatially white additive noise assumptions. Over the years
several alternative estimation algorithms have been proposed and tested.
Usually, these algorithms are shown, using computer simulations, to have
improved performance over the MDL estimator, and to be robust against
deviations from the assumed spatial model. Nevertheless, these robust
algorithms have high computational complexity, requiring several
multi-dimensional searches.
In this paper, motivated by real life problems, a systematic approach toward
the problem of robust estimation of the number of sources using information
theoretic criteria is taken. An MDL type estimator that is robust against
deviation from assumption of equal noise level across the array is studied. The
consistency of this estimator, even when deviations from the equal noise level
assumption occur, is proven. A novel low-complexity implementation method
avoiding the need for multi-dimensional searches is presented as well, making
this estimator a favorable choice for practical applications.Comment: To appear in the IEEE Transactions on Signal Processin
Sensing Throughput Tradeoff for Cognitive Radio Networks with Noise Variance Uncertainty
This paper proposes novel spectrum sensing algorithm, and examines the
sensing throughput tradeoff for cognitive radio (CR) networks under noise
variance uncertainty. It is assumed that there are one white sub-band, and one
target sub-band which is either white or non-white. Under this assumption,
first we propose a novel generalized energy detector (GED) for examining the
target sub-band by exploiting the noise information of the white sub-band,
then, we study the tradeoff between the sensing time and achievable throughput
of the CR network. To study this tradeoff, we consider the sensing time
optimization for maximizing the throughput of the CR network while
appropriately protecting the primary network. The sensing time is optimized by
utilizing the derived detection and false alarm probabilities of the GED. The
proposed GED does not suffer from signal to noise ratio (SNR) wall (i.e.,
robust against noise variance uncertainty) and outperforms the existing signal
detectors. Moreover, the relationship between the proposed GED and conventional
energy detector (CED) is quantified analytically. We show that the optimal
sensing times with perfect and imperfect noise variances are not the same. In
particular, when the frame duration is 2s, and SNR is -20dB, and each of the
bandwidths of the white and target sub-bands is 6MHz, the optimal sensing times
are 28.5ms and 50.6ms with perfect and imperfect noise variances, respectively.Comment: Accepted in CROWNCOM, June 2014, Oulu, Finlan
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