Detection Of non-Gaussian Signals Research Articles

Novel Adaptive Nonlinear Receivers for UWB Multiple Access Communications

Ultra-wide bandwidth communication systems are known to suffer from non-Gaussian interference. In general, wireless ad-hoc networks, due to the lack of perfect power control and the random placement of nodes, are very likely to experience non-Gaussian multiple access interference. In systems with additive non-Gaussian noise, non-Gaussian signal detection and nonlinear signal processing can play important roles, especially in suppressing the multiple access interference. Practical ultra-wide bandwidth receiver designs based on the α-stable non-Gaussian additive impairment model are proposed and evaluated. It is demonstrated that the α-stable model together with a fractile based parameter estimation technique constitute a robust technique for adaptive receiver designs. The proposed receivers based on the α-stable model suppress multiple access interference, adapt to the noise and the interference in the environment, and are robust to estimation errors in the receiver parameters. The proposed receivers provide much better bit error rates than linear detectors and previously known nonlinear detectors.

Joint signal detection algorithm of cognitive radio in UWB

With the progress of research on cognitive radio in ultra-wideband (UWB) open frequency-band, a joint detection algorithm integrating the energy and bi-spectrum detection is proposed in detail for non-Gaussian signal detection from Gaussian noise. The performance of the algorithm was evaluated by simulation, the result of which indicates that the joint detection not only solves the problem of the signal detection in low signal-to-noise ratio (SNR) but also improves the operational speed and the detection probability. Thus, the joint detection algorithm has definite prospect in practice.

Patterns in the weak shear 3-point correlation function

We explore the scale and angular dependence of the cosmic shear three-point correlation function. The shear field is found to have a much more complex three-point function than the convergence field, but it also exhibits specific motifs which show signatures of gravitational lensing. Exact shear patterns are inferred analytically for some geometrical shear triplets configurations, when simple interpretations can be derived. A more complete description of their geometrical properties is then carried out from ray-tracing numerical simulations and simple models. These patterns reveal typical features that can be utilized for non-Gaussian signal detection in cosmic shear surveys. We test the robustness of these properties against complex noise statistics and non-trivial survey topologies. From these conclusive checks, we predict that the VIRMOS-DESCART survey should allow a detection of a non-Gaussian signal with a comfortable significance for a low matter density Universe.

Detection of non-Gaussian signals by bispectrum-U detector

A method for detecting non-Gaussian stationary signals in additive Gaussian noise using a bispectrum-U test is presented. The performance of the proposed detection statistic is compared to the conventional bispectrum χ2 detector.

Performance analysis of cumulant-based detection of non-gaussian signals

Performance analysis of cumulant-based detection of non-gaussian signals

Corrections to "Detection of Non-Gaussian Signals Using Integrated Polyspectrum"

Corrections to "Detection of Non-Gaussian Signals Using Integrated Polyspectrum"

Detection of non-Gaussian signals: a paradigm for modern statistical signal processing

Non-Gaussian signals arise in a wide variety of applications, including sonar, digital communications, seismology, and radio astronomy. In this tutorial overview, a hierarchical approach to signal modeling and detector design for non-Gaussian signals is described. In addition to being of interest in applications, this problem serves as a paradigm within which most of the areas of active research in statistical signal processing arise. In particular, the methodologies of nonlinear signal processing, higher order statistical analysis, signal representations, and learning algorithms, all can be juxtaposed quite naturally in this framework. >

Detection of non-Gaussian signals using integrated polyspectrum

We consider the problem of detecting an unknown, random, stationary, non-Gaussian signal in Gaussian noise of unknown correlation structure. The same framework applies if one desires to determine whether the given random signal is non-Gaussian. The most commonly used method for detection of random signals is the so-called energy detector, which cannot distinguish between Gaussian and non-Gaussian signals and requires the knowledge of the noise power. Recently, the use of bispectrum and/or trispectrum of the signal has been suggested for detection of non-Gaussian signals. The higher order spectra-based detectors do not require the knowledge of the noise statistics if the noise is Gaussian. In this paper, we suggest the use of an integrated polyspectrum (bispectrum of trispectrum) to improve computational efficiency of the detectors based on polyspectrum and to possibly further enhance their detection performance. We investigate conditions under which use of the integrated polyspectrum is appropriate. The detector structure is derived, acid its performance is evaluated via simulations and comparisons with several other existing approaches. >

Two-channel tests for common non-gaussian signal detection

The problem of detecting an unknown, random, stationary, non-Gaussian signal that is common to two spatially separated sensors, is considered. The signal is assumed to have a nonvanishing bispectrum. The measurement noise sequences at the two sensors are either mutually independent with arbitrary cumulant spectra, or dependent with vanishing bispectra. Two statistical tests are presented for signal detection when the noise statistics are unknown. The performance of the tests is illustrated by computer simulation examples.

Suboptimal detection of non-Gaussian signals by third-order spectral analysis

The use of higher-order spectra (HOS) is proposed for improving detection performance in non-Gaussian signals. The method comprises two stages. First, the higher-order spectra of the received signal are estimated using conventional spectral estimation techniques; then, a (maximum) likelihood ratio test (LRT) is performed in the higher-order-spectra domain. It is shown that, under certain low signal-to-noise ratio (SNR) conditions, the HOS-based method performs much better than the conventional energy one. The required processor is derived and its performance is analyzed. While the method is demonstrated using the third-order spectrum (called bispectrum), it can easily be extended to higher-order analysis (e.g. trispectrum, etc.). >

Chernoff bounds on the error probability for the detection of non-Gaussian signals

Chernoff bounds on the error probability for the detection of non-Gaussian stochastic signals in additive white Gaussian noise are computed. By the use of Fokker-Planck (F-P) equations and a certain conditional expectation, the quasi-transition function, an equation for time evolution of the Chernoff bound is obtained. This time evolution equation is solved exactly to give all previously known results. Although the general non-Gaussian case cannot be conveniently solved for short time duratio ns, in the important special case of stationary processes and long integration times, bounding the error probability reduces to solving for the largest eigenvalue \lambda_0 of a differential operator. In particular, P(error) \leq \exp (\lambda_0T) , where T is the observation period. By iteratively determining \lambda_0 via the Galerkin variational procedure, we compare the performance of different receiver forms for a specific problem involving the detection of non-Gaussian random signal processes.

Chernoff bounds on the error probability for the detection of non-Gaussian signals (Ph.D. Thesis abstr.)

Chernoff bounds on the error probability for the detection of non-Gaussian signals (Ph.D. Thesis abstr.)