scholarly journals Eigenvalue-Based Spectrum Sensing with Small Samples Using Circulant Matrix

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2330
Author(s):  
Liping Du ◽  
Yuting Fu ◽  
Yueyun Chen ◽  
Xiaojian Wang ◽  
Xiaoyan Zhang
Keyword(s):  
Covariance Matrix ◽  
Circulant Matrix ◽  
Time Instant ◽  
Detection Performance ◽  
Distribution Functions ◽  
Small Samples ◽  
Dominant Eigenvalue ◽  
Ratio Test ◽  
Secondary Users ◽  
Short Period

In cognitive radio (CR) networks, eigenvalue-based detectors (EBDs) have attracted much attention due to their good performance of detecting secondary users (SUs). In order to further improve the detection performance of EBDs with short samples, we propose two new detectors: average circulant matrix-based Roy’s largest root test (ACM-RLRT) and average circulant matrix-based generalized likelihood ratio test (ACM-GLRT). In the proposed method, the circulant matrix of samples at each time instant from SUs is calculated, and then, the covariance matrix of the circulant matrix is averaged over a short period of time. The eigenvalues of the achieved average circulant matrix (ACM) are used to build our proposed detectors. Using a circulant matrix can improve the dominant eigenvalue of covariance matrix of signals and also the detection performance of EBDs even with short samples. The probability distribution functions of the detectors undernull hypothesis are analyzed, and the asymptotic expressions for the false-alarm and thresholds of two proposed detectors are derived, respectively. The simulation results verify the effectiveness of the proposed detectors.

scholarly journals Near-Exact Distributions for Likelihood Ratio Statistics Used in the Simultaneous Test of Conditions on Mean Vectors and Patterns of Covariance Matrices

2016 ◽  
Vol 2016 ◽  
pp. 1-25 ◽  
Author(s):  
Carlos A. Coelho ◽  
Filipe J. Marques ◽  
Sandra Oliveira
Keyword(s):  
Covariance Matrix ◽  
Likelihood Ratio ◽  
Exact Distribution ◽  
Covariance Matrices ◽  
Distribution Functions ◽  
Small Samples ◽  
Chi Square ◽  
Exact Distributions ◽  
Mean Vectors ◽  
Likelihood Ratio Statistics

The authors address likelihood ratio statistics used to test simultaneously conditions on mean vectors and patterns on covariance matrices. Tests for conditions on mean vectors, assuming or not a given structure for the covariance matrix, are quite common, since they may be easily implemented. But, on the other hand, the practical use of simultaneous tests for conditions on the mean vectors and a given pattern for the covariance matrix is usually hindered by the nonmanageability of the expressions for their exact distribution functions. The authors show the importance of being able to adequately factorize the c.f. of the logarithm of likelihood ratio statistics in order to obtain sharp and highly manageable near-exact distributions, or even the exact distribution in a highly manageable form. The tests considered are the simultaneous tests of equality or nullity of means and circularity, compound symmetry, or sphericity of the covariance matrix. Numerical studies show the high accuracy of the near-exact distributions and their adequacy for cases with very small samples and/or large number of variables. The exact and near-exact quantiles computed show how the common chi-square asymptotic approximation is highly inadequate for situations with small samples or large number of variables.

scholarly journals An Optimal Eigenvalue Based Spectrum Sensing Algorithm for Cognitive Radio

2015 ◽  
Vol 3 (10) ◽  
pp. 45-54
Author(s):  
Gevira Omondi ◽  
Vitalis K. Oduol
Keyword(s):  
Cognitive Radio ◽  
Covariance Matrix ◽  
Spectrum Sensing ◽  
Cognitive Radios ◽  
Sample Covariance Matrix ◽  
Dominant Eigenvalue ◽  
Noise Power ◽  
Secondary Users ◽  
Sample Covariance ◽  
Spectrum Holes

Spectrum is a scarce resource, and licensed spectrum is intended to be used only by the spectrum owners. Various measurements of spectrum utilization have shown unused resources in frequency, time and space. Cognitive radio is a new concept of reusing licensed spectrum in an unlicensed manner. The unused resources are often referred to as spectrum holes or white spaces. These spectrum holes could be reused by cognitive radios, sometimes called secondary users. All man-made signals have some structure that can be potentially exploited to improve their detection performance. This structure is intentionally introduced for example by the channel coding, the modulation and by the use of space-time codes. This structure, or correlation, is inherent in the sample covariance matrix of the received signal. In particular the eigenvalues of the sample covariance matrix have some spread, or in some cases some known features that can be exploited for detection. This work aims to implement, evaluate, and eventually improve on algorithms for efficient computation of eigenvalue-based spectrum sensing methods. The computations will be based on power methods for computation of the dominant eigenvalue of the covariance matrix of signals received at the secondary users. The proposed method endeavors to overcome the noise uncertainty problem, and perform better than the ideal energy detection method. The method should be used for various signal detection applications without requiring the knowledge of the signal, channel and noise power.

Ensemble estimation of polarization ellipse parameters

2007 ◽  
Vol 463 (2088) ◽  
pp. 3375-3394 ◽  
Author(s):  
A.T Walden ◽  
T Medkour
Keyword(s):  
Angular Distribution ◽  
Standard Deviation ◽  
Aspect Ratio ◽  
Plane Wave ◽  
Wave Field ◽  
Covariance Matrix ◽  
Time Instant ◽  
Azimuth Angle ◽  
Ensemble Estimation ◽  
Plane Wave Field

An ellipse describes the polarized part of a partially polarized quasi-monochromatic plane wave field. Its azimuth angle and aspect ratio are functions of the elements of the covariance matrix associated with the polarized part at a particular time instant. Given an ensemble of K independent samples at that time, the distributions of the estimators of these parameters are derived. The estimation is thus based on a sample ensemble at any time, and does not assume temporal stationarity. Additionally, the azimuth angle estimator has an angular distribution so that non-standard statistical methods are needed when deriving its mean and standard deviation.

Enhanced Spectrum Sensing Algorithm Based on MME Detection and OAS Shrinkage Estimator

2019 ◽  
Vol 10 (1) ◽  
pp. 83-97
Author(s):  
Amoon Khalil ◽  
Mohiedin Wainakh
Keyword(s):  
Cognitive Radio ◽  
Covariance Matrix ◽  
Spectrum Sensing ◽  
Detection Probability ◽  
Detection Performance ◽  
Shrinkage Estimator ◽  
Detection Window ◽  
Simulation Results

Spectrum Sensing is one of the major steps in Cognitive Radio. There are many methods to conduct Spectrum Sensing. Each method has different detection performances. In this article, the authors propose a modification of one of these methods based on MME algorithm and OAS estimator. In MME&OAS method, in each detection window, OAS estimates the covariance matrix of the signal then the MME algorithm detects the signal on the estimated matrix. In the proposed algorithm, authors assumed that there is correlation between two consecutive decisions, so authors suggest the OAS estimator depending on the last detection decision, and then detect the signal using MME algorithm. Simulation results showed enhancement in detection performance (about 2dB when detection probability is 0.9. compared to MME&OAS method).

scholarly journals Target Detection in Low Grazing Angle with Adaptive OFDM Radar

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Yang Xia ◽  
Zhiyong Song ◽  
Zaiqi Lu ◽  
Hao Wu ◽  
Qiang Fu
Keyword(s):  
Target Detection ◽  
Orthogonal Frequency Division Multiplexing ◽  
Multipath Propagation ◽  
Random Phase ◽  
Grazing Angle ◽  
Detection Performance ◽  
Propagation Model ◽  
Ratio Test ◽  
Multipath Effect ◽  
Adaptive Ofdm

Multipath effect is the main factor of deteriorating target detection performance in low grazing angle scenario, which results from reflections on the ground/sea surface. Amplitudes of the received signals fluctuate acutely due to the random phase variations of reflected signals along different paths; thereby the performances of target detection and tracking are heavily influenced. This paper deals with target detection in low grazing angle scenario with orthogonal frequency division multiplexing (OFDM) radar. Realistic physical and statistical effects are incorporated into the multipath propagation model. By taking advantage of multipath propagation that provides spatial diversity of radar system and frequency diversity of OFDM waveform, we derive a detection method based on generalized likelihood ratio test (GLRT). Then, we propose an algorithm to optimally design the transmitted subcarrier weights to improve the detection performance. Simulation results show that the detection performance can be improved due to the multipath effect and adaptive OFDM waveform design.

Refining chronologies by dating pollen concentrates – new approach of separating pollen using flow cytometry

2020 ◽  
Author(s):  
Christoph Steinhoff ◽  
Nadine Pickarski ◽  
Thomas Litt
Keyword(s):  
Flow Cytometry ◽  
Radiocarbon Dating ◽  
Sediment Cores ◽  
Pollen Grains ◽  
Plant Macrofossils ◽  
Small Samples ◽  
Large Lakes ◽  
Promising Alternative ◽  
Ams Radiocarbon Dating ◽  
Short Period

<p>Radiocarbon dating of terrestrial plant-remains is a traditional method for precise age estimations of lake sediments. The absence of sufficient large plant macrofossils required for AMS dating in continental records, especially large lakes, demands for a satisfactory alternative, such as carbon-containing microfossils. Due to their ubiquitous presence in sedimentary archives pollen grains may be considered for dating. Nevertheless, the isolation and enrichment of pollen without a significant carbon contamination is still challenging. Even though commonly applied separation techniques can be used to remove the predominant portions of foreign particles, the undesirable transfer of these particles into the pollen concentrate cannot be excluded, yet. However, flow cytometry, as a highly promising alternative, offers the possibility to sort huge quantities of particles in a short period of time and to generate pure pollen concentrates from heterogeneous samples suitable for AMS radiocarbon dating.</p><p>In this study we present the approach to sort limnic sediment samples using flow cytometry. We are able to unequivocally identify pollen populations in the heterogeneous composition of the sediments and isolate them. The sediments analyzed were taken from the continental record of Lake Van (Eastern Anatolia). Annually laminated layers from the Holocene section of the sediment cores allow a precise temporal classification and validation of generated radiocarbon ages derived from fossil pollen. Although it is now possible to produce pollen concentrates without the contamination of foreign particles, the isolation of a sufficient quantity of pollen grains to generate reliable radiocarbon ages is still difficult. An increase pollen yield is required. Due to the limitation of the initial material, it is therefore especially necessary to improve the efficiency during the cytometric analysis.</p><p>Our results show the importance to steadily optimize the processing steps during chemical pretreatment, cytometric analysis as well as the radiocarbon dating itself. This facilitates the handling of the ultra-small samples and ensures precise age estimations of the pollen concentrates. Furthermore improving the laboratory routine for the enrichment of pollen will allow the analysis of vast amounts of samples in a short period of time. In consequence, dating pollen concentrates generated by flow cytometry can be used as a robust contribution and independent time control for existing chronologies in continental climate records.</p>

scholarly journals Compressive Detection Using Sub-Nyquist Radars for Sparse Signals

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Ying Sun ◽  
Jianjun Huang ◽  
Jingxiong Huang ◽  
Li Kang ◽  
Li Lei ◽  
...  
Keyword(s):  
Signal To Noise Ratio ◽  
Computation Time ◽  
Detection Performance ◽  
High Signal ◽  
Sparse Signals ◽  
Ratio Test ◽  
Digital Conversion ◽  
Real Time Processing ◽  
Analog To Digital ◽  
Analog To Digital Conversion

This paper investigates the compression detection problem using sub-Nyquist radars, which is well suited to the scenario of high bandwidths in real-time processing because it would significantly reduce the computational burden and save power consumption and computation time. A compressive generalized likelihood ratio test (GLRT) detector for sparse signals is proposed for sub-Nyquist radars without ever reconstructing the signal involved. The performance of the compressive GLRT detector is analyzed and the theoretical bounds are presented. The compressive GLRT detection performance of sub-Nyquist radars is also compared to the traditional GLRT detection performance of conventional radars, which employ traditional analog-to-digital conversion (ADC) at Nyquist sampling rates. Simulation results demonstrate that the former can perform almost as well as the latter with a very small fraction of the number of measurements required by traditional detection in relatively high signal-to-noise ratio (SNR) cases.

A note on the variance-ratio distribution

1950 ◽  
Vol 10 (01) ◽  
pp. 62-64
Author(s):  
M. T. L. Bizley
Keyword(s):  
Simple Formula ◽  
Distribution Functions ◽  
Ratio Test ◽  
Variance Ratio ◽  
Ratio Distribution ◽  
Variance Ratio Test ◽  
Elementary Methods ◽  
The One

In his paper (J.S.S.Vol. VI, p. 172) Dr Wishart showed that the variance-ratio test can be very easily used with the aid of the appropriate tables. It may not have been obvious to the reader of that paper that, unlike most distribution functions, the one in question can be evaluated by elementary methods and that a simple formula can be established to give the required probability independently of any table. It is not suggested that the use of the formula to be demonstrated in this note is preferable to the ordinary employment of tables. It may be remarked, however, that in certain cases where a probability has to be directly calculated the formula has a big advantage, since the tables give only the values of F (orz) corresponding to a few specific ‘probability points’ and interpolation between these must be very unsatisfactory, as is obvious from a glance at Table 3 of Dr Wishart's paper.

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