Eigenvalue Detection Research Articles

A New Extended Target Detection Method Based on the Maximum Eigenvalue of the Hermitian Matrix

In the field of radar target detection, the conventional approach is to employ the range profile energy accumulation method for detecting extended targets. However, this method becomes ineffective when dealing with non-stationary and non-uniform radar clutter scenarios, as well as long-distance targets with weak radar cross sections (RCSs). In such cases, the signal-to-noise ratio (SNR) of the target echo is severely degraded, rendering the energy accumulation detection algorithm unreliable. To address this issue, this paper presents a new extended target detection method based on the maximum eigenvalue of the Hermitian matrix. This method utilizes a detection model that incorporates observed data and employs the likelihood ratio test (LRT) theory to derive the maximum eigenvalue detector at low SNR. Specifically, the detector constructs a matrix using a sliding window block with the available data and then computes the maximum eigenvalue of the covariance matrix. Subsequently, the maximum eigenvalue matrix is transformed into a one-dimensional eigenvalue image, enabling extended target detection through analogy with the energy accumulation detection method. Furthermore, this paper analyzes the proposed extended target detection method from both theoretical and experimental perspectives, validating it through field-measured data. The results obtained from the measured data demonstrate that the method effectively enhances the SNR in low SNR conditions, thereby improving target detection performance. Additionally, the method exhibits robustness across different scattering center targets.

Enhancing spectrum utilization and primary user detection in cognitive radio networks through greedy cooperative spectrum sensing

The utilization of the spectrum is optimized through which primary users of modern wireless communication technologies might obtain a higher chance of detection. The research aims to study how the NI-USRP hardware platform can be used to set up greedy cooperative spectrum sensing for cognitive radio networks. Research primarily deals with energy detection and eigenvalue-based detection approaches, both of which are highly recognized for their capacity to sense the spectrum without having prior knowledge of the primary user signals. In the hardware arrangement, there is one transmitter and two cognitive radio receivers. LABVIEW makes it simple to deploy and maximizes the detection probability across a large sample. Here, it was demonstrated that cooperative spectrum sensing is superior to non-cooperative spectrum sensing, which results in a reduction in the risk of errors occurring during detection. The research discovered that the OR combination rule has a higher detection probability than the AND rule at the same time. The research emphasizes the significance of expanding cooperative spectrum sensing to improve overall detection capabilities. SNRs that are more than 10 dB allow the energy detector to operate, and the eigenvalue detector continues to work when the SNR drops to –9 dB.

Comparative analysis of blind detectors in a cluster-based cooperative Spectrum Hole detection

Prevention of authorized users from interference determine the accurate detection of Spectrum Hole (SH) is of great importance in a Spectrum Shearing Network (SSN). However, multipath fading and shadowing affect the accurate detection of SH resulting in interference. Cluster-Based Cooperative Spectrum Hole Detection (CBCSHD) used to address this problem depends on detector and number of clusters. Hence, comparative analysis of blind detectors in CBCSHD is carried out to evaluate its performance with various blind detectors and number of clusters. The CBCSHD is carried out using six Cognitive Users (CUs) that jointly carry out detection of SH and each of the CUs performs local sensing using Eigenvalue Detector (EVD), Energy Detector (ED) and Cyclostationary Detector (CD). The CUs form clusters to reduce reporting overhead between CUs. The local sensing results from individual user are combined at the Cluster Head (CH) using majority fusion rule. The performance of each of the detectors in CBCSHD is evaluated using Probability of Detection (PD) and Sensing Time (ST). PD values of 0.7661, 0.7160 and 0.6229 are obtained at SNR of 4 dB for ED, CD and EVD, respectively, while ST values of 3.0707, 3.7163 and 4.0907 s are obtained for ED, CD and EVD, respectively. The results obtained show that ED has the highest detection rate, followed by CD, while EVD shows the worst detection rate.

Efficient Centralized Cooperative Spectrum Sensing Techniques for Cognitive Networks

Wireless Communication is a system for communicating information from one point to other, without utilizing any connections like wire, cable, or other physical medium. Cognitive Radio (CR) based systems and networks are a revolutionary new perception in wireless communications. Spectrum sensing is a vital task of CR to avert destructive intrusion with licensed primary or main users and discover the accessible spectrum for the efficient utilization of the spectrum. Centralized Cooperative Spectrum Sensing (CSS) is a kind of spectrum sensing. Most of the test metrics designed till now for sensing the spectrum is produced by using the Sample Covariance Matrix (SCM) of the received signal. Some of the methods that use the SCM for the process of detection are Pietra-Ricci Index Detector (PRIDe), Hadamard Ratio (HR) detector, Gini Index Detector (GID), etc. This paper presents the simulation and comparative performance analysis of PRIDe with various other detectors like GID, HR, Arithmetic to Geometric Mean (AGM), Volume-based Detector number 1 (VD1), Maximum-to-Minimum Eigenvalue Detection (MMED), and Generalized Likelihood Ratio Test (GLRT) using the MATLAB software. The PRIDe provides better performance in the presence of variations in the power of the signal and the noise power with less computational complexity.

RIS-Enhanced Spectrum Sensing: How Many Reflecting Elements are Required to Achieve a Detection Probability Close to 1?

In this paper, we propose a reconfigurable intelligent surface (RIS) enhanced spectrum sensing system, in which the primary transmitter is equipped with a single antenna, the secondary transmitter is equipped with multiple antennas, and the RIS is employed to reduce the required signal samples while realizing a high detection probability. Without loss of generality, we adopt the maximum eigenvalue detection approach, and propose a corresponding analytical framework based on random matrix theory, to evaluate the detection probability in the asymptotic regime. Besides, the RIS is configured with only the statistical channel state information to avoid realtime channel estimation. With the statistical configuration, the asymptotic distributions of the equivalent channel gains are derived. Then, we provide the theoretical predictions about the number of reflecting elements required to achieve a detection probability close to 1. Finally, we present the Monte-Carlo simulation results to evaluate the accuracy of the proposed asymptotic analytical framework for the detection probability and the validity of the theoretical predictions about the number of REs required to achieve a detection probability close to 1. Moreover, the simulation results show that the proposed RIS-enhanced spectrum sensing system can substantially improve the detection performance.

Maximum eigenvalue detection for local ionospheric anomaly - theory, cases, statistics, and potential application

At low latitudes in China, local ionospheric anomalies are frequent and difficult to capture, posing positioning errors and safety risks to GNSS users. This leads to conservative error bounds in GNSS augmentation systems. For example, in Satellite Based Augmentation System (SBAS), the presence of under-sampled regions and the ionospheric instability at low latitudes can result in an over-conservative error bound, i.e., Grid Ionospheric Vertical Error (GIVE) with reduced availability. Ionospheric irregularity detectors could be used to exclude anomalies from the grid model to share the integrity risk and tighten the GIVE. The detection method needs to have theoretical validity and sensitivity to small local anomalies. However, current irregularity detectors are designed for Ionospheric Grid Point (IGP), dealing with wide-area spatial anomalies. The problem of decreased availability resulting from the over-conservative error bound caused by the frequent local ionospheric anomalies is unsolved, especially at low latitudes and the equatorial region. To further enhance the GNSS performance, the applicability analysis of a maximum eigenvalue-based ionospheric irregularity detector, which is sensitive to local-scale spatial anomalies, is presented. The detection capability of MED for ionospheric anomalies is demonstrated by theory, cases, statistics, and simulation applications. This method can also be used for ionospheric monitoring in geodesy or geophysics.

A Neural Network Model for Business Performance Management Based on Random Matrix Theory

This paper uses random matrix theory to construct a neural network model for business performance management. The random sample covariance matrix of the random monitoring matrix is constructed, and the maximum eigenvalue and the minimum eigenvalue of the sample covariance matrix are solved. The ratio of eigenvalues is used to construct the eigenvalue detection index and determine the eigenvalue index detection threshold algorithm to judge the abnormal state of enterprise operation. The data of 66 listed Internet finance companies are selected, normalized, and correlation tested, and the index weights of each level are obtained using hierarchical analysis to derive the expected output of the BP neural network. Finally, the constructed BP neural network performance evaluation model is used for network training and simulation analysis, in which 192 data of 48 companies in the last four years are selected as training samples and 8 companies in the last four years are used as test samples to analyze the simulation output results. Using the original data instead of the main factor to join the BP neural network model, after two systematic optimizations, the final model with high accuracy, low mean square error, and low average error was formed. When applying the newly added data for testing, an accuracy of 95.98% was achieved for the ranking prediction, and the average deviation of 0.0021 points for the score prediction, which fully reflected the feasibility and adaptability of the model.

CNN-aided multiple PU spectrum sensing in uncalibrated massive antennas SU system

This paper deploys the Convolutional Neural Network (CNN) to learn and set the statistical test in Spectrum Sensing (SS) task of multiple primary user (PU) sources in massive uncalibrated antennas of secondary users (SU) sharing the same spectrum resources. The proposed deep learning-based SS method (DL-SS) is based on the CNN architecture that has the capability of extracting features of the sample covariance matrices (SCMs) that are given as the network input, improving the overall performance and robustness. The proposed CNN-SS method is compared with nine recent multiple-antennas SS methods, namely the arithmetic–geometric detector (AGM), John’s detector (JD), sphericity detector (SD), generalized likelihood test (GLRT), locally most powerful invariant test (LMPIT), maximum–minimum eigenvalue detector (MME), covariance detector (CAV), Hadamard detector (HD) and volume detector (VD) methods; besides, the proposed method is also compared with five recent state-of-art CNN-based SS methodologies. Performance-complexity trade-off of the proposed and reference SS methods are corroborated via Monte Carlo Simulations (MCS). The proposed CNN-SS method under uncalibrated massive antennas reveals substantial benefits w.r.t. the reference methods and is competitive with others CNN-SS methodologies, both in terms of complexity and performance, achieving detection probability of Pd=0.9(@SNR=−20dB) under very low false alarm probability Pf=0.1. Under different figures of merit, the performance of the CNN-based SS detector has revealed to be indubitably superior regarding the state-of-art SS detectors. However, the proposed CNN-based SS detector presents relative computational complexity increases. Hence, to be effective, such a superior operational performance requires a very efficient processing structure in the SU base stations.

Comprehensive review on spectrum sensing techniques in cognitive radio

In wireless communication, spectrum sensing (SS) is one of the important techniques to study about the radio environment. Spectrum sensing phenomenon is used to estimate the unutilized frequency band of whole radio spectrum. Utilization of available spectrum can be improved by enhancing the spectrum sensing techniques. The performance of available spectrum sensing techniques may degrade substantially in low signal to noise ratio, multipath fading & shadowing environments. This may lead to increase in probability of false alarms and decrease in probability of detection. This paper gives the categorization of different spectrum sensing techniques (SST) and it also explores the different methods used in spectrum sensing. Comparison of energy detector (ED), matched filter detection (MFD), cyclostationary feature detection (CFD), waveform detection (WD) and eigen value detection (EVD) based on their methodology and accuracy is also present in this paper. Various issues associated with these spectrum sensing techniques are highlighted here and futuristic solutions proposed for improvement in existing spectrum sensing techniques.

Energy-efficient cooperative spectrum sensing for detection of licensed users in a cognitive radio network using eigenvalue detector

Energy-efficient cooperative spectrum sensing for detection of licensed users in a cognitive radio network using eigenvalue detector

Constraint on Bounded Relative Distance for Robust MME Detection in Spaceborne Cluster Flight Netted Radar

In this paper, we investigate the robust maximum-minimum eigenvalue (MME) detection problem caused by this uncertainty of geometric configuration. Firstly, according to the proposed novel concept of spaceborne cluster flight netted radar (SCFNR) integrated cluster flight spacecraft with netted radar recently, we define the robust detector for the uncertainty of geometric configuration due to the mobility in SCFNR and give the condition about robust MME detector. Using the channel gain matrix in one CPI, the closed-form of the lower bound on the test statistic under the presence of target return, and the upper bound under the absence of target return are given respectively. Secondly, using the mobility model about transmitter-receiver pairs in SCFNR, we give the constraint on the bounded relative distance for robust MME detector in SCFNR. Finally, the effectiveness of the proposed constraint is validated through numerical calculations. The results show also that controlling the orbit elements about the transmitter and receiver platforms in SCFNR can make sure the robustness of MME and the relative distance bounded.

Ship Target Detection in SAR Imagery Based on Maximum Eigenvalue Detector

Ship target detection in synthetic aperture radar (SAR) imagery is of great significance in the field of ocean monitoring. Classical constant false alarm rate (CFAR) detectors and emerging information geometry methods are model-driven essentially, requiring precise modeling of the sea clutter distribution. In the complex and changeable ocean scenes, the performance of these two types of detectors is limited. To solve this problem, a ship target detection algorithm in SAR imagery based on the maximum eigenvalue of the sample covariance matrix is proposed in this letter. Without seeking the distribution model of clutter backgrounds, the difference between the target and the clutter background is fully captured by constructing the sample covariance matrix, and its maximum eigenvalue is utilized as the test statistic. Experimental results on measured SAR images show that the proposed method achieves better detection performance and faster calculation speed compared with the existing typical methods.

Spectrum Prediction in Cognitive Radio Network Using Machine Learning Techniques

Cognitive Radio (CR) aims to achieve efficient utilization of scarcely available radio spectrum. Spectrum sensing in CR is a basic process for identifying the existence or absence of primary users. In spectrum sensing, CR users suffer from deep fading effects and it requires additional sensing time to identify the primary user. To overcome these challenges, we frame Spectrum Prediction-Channel Allocation (SP-CA) algorithm which consists of three phases. First, clustering mechanisms to select the spectrum coordinator. Second, Eigenvalue based detection method to expand the sensing accuracy of the secondary user. Third, Bayesian inference approach to reduce the performance degradation of the secondary user. The Eigenvalue based detection method is compared with Energy detection method in terms of varying false alarm rates and samples. The Eigenvalue detection method achieves better performance than Energy detection method. The Simulation results show that our approach gives better performance in terms of reducing sensing time and increasing sensing accuracy.

Effect of random sampling on spectrum sensing for cognitive radio networks

Cognitive radio is a mechanism allowing dynamic access to spectrum channels. Since its beginnings, researchers have been working on using this inventive technology to control and manage the spectrum resources. Consequently, this research field has been progressing rapidly and important advances have been made. Spectrum sensing is a key function of cognitive radios that helps prevent the harmful interference with licensed users, as well as identifies the available spectrum to improve its utilization. Several spectrum sensing techniques are found in scientific literature. In this paper, we investigate the effect of the random sampling in spectrum sensing. We propose a spectrum sensing approach based on the energy detection and on the maximum eigenvalue detection (MED) combined with random sampling. The performance of the proposed approach is evaluated in terms of the receiver operating characteristics curves and in terms of the detection probability for different values of signal to noise ratio. The obtained results are compared to the uniform sampling case to show the added value of random sampling.

An Integrated Parallel Multistage Spectrum Sensing for Cognitive Radio

Spectrum sensing for cognitive radio requires speed and good detection performance at very low SNR ratios. There is no single-stage spectrum sensing technique that is perfect enough to be implemented in practical cognitive radio. In this paper, the authors propose a new parallel fully blind multistage detector. They assume the appropriate stage based on the estimated SNR values that are achieved from the SNR estimator. Energy detection is used in first stage for its simplicity and sensing accuracy at high SNR. For low SNRs, they adopt the maximum eigenvalues detector with different smoothing factor in higher stages. The sensing accuracy for the maximum eigenvalue detector technique improves with higher value of the smoothing factor. However, the computational complexity will increase significantly. They analyze the performance of two cases of the proposed detector: two-stage and three-stage schemes. The simulation results show that the proposed detector improves spectrum sensing in terms of accuracy and speed.

Eigenvalue‐based ground target detection in high‐resolution range profiles

In this study, the authors address the problem of range-distributed target detection in sequential high resolution range profiles (HRRPs). They propose a modified scaled largest eigenvalue detector for static target in homogenous ground clutter. A set of secondary data, which are free of target signal and have the same distribution as the clutter in the primary data, are assumed to be available. First, the sample covariance matrix (SCM) is estimated from the acquired multiple HRRPs in a short coherent processing interval. Then, the eigenvalue decomposition of the SCM is performed, and the eigenvalues are sorted in descending order. Finally, the largest eigenvalue scaled by the noise power estimated from the secondary data is selected as the detection statistic. Compared with existing methods of largest eigenvalue-based detection, the proposed method achieves better detection performance for coloured clutter by considering secondary data. Numerical and experimental results demonstrate the effectiveness of the proposed method.

Implementation of cooperative spectrum sensing using cognitive radio testbed

Objectives: To implement energy detection and eigenvalue based cooperative spectrum sensing in NI-USRP hardware platform and to obtain its performance.Cooperative spectrum sensing is to be implemented using O and AND fusion rules. Methodology: The hardware is implemented using one primary user transmitter and two cognitive radio users. The implementation is done using LABVIEW and detection performance is analyzed. In cooperative spectrum sensing (CSS), CR system shares its own sensing information with other sensing nodes and utilizes the sensing outcomes of others to give a decision. Findings: Energy detection performs well in high SNR region and eigenvalue based detection performs well even with low SNR region. Energy detector detects the signal completely with SNR greater than 10dB. Eigenvalue detector detects signal completely at SNR of -9dB. Detection probability with OR Cooperative rule is better than AND rule. It increases with number of samples and signal to noise ratio. It is found that cooperative spectrum sensing performs well than the noncooperative sensing by decreasing the chances of miss detection. Novelty: CSS is robust in sensing errors due to hidden node or fading channels and also it decreases the probabilities of false alarm as well as probabilities of miss detection. Keywords: Cognitive radio; Cooperative spectrum sensing; Primary users; Secondary users; Energy detection

An Overview of the Different Principal Spectrum Sensing Techniques in Cognitive Radio Systems

Cognitive radio is a technology proposed to increase the effective use of the spectrum. This can be done through the main function of cognitive radio technology, which is the spectrum sensing. In our work, we propose an analysis of the following spectrum sensing techniques: the matched filter detector, the cyclostationary feature detector, the energy detector and the maximum eigenvalue detector. More attention is given to blind sensing techniques that they do not need any knowledge of the primary user signal characteristics, namely the energy detection and maximum eigenvalue detection. These methods are evaluated in terms of Receiver Operational Characteristic curves and detection probability for various values of Signal to Noise Ratio based on Monte Carlo simulations, using MATLAB. As a result of this study, we found that the energy detection offers a good performance only for high SNR. Furthermore, with the maximum eigenvalue detector, the noise uncertainty problem encountered by the energy detection is solved when the value of the smoothing factor L ≥ 8 and. Finally, a summary of the comparative analysis is presented.

Enhanced Detection Algorithms Based on Eigenvalues and Energy in Random Matrix Theory Paradigm

This paper considers the problem of spectrum sensing in multi-antenna cognitive radio networks. Energy detection (ED) method for spectrum sensing does not require any information of the source signal and channel, as well as it is suitable for detecting independent identically distributed signals. Since covariance matrix catches the signal correlations well, the maximum eigenvalue detection (MED) method is more competitive than the ED method for correlated signals. Under the framework of random matrix theory, this paper firstly proposes two enhanced detection algorithms based on the maximum eigenvalue and energy of the signal to achieve performance improvement while preserving the advantages of the two algorithms. The proposed algorithms are a generalization of the ED and MED methods. To render the proposed algorithms more practical, we propose two other new blind spectrum sensing algorithms based on the maximum likelihood estimate of unknown noise variance. Using random matrix theory, the theoretical analysis on detection probability, false alarm probability and threshold are given. Finally, simulation results show the effectiveness and robustness of the proposed algorithms.

Improved Two-Stage Spectrum Sensing for Cognitive Radio Networks

Cognitive radio employs an opportunistic spectrum access approach to ensure efficient utilization of the available spectrum by secondary users (SUs). To allow SUs to access the spectrum opportunistically, the spectrum sensing process must be fast and accurate to avoid possible interference with the primary users. Previously, two-stage spectrum sensing methods were proposed that consider the sensing time and sensing accuracy parameters independently at the cost of a non-optimal spectrum sensing performance. To resolve this non-optimality issue, we consider both parameters in the design of our spectrum sensing scheme. In our scheme, we first derive optimal thresholds using an optimization equation with an objective function of maximizing the probability of detection, subject to the minimal probability of error. We then minimize the average spectrum sensing time using signal-to-noise ratio estimation. Our simulation results show that the proposed improved two-stage spectrum sensing (ITSS) scheme provides a 4%, 7%, and 6% better probability of detection accuracy rate than two-stage combinations of energy detection (ED) and maximum eigenvalue detection, energy detection and cyclostationary feature detection (CFD), and ED and combination of maximum-minimum eigenvalue (CMME) detection, respectively. The ITSS is superior also to single-stage ED by 19% and shows an improved average spectrum sensing time.