Maximum-minimum Eigenvalue Research Articles

Complete signed graphs with largest maximum or smallest minimum eigenvalue

In this paper, we deal with extremal eigenvalues of the adjacency matrices of complete signed graphs. The complete signed graphs with maximal index (i.e. the largest eigenvalue) with n vertices and m≤⌊n2/4⌋ negative edges have been already determined. We address the remaining case by characterizing those with m>⌊n2/4⌋ negative edges. We also identify the unique signed graph with maximal index among complete signed graphs whose negative edges induce a tree of diameter at least d for any given d. This extends a recent result by Li, Lin, and Meng [Discrete Math. 346 (2023), 113250] who established the same result for d=2. Finally, we prove that the smallest minimum eigenvalue of complete signed graphs with n vertices whose negative edges induce a tree is −n2−1−1+O(1n).

Evaluation Algorithm of Volleyball Players’ Competitive Ability Based on the Random Matrix Model

It is the trend of the development of modern competitive sports to put scientific and technological analysis methods and means into the study of volleyball, and it is also one of the powerful guarantee ways to promote the competitive level of all countries. The random matrix model algorithm has unique advantages to construct the team’s collective technical and tactical ability structure model. The quantitative relationship of the model describes the relationship between the technical and tactical ability structure and the result of victory and defeat and makes the advantages and disadvantages of the team clear, which is conducive to the subsequent targeted training and improvement. The technical and tactical abilities of the teams in different seasons were input to verify the prediction accuracy of the model for the teams in different seasons. In the face of the rapidly changing game situation, the coach team timely transmits the adjusted technical and tactical strategies to the players on the field and deals with the changes accurately and effectively. After the game, the opponent’s strengths and weaknesses should be clarified, and the team’s daily training details should be summarized to provide reference for the cultivation of collective technical and tactical consciousness. The random sample covariance matrix of the random monitoring matrix is constructed and the maximum and minimum eigenvalues of the sample covariance matrix are solved. The ratio of characteristic values is used to construct the detection index of characteristic values, and the detection threshold algorithm of characteristic values is determined to judge the competitive ability of volleyball players. In the case of false alarm rate and matrix size, based on Tracy-Widom distribution characteristics, the maximum eigenvalue and minimum eigenvalue approximations of sample covariance matrix are used to improve the eigenvalue index detection threshold algorithm, and the influence of false alarm rate, matrix size, and other parameters on the improved eigenvalue index detection threshold is further studied. Then, Iris data set was used to verify the effectiveness of the algorithm in terms of accuracy, recall rate, and comprehensive effective value, and the validation results proved that the accuracy of the algorithm reached more than 90%.

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.

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.

Multi-Path Hybrid Spectrum Sensing in Cognitive Radio

Inefficient utilization of the authorized spectrum emerges cognitive radio (CR) as a hopeful technology for both present and future telecommunications. It is owing to the potency to leverage the obtainable bandwidth of other wireless communication networks and thereby increase its occupancy. The key feature for the cognitive radio system for distinguishing the blank spectrum is spectrum sensing. This paper is intended to establish a hybrid sensing model for spectrum detection in CR to enhance the sensing efficiency of traditional techniques of spectrum sensing, which consists of two parallel paths of hybrid detectors. The first path is formed from two sequential detector stages; in the first phase, energy detector is used to recognize the PU signal existence where the signal has not been identified. Maximum–Minimum Eigenvalue (MME) is used as a second stage to detect the PU signal presence. The second path consists of two parallel stage detectors employing separate ED and MME to detect the PU signal individually, the two results are gathered to make a decision, and then the final detection decision is determined based on the two paths’ detection combined results. The proposed hybrid sensing approach adopted for enhancing the sensing performance is validated with conventional methods. Simulation results show that the proposed approach outperforms various traditional and hybrid approaches in terms of maximizing the detection probability on the specified limitations on the false alarm probability, as it can increase the detection probability to 94% instead of 79% for the parallel detector at SNR = − 10 dB and Pfa = 0.1.

An Adaptive Covariance Matrix Based on Combined Fully Blind Self Adapted Method for Cognitive Radio Spectrum Sensing

The main aim of this paper is to analysis and simulate existing methods such as energy detection, Maximum–Minimum Eigen value detectors (MME), MME with blind two stage detector and compare with the proposed adaptive covariance threshold method. This comparison is being made keeping in mind the complexity and accurateness in the terms of the sensing receiver operating characteristics curve. The influence of signal bandwidth of signal in comparison to the bandwidth of observation is done for every detector. As of the MME detector, the ratio between the bandwidth of the signal and the bandwidth of the observation is observed to be 0.5 when the reasonable values are used. The performance of the adaptive covariance threshold with combined full blind self-adapted detector are simulated on Matlab. The proposed method of detector shows a superior performance values when compared to three individual detectors. The performance metrics of proposed method are performed better than other three individual detector.

Optimized Complexity Problem Based on Combined Fully Blind Self Adapted Method using PSO for Cognitive Radio Spectrum Sensing

The main purpose of this paper is to solve the complexity problem and improved existing methods such as energy detection, Maximum-Minimum Eigen value detectors (MME), MME with blind two stage detector and adaptive covariance threshold method. PSO algorithm stands for Particle Swarm Optimization is utilized to novelty the optimal sensing time at that there will be maximum detection of probability for the Primary user. In which, we compare the optimal-PSO algorithm with non-optimal method. The simulation of the paper is depend on the performance of probability of detection based on the false alarm rate on the different region of the signal to noise ratio. The proposed optimized method of detector shows a superior performance values when compared to three individual detectors. The performance metrics of proposed method are performed better than other three individual detector.

Sensing and throughput analysis of a MU-MIMO based cognitive radio scheme for the Internet of Things

State-of-the-art energy detection (ED) based spectrum sensing requires perfect knowledge of noise power and is vulnerable to noise uncertainty. An eigenvalue-based spectrum sensing approach performs well in such an uncertain environment, but does not mitigate the spectrum scarcity problem, which evolves with the future Internet of Things (IoT) rollout. In this paper, we propose a multi-user multiple-input and multiple-output (MU-MIMO) based cognitive radio scheme for the Internet of Things (CR-IoT) with weighted-eigenvalue detection (WEVD) for the analysis of sensing, system throughput, energy efficiency and expected lifetime. In this scheme, each CR-IoT user is being equipped with MIMO antennas; we calculate the WEVD ratio, which is defined as the ratio between the difference of the maximum eigenvalue and minimum eigenvalue to the sum of the maximum eigenvalue and minimum eigenvalue. This mitigates against the spectrum scarcity problem, enhances system throughput, improves energy efficiency, prolongs expected lifetime and lowers error probability. Simulation results confirm the effectiveness of the proposed scheme; here the WEVD technique demonstrates a better detection gain and enhanced system throughput in comparison to the conventional scheme with eigenvalue based detection (EVD) and ED techniques in a noise uncertainty environment (i.e. SNR < -28). Furthermore, the proposed scheme has a lower energy consumption, prolonged expected lifetime and achieves a low error probability when compared with other schemes like the conventional single-input and single-output (SISO) based CR-IoT scheme with EVD and ED spectrum sensing.

Spectrum sensing based on deep learning classification for cognitive radios

Spectrum sensing is a key technology for cognitive radios. We present spectrum sensing as a classification problem and propose a sensing method based on deep learning classification. We normalize the received signal power to overcome the effects of noise power uncertainty. We train the model with as many types of signals as possible as well as noise data to enable the trained network model to adapt to untrained new signals. We also use transfer learning strategies to improve the performance for real-world signals. Extensive experiments are conducted to evaluate the performance of this method. The simulation results show that the proposed method performs better than two traditional spectrum sensing methods, i.e., maximum-minimum eigenvalue ratio-based method and frequency domain entropy-based method. In addition, the experimental results of the new untrained signal types show that our method can adapt to the detection of these new signals. Furthermore, the real-world signal detection experiment results show that the detection performance can be further improved by transfer learning. Finally, experiments under colored noise show that our proposed method has superior detection performance under colored noise, while the traditional methods have a significant performance degradation, which further validate the superiority of our method.

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.

Toward Overcoming a Hidden Terminal Problem Arising in MIMO Cognitive Radio Networks: A Tensor-Based Spectrum Sensing Algorithm

As the main enablers of cognitive radio (CR), numerous spectrum sensing techniques have been proposed to date. Despite the numerous techniques, the existing spectrum sensing techniques tend to fail in rendering an efficient spectrum sensing whenever a hidden terminal problem arises. Meanwhile, this problem can happen at any time in any severely fading primary-to-secondary channels resulting in very low primary signal-to-noise ratios (SNRs) and hence ineffective detection of the primary user. Toward overcoming this problem, by introducing a tensor-based hypothesis testing framework, this paper proposes an efficient tensor-based detector (TBD) for a multiple-input multiple-output (MIMO) CR networks over multi-path fading channels. For the proposed spectrum sensing technique, insightful asymptotic performance analyses are provided and Monte-Carlo simulations that assess its performance have been conducted. These simulations corroborate that TBD outperforms the generalized likelihood ratio test (GLRT) detector and the maximum-minimum eigenvalue (MME) detector, especially in the very low SNR regime which is a manifestation of the hidden terminal problem. Moreover, the simulations validate the derived asymptotic performance characterizations.

Primary signal detection algorithms for spectrum sensing at low SNR over fading channels in cognitive radio

The generalized detector (GD) can be implemented at the low signal-to-noise ratio (SNR) in cognitive radio (CR) systems to improve the spectrum sensing performance under correlated antenna array elements. The weighted GD (WGD) and the generalized likelihood ratio test for GD (GLRT-GD) are proposed to be used for coarse spectrum sensing when the noise power is known and unknown, respectively. The GD optimal detection threshold is defined based on the minimum probability of error criterion for various fading channels, namely, the additive white Gaussian noise (AWGN), Nakagami-m, and Rayleigh fading channels. The performance of the proposed algorithms are compared with the spectrum sensing performance of the energy detector (ED), weighted ED (WED), maximum-minimum eigenvalue (MME) detector, generalized likelihood ratio test for ED (GLRT-ED), matched filter (MF), arithmetic to geometric mean (AGM) detector, scaled largest eigenvalue (SLE) detector, moment based detector (MBD), covariance based detector (CBD), and others. The simulation results demonstrate superiority in the spectrum sensing performance of the proposed algorithms in comparison with the above-mentioned detectors. For example, the GLRT-GD achieves the SNR gain equal to 1.2 dB, 4.0 dB, and 4.5 dB in comparison with GLRT-ED, MME, and GM detectors, respectively, at the probability of false alarm PFA=0.1. The WGD and GLRT-GD implementation allows us to achieve a considerable spectrum sensing performance improvement at small number of samples under the low SNR and the correlated antenna array elements.

Improved Blind Spectrum Sensing by Covariance Matrix Cholesky Decomposition and RBF-SVM Decision Classification at Low SNRs

An improved blind spectrum sensing scheme is established by the covariance matrix Cholesky decomposition and radial basis function (RBF)-support vector machine (SVM) decision classification at low signal-to-noise ratios (SNRs). Under strong background noises, the proposed scheme improves the recognition rate of primary users (PUs) than that of the current blind spectrum sensing. First, the ratio of the maximum-to-minimum eigenvalue of a covariance matrix obtained by the Cholesky decomposition is used to construct the statistics. Second, the statistics are labeled with “+1” or “−1,” namely, the energy characteristics of the training samples are extracted and marked with “+1” for PUs and “−1” for noises. Finally, an RBF-SVM classification model, with an intelligent RBF as the SVM kernel function, is obtained by training the above-mentioned statistics and the labels. Thus, the received signals are classified as PUs or not be trained in the SVM model. The threshold possesses self-learning ability, and it distinguishes PU signals from noises effectively. The classification among PU signals and noises is implemented by the optimal SVM decision boundary, derived from maximizing the margin of the decision boundary of trained samples for efficient detection. In addition, the complexity of the statistic construction is lower than that of the conventional maximum minimum eigenvalue (MME). The simulation results show that the RBF in our scheme has 77.5% accuracy at −10 dB, and it outperforms linear kernel function significantly by about 27.5% in accuracy at −10 dB. In addition, the average error probability of the proposed scheme is reduced by about 26% when compared with those of original SVM schemes at −20 dB. The proposed scheme also outperforms the current MME detection in detection probability over 10% at −20 dB. Therefore, the proposed blind spectrum sensing scheme can be efficiently used to detect the PUs by the covariance matrix Cholesky decomposition and the RBF-SVM decision classification in the fifth-generation (5G) communications, especially at low SNRs.

Application of Wireless Sensor Network Technology in Security Control of Intelligent Buildings

When a wireless sensor network is used to perform real-time security monitoring inside a building, there are drawbacks like multi-path signal fading and difficulty in spectrum sensing. In light of these problems, this paper proposes an improved signal spectrum sensing algorithm based on support vector machine (SVM), which inhibits the impacts brought by the low signal-noise-ratio (SNR) environment in the transmission process of wireless sensor signals through the embedded cyclostationary characteristic parameters. Based on this, considering the low efficiency and poor fault tolerance of multi-task monitoring and scheduling inside the building, this paper also proposes a multi-task coordination and scheduling algorithm based on physical information integration, which achieves multi-task scheduling and execution through intelligent breakdown and prioritization of general tasks. The simulation test shows that, compared with the artificial neural network (ANN) algorithm and the maximum-minimum eigenvalue (MME) algorithm, the proposed algorithm has much better spectrum sensing effect under low SNR, takes less computation time, and achieves higher accuracy in large-scale multi-task coordination and scheduling. The research conclusions can provide new ideas for the application of wireless sensor network in intelligent building security monitoring.

On the first two largest distance Laplacian eigenvalues of unicyclic graphs

The distance Laplacian eigenvalues of a connected graph G are the eigenvalues of its distance Laplacian matrix L(G), defined as L(G)=Tr(G)−D(G), where Tr(G) is the diagonal matrix of vertex transmissions of G, and D(G) is the distance matrix of G. In this paper, we determine the unique unicyclic graphs with maximum largest distance Laplacian eigenvalue and minimum second largest distance Laplacian eigenvalue, respectively.

Noise Uncertainty Effect on a Modified Two-Stage Spectrum Sensing Technique

Detecting the presence or absence of primary user is the key task of cognitive radio networks. However, relying on single detector reduces the probability of detection and increases the probability of missed detection. Combining two conventional spectrum sensing techniques by integrating their individual features improves the probability of detection especially under noise uncertainty. This paper introduces a modified two-stage detection technique that depends on the energy detection as a first stage due to its ease and speed of detection, and the proposed Modified Combinational Maximum-Minimum Eigenvalue based detection as a second stage under noise uncertainty and comperes it with the case of using Maximum-Minimum Eigenvalue and Combinational Maximum-Minimum Eigenvalue as a second stage.

A Frequency Domain Approach to Eigenvalue-Based Detection With Diversity Reception and Spectrum Estimation

In this paper, we investigate a frequency domain approach for eigenvalue-based detection of a primary user, based on equal gain combining (EGC) and spectrum estimation with Bartlett’s method. This paper considers two techniques for eigenvalue detection which are Maximum Eigenvalue Detection (MED) and the Maximum-Minimum Eigenvalue (MME) detector. We exploit the eigenvalues that are associated with the Hermitian form representation of Bartlett’s estimate to assess the performance of the aforementioned eigenvalue techniques in the frequency domain. For each case, we quantify the performance based on the probabilities of false alarm and missed detection over Rayleigh and Rician fading. A bivariate Mellin transform approach is employed to obtain the probability distribution function for the ratio of the extreme eigenvalues under each hypothesis. All obtained formulas are validated via Monte-Carlo simulations, and the results give a clear insight into the performance of the investigated methods. In frequency domain, MED outperforms both the MME detector and Periodogram-based energy detection even in a worst case scenario of noise uncertainty, while the MME detector exhibits heavy-tailed statistical characteristics and thus its receiver operating characteristics tend to stay on the line of no-discrimination. The performance of MED is further enhanced by careful choice of combinations of the total length of the sensing frame and number of sub-slots.

Spectrum Sensing Algorithm to Detect Small-Scale Primary Users Based on Maximum-Minimum Eigenvalue

Spectrum Sensing Algorithm to Detect Small-Scale Primary Users Based on Maximum-Minimum Eigenvalue

Dynamic Digital Channelizer Based on Spectrum Sensing.

The ability to efficiently channelize a received signal with dynamic sub-channel bandwidths is a key requirement of software defined radio (SDR) systems. The digital channelizer, which is used to split the received signal into a number of sub-channels, plays an important role in SDR systems. In this paper, a design of dynamic digital channelizer is presented. The proposed method is novel in that it employs a cosine modulated filter bank (CMFB) to divide the received signal into multiple frequency sub-bands and a spectrum sensing technique, which is mostly used in cognitive radio, is introduced to detect the presence of signal of each sub-band. The method of spectrum sensing is carried out based on the eigenvalues of covariance matrix of received signal. The ratio of maximum-minimum eigenvalue of each sub-band is vulnerable to noise fluctuation. This paper suggests an optimized method to calculate the ratio of maximum-minimum eigenvalue. The simulation results imply that the design of digital channelizer can effectively separate the received signal with dynamically changeable sub-channel signals.

Spectrum sensing using low-complexity principal components for cognitive radios

Principal component (PC) algorithm has recently been shown as a very accurate blind detection technique in comparison with other covariance-based detection algorithms. However, it also has a higher complexity owing to the computation of the eigenvectors. We propose a low-complexity Lanczos principal component (LPC) algorithm that utilizes Lanczos iterative method to compute the eigenvectors. In comparison with the PC algorithm, the proposed LPC algorithm offers significant reduction in complexity while giving a similar detection performance. Low-complexity LPC algorithm allows for the use of larger sized covariance matrix that further improves the detection performance. Maximum-minimum eigenvalue (MME) algorithm is also included in the comparison and it gives an inferior performance as compared to both PC and LPC algorithm. All the algorithms were tested with experimental data while using universal software radio peripheral (USRP) testbed that was controlled by GNU radio software.