Maximum-minimum Eigenvalue Detection Research Articles

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.

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.

Decentralized Adaptive Eigenvalue-Based Spectrum Sensing for Multiantenna Cognitive Radio Systems

Eigenvalue-based spectrum sensing (EBSS) techniques may operate in a totally blind manner while they offer remarkably improved performance for specific types of signals compared with energy-based methods. In the literature so far, only batch and centralized cooperative EBSS techniques have been considered, which, however, suffer from limitations that render them impractical in several cases. Thus, the aim of this paper is to develop practical cooperative adaptive versions of typical EBSS techniques that could be applied in a completely decentralized manner. To this end, at first, novel adaptive EBSS techniques are developed for the maximum eigenvalue detector, the maximum-minimum eigenvalue detector, and the generalized likelihood ratio test scheme, respectively, for a single-user (no cooperation) case. Then, a novel distributed subspace tracking method is proposed, which enables the cooperating nodes to track the joint subspace of their received signals. Based on this method, cooperative decentralized versions of the adaptive EBSS techniques are subsequently developed that overcome the limitations of the existing batch centralized approaches. The performance of the proposed methods is verified via indicative simulations.

Energy and Eigenvalue Based Combined Fully Blind Self Adapted Spectrum Sensing Algorithm

In this paper, a comparison between energy and maximum-minimum eigenvalue (MME) detectors is performed. The comparison has been made concerning the sensing complexity and the sensing accuracy in terms of the receiver operating characteristic (ROC) curves. The impact of the signal bandwidth compared with the observation bandwidth is studied for each detector. For the energy detector, the probability of detection increases monotonically with the increase in the signal bandwidth. For the MME detector, an optimal value of the ratio between the signal bandwidth and the observation bandwidth is found to be 0.5 when reasonable values of the system dimensionality are used. Based on the comparison findings, a combined two-stage detector is proposed. The combined detector performance is evaluated based on simulations and measurements. The combined detector achieves better sensing accuracy than the two individual detectors with complexity that lies in between the two individual complexities. The combined detector is fully blind and self-adapted as the MME detector estimates the noise and feeds it back to the energy detector. The performance of the noise estimation process is evaluated in terms of the normalized mean square error (NMSE).

Signal Bandwidth Impact on Maximum-Minimum Eigenvalue Detection

The impact of the signal bandwidth and observation bandwidth on the detection performance of the maximum-minimum eigenvalue detector is studied in this letter. The considered signals are the Gaussian signals. The optimum ratio between the signal and the observation bandwidth is analytically proven to be 0.5 when reasonable values of the system dimensionality are used. The analytical proof is verified by simulations.

Performance Evaluation of Different Spectrum Sensing Techniques for Realistic Implementation Oriented Model in Cognitive Radio Networks

In this paper, the performance assessment of five different detection techniques from spectrum sensing perspective in cognitive radio networks is proposed and implemented using the realistic implementation oriented model (R-model) with signal processing operations. The performance assessment of the different sensing techniques in the existence of unknown or imprecisely known impulsive noise levels is done by considering the signal detection in cognitive radio networks under a non-parametric multisensory detection scenario. The examination focuses on performance comparison of basic spectrum sensing mechanisms as, energy detection (ED) and cyclostationary feature detection (CSFD) along with the eigenvalue-based detection methods namely, Maximum-minimum eigenvalue detection (MMED), Roy’s largest Root Test (RLRT) which requires knowledge of the noise variance and Generalized Likelihood Ratio Test (GLRT) which can be implemented as a test of the largest eigenvalues vs. Maximum-likelihood estimates a noise variance. From simulation results it is observed that the detection performance of the GLRT method is better than the other techniques in realistic implementation oriented model.

Improved Maximum-Minimum Eigenvalue Detection with a Single Antenna Using Jackknifing

Spectrum sensing is critical for cognitive radio networks as it allows a secondary user to find spectrum holes for opportunistic reuse. In this paper, an improved maximum-minimum eigenvalue detection method is proposed for a cognitive user equipped with a single receiving antenna. The proposed method utilizes the temporal smoothing technique to form a virtual multiple antennas structure. At the same time, the jackknifing resampling strategy is employed to improve the detection performance. Simulation results are presented to verify the effectiveness of the proposed method.

Spectrum Sensing in Multi-antenna OFDM System for Cognitive Radio Networks

This paper proposes an efficient spectrum sensing scheme for OFDM signal transmitted by the primary user with its Cyclic Prefix Correlation Coefficient (CPCC) based on multi-antenna. Inspired by the Maximum-minimum Eigenvalue Detection (MMED) algorithm, a CPCC-based MMED spectrum sensing algorithm is proposed. This algorithm uses inherent property of Cyclic Prefix (CP) resulting in nonzero correlation of the received OFDM primary signal. The maximum-to-minimum eigenvalue ratio of the covariance matrix of the received primary signal is used as a test statistic to detect signal existence. Based on the random matrix theory, we obtain the quantification of the detection ratio, threshold and probability. Finally, the performance of the algorithm is studied through computer simulations. A comparison of the proposed CPCC-MMED algorithm with MMED and ED algorithms is also carried out.

Performance of Cooperative Eigenvalue Spectrum Sensing with a Realistic Receiver Model under Impulsive Noise

In this paper we present a unified comparison of the performance of four detection techniques for centralized data-fusion cooperative spectrum sensing in cognitive radio networks under impulsive noise, namely, the eigenvalue-based generalized likelihood ratio test (GLRT), the maximum-minimum eigenvalue detection (MMED), the maximum eigenvalue detection (MED), and the energy detection (ED). We consider two system models: an implementation-oriented model that includes the most relevant signal processing tasks realized by a real cognitive radio receiver, and the theoretical model conventionally adopted in the literature. We show that under the implementation-oriented model, GLRT and MMED are quite robust under impulsive noise, whereas the performance of MED and ED is drastically degraded. We also show that performance under the conventional model can be too pessimistic if impulsive noise is present, whereas it can be too optimistic in the absence of this impairment. We also discuss the fact that impulsive noise is not such a severe problem when we take into account the more realistic implementation-oriented model.

Cooperative Spectrum Sensing Using Eigenvalue Fusion for OFDMA and Other Wideband Signals

In this paper, we propose a new approach for the detection of OFDMA and other wideband signals in the context of centralized cooperative spectrum sensing for cognitive radio (CR) applications. The approach is based on the eigenvalues of the received signal covariance matrix whose samples are in the frequency domain. Soft combining of the eigenvalues at the fusion center is the main novelty. This combining strategy is applied to variants of four test statistics for binary hypothesis test, namely: the eigenvalue-based generalized likelihood ratio test (GLRT), the maximum-minimum eigenvalue detection (MMED), the maximum eigenvalue detection (MED) and the energy detection (ED). It is shown that the eigenvalue fusion can outperform schemes based on decision fusion and sample fusion. A tradeoff is also established between complexity and volume of data sent to the fusion center in all combining strategies.

Blind Spectrum Sensing for Cognitive Radios Using Discriminant Analysis: A Novel Approach

In this paper, we present a new spectrum sensing technique for cognitive radios based on discriminant analysis called spectrum discriminator. The presented technique uses the knowledge of the noise uncertainty and a probabilistic validation to overcome the limitations of the discriminant analysis. A comparative study between the proposed technique and the maximum-minimum eigenvalue detection has been performed based on two performance metrics: the probability of false alarm and the probability of detection. The spectrum discriminator has been further developed to a peel-off technique where all primary users can be detected. The performance of the spectrum discriminator and the peel-off technique has been tested on simulations and experimentally verified. The comparative study is based on simulations as well as measurements.

PRIMARY USER SIGNAL DETECTION BASED ON VIRTUAL MULTIPLE ANTENNAS FOR COGNITIVE RADIO NETWORKS

Primary User (PU) signal detection is critical for cognitive radio networks as it allows a secondary user to flnd spectrum holes for opportunistic reuse. Eigenvalue based detection has many advantages, such as it does not require knowledge on primary user signal or noise power level. However, most of the work on eigenvalue based detection methods presented in the literature require multiple sensing nodes or receiving antennas so that they cannot be directly applied to single antenna systems. In this paper, an efiective eigenvalue based PU signal detection method is proposed for a cognitive user equipped with a single receiving antenna. The proposed method utilizes the temporal smoothing technique to form a virtual multi-antenna structure. The maximum and minimum eigenvalues of the covariance matrix obtained by the virtual multi-antenna structure are used to detect PU signal. Compared with the previous work, the presented method ofiers a number of advantages over other recently proposed algorithms. Firstly, the presented approach makes use of power method to calculate the maximum and minimum eigenvalues, it has lower computational complexity since the eigenvalue decomposition processing is avoided. Secondly, it can reduce system overhead since single antenna is used instead of multiple antennas or sensing nodes. Finally, simulation results show that performance of the proposed method is close to that of maximum-minimum eigenvalue detection using multiple antennas.

Implementation-Oriented Model for Centralized Data-Fusion Cooperative Spectrum Sensing

We propose a new model for a cognitive radio in the scenario of centralized data-fusion cooperative spectrum sensing. The model is grounded on a direct-conversion receiver architecture and was applied to four detection methods: the eigenvalue-based generalized likelihood ratio test, the maximum-minimum eigenvalue detection, the maximum eigenvalue detection and the energy detection. It is shown that the sensing performance under the conventional model typically adopted in the above scenario is overestimated when compared with the proposed one, which suggests that our model better suits for the spectrum sensing design and its performance assessment.