Scaled Largest Eigenvalue Detection for Stationary Time-Series

Abstract

Abstract-This paper studies the performance of the Scaled Largest Eigenvalue (SLE) detector used for the detection of stationary time-series. We focus on a singleantenna setup and a blind detection scenario (neither the signal covariance, nor the noise variance are known). The SLE detector has received much attention in the context of Cognitive Radios (CR) due to its simplicity, good performance and robustness to noise level uncertainties. Specifically, our goal is to analyze the detector based on the statistic Γ =, where λ1 ≥ λ2 ≥ . . . ≥ λp represent the ordered eigenvalues of the sample covariance matrix. We derive a large-sample-size closed-form approximation for the test statistic which allows us to derive its statistical distribution and set up the detector to achieve the required Probability of False-Alarm (P f a ) and Probability of Detection (P d ). We also study the robustness of the detector in the presence of noise uncertainty and impulsive-noise and investigate the benefits of the spatial sign filter for such scenarios.

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

“…Furthermore, the estimation of is obtained by combining to improve accuracy. is defined as the difference between sequences and as Then, by minimising , the estimation of can be obtained as After the determination of , the threshold T for a given false alarm rate can be derived according to the method in [44], in which in the hypothesis follows the selected normal distribution. However, the computation of T is complex due to the complicated explicit distribution of .…”

“…In addition, because homogenous clutter is composed of much small backscatter components, such clutter can be assumed to fluctuate more than the target in the HRRPs in a CPI. That is, the power of the clutter is distributed among all the eigenvalues of the SCM, and the signal power is mostly associated with the LE [44]. Therefore, the LE statistics can be used to improve the SCR.…”

“…In recent years, LE detectors have been used to detect radio signal sources in the field of wireless cognitive radio networks [44–50]. In [45], the LE of a source signal SCM was verified to follow the Tracy‐Widom distribution when the size of the matrix is sufficiently large.…”

“…Based on the discussion above, we propose a modified SLE (M‐SLE) detector for static ground target detection with a homogenous clutter background. Unlike the traditional SLE statistics, which are normalised with primary data, the M‐SLE utilises secondary data for normalisation, and this approach is more reasonable than that for traditional SLE statistics [44] based on the H 1 hypothesis.…”

Experimental Studies on Energy and Eigenvalue Based Spectrum Sensing Algorithms Using USRP Devices in OFDM Systems

“…Eigenvalue based detection techniques studied are maximum‐minimum eigenvalue (MME) detection (Zeng & Liang, 2009), scale largest eigenvalue detection (SLE) (Renard et al, 2015), energy with minimum eigenvalue (EME) detection (Yucek & Arslan, 2009), maximum eigenvalue detection (MED) (Zeng et al, 2008), and maximum eigenvalue to trace (MET) detection (Zeng & Liang, 2007, 2010). Eigenvalue based detection of PU signal is presented in Zeng and Liang (2009), where the ratio of maximum eigenvalue to the minimum eigenvalue is compared to the predefined threshold value.…”