Quickest Eigenvalue-Based Spectrum Sensing using Random Matrix Theory
Quickest Eigenvalue-Based Spectrum Sensing using Random Matrix Theory
复制标题
使用随机矩阵理论的最快基于特征值的频谱传感
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
R. Mathar
中科院分区：
文献类型：
--
作者：
Martijn Arts;Andreas Bollig;R. Mathar
我们研究了基于样本协方差矩阵的特征值的最快检测在频谱感知应用中的潜力。考虑了一个简单的具有加性高斯白噪声(AWGN)的相移键控(PSK)模型，该模型具有$1$主用户(PU)和$K$次用户(SU)。在两种检测假设下，样本协方差矩阵的特征值均服从Wishart分布。对于$K=2$sus的情形，我们推导了在数学{H}_1下最大-最小特征值(MME)检测器的概率密度函数(PDF)的解析表达式。利用文献中在数学{H}0下的结果，我们研究了两种检测方案。首先，我们根据分析结果计算了MME块检测器的接收算子特性(ROC)。其次，我们介绍了两种基于特征值的最快检测算法：当PU信号的信噪比(SNR)已知时的累积和(CUSUM)算法，以及在信噪比未知的情况下使用广义似然比的算法。给出了累积和算法的平均虚警时间$\tau_\Text{fa}$和平均检测时间$\tau_\Text{d}$的上界。数值模拟表明了最快检测方法相对于块检测方案的潜在优势。
We investigate the potential of quickest detection based on the eigenvalues of the sample covariance matrix for spectrum sensing applications. A simple phase shift keying (PSK) model with additive white Gaussian noise (AWGN), with $1$ primary user (PU) and $K$ secondary users (SUs) is considered. Under both detection hypotheses $\mathcal{H}_0$ (noise only) and $\mathcal{H}_1$ (signal + noise) the eigenvalues of the sample covariance matrix follow Wishart distributions. For the case of $K = 2$ SUs, we derive an analytical formulation of the probability density function (PDF) of the maximum-minimum eigenvalue (MME) detector under $\mathcal{H}_1$. Utilizing results from the literature under $\mathcal{H}_0$, we investigate two detection schemes. First, we calculate the receiver operator characteristic (ROC) for MME block detector based on analytical results. Second, we introduce two eigenvalue-based quickest detection algorithms: a cumulative sum (CUSUM) algorithm, when the signal-to-noise ratio (SNR) of the PU signal is known and an algorithm using the generalized likelihood ratio, in case the SNR is unknown. Bounds on the mean time to false-alarm $\tau_\text{fa}$ and the mean time to detection $\tau_\text{d}$ are given for the CUSUM algorithm. Numerical simulations illustrate the potential advantages of the quickest detection approach over the block detection scheme.