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Exact non-asymptotic threshold for eigenvalue-based spectrum sensing

机译：基于特征值的光谱感测的精确的非渐近阈值

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摘要

Eigenvalue-based detection is one of the most promising techniques proposed for spectrum sensing in cognitive radio as it is insensitive to the noise uncertainty problem. However, the eigenvalue-based detection schemes presented so far rely on asymptotic assumptions that are not suitable for many realistic scenarios, thus determining a substantial degradation of detection performance. In this paper, starting from the analytical distribution of the ordered eigenvalues of finite-dimension Wishart matrices, we derive an exact expression for the decision threshold as a function of the probability of false alarm. Since it is not based on asymptotical assumptions, the novel decision rule is valid for any, even small, number of samples and cooperating receivers. In addition to the exact expression, an alternative (approximated) formula is then derived to reduce the computational complexity. Simulation results show that the proposed detector, both with the exact and the approximated formula, outperforms the other existing eigenvalue-based techniques, especially when the receiver operates under non-asymptotical conditions.
机译：基于特征值检测是提出了频谱认知无线电检测，因为它是不敏感的噪声不确定性问题的最有前途的技术之一。但是，基于本征值检测方案提出迄今依赖渐近假设不适合于许多实际场景，由此确定的检测性能明显降低。在本文中，从有限维威沙特矩阵的本征值排序的分析分布开始，我们推导出的决定阈值作为假警报的概率的函数的精确表达。由于它不是基于渐近假设，新颖的决策规则是有效的任何，哪怕是很小的，样本数量和协作接收机。除了精确表达式，替代的（近似）公式然后导出以减少计算复杂度。仿真结果表明，所提出的检测器，二者与精确和近似式，优于其它现有的基于特征值的技术，特别是当接收机的非渐近条件下操作。

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