Cognitive radio has been proposed to alleviate the scarcity of available spectrum. However, sensing performance is quite poor due to the low sensing signal-to-noise ratio. Fortunately, reconfigurable intelligent surface (RIS)-aided spectrum sensing can effectively tackle the above challenge due to its high array gain. Nevertheless, the traditional passive RIS suffers from the ``double fading'' effect, which severely restricts the performance of passive RIS-aided spectrum sensing. To this end, we introduce the active RIS into spectrum sensing and respectively formulate two optimization problems for the passive RIS and the active RIS to maximize the detection probability. In light of the intractability of the formulated problems, we develop a one-stage optimization algorithm with inner approximation and a two-stage optimization algorithm with a bisection method to obtain sub-optimal solutions, and apply the Rayleigh quotient to obtain the upper and lower bounds of the detection probability. Furthermore, in order to gain more insight into the impact of the RIS on spectrum sensing, we respectively investigate the number configuration for passive RIS and active RIS and analyze how many reflecting elements are needed to achieve the detection probability close to 1. Simulation results verify the effectiveness of the proposed algorithms.

翻译：认知无线电已被提出用以缓解可用频谱的稀缺性问题。然而，由于感知信噪比过低，频谱感知性能较差。幸运的是，可重构智能表面（RIS）辅助的频谱感知凭借其高阵列增益可以有效应对上述挑战。但传统被动RIS存在"双重衰落"效应，这严重制约了被动RIS辅助频谱感知的性能。为此，我们将主动RIS引入频谱感知，并分别针对被动RIS和主动RIS构建两个优化问题以最大化检测概率。鉴于所构建问题的难解性，我们分别开发了基于内近似的单阶段优化算法和基于二分法的两阶段优化算法以获得次优解，并应用瑞利商推导出检测概率的上下界。此外，为深入探究RIS对频谱感知的影响，我们分别研究了被动RIS和主动RIS的单元数量配置，并分析了需要多少反射单元才能使检测概率趋近于1。仿真结果验证了所提算法的有效性。