Abstract
                                                                        Robust spectrum sensing is crucial for facilitating  opportunistic spectrum utilization for secondary users (SU) in the  absense of primary users (PU). However, propagation environment  factors such as multi-path fading, shadowing, and lack of line  of sight (LoS) often adversely affect detection performance. To  deal with these issues, this paper focuses on utilizing reconfig-  urable intelligent surfaces (RIS) to improve spectrum sensing  in the scenario wherein both the multi-path fading and noise  are correlated. In particular, to leverage the spatially correlated  fading, we propose to use maximum eigenvalue detection (MED)  for spectrum sensing. We first derive exact distributions of test  statistics, i.e., the largest eigenvalue of the sample covariance  matrix, observed under the null and signal present hypothesis.  Next, utilizing these results, we present the exact closed-form  expressions for the false alarm and detection probabilities. In  addition, we also optimally configure the phase shift matrix of  RIS such that the mean of the test statistics is maximized, thus  improving the detection performance. Our numerical analysis  demonstrates that the MED’s receiving operating characteristic  (ROC) curve improves with increased RIS elements, SNR, and  the utilization of statistically optimal configured RIS.  Index Terms—Reconfigurable Intelligent Surfaces, Spectrum  Sensing, Maximum Eigenvalue Detector, Correlated Fading, e