This paper proposes two eigenvalue-based spectrum sensing algorithms for cognitive radio systems. The algorithms are based on the ratio of the maximum eigenvalue to the minimum eigenvalue and the ratio of the average eigenvalue to the minimum eigenvalue of the covariance matrix of received signals. Using random matrix theory, the distributions of these ratios are quantified, and the probabilities of false alarm and detection are derived. The proposed methods overcome the noise uncertainty problem and can outperform energy detection when signals are highly correlated. The methods do not require knowledge of signal, channel, or noise power and are applicable to various signal detection applications. Simulations using randomly generated signals, wireless microphone signals, and captured ATSC DTV signals verify the effectiveness of the proposed methods. The results show that the proposed methods perform well in detecting signals without requiring prior knowledge of noise or channel conditions, and they are more reliable than energy detection in the presence of noise uncertainty. The methods are also less sensitive to signal correlation and can achieve better detection performance under varying noise conditions.This paper proposes two eigenvalue-based spectrum sensing algorithms for cognitive radio systems. The algorithms are based on the ratio of the maximum eigenvalue to the minimum eigenvalue and the ratio of the average eigenvalue to the minimum eigenvalue of the covariance matrix of received signals. Using random matrix theory, the distributions of these ratios are quantified, and the probabilities of false alarm and detection are derived. The proposed methods overcome the noise uncertainty problem and can outperform energy detection when signals are highly correlated. The methods do not require knowledge of signal, channel, or noise power and are applicable to various signal detection applications. Simulations using randomly generated signals, wireless microphone signals, and captured ATSC DTV signals verify the effectiveness of the proposed methods. The results show that the proposed methods perform well in detecting signals without requiring prior knowledge of noise or channel conditions, and they are more reliable than energy detection in the presence of noise uncertainty. The methods are also less sensitive to signal correlation and can achieve better detection performance under varying noise conditions.