This paper proposes two new spectrum sensing algorithms for cognitive radio based on the eigenvalues of the covariance matrix of received signals. The first algorithm, Maximum-Minimum Eigenvalue (MME) detection, compares the ratio of the maximum eigenvalue to the minimum eigenvalue with a threshold. The second algorithm, Energy with Minimum Eigenvalue (EME) detection, compares the ratio of the average power to the minimum eigenvalue. Both methods do not require knowledge of the signal, channel, or noise power, and they are robust to noise uncertainty. The paper uses random matrix theory to quantify the distributions of these ratios and derive the probabilities of false alarm and detection. Simulations using randomly generated signals, wireless microphone signals, and captured DTV signals demonstrate the effectiveness of the proposed methods, showing that they can outperform energy detection, especially in highly correlated signals. The proposed methods are also shown to be less sensitive to noise uncertainty compared to energy detection.This paper proposes two new spectrum sensing algorithms for cognitive radio based on the eigenvalues of the covariance matrix of received signals. The first algorithm, Maximum-Minimum Eigenvalue (MME) detection, compares the ratio of the maximum eigenvalue to the minimum eigenvalue with a threshold. The second algorithm, Energy with Minimum Eigenvalue (EME) detection, compares the ratio of the average power to the minimum eigenvalue. Both methods do not require knowledge of the signal, channel, or noise power, and they are robust to noise uncertainty. The paper uses random matrix theory to quantify the distributions of these ratios and derive the probabilities of false alarm and detection. Simulations using randomly generated signals, wireless microphone signals, and captured DTV signals demonstrate the effectiveness of the proposed methods, showing that they can outperform energy detection, especially in highly correlated signals. The proposed methods are also shown to be less sensitive to noise uncertainty compared to energy detection.