Eigenvalue based Spectrum Sensing Algorithms for Cognitive Radio (0804.2960v1)

Abstract: Spectrum sensing is a fundamental component is a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based on randomly generated signals, wireless microphone signals and captured ATSC DTV signals are presented to verify the effectiveness of the proposed methods.

• The paper introduces innovative eigenvalue-based detection methods (MME and EME) that sense primary users without prior signal, channel, or noise information.
• The study utilizes random matrix theory to derive robust thresholds, ensuring high detection probability even under significant noise uncertainty.
• Extensive simulations demonstrate superior performance in detecting correlated signals and scalability across variable sample sizes and smoothing factors.

Eigenvalue Based Spectrum Sensing Algorithms for Cognitive Radio

In their paper, "Eigenvalue based Spectrum Sensing Algorithms for Cognitive Radio," Yonghong Zeng and Ying-Chang Liang propose innovative spectrum sensing methods that leverage the eigenvalues of covariance matrices derived from signals at secondary users to enhance cognitive radio technology. The crux of their strategy is to use eigenvalue ratios to detect the presence or absence of primary users in a given spectrum band, a fundamental requirement for the effective implementation of cognitive radio systems like IEEE 802.22 WRAN.

Proposed Algorithms

The authors introduce two primary eigenvalue-based sensing algorithms:

1. Maximum-Minimum Eigenvalue (MME) Detection: This algorithm is based on the ratio of the maximum eigenvalue to the minimum eigenvalue of the covariance matrix of the received signal.
2. Energy with Minimum Eigenvalue (EME) Detection: This algorithm utilizes the ratio of the average signal power to the minimum eigenvalue.

Both methods are designed to operate without prior knowledge of the signal, channel, or noise power, classifying them as blind detection methods. They are particularly adept at solving the noise uncertainty problem, a significant challenge in spectrum sensing.

Theoretical Foundations and Analysis

Using recent advancements in random matrix theory (RMT), the authors derive the distribution profiles for the eigenvalue ratios. They provide explicit formulations for probabilities of false alarm (Pfa) and probabilities of detection (Pd). Both thresholds and statistical properties of the algorithms are grounded in RMT, making their theoretical derivations robust.

For instance, the threshold γ1 in MME detection, which decides whether a primary user is present, is computed using a theoretical framework that involves the Tracy-Widom distribution. This threshold setting ensures that the algorithms remain unaffected by the noise power, a contrast to traditional energy detection methods that require accurate noise power estimation.

Numerical Results and Simulations

The paper presents extensive simulation results to validate the proposed methods. These simulations cover a range of scenarios including randomly generated signals, wireless microphone signals, and captured DTV signals. Key findings from these simulations highlight:

• Performance under Noise Uncertainty: While energy detection performance degrades significantly under noise uncertainty, the proposed MME and EME methods maintain high detection probabilities.
• Effectiveness for Correlated Signals: MME, in particular, shows superior performance when dealing with correlated signal environments, underscoring its utility in practical cognitive radio applications where signals often exhibit correlation.
• Scalability with Samples and Smoothing Factor: The performance of these algorithms is robust across different numbers of samples and smoothing factors, with MME typically outperforming EME and ideal energy detection under realistic noise conditions.

Implications and Future Directions

The practical implications of Zeng and Liang's research are substantial. The eigenvalue-based detection schemes they propose can facilitate more reliable spectrum sensing in cognitive radio networks. This directly impacts the viability and efficiency of systems like IEEE 802.22 WRAN, which aim to use TV white spaces for broadband wireless access without interfering with incumbent users.

From a theoretical perspective, this work opens avenues for further exploration into the application of RMT in signal processing and spectrum sensing. Future research could focus on refining the detection thresholds using more precise distributions or extending these methods to other types of cognitive radio environments. Moreover, the empirical performance suggests opportunities to optimize these algorithms in a variety of noisy, real-world scenarios, thereby improving the robustness and adaptability of cognitive radio systems.

In summary, the eigenvalue-based spectrum sensing methods proposed by Zeng and Liang stand out as effective and practical solutions for enhancing spectrum sensing in cognitive radio. Their reliance on RMT not only solidifies their theoretical foundation but also propels spectrum sensing algorithms forward by offering robust performance in the face of the ubiquitous challenge of noise uncertainty.