Wideband Spectrum Sensing Based on Riemannian Distance for Cognitive Radio Networks
Abstract
:1. Introduction
2. System Model and the Proposed Detection Scheme
2.1. System Model
2.2. Riemannian Distance and Riemannian Mean
Algorithm 1: Iterative Calculation of the Riemannian Mean By a Gradient Descent Algorithm |
Input: and . |
Output: Estimates of Riemannian mean . |
Initialize: ; . |
repeat |
Compute gradient of objective function ; |
Obtain ; |
Update ; |
until convergence. |
2.3. The Riemannian Distance Based Test Statistic
- Determine the vacant subband. If there is only one vacant (noise-only) subband, then its sample covariance matrix is calculated and used as a reference matrix . If there are multiple vacant subbands, such as A, then the Riemannian mean of the noise covariance matrices of the multiple vacant subbands can be used as the reference matrix:
- Compute the sample covariance matrix of the i-th subband to be tested.
- Obtain the test statistic , where is the eigenvalue of with ordered .
- Compare the test statistic with the threshold, and get the sensing result:
3. Threshold and Probability of False Alarm
3.1. Moments of Test Statistics under
3.2. Gamma Approximation Approach
4. Numerical Results
4.1. Decision Threshold and PF
4.2. Detection Performance
4.3. Multiband Detection with Riemannian Mean
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A
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() | (TRD) Simulated | (TRD) Analytical | Simulated | Analytical |
---|---|---|---|---|
1.1708 | 1.1695 | 1.5489 | 1.5474 | |
(50,4) | 0.6750 | 0.6756 | 0.5147 | 0.5151 |
(50,8) | 2.8708 | 2.8667 | 8.5091 | 8.4914 |
(80,8) | 1.7135 | 1.7424 | 3.1125 | 3.14 |
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Lu, Q.; Yang, S.; Liu, F. Wideband Spectrum Sensing Based on Riemannian Distance for Cognitive Radio Networks. Sensors 2017, 17, 661. https://doi.org/10.3390/s17040661
Lu Q, Yang S, Liu F. Wideband Spectrum Sensing Based on Riemannian Distance for Cognitive Radio Networks. Sensors. 2017; 17(4):661. https://doi.org/10.3390/s17040661
Chicago/Turabian StyleLu, Qiuyuan, Shengzhi Yang, and Fan Liu. 2017. "Wideband Spectrum Sensing Based on Riemannian Distance for Cognitive Radio Networks" Sensors 17, no. 4: 661. https://doi.org/10.3390/s17040661