Compressive Covariance Sampling for Spectrum Sensing (CoCoSa)
Mathematics
Final Report Abstract
The contributions of this project is divided into two distinct parts that are also interrelated, one mainly in mathematical study of covariance estimation problems and the other one in spectrum sensing. The contributions in spectrum sensing are summarized as follows. We present an analytical derivation of the probability density functions (PDFs) of the maximum-minusminimum eigenvalue (MMME) detector for the special case of two cooperating secondary users (SUs) in a spectrum sensing scenario. This is considered for phase shift keying (PSK) modulated signals. We study a collaborative quickest detection scheme that uses a function of the eigenvalues of the sample covariance matrix for a spectrum sensing system with a fusion center. We analyze the two types of change detection problems in spectrum sensing, i.e., the channel becoming free when it was occupied before and vice versa. Performance evaluation is done by evaluating bounds and by comparing the presented quickest detection algorithms with the traditional block detection scheme. Cyclostationarity-based algorithms are extended to blind spectrum sensing. We propose two new cyclostationary spectrum sensing algorithms that make use of the inherent sparsity of the cyclic autocorrelation to make blind operation possible. Along with utilizing sparse recovery methods for estimating the cyclic autocorrelation, we take further advantage of its structure by introducing joint sparsity as well as general structure dictionaries into the recovery process. Furthermore, we extend a statistical test for cyclostationarity to accommodate sparse cyclic spectra. Our numerical results demonstrate that the new methods achieve a near constant false alarm rate behavior in contrast to earlier approaches from the literature. The effect of imperfect calibration in a collaborative spectrum sensing system with a fusion center, which utilizes the eigenvalues of the sample covariance matrix for detection, is investigated. The results show that a very large number of cooperating receivers is needed to enable detection at very low SNRs, which are customary in spectrum sensing. An SNR value below which a detector cannot perform robustly no matter how many observations are used. Up to now, the eigenvalue- based maximum-minimum-eigenvalue (MME) detector has been a notable exception. We prove that uncertainty in the amount of noise coloring does lead to an SNR-wall for the MME detector. We derive a lower bound on this SNR-wall and evaluate it for example scenarios. The findings are supported by numerical simulations. Masked Toeplitz covariance estimation was mathematically analyzed. New bounds have been derived under rather general assumptions on the distribution and for very general Toeplitz masks which show that for sparse Toeplitz covariance matrices, accurate covariance estimation can be performed with far fewer measurements than required for general covariance estimation problems.
Publications
- “Analytical test statistic distributions of the MMME eigenvalue-based detector for spectrum sensing”. In: The Twelfth International Symposium on Wireless Communication Systems (ISWCS 2015). Brussels, Belgium, Aug. 2015
Martijn Arts, Andreas Bollig, and Rudolf Mathar
(See online at https://doi.org/10.1109/ISWCS.2015.7454393) - “Compressive energy detection for blind coarse wideband sensing: comparative performance study”. In: The Twelfth International Symposium on Wireless Communication Systems. IEEE. Brussels, Aug. 2015, pp. 491–495
A. Lavrenko, A. Bollig, and R. S. Thomä
(See online at https://doi.org/10.1109/ISWCS.2015.7454392) - “Exact Quickest Spectrum Sensing Algorithms for Eigenvalue-Based Change Detection”. In: The Eighth International Conference on Ubiquitous and Future Networks ICUFN. Vienna, Austria, July 2016, pp. 235–240
Martijn Arts, Andreas Bollig, and Rudolf Mathar
(See online at https://doi.org/10.1109/ICUFN.2016.7537024) - “Performance Limits of Cooperative Eigenvalue-Based Spectrum Sensing Under Noise Calibration Uncertainty”. In: The Eighth International Conference on Ubiquitous and Future Networks ICUFN. Vienna, Austria, July 2016, pp. 241–246
Martijn Arts and Rudolf Mathar
(See online at https://doi.org/10.1109/ICUFN.2016.7537025) - Masked Toeplitz covariance estimation
Maryia Kabanava and Holger Rauhut
- “Compressive cyclostationary spectrum sensing with a constant false alarm rate”. In: EURASIP Journal on Wireless Communications and Networking 2017.1 (Aug. 2017), p. 13
A. Bollig, A. Lavrenko, M. Arts, and R. Mathar
(See online at https://doi.org/10.1186/s13638-017-0920-5) - “SNR-Walls in Eigenvaluebased Spectrum Sensing”. In: EURASIP Journal on Wireless Communications and Networking 2017.1 (June 2017), pp. 1–10
Andreas Bollig, Constantin Disch, Martijn Arts, and Rudolf Mathar
(See online at https://doi.org/10.1186/s13638-017-0899-y)
