nd right-multiplying XX, we have (A.9) After a simple transformation, we have (A.10) Appendix A Proof of Theorem 5.1 From the fact that (5.11) is a positive semidefinite matrix, (I+Ck - would be a non-singular matrix, thus the rank of the left term of the above equation is the same as . Also, it is easy to verify that the right term has a rank 1. Similarly, we can prove that ) = 1. Therefore, the following equation holds. Rank Rank +Rank (Exp.x.)=z (A.11) which proves the theorem. Bibliography 1 M. E. Ahmed, J. B. Song, and Z. Han. Mitigating malicious attacks using Bayesian nonparametric clustering in collaborative cognitive radio networks. In 2014 IEEE Global Communications Conference, pages 999-1004, 2014. 2 I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty. Next generation/dynamic spectrum access/cognitive radio wireless networks: A survey. Computer Networks, 50(13):2127-2159, 2006. 3 M. M. Al-Wani, A. Sali, B. M. Ali, A. A. Salah, K. Navaie, C. Y. Leow, N. K. Noordin, and S. J. Hashim. On short term fairness and throughput of user clus- tering for downlink non-orthogonal multiple access system. In 2019 IEEE 89th Vehicular Technology Conference (VTC2019-Spring), pages 1-6, 2019. doi: 10.1109/ 7TCSpring.2019.8746330. 4 A. Albehadili, A. Ali, F. Jahan, A. Y. Javaid, J. Oluochy, and V. Devabhaktuniz. Machine learning-based primary user emulation attack detection in cognitive radio networks using pattern described link-signature (PDLS). In 2019 Wireless Telecommunications Symposium (WTS), pages 1-7, 2019. H. Alhosani, M. H. ur Rehman, K. Salah, C. Lima, and D. Svetinovic. Blockchain- based solution for multiple operator spectrum sharing (MOSS) in 5G networks. In 2020 IEEE Globecom Workshops (GC Wkshps, pages 1-6, 2020. doi: 10.1109/ GCWkshps50303.2020.9367561. 6 M. M. Amiri and D. Gündüz. Machine learning at the wireless edge: Distributed stochastic gradient descent over-the-air. IEEE Transactions on Signal Processing, 68:2155-2169, 2020. 7 S. Amuru and R. M. Buehrer. Optimal jamming using delayed learning. 