# A Novel Matrix Optimization for Compressive Sampling-Based Sub-Nyquist OFDM Receiver in Cognitive Radio

- 11 Downloads

## Abstract

Modulated wideband converter is the most commonly accepted technique for implementing sub-Nyquist compressive sampling-based wireless receiver to reduce the analog and digital processing complexity when detecting wideband spectrum for cognitive radio systems. However, the issue of non-optimal mutual coherence, which leads to a higher receiving bit error rate, has not been considered in existing compressive sampling-based cognitive radio studies. Furthermore, existing theoretical compressive sampling-based solutions cannot be directly applied because typical modulated wideband converter-based designs use fixed parameters that cannot be easily updated during their sampling operations. This paper presents a novel matrix optimization which can be incorporated into modulated wideband converter-based cognitive radio to enhance its detection accuracy for OFDM signals. The proposed approach can also be predetermined to reduce the computation complexity, while remains compatible with standard digital OFDM receiver’s operation. Simulation results show that our proposed system can consistently produce smaller compressive sampling reconstruction error in terms of lower bit error rate under various operating conditions compared to existing systems.

## Keywords

Cognitive radio Sub-Nyquist OFDM receiver Compressive sampling Mutual coherence optimization## References

- 1.T. Agrawal, V. Lakkundi, A. Griffin, P. Tsakalides, Compressed sensing for ofdm uwb systems. in
*2011 IEEE Radio and Wireless Symposium*(IEEE, 2011), pp. 190–193Google Scholar - 2.H. Bai, G. Li, S. Li, Q. Li, Q. Jiang, L. Chang, Alternating optimization of sensing matrix and sparsifying dictionary for compressed sensing. IEEE Trans. Signal Process.
**63**(6), 1581–1594 (2015)MathSciNetCrossRefGoogle Scholar - 3.E.J. Candes, J.K. Romberg, T. Tao, Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math.
**59**(8), 1207–1223 (2006)MathSciNetCrossRefMATHGoogle Scholar - 4.E.J. Candès et al., Compressive sampling. in
*Proceedings of the International Congress of Mathematicians*, Madrid, Spain, vol. 3, pp. 1433–1452 (2006)Google Scholar - 5.E.J. Cands, M.B. Wakin, An introduction to compressive sampling. Signal Process. Mag.
**25**(2), 21–30 (2008). (**1stV**)CrossRefGoogle Scholar - 6.M.F. Duarte, Y.C. Eldar, Structured compressed sensing: from theory to applications. IEEE Trans. Signal Process.
**59**(9), 4053–4085 (2011)MathSciNetCrossRefGoogle Scholar - 7.M. Elad, Optimized projections for compressed sensing. IEEE Trans. Signal Process.
**55**(12), 5695–5702 (2007)MathSciNetCrossRefGoogle Scholar - 8.A. Ghasemi, E.S. Sousa, Spectrum sensing in cognitive radio networks: requirements, challenges and design trade-offs. IEEE Commun. Mag.
**46**(4), 32–39 (2008)CrossRefGoogle Scholar - 9.S. Haykin, Cognitive radio: brain-empowered wireless communications. IEEE J. Sel. Areas Commun.
**23**(2), 201–220 (2005)CrossRefGoogle Scholar - 10.M. Holmes, A. Gray, C. Isbell, Fast svd for large-scale matrices. in
*Workshop on Efficient Machine Learning at NIPS*, vol. 58, pp. 249–252 (2007)Google Scholar - 11.M.H. Islam, C.L. Koh, S.W. Oh, X. Qing, Y.Y. Lai, C. Wang, Y.C. Liang, B.E. Toh, F. Chin, G.L. Tan, et al , Spectrum survey in Singapore: occupancy measurements and analyses. in
*3rd International Conference on Cognitive Radio Oriented Wireless Networks and Communications, 2008. CrownCom 2008*(IEEE, 2008), pp. 1–7Google Scholar - 12.G. Li, Z. Zhu, D. Yang, L. Chang, H. Bai, On projection matrix optimization for compressive sensing systems. IEEE Trans. Signal Process.
**61**(11), 2887–2898 (2013)MathSciNetCrossRefGoogle Scholar - 13.Z. Lin, C. Lu,H. Li, Optimized projections for compressed sensing via direct mutual coherence minimization (2015). arXiv:1508.03117
- 14.H. Lu, X. Long, J. Lv, A fast algorithm for recovery of jointly sparse vectors based on the alternating direction methods. in
*AISTATS*, pp. 461–469 (2011)Google Scholar - 15.M. Mishali, Y.C. Eldar, Reduce and boost: recovering arbitrary sets of jointly sparse vectors. IEEE Trans. Signal Process.
**56**(10), 4692–4702 (2008)MathSciNetCrossRefGoogle Scholar - 16.M. Mishali, Y.C. Eldar, Blind multiband signal reconstruction: compressed sensing for analog signals. IEEE Trans. Signal Process.
**57**(3), 993–1009 (2009)MathSciNetCrossRefGoogle Scholar - 17.M. Mishali, Y.C. Eldar, From theory to practice: sub-nyquist sampling of sparse wideband analog signals. IEEE J. Sel. Top. Signal Process.
**4**(2), 375–391 (2010)CrossRefGoogle Scholar - 18.D.B. Rawat, Evaluating performance of cognitive radio users in mimo-ofdm-based wireless networks. IEEE Wirel. Commun. Lett.
**5**(5), 476–479 (2016)CrossRefGoogle Scholar - 19.J. Van Wyk, L. Linde, Bit error probability for a m-ary qam ofdm-based system. in
*AFRICON 2007*(IEEE, 2007), pp. 1–5Google Scholar - 20.J. Xu, G. Choi, Compressive sensing and reception for mimo-ofdm based cognitive radio. in
*International Conference on Computing, Networking and Communications (ICNC)*(IEEE, 2015), pp. 884–888Google Scholar - 21.B. Yang, S. Li, Pixel-level image fusion with simultaneous orthogonal matching pursuit. Inf. fus.
**13**(1), 10–19 (2012)CrossRefGoogle Scholar - 22.Z. Yu, S. Hoyos, B.M. Sadler, Mixed-signal parallel compressed sensing and reception for cognitive radio, in
*2008 IEEE International Conference on Acoustics Speech and Signal Processing*(IEEE, 2008), pp. 3861–3864Google Scholar - 23.T. Zahavy, O. Shayer, D. Cohen, A. Tolmachev, Y.C. Eldar, Sub-nyquist sampling of ofdm signals for cognitive radios. in
*2014 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP)*(IEEE, 2014), pp. 8092–8096Google Scholar