Compressive Sensing Based Channel Estimator and LDPC Theory for OFDM using SDR
Main Article Content
Abstract
This work proposes the application of a channel estimator based on Compressive Sensing (CS) over a system that uses Orthogonal Frequency Division Multiplexing (OFDM) using Software Defined Radio (SDR) devices. The application of the CS theory is given through the use of sparse reconstruction algorithms such as Orthogonal Matching Pursuit (OMP) and Compressive Sampling Matching Pursuit (CoSaMP) in order to take advantage of the sparse nature of the pilot subcarriers used in OFDM, optimizing the bandwidth of system. In addition, to improve the performance of these algorithms, the sparse parity checking matrix concept is used, which is implemented in the deployment of low density parity check codes (LDPC) to obtain a sensing matrix that improves the isometric restriction property (RIP) belonging to the CS paradigm. The document shows the model implemented in the SDR equipment and analyze the bit error rate and the number of pilot symbols used.
Keywords
Channel Estimation, Compressed Sensing, LDPC, OFDM, SDR Sensado Compresivo, Estimación de Canal, LDPC, OFDM, SDR
References
[1] J. Sterba and D. Kocur, “Pilot symbol aided channel estimation for ofdm system in frequency selective rayleigh fading channel,” in 2009 19th International Conference Radioelektronika, April 2009, pp. 77–80. [Online]. Available: https://doi.org/10.1109/RADIOELEK.2009.5158729
[2] C. Tzi-Dar and T. Pei-Yun, OFDM Baseband Receiver Design OFDM Baseband Receiver Design for Wireless Communications, J. W. S. A. P. Ltd, Ed., 2007. [Online]. Available: http://doi.org/10.1002/9780470822500
[3] M. R. Raghavendra, S. Bhashyam, and K. Giridhar, “Exploiting hopping pilots for parametric channel estimation in ofdm systems,” IEEE Signal Processing Letters, vol. 12, no. 11, pp. 737–740, Nov 2005.
[4] N. N. Jimenez Castro Martínez, “Identificación ciega de canal disperso basado en algoritmos de sub-espacio,” Master’s thesis, 2016. [Online]. Available: http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/40
[5] M. Cordero Limón, “Técnicas de estimación de canal en la capa física wirelessman-ofdm de la norma ieee 802.16e,” 2009. [Online]. Available: https://bit.ly/2P9Q1co
[6] S. Zhang, J. Kang, Y. Song, and N. Wang, “An optimization for channel estimation based on compressed channel sensing,” in 2012 13th ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing, Aug 2012, pp. 597–602. [Online]. Available: https://doi.org/10.1109/SNPD.2012.128
[7] Y. Liao, G. Sun, X. Shen, S. Zhang, X. Yang, X. Zhang, H. Yao, and N. Zhang, “Bem-based channel estimation and interpolation methods for doubly-selective ofdm channel,” in 2018 IEEE International Conference on Smart Internet of Things (SmartIoT), Aug 2018, pp. 70–75. [Online]. Available: https://doi.org/10.1109/SmartIoT.2018.00022
[8] Y. A. Al-Jawhar, K. N. Ramli, M. A. Taher, N. S. Mohd Shah, L. Audah, and M. S. Ahmed, “Zero-padding techniques in ofdm systems,” International Journal on Electrical Engineering and Informatics, vol. 10, no. 4, pp. 704–725, 2018. [Online]. Available: https://bit.ly/2YAQGqc
[9] P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Transactions on Communications, vol. 42, no. 10, pp. 2908–2914, Oct 1994. [Online]. Available: https://doi.org/10.1109/26.328961
[10] J. van de Beek, M. Sandell, and P. O. Börjesson, ML estimation of timing and frequency offset in multicarrier systems, div. of signal processing lulea university of technology s–971 87 lulea, sweden ed. Luleå tekniska universitet, 1996. [Online]. Available: https://bit.ly/38qaO2W
[11] D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, April 2006. [Online]. Available: https://doi.org/10.1109/TIT.2006.871582
[12] R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Processing Magazine, vol. 24, no. 4, pp. 118–121, July 2007. [Online]. Available: https://doi.org/10.1109/MSP.2007.4286571
84 INGENIUS N. 23, enero-junio de 2020 [13] R. Baraniuk, M. A. Davenport, M. F. Duarte, and C. Hegde, An introduction to compressive sensing, 2011. [Online]. Available: https://bit.ly/38uCOCG
[14] Milliarde. (2016) Compressed sensing intro & tutorial w/ matlab. CODE PROJECT for those who code. [Online]. Available: https://bit.ly/2YC5Ewa
[15] J. Inga-Ortega, E. Inga-Ortega, C. Gómez, and R. Hincapié, “Electrical load curve reconstruction required for demand response using compressed sensing techniques,” in 2017 IEEE PES Innovative Smart Grid Technologies Conference - Latin America (ISGT Latin America), Sep. 2017, pp. 1–6. [Online]. Available: https://doi.org/10.1109/ISGT-LA.2017.8126731
[16] M. Pinos and J. Inga, “Predicción de consumo eléctrico en la UPS de Cuenca usando P1P y censado comprimido,” 2018.
[17] E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21–30, March 2008. [Online]. Available: https://doi.org/10.1109/MSP.2007.914731
[18] E. J. Candés, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique, vol. 346, no. 9, pp. 589–592, 2008. [Online]. Available: https://doi.org/10.1016/j.crma.2008.03.014
[19] E.-G. Astaiza-Hoyos and H. F. Pablo Emilio Bermúdez-Orozco, “Compressive sensing: A methodological approach to an efficient signal processing,” Dyna, 2015. [Online]. Available: https://bit.ly/2qLx8TI
[20] H. Yuan, H. Song, X. Sun, K. Guo, and Z. Ju, “Compressive sensing measurement matrix construction based on improved size compatible array ldpc code,” IET Image Processing, vol. 9, no. 11, pp. 993–1001, 2015. [Online]. Available: https://doi.org/10.1049/iet-ipr.2015.0117
[21] A. G. Dimakis, R. Smarandache, and P. O. Vontobel, “Ldpc codes for compressed sensing,” IEEE Transactions on Information Theory, vol. 58, no. 5, pp. 3093–3114, May 2012. [Online]. Available: https://doi.org/10.1109/TIT.2011.2181819
[22] S. Pawar and K. Ramchandran, “A hybrid dft-ldpc framework for fast, efficient and robust compressive sensing,” in 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Oct 2012, pp. 1943–1950. [Online]. Available: https://doi.org/10.1109/Allerton.2012.6483460
[23] H. Wang, W. Du, and Y. Bai, “Compressed sensing based channel estimation for OFDM transmission under 3 GPP channels,” International Journal of Future Generation Communication and Networking, vol. 9, no. 4, pp. 85–94, 2016. [Online]. Available: http://dx.doi.org/10.14257/ijfgcn.2016.9.4.08
[24] D. Needell and J. A. Tropp, “Cosamp: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis, vol. 26, no. 3, pp. 301–321, 2009. [Online]. Available: https://doi.org/10.1016/j.acha.2008.07.002
[25] B. L. Sturn. (2011) Algorithm power hour: Compressive sampling matching pursuit (cosamp). [Online]. Available: https://bit.ly/2RS0DOX
[26] I. D. F. Lava, “Implementación y evaluación de la codificación ldpc para la transmisión de ficheros en entornos unidireccionales,” in Computer Science, 2013. [Online]. Available: https://bit.ly/2YCauJQ
[27] R. Gallager, “Low-density parity-check codes,” IRE Transactions on Information Theory, vol. 8, no. 1, pp. 21–28, January 1962. [Online]. Available: https://doi.org/10.1109/TIT.1962.1057683
[28] D. J. C. Mackay, Information Theory, Inference and Learning Algorithms. Cambridge University Press, 2003. [Online]. Available: https://bit.ly/2E5yfQX
[29] G. G. Andrade Salinas, “Implementación de la codificación y decodificación del código LDPC (low density parity check) en MATLAB,” 2017. [Online]. Available: https://bit.ly/34ahKxG
[30] V. Roca, C. Neumann, and D. Furodet. (2008) Low density parity check (ldpc) staircase and triangle forward error correction (fec) schemes. [Online]. Available: https://bit.ly/2RH8PBq
[31] E. Seidel, “Overview lte phy: Part 1 - principles and numerology etc,” NOMOR Research, 2007. [Online]. Available: https://bit.ly/35cxH7R
[32] R. Prieto, A. Abril, and A. Ortega, “Experimental alamouti-stbc using ldpc codes for mimo channels over sdr systems,” in 2017 IEEE 30th Canadian Conference on Electrical and Computer Engineering (CCECE), April 2017, pp. 1–5. [Online]. Available: https://doi.org/10.1109/CCECE.2017.7946842
[33] B. Peñafiel and A. Ortega, “A joint multilevel modulator and robust ldpc codes processing over optical systems by providing solutions for holistc Yanza-Verdugo et al. / Estimador de canal basado en sensado compresivo y LDPC para OFDM usando SDR 85 5g backhaul,” in 2017 IEEE 13th Malaysia International Conference on Communications (MICC), Nov 2017, pp. 197–202. [Online]. Available: https://doi.org/10.1109/MICC.2017.8311758
[34] J. Zyren, “Overview of the 3gpp long term evolution physical layer,” NXP Semiconductors, Tech. Rep., 2007. [Online]. Available: https://bit.ly/35gg8E0
[2] C. Tzi-Dar and T. Pei-Yun, OFDM Baseband Receiver Design OFDM Baseband Receiver Design for Wireless Communications, J. W. S. A. P. Ltd, Ed., 2007. [Online]. Available: http://doi.org/10.1002/9780470822500
[3] M. R. Raghavendra, S. Bhashyam, and K. Giridhar, “Exploiting hopping pilots for parametric channel estimation in ofdm systems,” IEEE Signal Processing Letters, vol. 12, no. 11, pp. 737–740, Nov 2005.
[4] N. N. Jimenez Castro Martínez, “Identificación ciega de canal disperso basado en algoritmos de sub-espacio,” Master’s thesis, 2016. [Online]. Available: http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/40
[5] M. Cordero Limón, “Técnicas de estimación de canal en la capa física wirelessman-ofdm de la norma ieee 802.16e,” 2009. [Online]. Available: https://bit.ly/2P9Q1co
[6] S. Zhang, J. Kang, Y. Song, and N. Wang, “An optimization for channel estimation based on compressed channel sensing,” in 2012 13th ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing, Aug 2012, pp. 597–602. [Online]. Available: https://doi.org/10.1109/SNPD.2012.128
[7] Y. Liao, G. Sun, X. Shen, S. Zhang, X. Yang, X. Zhang, H. Yao, and N. Zhang, “Bem-based channel estimation and interpolation methods for doubly-selective ofdm channel,” in 2018 IEEE International Conference on Smart Internet of Things (SmartIoT), Aug 2018, pp. 70–75. [Online]. Available: https://doi.org/10.1109/SmartIoT.2018.00022
[8] Y. A. Al-Jawhar, K. N. Ramli, M. A. Taher, N. S. Mohd Shah, L. Audah, and M. S. Ahmed, “Zero-padding techniques in ofdm systems,” International Journal on Electrical Engineering and Informatics, vol. 10, no. 4, pp. 704–725, 2018. [Online]. Available: https://bit.ly/2YAQGqc
[9] P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Transactions on Communications, vol. 42, no. 10, pp. 2908–2914, Oct 1994. [Online]. Available: https://doi.org/10.1109/26.328961
[10] J. van de Beek, M. Sandell, and P. O. Börjesson, ML estimation of timing and frequency offset in multicarrier systems, div. of signal processing lulea university of technology s–971 87 lulea, sweden ed. Luleå tekniska universitet, 1996. [Online]. Available: https://bit.ly/38qaO2W
[11] D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, April 2006. [Online]. Available: https://doi.org/10.1109/TIT.2006.871582
[12] R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Signal Processing Magazine, vol. 24, no. 4, pp. 118–121, July 2007. [Online]. Available: https://doi.org/10.1109/MSP.2007.4286571
84 INGENIUS N. 23, enero-junio de 2020 [13] R. Baraniuk, M. A. Davenport, M. F. Duarte, and C. Hegde, An introduction to compressive sensing, 2011. [Online]. Available: https://bit.ly/38uCOCG
[14] Milliarde. (2016) Compressed sensing intro & tutorial w/ matlab. CODE PROJECT for those who code. [Online]. Available: https://bit.ly/2YC5Ewa
[15] J. Inga-Ortega, E. Inga-Ortega, C. Gómez, and R. Hincapié, “Electrical load curve reconstruction required for demand response using compressed sensing techniques,” in 2017 IEEE PES Innovative Smart Grid Technologies Conference - Latin America (ISGT Latin America), Sep. 2017, pp. 1–6. [Online]. Available: https://doi.org/10.1109/ISGT-LA.2017.8126731
[16] M. Pinos and J. Inga, “Predicción de consumo eléctrico en la UPS de Cuenca usando P1P y censado comprimido,” 2018.
[17] E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21–30, March 2008. [Online]. Available: https://doi.org/10.1109/MSP.2007.914731
[18] E. J. Candés, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique, vol. 346, no. 9, pp. 589–592, 2008. [Online]. Available: https://doi.org/10.1016/j.crma.2008.03.014
[19] E.-G. Astaiza-Hoyos and H. F. Pablo Emilio Bermúdez-Orozco, “Compressive sensing: A methodological approach to an efficient signal processing,” Dyna, 2015. [Online]. Available: https://bit.ly/2qLx8TI
[20] H. Yuan, H. Song, X. Sun, K. Guo, and Z. Ju, “Compressive sensing measurement matrix construction based on improved size compatible array ldpc code,” IET Image Processing, vol. 9, no. 11, pp. 993–1001, 2015. [Online]. Available: https://doi.org/10.1049/iet-ipr.2015.0117
[21] A. G. Dimakis, R. Smarandache, and P. O. Vontobel, “Ldpc codes for compressed sensing,” IEEE Transactions on Information Theory, vol. 58, no. 5, pp. 3093–3114, May 2012. [Online]. Available: https://doi.org/10.1109/TIT.2011.2181819
[22] S. Pawar and K. Ramchandran, “A hybrid dft-ldpc framework for fast, efficient and robust compressive sensing,” in 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Oct 2012, pp. 1943–1950. [Online]. Available: https://doi.org/10.1109/Allerton.2012.6483460
[23] H. Wang, W. Du, and Y. Bai, “Compressed sensing based channel estimation for OFDM transmission under 3 GPP channels,” International Journal of Future Generation Communication and Networking, vol. 9, no. 4, pp. 85–94, 2016. [Online]. Available: http://dx.doi.org/10.14257/ijfgcn.2016.9.4.08
[24] D. Needell and J. A. Tropp, “Cosamp: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis, vol. 26, no. 3, pp. 301–321, 2009. [Online]. Available: https://doi.org/10.1016/j.acha.2008.07.002
[25] B. L. Sturn. (2011) Algorithm power hour: Compressive sampling matching pursuit (cosamp). [Online]. Available: https://bit.ly/2RS0DOX
[26] I. D. F. Lava, “Implementación y evaluación de la codificación ldpc para la transmisión de ficheros en entornos unidireccionales,” in Computer Science, 2013. [Online]. Available: https://bit.ly/2YCauJQ
[27] R. Gallager, “Low-density parity-check codes,” IRE Transactions on Information Theory, vol. 8, no. 1, pp. 21–28, January 1962. [Online]. Available: https://doi.org/10.1109/TIT.1962.1057683
[28] D. J. C. Mackay, Information Theory, Inference and Learning Algorithms. Cambridge University Press, 2003. [Online]. Available: https://bit.ly/2E5yfQX
[29] G. G. Andrade Salinas, “Implementación de la codificación y decodificación del código LDPC (low density parity check) en MATLAB,” 2017. [Online]. Available: https://bit.ly/34ahKxG
[30] V. Roca, C. Neumann, and D. Furodet. (2008) Low density parity check (ldpc) staircase and triangle forward error correction (fec) schemes. [Online]. Available: https://bit.ly/2RH8PBq
[31] E. Seidel, “Overview lte phy: Part 1 - principles and numerology etc,” NOMOR Research, 2007. [Online]. Available: https://bit.ly/35cxH7R
[32] R. Prieto, A. Abril, and A. Ortega, “Experimental alamouti-stbc using ldpc codes for mimo channels over sdr systems,” in 2017 IEEE 30th Canadian Conference on Electrical and Computer Engineering (CCECE), April 2017, pp. 1–5. [Online]. Available: https://doi.org/10.1109/CCECE.2017.7946842
[33] B. Peñafiel and A. Ortega, “A joint multilevel modulator and robust ldpc codes processing over optical systems by providing solutions for holistc Yanza-Verdugo et al. / Estimador de canal basado en sensado compresivo y LDPC para OFDM usando SDR 85 5g backhaul,” in 2017 IEEE 13th Malaysia International Conference on Communications (MICC), Nov 2017, pp. 197–202. [Online]. Available: https://doi.org/10.1109/MICC.2017.8311758
[34] J. Zyren, “Overview of the 3gpp long term evolution physical layer,” NXP Semiconductors, Tech. Rep., 2007. [Online]. Available: https://bit.ly/35gg8E0
Article Sidebar
PDF
PDF (Español (España))
EPUB (Español (España))
XML (Español (España))
HTML (Español (España))
HTML
Published
Dec 27, 2019
Article Details
Section
Scientific Paper
Author Biography