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August & September  2019, 12(4&5): 783-793. doi: 10.3934/dcdss.2019052

## On the design of full duplex wireless system with chaotic sequences

 1 School of Electronics Engineering and Computer Science, Peking University, Beijing, China 2 Department of Computer Science, Yale University, New Haven, CT, USA

* Corresponding author: Ruwu Xiao

Received  September 2017 Revised  January 2018 Published  November 2018

Fund Project: The first author is supported by the NNSFC under grant No. 61371072

This paper proposes a novel approach for full duplex using chaotic sequences which is known as the asynchronous code-division duplex (Async-CDD) system. The Async-CDD system can transmit and receive signals at the same time and in the same frequency channel without time slot synchronization. The data rate of the Async-CDD system is 8 times higher than the conventional CDD system and is the same as a non-spreading system. The property of low block cross-correlation of the chaotic sequence allows the Async-CDD system achieve duplex interference suppression at any duplex delay. And the huge number of available code words/blocks of the chaotic sequence allows the Async-CDD system increase the data rate by increasing the number of multiplexed sub-channels. When both of the code length of the orthogonal chaotic code and the number of multiplexed sub-channels are 128, the orthogonal chaotic code provides 30.40 dBc self-interference suppression in average, which is 6.99 dB better than the orthogonal Gold code.

Citation: Ruwu Xiao, Geng Li, Yuping Zhao. On the design of full duplex wireless system with chaotic sequences. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 783-793. doi: 10.3934/dcdss.2019052
##### References:
 [1] A. L. A. Aboltins, Selection and performance analysis of chaotic spreading sequences for DS-CDMA systems, in Advances in Wireless and Optical Communications (RTUWO), 2016, 38–45. [2] E. Ahmed and A. M. Eltawil, All-digital self-interference cancellation technique for full-duplex systems, IEEE Transactions on Wireless Communications, 14 (2015), 3519-3532. [3] M. Duarte, C. Dick and A. Sabharwal, Experiment-driven characterization of full-duplex wireless systems, IEEE Transactions on Wireless Communications, 11 (2012), 4296-4307. [4] M. Duarte, A. Sabharwal, V. Aggarwal, R. Jana, K. K. Ramakrishnan, C. W. Rice and N. K. Shankaranarayanan, Design and characterization of a full-duplex multiantenna system for WiFi networks, IEEE Transactions on Vehicular Technology, 63 (2014), 1160-1177. [5] E. Everett, A. Sahai and A. Sabharwal, Passive self-interference suppression for full-duplex infrastructure nodes, IEEE Transactions on Wireless Communications, 13 (2014), 680-694. [6] Y. Hua, Y. Ma, A. Gholian, Y. Li, A. C. Cirik and P. Liang, Radio self-interference cancellation by transmit beamforming, all-analog cancellation and blind digital tuning, Signal Processing, 108 (2015), 322-340. [7] F. Jian and S. Dandan, Complex Network Theory and Its Application Research on P2P Networks, Applied Mathematics and Nonlinear Sciences, 1 (2016), 45-52. [8] B. Jiao, M. Wen, M. Ma and H. V. Poor, Spatial modulated full duplex, IEEE Wireless Communications Letters, 3 (2014), 641-644. [9] X. Jin, M. Ma, B. Jiao and W. C. Y. Lee, Studies on spectral efficiency of the cdd system, in Vehicular Technology Conference Fall, 2009, 1–5. [10] A. S. B. T. Krishna, Generation of biphase sequences using different logistic maps, in International Conference on Communication and Signal Processing (ICCSP), 2016, 2102–2104. [11] P. Kumar and S. Chakrabarti, A new overloading scheme for cellular DS-CDMA using orthogonal Gold codes, in Vehicular Technology Conference (VTC), 2008, 1042–1046. [12] W. C. Y. Lee, The most spectrum-efficient duplexing system: CDD, IEEE Communications Magazine, 40 (2002), 163–166. [13] A. Murua and J. Sanz-Serna, Vibrational resonance: a study with high-order word-series averaging, Applied Mathematics and Nonlinear Sciences, 1 (2016), 239-246. [14] M. Pal and S. Chattopadhyay, A novel orthogonal minimum cross-correlation spreading code in CDMA system, in International Conference on Emerging Trends in Robotics and Communication Technologies, 2010, 80–84. [15] J. S. Pereira and H. J. A. D. Silva, M-ary mutually orthogonal complementary gold codes, in Signal Processing Conference, 2009 European, 2009, 1636–1640. [16] J. G. Proakis, Digital Communications Fourth Edition, McGraw-Hill Companies, Inc., New York, NY, 1998. [17] S. Shao, X. Quan, Y. Shen and Y. Tang, Effect of phase noise on digital self-interference cancellation in wireless full duplex, 2759–2763. [18] Y. Shen, J. Zhou and Y. Tang, Digital self-interference cancellation in wireless co-time and co-frequency full-duplex system, Wireless Personal Communications, 82 (2015), 2557-2565. [19] X. H. Tang, P. Z. Fan and S. Matsufuji, Lower bounds on correlation of spreading sequence set with low or zero correlation zone, Electronics Letters, 36 (2002), 551-552.

show all references

##### References:
 [1] A. L. A. Aboltins, Selection and performance analysis of chaotic spreading sequences for DS-CDMA systems, in Advances in Wireless and Optical Communications (RTUWO), 2016, 38–45. [2] E. Ahmed and A. M. Eltawil, All-digital self-interference cancellation technique for full-duplex systems, IEEE Transactions on Wireless Communications, 14 (2015), 3519-3532. [3] M. Duarte, C. Dick and A. Sabharwal, Experiment-driven characterization of full-duplex wireless systems, IEEE Transactions on Wireless Communications, 11 (2012), 4296-4307. [4] M. Duarte, A. Sabharwal, V. Aggarwal, R. Jana, K. K. Ramakrishnan, C. W. Rice and N. K. Shankaranarayanan, Design and characterization of a full-duplex multiantenna system for WiFi networks, IEEE Transactions on Vehicular Technology, 63 (2014), 1160-1177. [5] E. Everett, A. Sahai and A. Sabharwal, Passive self-interference suppression for full-duplex infrastructure nodes, IEEE Transactions on Wireless Communications, 13 (2014), 680-694. [6] Y. Hua, Y. Ma, A. Gholian, Y. Li, A. C. Cirik and P. Liang, Radio self-interference cancellation by transmit beamforming, all-analog cancellation and blind digital tuning, Signal Processing, 108 (2015), 322-340. [7] F. Jian and S. Dandan, Complex Network Theory and Its Application Research on P2P Networks, Applied Mathematics and Nonlinear Sciences, 1 (2016), 45-52. [8] B. Jiao, M. Wen, M. Ma and H. V. Poor, Spatial modulated full duplex, IEEE Wireless Communications Letters, 3 (2014), 641-644. [9] X. Jin, M. Ma, B. Jiao and W. C. Y. Lee, Studies on spectral efficiency of the cdd system, in Vehicular Technology Conference Fall, 2009, 1–5. [10] A. S. B. T. Krishna, Generation of biphase sequences using different logistic maps, in International Conference on Communication and Signal Processing (ICCSP), 2016, 2102–2104. [11] P. Kumar and S. Chakrabarti, A new overloading scheme for cellular DS-CDMA using orthogonal Gold codes, in Vehicular Technology Conference (VTC), 2008, 1042–1046. [12] W. C. Y. Lee, The most spectrum-efficient duplexing system: CDD, IEEE Communications Magazine, 40 (2002), 163–166. [13] A. Murua and J. Sanz-Serna, Vibrational resonance: a study with high-order word-series averaging, Applied Mathematics and Nonlinear Sciences, 1 (2016), 239-246. [14] M. Pal and S. Chattopadhyay, A novel orthogonal minimum cross-correlation spreading code in CDMA system, in International Conference on Emerging Trends in Robotics and Communication Technologies, 2010, 80–84. [15] J. S. Pereira and H. J. A. D. Silva, M-ary mutually orthogonal complementary gold codes, in Signal Processing Conference, 2009 European, 2009, 1636–1640. [16] J. G. Proakis, Digital Communications Fourth Edition, McGraw-Hill Companies, Inc., New York, NY, 1998. [17] S. Shao, X. Quan, Y. Shen and Y. Tang, Effect of phase noise on digital self-interference cancellation in wireless full duplex, 2759–2763. [18] Y. Shen, J. Zhou and Y. Tang, Digital self-interference cancellation in wireless co-time and co-frequency full-duplex system, Wireless Personal Communications, 82 (2015), 2557-2565. [19] X. H. Tang, P. Z. Fan and S. Matsufuji, Lower bounds on correlation of spreading sequence set with low or zero correlation zone, Electronics Letters, 36 (2002), 551-552.
Application Scenario of the CDD System
The block-correlation performance of the OG code
The block-correlation performance of the OC code
The Average Duplex Self-interference Suppression Performance with Different $N$
 Code Type $N$ $Q$ ${C}_{aver}$ (dBc) ${C}_{worst}$ (dBc) OG 128 128 23.28 18.99 512 512 29.80 27.21 1024 1024 32.68 31.18 OC 128 128 33.79 24.69 256 256 37.11 26.35 512 512 39.77 26.95 1024 1024 42.65 25.29
 Code Type $N$ $Q$ ${C}_{aver}$ (dBc) ${C}_{worst}$ (dBc) OG 128 128 23.28 18.99 512 512 29.80 27.21 1024 1024 32.68 31.18 OC 128 128 33.79 24.69 256 256 37.11 26.35 512 512 39.77 26.95 1024 1024 42.65 25.29
System parameter of the compared system
 $N$ $W$ Max. $Q$ $Q$ CDD 128+8 8 16 16 Async-CDD with OG code 128 - 128 16 Async-CDD with OC code 128 - 128 16
 $N$ $W$ Max. $Q$ $Q$ CDD 128+8 8 16 16 Async-CDD with OG code 128 - 128 16 Async-CDD with OC code 128 - 128 16
The self-interference suppression performance with different delay
 $Q$ $N$ The number of $C(p, q)$ $\leq$ 24 dBc The number of $C(p, q)$ $\leq$ 28 dBc The number of $C(p, q)$ $\leq$ 30 dBc CDD with 16 128 0 168 256 ZCZ code Async-CDD 16 128 225 256 256 with OG code Async-CDD 16 128 0 10 33 with OC code
 $Q$ $N$ The number of $C(p, q)$ $\leq$ 24 dBc The number of $C(p, q)$ $\leq$ 28 dBc The number of $C(p, q)$ $\leq$ 30 dBc CDD with 16 128 0 168 256 ZCZ code Async-CDD 16 128 225 256 256 with OG code Async-CDD 16 128 0 10 33 with OC code
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