Abstract

In this paper, the peak-to-average power ratio (PAPR) reduction problem with tone injection (TI) in the direct current-biased optical orthogonal frequency division multiplexing (DCO-OFDM) system is investigated, which is formulated as a tough integer combinatorial optimization problem. Since it is a challenging task to find the global optimal solution, the branch-and-bound method (BBM), which is extensively employed to deal with the NP-hard problem, is introduced to solve this problem. By splitting the superior branches and pruning the inferior branches, the close optimal solution is obtained. Simulation results reveal that the proposed BBM-based TI method has superior PAPR reduction and bit error rate (BER) performance compared with some existing algorithms. The proposed algorithm ensures a relatively low peak value, and thus provides an important benchmark in performance evaluations relative to other existing algorithms targeting at the same problem.

© 2017 Optical Society of America

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References

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  1. S. Rajagopal, R. Roberts, and S. K. Lim, “IEEE 802.15.7 visible light communication: Modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
    [Crossref]
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    [Crossref]
  3. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009).
    [Crossref]
  4. Z. Yu, R. J. Baxley, and G. T. Zhou, “EVM and achievable data rate analysis of clipped OFDM signals in visible light communication,” EURASIP J. Wirel. Commun. Netw. 2012(1), 1–16 (2013).
  5. H. Elgala, R. Mesleh, and H. Haas, “A study of LED nonlinearity effectson optical wireless transmission using OFDM,” in Proc. Wireless Opt. Commun. Netw. (WOCN), 1–5(2009).
  6. Z. H. Yu, R. J. Baxley, and G. T. Zhou, “Iterative clipping for PAPR reduction in visible light OFDM communications,” Military Communications Conference (IEEE,2014), pp. 1681–1686.
    [Crossref]
  7. K. Bandara, P. Niroopan, and Y.-H. Chung, “PAPR reduced OFDM visible light communication using exponential nonlinear companding,” International Conference on Microwaves, Communications, Antennas and Electronic Systems (IEEE, 2013), pp. 1–5.
    [Crossref]
  8. W. O. Popoola, Z. Ghassemlooy, and B. G. Stewart, “Pilot-assisted PAPR reduction technique for optical OFDM communication systems,” J. Lightwave Technol. 32(7), 1374–1382 (2014).
    [Crossref]
  9. H. Zhang, Y. Yuan, and W. Xu, “PAPR reduction for DCO-OFDM visible light communications via semidefinite relaxation,” IEEE Photonics Technol. Lett. 26(17), 1718–1721 (2014).
    [Crossref]
  10. N. Jacklin and Z. Ding, “A linear programming based tone injection algorithm for PAPR reduction of OFDM and linearly precoded systems,” IEEE Trans. Circ. Syst. 60(7), 1937–1945 (2013).
  11. K. Cumanan, R. Krishna, L. Musavian, and S. Lambotharan, “Joint beamforming and user maximization techniques for cognitive radio networks based on branch and bound method,” IEEE Trans. Wirel. Commun. 9(10), 3082–3092 (2010).
    [Crossref]
  12. T. Ding, R. Bo, F. Li, and H. Sun, “A bi-level branch and bound method for economic dispatch with disjoint prohibited zones considering network losses,” IEEE Trans. Power Syst. 30(6), 2841–2855 (2015).
    [Crossref]
  13. T. Jiang and Y. Y. Wu, “An overview: peak-to-average power ratio reduction techniques for OFDM signals,” IEEE Trans. Broadcast 54(2), 257–268 (2008).
    [Crossref]
  14. J. C. Chen and C. K. Wen, “PAPR reduction of OFDM Signal using cross-entropy-based tone injection schemes,” IEEE Signal Process. Lett. 17(8), 727–730 (2010).
    [Crossref]
  15. I. W. H. Tsang and J. T. Y. Kwok, “Efficient hyperkernel learning using second-order cone programming,” IEEE Trans. Neural Netw. 17(1), 48–58 (2006).
    [Crossref] [PubMed]
  16. Y. Nesterov and A. Nemirovskii, “Interior-point polynomial algorithms in convex programming,” Soc. Indust. Appl. Math. Rev. 36(4), 682–683 (1994).
    [Crossref]
  17. S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge, U.K.: Cambridge Univ. Press, 2004).

2015 (1)

T. Ding, R. Bo, F. Li, and H. Sun, “A bi-level branch and bound method for economic dispatch with disjoint prohibited zones considering network losses,” IEEE Trans. Power Syst. 30(6), 2841–2855 (2015).
[Crossref]

2014 (2)

H. Zhang, Y. Yuan, and W. Xu, “PAPR reduction for DCO-OFDM visible light communications via semidefinite relaxation,” IEEE Photonics Technol. Lett. 26(17), 1718–1721 (2014).
[Crossref]

W. O. Popoola, Z. Ghassemlooy, and B. G. Stewart, “Pilot-assisted PAPR reduction technique for optical OFDM communication systems,” J. Lightwave Technol. 32(7), 1374–1382 (2014).
[Crossref]

2013 (2)

Z. Yu, R. J. Baxley, and G. T. Zhou, “EVM and achievable data rate analysis of clipped OFDM signals in visible light communication,” EURASIP J. Wirel. Commun. Netw. 2012(1), 1–16 (2013).

N. Jacklin and Z. Ding, “A linear programming based tone injection algorithm for PAPR reduction of OFDM and linearly precoded systems,” IEEE Trans. Circ. Syst. 60(7), 1937–1945 (2013).

2012 (1)

S. Rajagopal, R. Roberts, and S. K. Lim, “IEEE 802.15.7 visible light communication: Modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[Crossref]

2010 (2)

J. C. Chen and C. K. Wen, “PAPR reduction of OFDM Signal using cross-entropy-based tone injection schemes,” IEEE Signal Process. Lett. 17(8), 727–730 (2010).
[Crossref]

K. Cumanan, R. Krishna, L. Musavian, and S. Lambotharan, “Joint beamforming and user maximization techniques for cognitive radio networks based on branch and bound method,” IEEE Trans. Wirel. Commun. 9(10), 3082–3092 (2010).
[Crossref]

2009 (1)

2008 (1)

T. Jiang and Y. Y. Wu, “An overview: peak-to-average power ratio reduction techniques for OFDM signals,” IEEE Trans. Broadcast 54(2), 257–268 (2008).
[Crossref]

2006 (1)

I. W. H. Tsang and J. T. Y. Kwok, “Efficient hyperkernel learning using second-order cone programming,” IEEE Trans. Neural Netw. 17(1), 48–58 (2006).
[Crossref] [PubMed]

2005 (1)

S. Hranilovic, “On the design of bandwidth efficient signaling for indoor wireless optical channels,” Int. J. Commun. Syst. 18(3), 205–228 (2005).
[Crossref]

1994 (1)

Y. Nesterov and A. Nemirovskii, “Interior-point polynomial algorithms in convex programming,” Soc. Indust. Appl. Math. Rev. 36(4), 682–683 (1994).
[Crossref]

Armstrong, J.

Bandara, K.

K. Bandara, P. Niroopan, and Y.-H. Chung, “PAPR reduced OFDM visible light communication using exponential nonlinear companding,” International Conference on Microwaves, Communications, Antennas and Electronic Systems (IEEE, 2013), pp. 1–5.
[Crossref]

Baxley, R. J.

Z. Yu, R. J. Baxley, and G. T. Zhou, “EVM and achievable data rate analysis of clipped OFDM signals in visible light communication,” EURASIP J. Wirel. Commun. Netw. 2012(1), 1–16 (2013).

Z. H. Yu, R. J. Baxley, and G. T. Zhou, “Iterative clipping for PAPR reduction in visible light OFDM communications,” Military Communications Conference (IEEE,2014), pp. 1681–1686.
[Crossref]

Bo, R.

T. Ding, R. Bo, F. Li, and H. Sun, “A bi-level branch and bound method for economic dispatch with disjoint prohibited zones considering network losses,” IEEE Trans. Power Syst. 30(6), 2841–2855 (2015).
[Crossref]

Chen, J. C.

J. C. Chen and C. K. Wen, “PAPR reduction of OFDM Signal using cross-entropy-based tone injection schemes,” IEEE Signal Process. Lett. 17(8), 727–730 (2010).
[Crossref]

Chung, Y.-H.

K. Bandara, P. Niroopan, and Y.-H. Chung, “PAPR reduced OFDM visible light communication using exponential nonlinear companding,” International Conference on Microwaves, Communications, Antennas and Electronic Systems (IEEE, 2013), pp. 1–5.
[Crossref]

Cumanan, K.

K. Cumanan, R. Krishna, L. Musavian, and S. Lambotharan, “Joint beamforming and user maximization techniques for cognitive radio networks based on branch and bound method,” IEEE Trans. Wirel. Commun. 9(10), 3082–3092 (2010).
[Crossref]

Ding, T.

T. Ding, R. Bo, F. Li, and H. Sun, “A bi-level branch and bound method for economic dispatch with disjoint prohibited zones considering network losses,” IEEE Trans. Power Syst. 30(6), 2841–2855 (2015).
[Crossref]

Ding, Z.

N. Jacklin and Z. Ding, “A linear programming based tone injection algorithm for PAPR reduction of OFDM and linearly precoded systems,” IEEE Trans. Circ. Syst. 60(7), 1937–1945 (2013).

Ghassemlooy, Z.

Hranilovic, S.

S. Hranilovic, “On the design of bandwidth efficient signaling for indoor wireless optical channels,” Int. J. Commun. Syst. 18(3), 205–228 (2005).
[Crossref]

Jacklin, N.

N. Jacklin and Z. Ding, “A linear programming based tone injection algorithm for PAPR reduction of OFDM and linearly precoded systems,” IEEE Trans. Circ. Syst. 60(7), 1937–1945 (2013).

Jiang, T.

T. Jiang and Y. Y. Wu, “An overview: peak-to-average power ratio reduction techniques for OFDM signals,” IEEE Trans. Broadcast 54(2), 257–268 (2008).
[Crossref]

Krishna, R.

K. Cumanan, R. Krishna, L. Musavian, and S. Lambotharan, “Joint beamforming and user maximization techniques for cognitive radio networks based on branch and bound method,” IEEE Trans. Wirel. Commun. 9(10), 3082–3092 (2010).
[Crossref]

Kwok, J. T. Y.

I. W. H. Tsang and J. T. Y. Kwok, “Efficient hyperkernel learning using second-order cone programming,” IEEE Trans. Neural Netw. 17(1), 48–58 (2006).
[Crossref] [PubMed]

Lambotharan, S.

K. Cumanan, R. Krishna, L. Musavian, and S. Lambotharan, “Joint beamforming and user maximization techniques for cognitive radio networks based on branch and bound method,” IEEE Trans. Wirel. Commun. 9(10), 3082–3092 (2010).
[Crossref]

Li, F.

T. Ding, R. Bo, F. Li, and H. Sun, “A bi-level branch and bound method for economic dispatch with disjoint prohibited zones considering network losses,” IEEE Trans. Power Syst. 30(6), 2841–2855 (2015).
[Crossref]

Lim, S. K.

S. Rajagopal, R. Roberts, and S. K. Lim, “IEEE 802.15.7 visible light communication: Modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[Crossref]

Musavian, L.

K. Cumanan, R. Krishna, L. Musavian, and S. Lambotharan, “Joint beamforming and user maximization techniques for cognitive radio networks based on branch and bound method,” IEEE Trans. Wirel. Commun. 9(10), 3082–3092 (2010).
[Crossref]

Nemirovskii, A.

Y. Nesterov and A. Nemirovskii, “Interior-point polynomial algorithms in convex programming,” Soc. Indust. Appl. Math. Rev. 36(4), 682–683 (1994).
[Crossref]

Nesterov, Y.

Y. Nesterov and A. Nemirovskii, “Interior-point polynomial algorithms in convex programming,” Soc. Indust. Appl. Math. Rev. 36(4), 682–683 (1994).
[Crossref]

Niroopan, P.

K. Bandara, P. Niroopan, and Y.-H. Chung, “PAPR reduced OFDM visible light communication using exponential nonlinear companding,” International Conference on Microwaves, Communications, Antennas and Electronic Systems (IEEE, 2013), pp. 1–5.
[Crossref]

Popoola, W. O.

Rajagopal, S.

S. Rajagopal, R. Roberts, and S. K. Lim, “IEEE 802.15.7 visible light communication: Modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[Crossref]

Roberts, R.

S. Rajagopal, R. Roberts, and S. K. Lim, “IEEE 802.15.7 visible light communication: Modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[Crossref]

Stewart, B. G.

Sun, H.

T. Ding, R. Bo, F. Li, and H. Sun, “A bi-level branch and bound method for economic dispatch with disjoint prohibited zones considering network losses,” IEEE Trans. Power Syst. 30(6), 2841–2855 (2015).
[Crossref]

Tsang, I. W. H.

I. W. H. Tsang and J. T. Y. Kwok, “Efficient hyperkernel learning using second-order cone programming,” IEEE Trans. Neural Netw. 17(1), 48–58 (2006).
[Crossref] [PubMed]

Wen, C. K.

J. C. Chen and C. K. Wen, “PAPR reduction of OFDM Signal using cross-entropy-based tone injection schemes,” IEEE Signal Process. Lett. 17(8), 727–730 (2010).
[Crossref]

Wu, Y. Y.

T. Jiang and Y. Y. Wu, “An overview: peak-to-average power ratio reduction techniques for OFDM signals,” IEEE Trans. Broadcast 54(2), 257–268 (2008).
[Crossref]

Xu, W.

H. Zhang, Y. Yuan, and W. Xu, “PAPR reduction for DCO-OFDM visible light communications via semidefinite relaxation,” IEEE Photonics Technol. Lett. 26(17), 1718–1721 (2014).
[Crossref]

Yu, Z.

Z. Yu, R. J. Baxley, and G. T. Zhou, “EVM and achievable data rate analysis of clipped OFDM signals in visible light communication,” EURASIP J. Wirel. Commun. Netw. 2012(1), 1–16 (2013).

Yu, Z. H.

Z. H. Yu, R. J. Baxley, and G. T. Zhou, “Iterative clipping for PAPR reduction in visible light OFDM communications,” Military Communications Conference (IEEE,2014), pp. 1681–1686.
[Crossref]

Yuan, Y.

H. Zhang, Y. Yuan, and W. Xu, “PAPR reduction for DCO-OFDM visible light communications via semidefinite relaxation,” IEEE Photonics Technol. Lett. 26(17), 1718–1721 (2014).
[Crossref]

Zhang, H.

H. Zhang, Y. Yuan, and W. Xu, “PAPR reduction for DCO-OFDM visible light communications via semidefinite relaxation,” IEEE Photonics Technol. Lett. 26(17), 1718–1721 (2014).
[Crossref]

Zhou, G. T.

Z. Yu, R. J. Baxley, and G. T. Zhou, “EVM and achievable data rate analysis of clipped OFDM signals in visible light communication,” EURASIP J. Wirel. Commun. Netw. 2012(1), 1–16 (2013).

Z. H. Yu, R. J. Baxley, and G. T. Zhou, “Iterative clipping for PAPR reduction in visible light OFDM communications,” Military Communications Conference (IEEE,2014), pp. 1681–1686.
[Crossref]

EURASIP J. Wirel. Commun. Netw. (1)

Z. Yu, R. J. Baxley, and G. T. Zhou, “EVM and achievable data rate analysis of clipped OFDM signals in visible light communication,” EURASIP J. Wirel. Commun. Netw. 2012(1), 1–16 (2013).

IEEE Commun. Mag. (1)

S. Rajagopal, R. Roberts, and S. K. Lim, “IEEE 802.15.7 visible light communication: Modulation schemes and dimming support,” IEEE Commun. Mag. 50(3), 72–82 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (1)

H. Zhang, Y. Yuan, and W. Xu, “PAPR reduction for DCO-OFDM visible light communications via semidefinite relaxation,” IEEE Photonics Technol. Lett. 26(17), 1718–1721 (2014).
[Crossref]

IEEE Signal Process. Lett. (1)

J. C. Chen and C. K. Wen, “PAPR reduction of OFDM Signal using cross-entropy-based tone injection schemes,” IEEE Signal Process. Lett. 17(8), 727–730 (2010).
[Crossref]

IEEE Trans. Broadcast (1)

T. Jiang and Y. Y. Wu, “An overview: peak-to-average power ratio reduction techniques for OFDM signals,” IEEE Trans. Broadcast 54(2), 257–268 (2008).
[Crossref]

IEEE Trans. Circ. Syst. (1)

N. Jacklin and Z. Ding, “A linear programming based tone injection algorithm for PAPR reduction of OFDM and linearly precoded systems,” IEEE Trans. Circ. Syst. 60(7), 1937–1945 (2013).

IEEE Trans. Neural Netw. (1)

I. W. H. Tsang and J. T. Y. Kwok, “Efficient hyperkernel learning using second-order cone programming,” IEEE Trans. Neural Netw. 17(1), 48–58 (2006).
[Crossref] [PubMed]

IEEE Trans. Power Syst. (1)

T. Ding, R. Bo, F. Li, and H. Sun, “A bi-level branch and bound method for economic dispatch with disjoint prohibited zones considering network losses,” IEEE Trans. Power Syst. 30(6), 2841–2855 (2015).
[Crossref]

IEEE Trans. Wirel. Commun. (1)

K. Cumanan, R. Krishna, L. Musavian, and S. Lambotharan, “Joint beamforming and user maximization techniques for cognitive radio networks based on branch and bound method,” IEEE Trans. Wirel. Commun. 9(10), 3082–3092 (2010).
[Crossref]

Int. J. Commun. Syst. (1)

S. Hranilovic, “On the design of bandwidth efficient signaling for indoor wireless optical channels,” Int. J. Commun. Syst. 18(3), 205–228 (2005).
[Crossref]

J. Lightwave Technol. (2)

Soc. Indust. Appl. Math. Rev. (1)

Y. Nesterov and A. Nemirovskii, “Interior-point polynomial algorithms in convex programming,” Soc. Indust. Appl. Math. Rev. 36(4), 682–683 (1994).
[Crossref]

Other (4)

S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge, U.K.: Cambridge Univ. Press, 2004).

H. Elgala, R. Mesleh, and H. Haas, “A study of LED nonlinearity effectson optical wireless transmission using OFDM,” in Proc. Wireless Opt. Commun. Netw. (WOCN), 1–5(2009).

Z. H. Yu, R. J. Baxley, and G. T. Zhou, “Iterative clipping for PAPR reduction in visible light OFDM communications,” Military Communications Conference (IEEE,2014), pp. 1681–1686.
[Crossref]

K. Bandara, P. Niroopan, and Y.-H. Chung, “PAPR reduced OFDM visible light communication using exponential nonlinear companding,” International Conference on Microwaves, Communications, Antennas and Electronic Systems (IEEE, 2013), pp. 1–5.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 The schematic diagram of the DCO-OFDM VLC system.
Fig. 2
Fig. 2 The extended 16-QAM constellation diagram.
Fig. 3
Fig. 3 PAPR reduction comparison of different TI methods with N=128 and 16-QAM.
Fig. 4
Fig. 4 Peak power comparison of different TI methods.
Fig. 5
Fig. 5 Mean power comparison of different TI methods.
Fig. 6
Fig. 6 BER comparison of different TI methods with N=128 and 16-QAM.

Tables (1)

Tables Icon

Algorithm 1 BBM-based TI method for PAPR reduction

Equations (13)

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X k ={ X k k=1,2,,N/2 1 X Nk * k=N/2 +1,,N1 ,
x n = 1 N k=0 N1 X k e j2πkn / NL ,n=0,1,2,,LN1.
PAPR=10 log 10 max 0nLN1 | x n | 2 E[ | x n | 2 ] ,
X ¯ k =( 1 ω k ) X k + ω k C k ,
C k ={ (d/2 ) a k j(d/2 ) M '' , ( a k > M ' , b k = M ' ) (d/2 ) a k +j(d/2 ) M '' , ( a k < M ' , b k = M ' ) (d/2 ) M '' j(d/2 ) b k , ( a k = M ' , M ' < b k < M ' ) (d/2 ) M '' j(d/2 ) b k , ( a k = M ' , M ' < b k < M ' ) (d/2 ) a k j(d/2 ) M '' , ( a k = M ' , b k = M ' ) (d/2 ) a k +j(d/2 ) M '' , ( a k = M ' , b k = M ' ) ,
Y k ={ { X ¯ 0 }, k=0 X ¯ k , k=1,, N 2 1 { X ¯ 0 }, k= N 2 X ¯ Nk * , k= N 2 +1,,N1 ,
y n = 1 N k=0 N1 Y k e j2πkn / LN ,n=0,1,2,,LN1.
min ω C sel (ω) C sel (ω)=max| y n (ω) | 2 subject to ω {0,1} N ,
min ω C sel (ω) s.t. Q 0 .
min ω C sel (ω) s.t. Q 1 : ω k [ 0,1 ] ,kl, ω l =0,
min ω C sel (ω) s.t. Q 2 : ω k [ 0,1 ] ,kl, ω l =1.
k * =arg min k{1,,N} | ω k 1 2 |.
y n, DCO ={ A m , y n > A m y n ,0 y n A m 0, y n 0 .

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