Abstract

In this paper, we consider the design of space code for an intensity modulated direct detection multi-input-multi-output optical wireless communication (IM/DD MIMO-OWC) system, in which channel coefficients are independent and non-identically log-normal distributed, with variances and means known at the transmitter and channel state information available at the receiver. Utilizing the existing space code design criterion for IM/DD MIMO-OWC with a maximum likelihood (ML) detector, we design a diversity-optimal space code (DOSC) that maximizes both large-scale diversity and small-scale diversity gains and prove that the spatial repetition code (RC) with a diversity-optimized power allocation is diversity-optimal among all the high dimensional nonnegative space code schemes under a commonly used optical power constraint. In addition, we show that one of significant advantages of the DOSC is to allow low-complexity ML detection. Simulation results indicate that in high signal-to-noise ratio (SNR) regimes, our proposed DOSC significantly outperforms RC, which is the best space code currently available for such system.

© 2016 Optical Society of America

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  1. D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).
  2. M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
    [Crossref]
  3. S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014).
    [Crossref]
  4. A. K. Majumdar, Free-space Optical (FSO) Platforms: Unmanned Aerial Vehicle (UAV) and Mobile (Springer, 2015).
  5. M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
    [Crossref]
  6. S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
    [Crossref]
  7. M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
    [Crossref]
  8. H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
    [Crossref]
  9. R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
    [Crossref]
  10. E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
    [Crossref]
  11. M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
    [Crossref]
  12. Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.
  13. Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Space codes for MIMO optical wireless communications: Error performance criterion and code construction,” http://arxiv.org/abs/1509.07470 (2015).
  14. V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
    [Crossref]
  15. J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
    [Crossref]
  16. J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
    [Crossref]
  17. D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
    [Crossref]
  18. S. M. Aghajanzadeh and M. Uysal, “Diversity–multiplexing trade-off in coherent free-space optical systems with multiple receivers,” J. Opt. Commun. Netw 2(12), 1087–1094 (2010).
    [Crossref]
  19. E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012).
    [Crossref]
  20. M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
    [Crossref] [PubMed]
  21. X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).
  22. M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
    [Crossref]
  23. J. R. Barry, Wireless Infrared Communications (Kluwer Academic, 1994).
    [Crossref]
  24. A. García-Zambrana, C. Castillo-Vázquez, B. Castillo-Vázquez, and A. Hiniesta-Gómez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photonics Technol. Lett. 21(14), 1017–1019 (2009).
    [Crossref]
  25. A. García-Zambrana, C. Castillo-Vázquez, and B. Castillo-Vázquez, “Space-time trellis coding with transmit laser selection for FSO links over strong atmospheric turbulence channels,” Opt. Express 18(6), 5356–5366 (2010).
    [Crossref] [PubMed]
  26. A. García-Zambrana, B. Castillo-Vázquez, and C. Castillo-Vázquez, “Average capacity of FSO links with transmit laser selection using non-uniform OOK signaling over exponential atmospheric turbulence channels,” Opt. Express 18(19), 20445–20454 (2010).
    [Crossref] [PubMed]
  27. C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
    [Crossref]
  28. N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Commun. Technol. 53(2), 479–489 (2004).
  29. D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008).
    [Crossref]
  30. S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
    [Crossref]
  31. L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
    [Crossref]
  32. D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9(4), 505–513 (1991).
    [Crossref]
  33. M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels (John Wiley and Sons, 2000).
    [Crossref]
  34. J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008).
    [Crossref]
  35. J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
    [Crossref]
  36. Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
    [Crossref]
  37. X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).
  38. T. M. Cover and J. A. Thomas, Information Theory (John Wiley and Sons, 1991).

2015 (1)

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

2014 (5)

M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
[Crossref]

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014).
[Crossref]

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

2013 (2)

D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
[Crossref]

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

2012 (4)

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
[Crossref] [PubMed]

E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012).
[Crossref]

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

2011 (1)

C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
[Crossref]

2010 (4)

2009 (2)

A. García-Zambrana, C. Castillo-Vázquez, B. Castillo-Vázquez, and A. Hiniesta-Gómez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photonics Technol. Lett. 21(14), 1017–1019 (2009).
[Crossref]

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
[Crossref]

2008 (4)

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
[Crossref]

J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
[Crossref]

J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008).
[Crossref]

D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008).
[Crossref]

2007 (2)

J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
[Crossref]

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[Crossref]

2005 (1)

M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[Crossref]

2004 (1)

N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Commun. Technol. 53(2), 479–489 (2004).

1998 (1)

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

1991 (1)

D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9(4), 505–513 (1991).
[Crossref]

Abaza, M.

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

Abou-Rjeily, C.

C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
[Crossref]

Aggoune, E.-H. M.

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

Aghajanzadeh, S. M.

S. M. Aghajanzadeh and M. Uysal, “Diversity–multiplexing trade-off in coherent free-space optical systems with multiple receivers,” J. Opt. Commun. Netw 2(12), 1087–1094 (2010).
[Crossref]

Agrell, E.

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

Alouini, M.-S.

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels (John Wiley and Sons, 2000).
[Crossref]

X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).

Amphawan, A.

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014).
[Crossref]

Andrews, L. C.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[Crossref]

Armstrong, J.

J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008).
[Crossref]

Barry, J. R.

J. R. Barry, Wireless Infrared Communications (Kluwer Academic, 1994).
[Crossref]

Bayaki, E.

E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012).
[Crossref]

E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
[Crossref]

Beaulieu, N. C.

N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Commun. Technol. 53(2), 479–489 (2004).

Borah, D. K.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

Boucouvalas, A. C.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

Calderbank, A. R.

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

Castillo-Vázquez, B.

Castillo-Vázquez, C.

Chaudhary, S.

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014).
[Crossref]

Chen, G.

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

Cheng, J.

M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
[Crossref]

M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
[Crossref] [PubMed]

X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).

Cover, T. M.

T. M. Cover and J. A. Thomas, Information Theory (John Wiley and Sons, 1991).

Davis, C. C.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

Ding, Z.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

Dumitrescu, S.

D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
[Crossref]

Gagliardi, R. M.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
[Crossref]

Gao, Q.

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

García-Zambrana, A.

Ge-Shi, T.

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

Giggenbach, D.

D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008).
[Crossref]

Guan, Y.

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

Henniger, H.

D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008).
[Crossref]

Hiniesta-Gómez, A.

A. García-Zambrana, C. Castillo-Vázquez, B. Castillo-Vázquez, and A. Hiniesta-Gómez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photonics Technol. Lett. 21(14), 1017–1019 (2009).
[Crossref]

Holzman, J. F.

M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
[Crossref]

M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
[Crossref] [PubMed]

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[Crossref]

Hranilovic, S.

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

Hua, Y.

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

Karlsson, M.

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

Karout, J.

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

Karp, S.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
[Crossref]

Kavehrad, M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[Crossref]

Ke, X.

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
[Crossref]

Khalighi, M. A.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

Liang, X.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

Ling, X.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

Liu, J.

J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
[Crossref]

J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
[Crossref]

Majumdar, A. K.

A. K. Majumdar, Free-space Optical (FSO) Platforms: Unmanned Aerial Vehicle (UAV) and Mobile (Springer, 2015).

Mansour, A.

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

Manton, J.

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

Marcuse, D.

D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9(4), 505–513 (1991).
[Crossref]

Mesleh, R.

M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
[Crossref]

Moran, S. E.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
[Crossref]

Navidpour, S. M.

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[Crossref]

Niu, M.

M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
[Crossref]

M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
[Crossref] [PubMed]

Phillips, R. L.

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
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Safari, M.

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
[Crossref]

Schmidt, B. J. C.

J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008).
[Crossref]

Schober, R.

E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012).
[Crossref]

E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
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Seshadri, N.

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

Simon, M. K.

M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[Crossref]

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels (John Wiley and Sons, 2000).
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Song, X.

M. Niu, X. Song, J. Cheng, and J. F. Holzman, “Performance analysis of coherent wireless optical communications with atmospheric turbulence,” Opt. Express 20(6), 6515–6520 (2012).
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X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).

Stotts, L. B.

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
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Szczerba, K.

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
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Tarokh, V.

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
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Thomas, J. A.

T. M. Cover and J. A. Thomas, Information Theory (John Wiley and Sons, 1991).

Tian-Peng, R.

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
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Uysal, M.

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
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S. M. Aghajanzadeh and M. Uysal, “Diversity–multiplexing trade-off in coherent free-space optical systems with multiple receivers,” J. Opt. Commun. Netw 2(12), 1087–1094 (2010).
[Crossref]

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
[Crossref]

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[Crossref]

Vilnrotter, V. A.

M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[Crossref]

Wang, H.

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
[Crossref]

Wang, J.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

Wang, J.-L.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Wang, T.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Wong, K. M.

J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
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J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
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D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
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Yu, H.-Y.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Yuen, C.

R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

Zhang, J.-K.

D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
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J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
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J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
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Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Zhang, Y.-Y.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Zhao, C.

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

Zhao, L.

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
[Crossref]

Zhu, Y.-J.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Commun. Surveys Tuts. (1)

M. A. Khalighi and M. Uysal, “Survey on free space optical communication: A communication theory perspective,” Commun. Surveys Tuts. 16(4), 2231–2258 (2014).
[Crossref]

EURASIP J. Wireless Commun. Netw. (1)

D. K. Borah, A. C. Boucouvalas, C. C. Davis, S. Hranilovic, and K. Yiannopoulos, “A review of communication-oriented optical wireless systems,” EURASIP J. Wireless Commun. Netw. 91(1), 1–28 (2012).

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C. Abou-Rjeily, “On the optimality of the selection transmit diversity for MIMO-FSO links with feedback,” IEEE Commun. Lett. 15(6), 641–643 (2011).
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R. Tian-Peng, C. Yuen, Y. Guan, and T. Ge-Shi, “High-order intensity modulations for OSTBC in free-space optical MIMO communications,” IEEE Commun. Lett. 2(6), 607–610 (2013).
[Crossref]

J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett. 12(5), 343–345 (2008).
[Crossref]

IEEE Photonics J. (1)

M. Niu, J. Cheng, and J. F. Holzman, “Alamouti-type STBC for atmospheric optical communication using coherent detection,” IEEE Photonics J. 6(1), 1–17 (2014).
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IEEE Photonics Technol. Lett. (1)

A. García-Zambrana, C. Castillo-Vázquez, B. Castillo-Vázquez, and A. Hiniesta-Gómez, “Selection transmit diversity for FSO links over strong atmospheric turbulence channels,” IEEE Photonics Technol. Lett. 21(14), 1017–1019 (2009).
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IEEE Trans. Commun. (2)

Q. Gao, J. Manton, G. Chen, and Y. Hua, “Constellation design for a multicarrier optical wireless communication channel,” IEEE Trans. Commun. 62(1), 214–225 (2014).
[Crossref]

E. Bayaki and R. Schober, “On space-time coding for free-space optical systems,” IEEE Trans. Commun. 58(1), 58–62 (2010).
[Crossref]

IEEE Trans. Commun. Technol. (1)

N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Commun. Technol. 53(2), 479–489 (2004).

IEEE Trans. Inf. Theory (4)

V. Tarokh, N. Seshadri, and A. R. Calderbank, “Space-time codes for high date rate wireless communication: performance criterion and code construction,” IEEE Trans. Inf. Theory 44(2), 744–765 (1998).
[Crossref]

J. Liu, J.-K. Zhang, and K. M. Wong, “Full diversity codes for MISO systems equipped with linear or ML detectors,” IEEE Trans. Inf. Theory 54(10) 4511–4527 (2008).
[Crossref]

D. Xia, J.-K. Zhang, and S. Dumitrescu, “Energy-efficient full diversity collaborative unitary space-time block code designs via unique factorization of signals,” IEEE Trans. Inf. Theory 59(3), 1678–1703 (2013).
[Crossref]

J. Karout, E. Agrell, K. Szczerba, and M. Karlsson, “Optimizing constellations for single-subcarrier intensity-modulated optical systems,” IEEE Trans. Inf. Theory 58(7), 4645–4659 (2012).
[Crossref]

IEEE Trans. Signal Process. (2)

X. Ling, J. Wang, X. Liang, Z. Ding, and C. Zhao, “Offset and power optimization for DCO-OFDM in visible light communication systems,” IEEE Trans. Signal Process. 31(1), 278 (2015).

J.-K. Zhang, J. Liu, and K. M. Wong, “Trace-orthonormal full diversity cyclotomic space-time codes,” IEEE Trans. Signal Process. 55(2), 618–630 (2007).
[Crossref]

IEEE Trans. Wireless Commun. (3)

M. K. Simon and V. A. Vilnrotter, “Alamouti-type space-time coding for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 4(1), 35–39 (2005).
[Crossref]

S. M. Navidpour, M. Uysal, and M. Kavehrad, “BER performance of free-space optical transmission with spatial diversity,” IEEE Trans. Wireless Commun. 6(8), 2813–2819 (2007).
[Crossref]

M. Safari and M. Uysal, “Do we really need OSTBCs for free-space optical communication with direct detection,” IEEE Trans. Wireless Commun. 7(11), 4445–4448 (2008).
[Crossref]

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D. Marcuse, “Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise,” J. Lightwave Technol. 9(4), 505–513 (1991).
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E. Bayaki and R. Schober, “Performance and design of coherent and differential space-time coded FSO systems,” J. Lightwave Technol. 30(11), 1569–1577 (2012).
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J. Opt. Commun. (1)

S. Chaudhary and A. Amphawan, “The role and challenges of free-space optical systems,” J. Opt. Commun. 35(4), 327–334 (2014).
[Crossref]

J. Opt. Commun. Netw (1)

S. M. Aghajanzadeh and M. Uysal, “Diversity–multiplexing trade-off in coherent free-space optical systems with multiple receivers,” J. Opt. Commun. Netw 2(12), 1087–1094 (2010).
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D. Giggenbach and H. Henniger, “Fading-loss assessment in atmospheric free-space optical communication links with on-off keying,” Opt. Eng. 47(4), 046001 (2008).
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M. Abaza, R. Mesleh, A. Mansour, and E.-H. M. Aggoune, “Diversity techniques for a free-space optical communication system in correlated log-normal channels,” Opt. Eng. 53(1), 259–268 (2014).
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Opt. Express (3)

Science Chin. Series F: Inf. Sci. (1)

H. Wang, X. Ke, and L. Zhao, “MIMO free space optical communication based on orthogonal space time block code,” Science Chin. Series F: Inf. Sci. 52(8), 1483–1490 (2009).
[Crossref]

Other (9)

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Full large-scale diversity space codes for MIMO optical wireless communications,” in Proc. IEEE Int. Symp. Inf. Theory (IEEE, 2015), pp. 1671–1675.

Y.-Y. Zhang, H.-Y. Yu, J.-K. Zhang, Y.-J. Zhu, J.-L. Wang, and T. Wang, “Space codes for MIMO optical wireless communications: Error performance criterion and code construction,” http://arxiv.org/abs/1509.07470 (2015).

S. Karp, R. M. Gagliardi, S. E. Moran, and L. B. Stotts, Optical Channels (Springer, 1988).
[Crossref]

L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE, 2001).
[Crossref]

A. K. Majumdar, Free-space Optical (FSO) Platforms: Unmanned Aerial Vehicle (UAV) and Mobile (Springer, 2015).

J. R. Barry, Wireless Infrared Communications (Kluwer Academic, 1994).
[Crossref]

M. K. Simon and M.-S. Alouini, Digital Communication Over Fading Channels (John Wiley and Sons, 2000).
[Crossref]

T. M. Cover and J. A. Thomas, Information Theory (John Wiley and Sons, 1991).

X. Song, J. Cheng, and M.-S. Alouini, “High SNR BER comparison of coherent and differentially coherent modulation schemes in lognormal fading channels,” arXiv preprint arXiv:1407.7097 (2014).

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Figures (4)

Fig. 1
Fig. 1 Performance comparison of DOSC and RC with M = 1, N = 2 and K = 2.

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Fig. 2
Fig. 2 Performance comparison of DOSC and RC with M = N = 2 and varied K.

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Fig. 3
Fig. 3 Performance comparison of DOSC and RC with M = 1, N = K = 2 and varied μn .

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Fig. 4
Fig. 4 Performance comparison of DOSC and RC with N = 2, K = 3 and varied M.

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Equations (10)

Equations on this page are rendered with MathJax. Learn more.

y = Hs + n ,
P D ( s → s ^ ) = C D 𝒢 ( e )     ( ρ / ln 2 ρ ) σ ¯ 4 ln ( N σ ¯ M ) − 3 4 ln 𝒟 small ( e ) ( ln ρ ) − M N e − 𝒟 large 8 ln 2 ρ ln 2 ρ
P ˜ D ( s → s ^ ) = P D ( s → s ^ ) ∏ n = 1 N | e n | − ∑ m = 1 M μ m n σ m n − 2 ( ρ / ln 2 ρ ) − 1 4 ∑ n = 1 N ∑ m = 1 M μ m n σ m n − 2
∏ n = 1 N ( s n ( k + 1 ) − s nk ) σ ¯ n ≤ ( ∑ n = 1 N ( s n ( k + 1 ) ) − s nk ) σ ¯ ∏ n = 1 N ( σ ¯ n σ ¯ ) σ ¯ n .
min 0 ≤ k ≤ 2 K − 2 ∏ n = 1 N ( s n ( k + 1 ) − s nk ) σ ¯ n ≤ 2 σ ¯ ∏ n = 1 N σ ¯ n σ ¯ n ( ( 2 K − 1 ) σ ¯ ) σ ¯
∏ n = 1 N ( s ˜ n ( k + 1 ) − s ˜ nk ) σ ¯ n > 2 σ ¯ ∏ n = 1 N σ ¯ n σ ¯ n ( ( 2 K − 1 ) σ ¯ ) σ ¯
𝒮 opt = { k w } k = 0 k = 2 K − 1
y = Hw k + n , 0 ≤ k ≤ 2 K − 1
k ^ = arg min 0 ≤ k ≤ 2 K − 1 ‖ y − Hw k ‖ 2 2 = arg min 0 ≤ k ≤ 2 K − 1 ( k 2 ‖ Hw k ‖ 2 2 − 2 k y T Hw + ‖ y ‖ 2 2 ) = arg min 0 ≤ k ≤ 2 K − 1 ( ‖ Hw ‖ 2 2 × | k − y T Hw / ‖ Hw ‖ 2 2 | 2 − ( y T Hw ) 2 / ‖ Hw k ‖ 2 2 + ‖ y ‖ 2 2 ) = arg min 0 ≤ k ≤ 2 K − 1 | k − y T Hw / ‖ Hw ‖ 2 2 |
s ^ k = { 0 , y T Hw / ‖ Hw ‖ 2 2 < 0 ; ⌊ y T Hw / ‖ Hw ‖ 2 2 + 1 2 ⌋ w , 0 ≤ y T Hw / ‖ Hw ‖ 2 2 ≤ 2 K − 1 ; ( 2 K − 1 ) w , y T Hw / ‖ Hw ‖ 2 2 > 2 K − 1 .

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