Abstract

Multi-layer modulation (MLM)-aided intensity-modulated direct-detection (IM/DD) DC-biased optical orthogonal frequency division multiplexing (DCO-OFDM) and asymmetrically clipped optical OFDM (ACO-OFDM) are considered. More explicitly, we propose a double turbo receiver (DTR) for jointly detecting the MLM and for compensating the clipping distortion. Additionally, a genetic-algorithm-aided weight optimization is pursued for seeking an increased MLM bits per symbol (BPS) throughput. Our numerical results demonstrate that for ACO-OFDM, at the throughput of η=3 BPS, a 3 dB gain was attained for Q=15 DTR iterations without requiring weight optimization. For DCO-OFDM, an even more significant gain of 12 and 8 dB was observed at the throughput of η=3 BPS and η=4 BPS, respectively, without any clipping distortion compensation.

© 2013 Optical Society of America

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  1. L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for Broadcasting Multi-user Communications, WLANs and Broadcasting. Wiley-IEEE, 2003.
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  24. D. Kim and G. L. Stüber, “Clipping noise mitigation for OFDM by decision-aided reconstruction,” IEEE Commun. Lett., vol.  3, pp. 217–219, 1999.
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  25. H. Chen and A. M. Haimovich, “Iterative estimation and cancellation of clipping noise for OFDM signals,” IEEE Commun. Lett., vol.  7, no. 7, pp. 305–307, 2003.
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  26. H. Nikopour, A. K. Khandani, and S. H. Jamali, “Turbo-coded OFDM transmission over a nonlinear channel,” IEEE Trans. Veh. Technol., vol.  54, no. 4, pp. 1361–1371, 2005.
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  29. S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenated codes,” IEEE Trans. Commun., vol.  49, no. 10, pp. 1727–1737, 2001.
    [CrossRef]
  30. G. K. S. ten Brink and A. Ashikhmin, “Design of low-density parity-check codes for modulation and detection,” IEEE Trans. Commun., vol.  52, no. 4, pp. 670–678, 2004.
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2011 (2)

R. Zhang and L. Hanzo, “A unified treatment of power-efficient superposition coding aided communications: Theory and practice,” IEEE Commun. Surv. Tutorials, vol.  13, no. 3, pp. 503–520, 2011.
[CrossRef]

R. Mesleh, H. Elgala, and H. Haas, “On the performance of different OFDM based optical wireless communication systems,” J. Opt. Commun. Netw., vol.  3, no. 8, pp. 620–628, 2011.
[CrossRef]

2010 (4)

M. Moreolo, R. Muoz, and G. Junyent, “Novel power efficient optical OFDM based on Hartley transform for intensity-modulated direct-detection systems,” J. Lightwave Technol., vol.  28, no. 5, pp. 798–805, 2010.
[CrossRef]

A. A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory, vol.  56, no. 12, pp. 6066–6077, 2010.
[CrossRef]

R. Zhang and L. Hanzo, “Wireless cellular networks,” IEEE Veh. Technol. Mag., vol.  5, no. 4, pp. 31–39, 2010.
[CrossRef]

J. Grubor and K.-D. Langer, “Efficient signal processing in OFDM-based indoor optical wireless links,” J. Networks, vol.  5, no. 2, pp. 197–211, 2010.
[CrossRef]

2009 (2)

2008 (3)

B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol., vol.  26, no. 1, pp. 196–203, 2008.
[CrossRef]

F. Peng and W. E. Ryan, “MLSD bounds and receiver design for clipped OFDM channels,” IEEE Trans. Wireless Commun., vol.  7, no. 9, pp. 3568–3578, 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., vol.  12, no. 5, pp. 343–345, 2008.
[CrossRef]

2007 (2)

2006 (3)

I. B. Djordjevic and B. Vasic, “Multilevel coding in M-ary DPSK/differential QAM high-speed optical transmission with direct detection,” J. Lightwave Technol., vol.  24, no. 1, pp. 420–428, 2006.
[CrossRef]

J. Armstrong and A. J. Lowery, “Power efficient optical OFDM,” Electron. Lett., vol.  42, no. 6, pp. 370–371, 2006.
[CrossRef]

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett., vol.  42, no. 10, pp. 587–589, 2006.
[CrossRef]

2005 (1)

H. Nikopour, A. K. Khandani, and S. H. Jamali, “Turbo-coded OFDM transmission over a nonlinear channel,” IEEE Trans. Veh. Technol., vol.  54, no. 4, pp. 1361–1371, 2005.
[CrossRef]

2004 (2)

X. Ma and P. Li, “Coded modulation using superimposed binary codes,” IEEE Trans. Inf. Theory, vol.  50, no. 12, pp. 3331–3343, 2004.
[CrossRef]

G. K. S. ten Brink and A. Ashikhmin, “Design of low-density parity-check codes for modulation and detection,” IEEE Trans. Commun., vol.  52, no. 4, pp. 670–678, 2004.
[CrossRef]

2003 (1)

H. Chen and A. M. Haimovich, “Iterative estimation and cancellation of clipping noise for OFDM signals,” IEEE Commun. Lett., vol.  7, no. 7, pp. 305–307, 2003.
[CrossRef]

2002 (1)

J. Boutros and G. Caire, “Iterative multiuser decoding: Unified framework and asymptotic performance analysis,” IEEE Trans. Inf. Theory, vol.  48, no. 7, pp. 1772–1793, 2002.
[CrossRef]

2001 (1)

S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenated codes,” IEEE Trans. Commun., vol.  49, no. 10, pp. 1727–1737, 2001.
[CrossRef]

2000 (1)

D. Dardari, V. Tralli, and A. Vaccari, “A theoretical characterization of nonlinear distortion effects in OFDM systems,” IEEE Trans. Commun., vol.  48, no. 10, pp. 1755–1764, 2000.
[CrossRef]

1999 (1)

D. Kim and G. L. Stüber, “Clipping noise mitigation for OFDM by decision-aided reconstruction,” IEEE Commun. Lett., vol.  3, pp. 217–219, 1999.
[CrossRef]

1998 (1)

K. Kitayama, “Code division multiplexing lightwave networks based upon optical code conversion,” IEEE J. Sel. Areas Commun., vol.  16, no. 7, pp. 1309–1319, 1998.
[CrossRef]

1996 (1)

J. B. Carruthers and J. M. Kahn, “Multiple-subcarrier modulation for nondirected wireless infrared communication,” IEEE J. Sel. Areas Commun., vol.  14, no. 3, pp. 538–546, 1996.
[CrossRef]

1977 (1)

H. Imai and S. Hirakawa, “A new multilevel coding method using error-correcting codes,” IEEE Trans. Inf. Theory, vol.  23, no. 3, pp. 371–377, 1977.
[CrossRef]

Armstrong, J.

Asadzadeh, A. D. K.

A. D. K. Asadzadeh and S. Hranilovic, “Receiver design for asymmetrically clipped optical OFDM,” in Proc. of IEEE GLOBECOM OWC Workshop, Houston, TX, USA, Dec. 2011.

Ashikhmin, A.

G. K. S. ten Brink and A. Ashikhmin, “Design of low-density parity-check codes for modulation and detection,” IEEE Trans. Commun., vol.  52, no. 4, pp. 670–678, 2004.
[CrossRef]

Athaudage, C.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett., vol.  42, no. 10, pp. 587–589, 2006.
[CrossRef]

Boutros, J.

J. Boutros and G. Caire, “Iterative multiuser decoding: Unified framework and asymptotic performance analysis,” IEEE Trans. Inf. Theory, vol.  48, no. 7, pp. 1772–1793, 2002.
[CrossRef]

Caire, G.

J. Boutros and G. Caire, “Iterative multiuser decoding: Unified framework and asymptotic performance analysis,” IEEE Trans. Inf. Theory, vol.  48, no. 7, pp. 1772–1793, 2002.
[CrossRef]

Carruthers, J. B.

J. B. Carruthers and J. M. Kahn, “Multiple-subcarrier modulation for nondirected wireless infrared communication,” IEEE J. Sel. Areas Commun., vol.  14, no. 3, pp. 538–546, 1996.
[CrossRef]

Chen, H.

H. Chen and A. M. Haimovich, “Iterative estimation and cancellation of clipping noise for OFDM signals,” IEEE Commun. Lett., vol.  7, no. 7, pp. 305–307, 2003.
[CrossRef]

Choi, B. J.

L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for Broadcasting Multi-user Communications, WLANs and Broadcasting. Wiley-IEEE, 2003.

Dardari, D.

D. Dardari, V. Tralli, and A. Vaccari, “A theoretical characterization of nonlinear distortion effects in OFDM systems,” IEEE Trans. Commun., vol.  48, no. 10, pp. 1755–1764, 2000.
[CrossRef]

Djordjevic, I.

W. Shieh and I. Djordjevic, OFDM for Optical Communications. Academic, 2009.

Djordjevic, I. B.

Du, L. B.

Elgala, H.

Evans, J.

B. K. C. Liang and J. Evans, “Diversity combining for asymmetrically clipped optical OFDM in IM/DD channels,” in Proc. of IEEE GLOBECOM OWC Workshop, Honolulu, HI, USA, Dec. 2009.

Farid, A. A.

A. A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory, vol.  56, no. 12, pp. 6066–6077, 2010.
[CrossRef]

Grubor, J.

J. Grubor and K.-D. Langer, “Efficient signal processing in OFDM-based indoor optical wireless links,” J. Networks, vol.  5, no. 2, pp. 197–211, 2010.
[CrossRef]

Haas, H.

Haimovich, A. M.

H. Chen and A. M. Haimovich, “Iterative estimation and cancellation of clipping noise for OFDM signals,” IEEE Commun. Lett., vol.  7, no. 7, pp. 305–307, 2003.
[CrossRef]

Hanzo, L.

R. Zhang and L. Hanzo, “A unified treatment of power-efficient superposition coding aided communications: Theory and practice,” IEEE Commun. Surv. Tutorials, vol.  13, no. 3, pp. 503–520, 2011.
[CrossRef]

R. Zhang and L. Hanzo, “Wireless cellular networks,” IEEE Veh. Technol. Mag., vol.  5, no. 4, pp. 31–39, 2010.
[CrossRef]

L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for Broadcasting Multi-user Communications, WLANs and Broadcasting. Wiley-IEEE, 2003.

Hirakawa, S.

H. Imai and S. Hirakawa, “A new multilevel coding method using error-correcting codes,” IEEE Trans. Inf. Theory, vol.  23, no. 3, pp. 371–377, 1977.
[CrossRef]

Hranilovic, S.

A. A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory, vol.  56, no. 12, pp. 6066–6077, 2010.
[CrossRef]

A. D. K. Asadzadeh and S. Hranilovic, “Receiver design for asymmetrically clipped optical OFDM,” in Proc. of IEEE GLOBECOM OWC Workshop, Houston, TX, USA, Dec. 2011.

Imai, H.

H. Imai and S. Hirakawa, “A new multilevel coding method using error-correcting codes,” IEEE Trans. Inf. Theory, vol.  23, no. 3, pp. 371–377, 1977.
[CrossRef]

Jamali, S. H.

H. Nikopour, A. K. Khandani, and S. H. Jamali, “Turbo-coded OFDM transmission over a nonlinear channel,” IEEE Trans. Veh. Technol., vol.  54, no. 4, pp. 1361–1371, 2005.
[CrossRef]

Junyent, G.

Kahn, J. M.

J. B. Carruthers and J. M. Kahn, “Multiple-subcarrier modulation for nondirected wireless infrared communication,” IEEE J. Sel. Areas Commun., vol.  14, no. 3, pp. 538–546, 1996.
[CrossRef]

Keller, T.

L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for Broadcasting Multi-user Communications, WLANs and Broadcasting. Wiley-IEEE, 2003.

Khandani, A. K.

H. Nikopour, A. K. Khandani, and S. H. Jamali, “Turbo-coded OFDM transmission over a nonlinear channel,” IEEE Trans. Veh. Technol., vol.  54, no. 4, pp. 1361–1371, 2005.
[CrossRef]

Kim, D.

D. Kim and G. L. Stüber, “Clipping noise mitigation for OFDM by decision-aided reconstruction,” IEEE Commun. Lett., vol.  3, pp. 217–219, 1999.
[CrossRef]

Kitayama, K.

K. Kitayama, “Code division multiplexing lightwave networks based upon optical code conversion,” IEEE J. Sel. Areas Commun., vol.  16, no. 7, pp. 1309–1319, 1998.
[CrossRef]

Langer, K.-D.

J. Grubor and K.-D. Langer, “Efficient signal processing in OFDM-based indoor optical wireless links,” J. Networks, vol.  5, no. 2, pp. 197–211, 2010.
[CrossRef]

Li, P.

X. Ma and P. Li, “Coded modulation using superimposed binary codes,” IEEE Trans. Inf. Theory, vol.  50, no. 12, pp. 3331–3343, 2004.
[CrossRef]

Liang, B. K. C.

B. K. C. Liang and J. Evans, “Diversity combining for asymmetrically clipped optical OFDM in IM/DD channels,” in Proc. of IEEE GLOBECOM OWC Workshop, Honolulu, HI, USA, Dec. 2009.

Lowery, A. J.

Ma, X.

X. Ma and P. Li, “Coded modulation using superimposed binary codes,” IEEE Trans. Inf. Theory, vol.  50, no. 12, pp. 3331–3343, 2004.
[CrossRef]

MacKay, J. C.

J. C. MacKay, Information Theory, Inference and Learning Algorithms. Cambridge University, 2003.

Mesleh, R.

Moreolo, M.

Munster, M.

L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for Broadcasting Multi-user Communications, WLANs and Broadcasting. Wiley-IEEE, 2003.

Muoz, R.

Nikopour, H.

H. Nikopour, A. K. Khandani, and S. H. Jamali, “Turbo-coded OFDM transmission over a nonlinear channel,” IEEE Trans. Veh. Technol., vol.  54, no. 4, pp. 1361–1371, 2005.
[CrossRef]

Peng, F.

F. Peng and W. E. Ryan, “MLSD bounds and receiver design for clipped OFDM channels,” IEEE Trans. Wireless Commun., vol.  7, no. 9, pp. 3568–3578, 2008.
[CrossRef]

Ryan, W. E.

F. Peng and W. E. Ryan, “MLSD bounds and receiver design for clipped OFDM channels,” IEEE Trans. Wireless Commun., vol.  7, no. 9, pp. 3568–3578, 2008.
[CrossRef]

Schmidt, B. J. C.

B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol., vol.  26, no. 1, pp. 196–203, 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., vol.  12, no. 5, pp. 343–345, 2008.
[CrossRef]

Shieh, W.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett., vol.  42, no. 10, pp. 587–589, 2006.
[CrossRef]

W. Shieh and I. Djordjevic, OFDM for Optical Communications. Academic, 2009.

Shore, K. A.

Stüber, G. L.

D. Kim and G. L. Stüber, “Clipping noise mitigation for OFDM by decision-aided reconstruction,” IEEE Commun. Lett., vol.  3, pp. 217–219, 1999.
[CrossRef]

Tang, J. M.

ten Brink, G. K. S.

G. K. S. ten Brink and A. Ashikhmin, “Design of low-density parity-check codes for modulation and detection,” IEEE Trans. Commun., vol.  52, no. 4, pp. 670–678, 2004.
[CrossRef]

ten Brink, S.

S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenated codes,” IEEE Trans. Commun., vol.  49, no. 10, pp. 1727–1737, 2001.
[CrossRef]

Tralli, V.

D. Dardari, V. Tralli, and A. Vaccari, “A theoretical characterization of nonlinear distortion effects in OFDM systems,” IEEE Trans. Commun., vol.  48, no. 10, pp. 1755–1764, 2000.
[CrossRef]

Vaccari, A.

D. Dardari, V. Tralli, and A. Vaccari, “A theoretical characterization of nonlinear distortion effects in OFDM systems,” IEEE Trans. Commun., vol.  48, no. 10, pp. 1755–1764, 2000.
[CrossRef]

Vasic, B.

Yu, J.

Zhang, R.

R. Zhang and L. Hanzo, “A unified treatment of power-efficient superposition coding aided communications: Theory and practice,” IEEE Commun. Surv. Tutorials, vol.  13, no. 3, pp. 503–520, 2011.
[CrossRef]

R. Zhang and L. Hanzo, “Wireless cellular networks,” IEEE Veh. Technol. Mag., vol.  5, no. 4, pp. 31–39, 2010.
[CrossRef]

Zhou, X.

Electron. Lett. (2)

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett., vol.  42, no. 10, pp. 587–589, 2006.
[CrossRef]

J. Armstrong and A. J. Lowery, “Power efficient optical OFDM,” Electron. Lett., vol.  42, no. 6, pp. 370–371, 2006.
[CrossRef]

IEEE Commun. Lett. (3)

J. Armstrong and B. J. C. Schmidt, “Comparison of asymmetrically clipped optical OFDM and DC-biased optical OFDM in AWGN,” IEEE Commun. Lett., vol.  12, no. 5, pp. 343–345, 2008.
[CrossRef]

D. Kim and G. L. Stüber, “Clipping noise mitigation for OFDM by decision-aided reconstruction,” IEEE Commun. Lett., vol.  3, pp. 217–219, 1999.
[CrossRef]

H. Chen and A. M. Haimovich, “Iterative estimation and cancellation of clipping noise for OFDM signals,” IEEE Commun. Lett., vol.  7, no. 7, pp. 305–307, 2003.
[CrossRef]

IEEE Commun. Surv. Tutorials (1)

R. Zhang and L. Hanzo, “A unified treatment of power-efficient superposition coding aided communications: Theory and practice,” IEEE Commun. Surv. Tutorials, vol.  13, no. 3, pp. 503–520, 2011.
[CrossRef]

IEEE J. Sel. Areas Commun. (2)

J. B. Carruthers and J. M. Kahn, “Multiple-subcarrier modulation for nondirected wireless infrared communication,” IEEE J. Sel. Areas Commun., vol.  14, no. 3, pp. 538–546, 1996.
[CrossRef]

K. Kitayama, “Code division multiplexing lightwave networks based upon optical code conversion,” IEEE J. Sel. Areas Commun., vol.  16, no. 7, pp. 1309–1319, 1998.
[CrossRef]

IEEE Trans. Commun. (3)

S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenated codes,” IEEE Trans. Commun., vol.  49, no. 10, pp. 1727–1737, 2001.
[CrossRef]

G. K. S. ten Brink and A. Ashikhmin, “Design of low-density parity-check codes for modulation and detection,” IEEE Trans. Commun., vol.  52, no. 4, pp. 670–678, 2004.
[CrossRef]

D. Dardari, V. Tralli, and A. Vaccari, “A theoretical characterization of nonlinear distortion effects in OFDM systems,” IEEE Trans. Commun., vol.  48, no. 10, pp. 1755–1764, 2000.
[CrossRef]

IEEE Trans. Inf. Theory (4)

J. Boutros and G. Caire, “Iterative multiuser decoding: Unified framework and asymptotic performance analysis,” IEEE Trans. Inf. Theory, vol.  48, no. 7, pp. 1772–1793, 2002.
[CrossRef]

A. A. Farid and S. Hranilovic, “Capacity bounds for wireless optical intensity channels with Gaussian noise,” IEEE Trans. Inf. Theory, vol.  56, no. 12, pp. 6066–6077, 2010.
[CrossRef]

H. Imai and S. Hirakawa, “A new multilevel coding method using error-correcting codes,” IEEE Trans. Inf. Theory, vol.  23, no. 3, pp. 371–377, 1977.
[CrossRef]

X. Ma and P. Li, “Coded modulation using superimposed binary codes,” IEEE Trans. Inf. Theory, vol.  50, no. 12, pp. 3331–3343, 2004.
[CrossRef]

IEEE Trans. Veh. Technol. (1)

H. Nikopour, A. K. Khandani, and S. H. Jamali, “Turbo-coded OFDM transmission over a nonlinear channel,” IEEE Trans. Veh. Technol., vol.  54, no. 4, pp. 1361–1371, 2005.
[CrossRef]

IEEE Trans. Wireless Commun. (1)

F. Peng and W. E. Ryan, “MLSD bounds and receiver design for clipped OFDM channels,” IEEE Trans. Wireless Commun., vol.  7, no. 9, pp. 3568–3578, 2008.
[CrossRef]

IEEE Veh. Technol. Mag. (1)

R. Zhang and L. Hanzo, “Wireless cellular networks,” IEEE Veh. Technol. Mag., vol.  5, no. 4, pp. 31–39, 2010.
[CrossRef]

J. Lightwave Technol. (7)

J. Networks (1)

J. Grubor and K.-D. Langer, “Efficient signal processing in OFDM-based indoor optical wireless links,” J. Networks, vol.  5, no. 2, pp. 197–211, 2010.
[CrossRef]

J. Opt. Commun. Netw. (1)

Other (5)

J. C. MacKay, Information Theory, Inference and Learning Algorithms. Cambridge University, 2003.

W. Shieh and I. Djordjevic, OFDM for Optical Communications. Academic, 2009.

B. K. C. Liang and J. Evans, “Diversity combining for asymmetrically clipped optical OFDM in IM/DD channels,” in Proc. of IEEE GLOBECOM OWC Workshop, Honolulu, HI, USA, Dec. 2009.

A. D. K. Asadzadeh and S. Hranilovic, “Receiver design for asymmetrically clipped optical OFDM,” in Proc. of IEEE GLOBECOM OWC Workshop, Houston, TX, USA, Dec. 2011.

L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for Broadcasting Multi-user Communications, WLANs and Broadcasting. Wiley-IEEE, 2003.

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Figures (7)

Fig. 1.
Fig. 1.

Transceiver architecture with many-to-one type MLM constellation. Moreover, the acronyms used are the following: SPR, spreading; π/π, interleaving/deinterleaving; MLM, multi-layer modulation; MAP, mapping; IFFT/FFT, inverse fast Fourier transform/fast Fourier transform; CP+/-, add/remove cyclic prefix; IM, intensity modulation; DD, direct detection; DEM, demapping; DET, detector; DES, despreading; CDE, clipping distortion estimation; ACO, asymmetrically clipped optical; DCO, DC-biased optical.

Fig. 2.
Fig. 2.

Optimized amplitude of MLM for OOFDM for K=16, 20, 24 layers associated with Q=20, 30, 40 iterations and the spreading code rate of Rc=1/8 at the target BER of Pb*=104 in the context of relative amplitude pattern, where the amplitude of each layer was normalized to the maximum amplitude.

Fig. 3.
Fig. 3.

BER performance comparison of MLM-aided ACO-OFDM to conventional PSK-aided ACO-OFDM for comparable BPS throughput values, namely η={2,3,4,5,6}.

Fig. 4.
Fig. 4.

BER performance comparison of MLM-aided ACO-OFDM to conventional QAM-aided ACO-OFDM for comparable BPS throughput values, namely η={2,3,4,5,6}.

Fig. 5.
Fig. 5.

BER performance comparison of MLM-aided DCO-OFDM to conventional PSK-aided DCO-OFDM by arranging for the BPS throughput to be η={2,3,4,5,6} and for a DC bias of ρ0dB=7dB.

Fig. 6.
Fig. 6.

BER performance comparison of MLM-aided DCO-OFDM to conventional QAM-aided DCO-OFDM by arranging for the BPS throughput to be η={2,3,4,5,6} and for a DC bias of ρ0dB=7dB.

Fig. 7.
Fig. 7.

Comparison of the required Eb(opt)/N0 of MLM and conventional modulation for achieving BER of 105 for both ACO-OFDM and DCO-OFDM with DC bias ρ0dB=7dB.

Tables (3)

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Algorithm 1 Pseudocode of DTR

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TABLE I GA Optimized Amplitude Pattern for K=16, 20, 24 With Q=20, 30, 40 Iterations and Spreading Code Rate of Rc=1/8 at Target BER of Pb*=104

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Algorithm 2: GA-Aided Amplitude Pattern Optimization

Equations (35)

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s=k=1Kρkfm[c˜k],
S={S(n,l),n=1,,N/4,l=1,,Lo},
X(n,l)={S(n/2,l)ifnN/2and is evenS*(Nn+22,l)ifn>N/2and is even0ifnis odd.
x={x[(l1)N+m],m=1,,N,l=1,,Lo},
ϕ(x):xc={xulifxxulxif0<x<xul0ifx0.
S={S(n,l),n=1,,N/21,l=1,,Lo},
X(n,l)={S(n1,l)ifnN/2,n1S*(Nn+1,l)ifn>N/2,nN/2+10ifn=1,n=N/2+1,
ϕ(x):xc={xulifx+ρ0xulx+ρ0if0<x+ρ0<xul0ifx+ρ00.
ϕ(x)=αx+d,
r(l)=FHtxc(l)+W(l)
=FHt[αFX(l)+d(l)]+W(l)
=αHfX(l)+HfD(l)+W(l),
y(l)=αHS(l)+HSd(l)+N(l),
y=αhs+hsd+n.
P(c˜k|y)=likelihoodp(y,{c˜i}ik,sd|c˜k)probabilityP(c˜k)
=p(y|{c˜i}ik,sd,c˜k)ikP(c˜i)P(sd)extrinsicaprioriP(c˜k),
y=αhkc˜k+ikαhic˜i+hsd+n,
yI=αhkc˜k+ikαhi(c˜iMc˜i)+h(sdMsd)+n,
Ldete,k(c˜k)=lnp(yI|c˜k=+1)p(yI|c˜k=1)
=2αhk(yI)/V,
I=ikαhiMc˜i+hMsd,
V=ik|αhi|2Vc˜i+|h|2Vsd+σ2.
Md=E[xcαx]=[ϕ(x)αx]p(x)dx,
Vd=E[|dMd|2]=|ϕ(x)αxMd|2p(x)dx,
I=αikhiMc˜i,
V=α2ik|hi|2Vc˜i+σ2.
γkq=|αρk|2ik|αρi|2E[Vc˜i]+E[Vsd]+σe2,
Ides,ke,q=J((Rc11)J1[(Ides,ka,q)2]).
E[Vc˜k]=T1(Idet,ka,q),
E[Vsd]=T2(Idet,ka,q,k).
γkq+1=|αρk|2ik|αρi|2T1(Idet,ia,q)+T2(Idet,ka,q,k)+σe2.
Ides,kp,Q=J(J1[(Ides,ka,Q)2]/Rc)
mink=1K|ρk|2
s.t.Pb,k<=Pb*k=1,,K,
ρk>0k=1,,K.