Adaptively loaded IM/DD optical OFDM based on set-partitioned QAM formats

Jian Zhao; Lian-Kuan Chen

doi:10.1364/OE.25.009368

Abstract

We investigate the constellation design and symbol error rate (SER) of set-partitioned (SP) quadrature amplitude modulation (QAM) formats. Based on the SER analysis, we derive the adaptive bit and power loading algorithm for SP QAM based intensity-modulation direct-detection (IM/DD) orthogonal frequency division multiplexing (OFDM). We experimentally show that the proposed system significantly outperforms the conventional adaptively-loaded IM/DD OFDM and can increase the data rate from 36 Gbit/s to 42 Gbit/s in the presence of severe dispersion-induced spectral nulls after 40-km single-mode fiber. It is also shown that the adaptive algorithm greatly enhances the tolerance to fiber nonlinearity and allows for more power budget.

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References

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Year
Author
Publication

Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing,” Opt. Express 20(3), 2379–2385 (2012).
[Crossref] [PubMed]
J. Zhao, “DFT-based offset-QAM OFDM for optical communications,” Opt. Express 22(1), 1114–1126 (2014).
[Crossref] [PubMed]
P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multi-tone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(2), 773–776 (1995).
[Crossref]
E. Giacoumidis, A. Kavatzikidis, A. Tsokanos, J. M. Tang, and I. Tomkos, “Adaptive loading algorithms for IMDD optical OFDM PON systems using directly modulated lasers,” J. Opt. Commun. Netw. 4(10), 769–778 (2012).
[Crossref]
B. Cardiff, M. F. Flanagan, F. Smyth, L. P. Barry, and A. D. Fagan, “On bit and power loading for OFDM over SI-POF,” J. Lightwave Technol. 29(10), 1547–1554 (2011).
[Crossref]
D. Bykhovsky and S. Arnon, “An experimental comparison of different bit-and-power allocation algorithms for DCO-OFDM,” J. Lightwave Technol. 32(8), 1559–1564 (2014).
[Crossref]
Z. Yu, H. Chen, M. Chen, S. Yang, and S. Xie, “Bandwidth improvement using adaptive loading scheme in optical direct-detection OFDM,” IEEE J. Quantum Electron. 52(10), 8000106 (2016).
[Crossref]
M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17(13), 10814–10819 (2009).
[Crossref] [PubMed]
I. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Four-dimensional optical multiband-OFDM for beyond 1.4 Tb/s serial optical transmission,” Opt. Express 19(2), 876–882 (2011).
[Crossref] [PubMed]
H. Zhang, C. R. Davidson, H. G. Batshon, M. Mazurczyk, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “DP-16QAM based coded modulation transmission in C+L band system at transoceanic distance,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), paper W1I.2.
[Crossref]
R. R. Muller, J. Renaudier, M. A. Mestre, H. Mardoyan, A. Konczykowska, F. Jorge, B. Duval, and J. Y. Dupuy, “Multi-dimension coded PAM4 signaling for 100Gb/s short reach transceivers,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), Paper Th1G.4.
J. Zhao, S. K. Ibrahim, D. Rafique, P. Gunning, and A. D. Ellis, “Symbol synchronization exploiting the symmetric property in optical fast OFDM,” IEEE Photonics Technol. Lett. 23(9), 594–596 (2011).
[Crossref]

2016 (1)

Z. Yu, H. Chen, M. Chen, S. Yang, and S. Xie, “Bandwidth improvement using adaptive loading scheme in optical direct-detection OFDM,” IEEE J. Quantum Electron. 52(10), 8000106 (2016).
[Crossref]

J. Zhao, S. K. Ibrahim, D. Rafique, P. Gunning, and A. D. Ellis, “Symbol synchronization exploiting the symmetric property in optical fast OFDM,” IEEE Photonics Technol. Lett. 23(9), 594–596 (2011).
[Crossref]

2009 (1)

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17(13), 10814–10819 (2009).
[Crossref] [PubMed]

1995 (1)

P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multi-tone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(2), 773–776 (1995).
[Crossref]

Agrell, E.

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17(13), 10814–10819 (2009).
[Crossref] [PubMed]

Arnon, S.

D. Bykhovsky and S. Arnon, “An experimental comparison of different bit-and-power allocation algorithms for DCO-OFDM,” J. Lightwave Technol. 32(8), 1559–1564 (2014).
[Crossref]

Barry, L. P.

B. Cardiff, M. F. Flanagan, F. Smyth, L. P. Barry, and A. D. Fagan, “On bit and power loading for OFDM over SI-POF,” J. Lightwave Technol. 29(10), 1547–1554 (2011).
[Crossref]

Batshon, H. G.

I. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Four-dimensional optical multiband-OFDM for beyond 1.4 Tb/s serial optical transmission,” Opt. Express 19(2), 876–882 (2011).
[Crossref] [PubMed]

H. Zhang, C. R. Davidson, H. G. Batshon, M. Mazurczyk, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “DP-16QAM based coded modulation transmission in C+L band system at transoceanic distance,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), paper W1I.2.
[Crossref]

Bingham, J. A. C.

P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multi-tone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(2), 773–776 (1995).
[Crossref]

Bolshtyansky, M.

H. Zhang, C. R. Davidson, H. G. Batshon, M. Mazurczyk, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “DP-16QAM based coded modulation transmission in C+L band system at transoceanic distance,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), paper W1I.2.
[Crossref]

Bykhovsky, D.

D. Bykhovsky and S. Arnon, “An experimental comparison of different bit-and-power allocation algorithms for DCO-OFDM,” J. Lightwave Technol. 32(8), 1559–1564 (2014).
[Crossref]

Cardiff, B.

B. Cardiff, M. F. Flanagan, F. Smyth, L. P. Barry, and A. D. Fagan, “On bit and power loading for OFDM over SI-POF,” J. Lightwave Technol. 29(10), 1547–1554 (2011).
[Crossref]

Chen, H.

Z. Yu, H. Chen, M. Chen, S. Yang, and S. Xie, “Bandwidth improvement using adaptive loading scheme in optical direct-detection OFDM,” IEEE J. Quantum Electron. 52(10), 8000106 (2016).
[Crossref]

Chen, M.

Z. Yu, H. Chen, M. Chen, S. Yang, and S. Xie, “Bandwidth improvement using adaptive loading scheme in optical direct-detection OFDM,” IEEE J. Quantum Electron. 52(10), 8000106 (2016).
[Crossref]

Chow, P. S.

P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multi-tone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(2), 773–776 (1995).
[Crossref]

Cioffi, J. M.

P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multi-tone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(2), 773–776 (1995).
[Crossref]

Davidson, C. R.

H. Zhang, C. R. Davidson, H. G. Batshon, M. Mazurczyk, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “DP-16QAM based coded modulation transmission in C+L band system at transoceanic distance,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), paper W1I.2.
[Crossref]

Djordjevic, I.

I. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Four-dimensional optical multiband-OFDM for beyond 1.4 Tb/s serial optical transmission,” Opt. Express 19(2), 876–882 (2011).
[Crossref] [PubMed]

Ellis, A. D.

J. Zhao, S. K. Ibrahim, D. Rafique, P. Gunning, and A. D. Ellis, “Symbol synchronization exploiting the symmetric property in optical fast OFDM,” IEEE Photonics Technol. Lett. 23(9), 594–596 (2011).
[Crossref]

Fagan, A. D.

B. Cardiff, M. F. Flanagan, F. Smyth, L. P. Barry, and A. D. Fagan, “On bit and power loading for OFDM over SI-POF,” J. Lightwave Technol. 29(10), 1547–1554 (2011).
[Crossref]

Flanagan, M. F.

B. Cardiff, M. F. Flanagan, F. Smyth, L. P. Barry, and A. D. Fagan, “On bit and power loading for OFDM over SI-POF,” J. Lightwave Technol. 29(10), 1547–1554 (2011).
[Crossref]

Foursa, D. G.

H. Zhang, C. R. Davidson, H. G. Batshon, M. Mazurczyk, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “DP-16QAM based coded modulation transmission in C+L band system at transoceanic distance,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), paper W1I.2.
[Crossref]

Giacoumidis, E.

E. Giacoumidis, A. Kavatzikidis, A. Tsokanos, J. M. Tang, and I. Tomkos, “Adaptive loading algorithms for IMDD optical OFDM PON systems using directly modulated lasers,” J. Opt. Commun. Netw. 4(10), 769–778 (2012).
[Crossref]

Gunning, P.

J. Zhao, S. K. Ibrahim, D. Rafique, P. Gunning, and A. D. Ellis, “Symbol synchronization exploiting the symmetric property in optical fast OFDM,” IEEE Photonics Technol. Lett. 23(9), 594–596 (2011).
[Crossref]

He, Z.

Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing,” Opt. Express 20(3), 2379–2385 (2012).
[Crossref] [PubMed]

Ibrahim, S. K.

J. Zhao, S. K. Ibrahim, D. Rafique, P. Gunning, and A. D. Ellis, “Symbol synchronization exploiting the symmetric property in optical fast OFDM,” IEEE Photonics Technol. Lett. 23(9), 594–596 (2011).
[Crossref]

Karlsson, M.

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17(13), 10814–10819 (2009).
[Crossref] [PubMed]

Kavatzikidis, A.

E. Giacoumidis, A. Kavatzikidis, A. Tsokanos, J. M. Tang, and I. Tomkos, “Adaptive loading algorithms for IMDD optical OFDM PON systems using directly modulated lasers,” J. Opt. Commun. Netw. 4(10), 769–778 (2012).
[Crossref]

Mazurczyk, M.

H. Zhang, C. R. Davidson, H. G. Batshon, M. Mazurczyk, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “DP-16QAM based coded modulation transmission in C+L band system at transoceanic distance,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), paper W1I.2.
[Crossref]

Pilipetskii, A.

H. Zhang, C. R. Davidson, H. G. Batshon, M. Mazurczyk, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “DP-16QAM based coded modulation transmission in C+L band system at transoceanic distance,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), paper W1I.2.
[Crossref]

Rafique, D.

J. Zhao, S. K. Ibrahim, D. Rafique, P. Gunning, and A. D. Ellis, “Symbol synchronization exploiting the symmetric property in optical fast OFDM,” IEEE Photonics Technol. Lett. 23(9), 594–596 (2011).
[Crossref]

Shieh, W.

Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing,” Opt. Express 20(3), 2379–2385 (2012).
[Crossref] [PubMed]

Smyth, F.

B. Cardiff, M. F. Flanagan, F. Smyth, L. P. Barry, and A. D. Fagan, “On bit and power loading for OFDM over SI-POF,” J. Lightwave Technol. 29(10), 1547–1554 (2011).
[Crossref]

Tang, J. M.

E. Giacoumidis, A. Kavatzikidis, A. Tsokanos, J. M. Tang, and I. Tomkos, “Adaptive loading algorithms for IMDD optical OFDM PON systems using directly modulated lasers,” J. Opt. Commun. Netw. 4(10), 769–778 (2012).
[Crossref]

Tomkos, I.

E. Giacoumidis, A. Kavatzikidis, A. Tsokanos, J. M. Tang, and I. Tomkos, “Adaptive loading algorithms for IMDD optical OFDM PON systems using directly modulated lasers,” J. Opt. Commun. Netw. 4(10), 769–778 (2012).
[Crossref]

Tsokanos, A.

E. Giacoumidis, A. Kavatzikidis, A. Tsokanos, J. M. Tang, and I. Tomkos, “Adaptive loading algorithms for IMDD optical OFDM PON systems using directly modulated lasers,” J. Opt. Commun. Netw. 4(10), 769–778 (2012).
[Crossref]

Wang, T.

I. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Four-dimensional optical multiband-OFDM for beyond 1.4 Tb/s serial optical transmission,” Opt. Express 19(2), 876–882 (2011).
[Crossref] [PubMed]

Xie, S.

Z. Yu, H. Chen, M. Chen, S. Yang, and S. Xie, “Bandwidth improvement using adaptive loading scheme in optical direct-detection OFDM,” IEEE J. Quantum Electron. 52(10), 8000106 (2016).
[Crossref]

Xu, L.

I. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Four-dimensional optical multiband-OFDM for beyond 1.4 Tb/s serial optical transmission,” Opt. Express 19(2), 876–882 (2011).
[Crossref] [PubMed]

Yang, Q.

Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing,” Opt. Express 20(3), 2379–2385 (2012).
[Crossref] [PubMed]

Yang, S.

Z. Yu, H. Chen, M. Chen, S. Yang, and S. Xie, “Bandwidth improvement using adaptive loading scheme in optical direct-detection OFDM,” IEEE J. Quantum Electron. 52(10), 8000106 (2016).
[Crossref]

Yang, Z.

Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing,” Opt. Express 20(3), 2379–2385 (2012).
[Crossref] [PubMed]

Yi, X.

Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing,” Opt. Express 20(3), 2379–2385 (2012).
[Crossref] [PubMed]

Yu, S.

Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing,” Opt. Express 20(3), 2379–2385 (2012).
[Crossref] [PubMed]

Yu, Z.

Z. Yu, H. Chen, M. Chen, S. Yang, and S. Xie, “Bandwidth improvement using adaptive loading scheme in optical direct-detection OFDM,” IEEE J. Quantum Electron. 52(10), 8000106 (2016).
[Crossref]

Zhang, H.

H. Zhang, C. R. Davidson, H. G. Batshon, M. Mazurczyk, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “DP-16QAM based coded modulation transmission in C+L band system at transoceanic distance,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), paper W1I.2.
[Crossref]

Zhao, J.

J. Zhao, “DFT-based offset-QAM OFDM for optical communications,” Opt. Express 22(1), 1114–1126 (2014).
[Crossref] [PubMed]

J. Zhao, S. K. Ibrahim, D. Rafique, P. Gunning, and A. D. Ellis, “Symbol synchronization exploiting the symmetric property in optical fast OFDM,” IEEE Photonics Technol. Lett. 23(9), 594–596 (2011).
[Crossref]

IEEE J. Quantum Electron. (1)

Z. Yu, H. Chen, M. Chen, S. Yang, and S. Xie, “Bandwidth improvement using adaptive loading scheme in optical direct-detection OFDM,” IEEE J. Quantum Electron. 52(10), 8000106 (2016).
[Crossref]

IEEE Photonics Technol. Lett. (1)

J. Zhao, S. K. Ibrahim, D. Rafique, P. Gunning, and A. D. Ellis, “Symbol synchronization exploiting the symmetric property in optical fast OFDM,” IEEE Photonics Technol. Lett. 23(9), 594–596 (2011).
[Crossref]

IEEE Trans. Commun. (1)

P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, “A practical discrete multi-tone transceiver loading algorithm for data transmission over spectrally shaped channels,” IEEE Trans. Commun. 43(2), 773–776 (1995).
[Crossref]

J. Lightwave Technol. (2)

B. Cardiff, M. F. Flanagan, F. Smyth, L. P. Barry, and A. D. Fagan, “On bit and power loading for OFDM over SI-POF,” J. Lightwave Technol. 29(10), 1547–1554 (2011).
[Crossref]

D. Bykhovsky and S. Arnon, “An experimental comparison of different bit-and-power allocation algorithms for DCO-OFDM,” J. Lightwave Technol. 32(8), 1559–1564 (2014).
[Crossref]

J. Opt. Commun. Netw. (1)

E. Giacoumidis, A. Kavatzikidis, A. Tsokanos, J. M. Tang, and I. Tomkos, “Adaptive loading algorithms for IMDD optical OFDM PON systems using directly modulated lasers,” J. Opt. Commun. Netw. 4(10), 769–778 (2012).
[Crossref]

Opt. Express (4)

Q. Yang, Z. He, Z. Yang, S. Yu, X. Yi, and W. Shieh, “Coherent optical DFT-spread OFDM transmission using orthogonal band multiplexing,” Opt. Express 20(3), 2379–2385 (2012).
[Crossref] [PubMed]

J. Zhao, “DFT-based offset-QAM OFDM for optical communications,” Opt. Express 22(1), 1114–1126 (2014).
[Crossref] [PubMed]

M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17(13), 10814–10819 (2009).
[Crossref] [PubMed]

I. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Four-dimensional optical multiband-OFDM for beyond 1.4 Tb/s serial optical transmission,” Opt. Express 19(2), 876–882 (2011).
[Crossref] [PubMed]

Other (2)

H. Zhang, C. R. Davidson, H. G. Batshon, M. Mazurczyk, M. Bolshtyansky, D. G. Foursa, and A. Pilipetskii, “DP-16QAM based coded modulation transmission in C+L band system at transoceanic distance,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), paper W1I.2.
[Crossref]

R. R. Muller, J. Renaudier, M. A. Mestre, H. Mardoyan, A. Konczykowska, F. Jorge, B. Duval, and J. Y. Dupuy, “Multi-dimension coded PAM4 signaling for 100Gb/s short reach transceivers,” in Technical Digest of Optical Fiber Communication Conference (OFC) (2016), Paper Th1G.4.

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Fig. 1 Constellation of SP-2QAM, SP-8QAM, SP-32QAM, SP-128QAM, SP-512QAM, and SP-2048QAM. In each format, circled points in symbol #2 represent all possible constellation points when the circled point in symbol #1 is selected.

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Fig. 2 Constellation of SP-128QAM, which is divided into two subgroups represented by solid and empty circles, respectively. The minimal distance between the 16 points in the constellation of either symbol #1 or symbol #2 is assumed to be 2.

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Fig. 3 Experimental setup.

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Fig. 4 (a) BER performance versus signal data rate at back-to-back when the signal formats are 8QAM, 16QAM, adaptively-loaded conventional QAM, adaptively-loaded SP QAM, and SP QAM with the finer SE granularity. The received signal power is −3 dBm. (b) BER versus the received power for different formats when the data rate is 40.2 Gbit/s.

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Fig. 5 (a) BER performance versus signal data rate after 40 km when the signal formats are 8QAM, 16QAM, adaptively-loaded conventional QAM, adaptively-loaded SP QAM, and SP QAM with the finer SE granularity. (b) SE versus subcarrier index for adaptively-loaded conventional QAM, SP QAM, and SP QAM with the finer SE granularity at 40.2 Gbit/s. The dashed line represents the estimated SNR profile ( = SNR (dB) /3). In (a) and (b), the received signal power is −3 dBm and the signal launch power into the fiber is 10 dBm.

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Fig. 6 BER versus received power after 40 km when the data rate is (a) 30.7 Gbit/s and (b) 40.2 Gbit/s. The signal launch power is 10 dBm and the MZM bias is 2.4 V.

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Fig. 7 (a) BER versus the launch power into the 40-km SMF when channel estimation and bit loading are performed for each power (circles) or are fixed using the SNR profile obtained at 10-dBm launch power (diamonds). (b) SE versus subcarrier index when the bits are loaded using the SNR profiles estimated at 10-dBm and 15-dBm launch power. Dashed and dotted lines represent the SNR profiles ( = SNR (dB) / 3). In (a) and (b), the data rate is 30.7 Gbit/s.

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Fig. 8 (a) BER versus the MZM bias when the channel estimation and bit loading are performed for each bias (circles) or are fixed using the SNR profile obtained at 2.4-V bias (diamonds). (b) SE versus subcarrier index when the bits are loaded using the SNR profiles estimated at 1.8-V and 3-V bias. Dashed and dotted lines represent the SNR profiles ( = SNR (dB) / 3). In (a) and (b), the signal data rate is 30.7 Gbit/s.

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Tables (1)

Table 1 Upper bound of SER for different SP QAM formats

View Table

Equations (8)

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

S E R_{} = K \cdot Q (\frac{d_{\min}}{\sqrt{2 N_{0}}})

S E R \approx 4 \times (1 - \frac{1}{2^{m / 2}}) Q (\sqrt{\frac{3}{2^{m} - 1} S N R}) < 4 \times Q (\sqrt{\frac{3}{2^{m} - 1} S N R})

S N R = E_{s} / N_{0}

S E R < K \times Q (\sqrt{\frac{3 \times 2}{2^{m + 1 / 2} - 1} S N R})

m_{i} = \log_{2} (1 + \frac{3 \times 2 \times S N R_{i}}{{(Q^{- 1} (S E R_{p r e - s e t} / K))}^{2}}) - 0.5

{\overset{\land}{m}}_{i} = r o u n d (m_{i} + 1 / 2) - 1 / 2

m_{i} = \log_{2} (1 + \frac{3 \times 2 \times S N R_{i}}{{(Q^{- 1} (S E R_{p r e - s e t} / K))}^{2} \cdot γ}) - 0.5

S N R_{i} = \frac{{| E (r_{i}^{*} \cdot s_{i}) |}^{2}}{E ({| r_{i} |}^{2}) E ({| s_{i} |}^{2}) - | E (r_{i}^{*} \cdot s_{i}) |}

Format	SP-2QAM	SP-8QAM	SP-32QAM	SP-128QAM	SP-512QAM	SP-2048QAM
Equation (1)	$Q (\sqrt{4 S N R})$	$3 \cdot Q (\sqrt{2 S N R})$	$10 \cdot Q (\sqrt{\frac{4 S N R}{5}})$	$12 \cdot Q (\sqrt{\frac{2 S N R}{5}})$	$12 \cdot Q (\sqrt{\frac{S N R}{5}})$	$12 \cdot Q (\sqrt{\frac{2 S N R}{21}})$
Equation (4)	$K \cdot Q (\sqrt{6 S N R})$	$K \cdot Q (\sqrt{2 S N R})$	$K \cdot Q (\sqrt{\frac{6 S N R}{7}})$	$K \cdot Q (\sqrt{\frac{2 S N R}{5}})$	$K \cdot Q (\sqrt{\frac{6 S N R}{31}})$	$K \cdot Q (\sqrt{\frac{2 S N R}{21}})$

Abstract

References

2016 (1)

2014 (2)

2012 (2)

2011 (3)

2009 (1)

1995 (1)

Agrell, E.

Arnon, S.

Barry, L. P.

Batshon, H. G.

Bingham, J. A. C.

Bolshtyansky, M.

Bykhovsky, D.

Cardiff, B.

Chen, H.

Chen, M.

Chow, P. S.

Cioffi, J. M.

Davidson, C. R.

Djordjevic, I.

Ellis, A. D.

Fagan, A. D.

Flanagan, M. F.

Foursa, D. G.

Giacoumidis, E.

Gunning, P.

He, Z.

Ibrahim, S. K.

Karlsson, M.

Kavatzikidis, A.

Mazurczyk, M.

Pilipetskii, A.

Rafique, D.

Shieh, W.

Smyth, F.

Tang, J. M.

Tomkos, I.

Tsokanos, A.

Wang, T.

Xie, S.

Xu, L.

Yang, Q.

Yang, S.

Yang, Z.

Yi, X.

Yu, S.

Yu, Z.

Zhang, H.

Zhao, J.

IEEE J. Quantum Electron. (1)

IEEE Photonics Technol. Lett. (1)

IEEE Trans. Commun. (1)

J. Lightwave Technol. (2)

J. Opt. Commun. Netw. (1)

Opt. Express (4)

Other (2)

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Optics Express

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