Abstract

This paper introduces subcarrier pairing to optical OFDM systems and shows, using simulations, that the sensitivity of Direct-Detection Optical Orthogonal Frequency Division Multiplexed (DDO-OFDM) systems can be improved by 0.7 dB, without any coding overheads. Subcarrier pairing works because each subcarrier acquires a different electrical Signal to Interference plus Noise Ratio (SINR), which typically increases with the subcarrier’s frequency. Pairing the good and bad subcarriers, so that information is split between them, improves the performance of the bad subcarrier more than it degrades the performance of the good subcarrier. This lowers the required Optical Signal to Noise Ratio (OSNR) for the system to give a certain Bit Error Ratio (BER).

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. R. Knopp and G. Caire, “Power control schemes for TDD systems with multiple transmit and receive antennas,” in Proc. of IEEE Global Telecommunications Conference (Globecom) (Rio de Janeiro, 1999), pp. 2326–2330.
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    [CrossRef]
  10. J. Boutros and E. Viterbo, “Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel,” IEEE Trans. Inf. Theory 44(4), 1453–1467 (1998).
    [CrossRef]
  11. Y. Hong, E. Viterbo, and A. J. Lowery, “Improving the sensitivity of direct-detection optical OFDM systems by pairing of the optical subcarriers,” in European Conference on Optical Communications (Geneva, 2011), p. Th.11.B.2.
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    [CrossRef]
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    [CrossRef]
  14. C. S. Park and K. B. Lee, “Transmit power allocation for BER performance improvement in multicarrier systems,” IEEE Trans. Commun. 52(10), 1658–1663 (2004).
    [CrossRef]
  15. Q. Yang, W. Shieh, and Y. Ma, “Bit and power loading for coherent optical OFDM,” IEEE Photon. Technol. Lett. 20(15), 1305–1307 (2008).
    [CrossRef]
  16. 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]

2011 (2)

S. K. Mohammed, E. Viterbo, Y. Hong, and A. Chockalingam, “MIMO precoding with X- and Y-codes,” IEEE Trans. Inf. Theory 57(6), 3542–3566 (2011).
[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]

2010 (1)

2008 (2)

Q. Yang, W. Shieh, and Y. Ma, “Bit and power loading for coherent optical OFDM,” IEEE Photon. Technol. Lett. 20(15), 1305–1307 (2008).
[CrossRef]

A. J. Lowery, “Amplified-spontaneous noise limit of optical OFDM lightwave systems,” Opt. Express 16(2), 860–865 (2008).
[CrossRef] [PubMed]

2006 (3)

2004 (1)

C. S. Park and K. B. Lee, “Transmit power allocation for BER performance improvement in multicarrier systems,” IEEE Trans. Commun. 52(10), 1658–1663 (2004).
[CrossRef]

1998 (3)

G. Raleigh and J. Cioffi, “Spatio-temporal coding for wireless communication,” IEEE Trans. Commun. 46(3), 357–366 (1998).
[CrossRef]

J. Boutros and E. Viterbo, “Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel,” IEEE Trans. Inf. Theory 44(4), 1453–1467 (1998).
[CrossRef]

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44(3), 927–946 (1998).
[CrossRef]

Armstrong, J.

Athaudage, C.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–588 (2006).
[CrossRef]

Barry, L. P.

Biglieri, E.

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44(3), 927–946 (1998).
[CrossRef]

Boutros, J.

J. Boutros and E. Viterbo, “Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel,” IEEE Trans. Inf. Theory 44(4), 1453–1467 (1998).
[CrossRef]

Caire, G.

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44(3), 927–946 (1998).
[CrossRef]

Cardiff, B.

Chockalingam, A.

S. K. Mohammed, E. Viterbo, Y. Hong, and A. Chockalingam, “MIMO precoding with X- and Y-codes,” IEEE Trans. Inf. Theory 57(6), 3542–3566 (2011).
[CrossRef]

Cioffi, J.

G. Raleigh and J. Cioffi, “Spatio-temporal coding for wireless communication,” IEEE Trans. Commun. 46(3), 357–366 (1998).
[CrossRef]

Du, L. B.

Fagan, A. D.

Flanagan, M. F.

Hong, Y.

S. K. Mohammed, E. Viterbo, Y. Hong, and A. Chockalingam, “MIMO precoding with X- and Y-codes,” IEEE Trans. Inf. Theory 57(6), 3542–3566 (2011).
[CrossRef]

Lane, P. M.

Lee, K. B.

C. S. Park and K. B. Lee, “Transmit power allocation for BER performance improvement in multicarrier systems,” IEEE Trans. Commun. 52(10), 1658–1663 (2004).
[CrossRef]

Lowery, A. J.

Ma, Y.

Q. Yang, W. Shieh, and Y. Ma, “Bit and power loading for coherent optical OFDM,” IEEE Photon. Technol. Lett. 20(15), 1305–1307 (2008).
[CrossRef]

Mohammed, S. K.

S. K. Mohammed, E. Viterbo, Y. Hong, and A. Chockalingam, “MIMO precoding with X- and Y-codes,” IEEE Trans. Inf. Theory 57(6), 3542–3566 (2011).
[CrossRef]

Park, C. S.

C. S. Park and K. B. Lee, “Transmit power allocation for BER performance improvement in multicarrier systems,” IEEE Trans. Commun. 52(10), 1658–1663 (2004).
[CrossRef]

Raleigh, G.

G. Raleigh and J. Cioffi, “Spatio-temporal coding for wireless communication,” IEEE Trans. Commun. 46(3), 357–366 (1998).
[CrossRef]

Schmidt, B. J. C.

Shieh, W.

Q. Yang, W. Shieh, and Y. Ma, “Bit and power loading for coherent optical OFDM,” IEEE Photon. Technol. Lett. 20(15), 1305–1307 (2008).
[CrossRef]

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–588 (2006).
[CrossRef]

Shore, K. A.

Smyth, F.

Tang, J. M.

Taricco, G.

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44(3), 927–946 (1998).
[CrossRef]

Viterbo, E.

S. K. Mohammed, E. Viterbo, Y. Hong, and A. Chockalingam, “MIMO precoding with X- and Y-codes,” IEEE Trans. Inf. Theory 57(6), 3542–3566 (2011).
[CrossRef]

J. Boutros and E. Viterbo, “Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel,” IEEE Trans. Inf. Theory 44(4), 1453–1467 (1998).
[CrossRef]

Yang, Q.

Q. Yang, W. Shieh, and Y. Ma, “Bit and power loading for coherent optical OFDM,” IEEE Photon. Technol. Lett. 20(15), 1305–1307 (2008).
[CrossRef]

Zan, Z.

Electron. Lett. (1)

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–588 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Q. Yang, W. Shieh, and Y. Ma, “Bit and power loading for coherent optical OFDM,” IEEE Photon. Technol. Lett. 20(15), 1305–1307 (2008).
[CrossRef]

IEEE Trans. Commun. (2)

C. S. Park and K. B. Lee, “Transmit power allocation for BER performance improvement in multicarrier systems,” IEEE Trans. Commun. 52(10), 1658–1663 (2004).
[CrossRef]

G. Raleigh and J. Cioffi, “Spatio-temporal coding for wireless communication,” IEEE Trans. Commun. 46(3), 357–366 (1998).
[CrossRef]

IEEE Trans. Inf. Theory (3)

S. K. Mohammed, E. Viterbo, Y. Hong, and A. Chockalingam, “MIMO precoding with X- and Y-codes,” IEEE Trans. Inf. Theory 57(6), 3542–3566 (2011).
[CrossRef]

J. Boutros and E. Viterbo, “Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel,” IEEE Trans. Inf. Theory 44(4), 1453–1467 (1998).
[CrossRef]

G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory 44(3), 927–946 (1998).
[CrossRef]

J. Lightwave Technol. (3)

Opt. Express (2)

Other (4)

S. L. Jansen, I. Morita, and H. Tanaka, “Carrier-to-signal power in fiber-optic SSB-OFDM transmission systems” in IEICE General Conference (Nagoya, 2007), pp. B-10–24, 363.

S. L. Jansen, I. Morita, N. Tadeka, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSMF enabled by RF-pilot tone phase noise compensation,” in Conference on Optical Fiber Communication, OFC (Anaheim, CA., 2007), p. PDP15.

Y. Hong, E. Viterbo, and A. J. Lowery, “Improving the sensitivity of direct-detection optical OFDM systems by pairing of the optical subcarriers,” in European Conference on Optical Communications (Geneva, 2011), p. Th.11.B.2.

R. Knopp and G. Caire, “Power control schemes for TDD systems with multiple transmit and receive antennas,” in Proc. of IEEE Global Telecommunications Conference (Globecom) (Rio de Janeiro, 1999), pp. 2326–2330.

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Figures (10)

Fig. 1
Fig. 1

Direct detection optical OFDM schematic. The Rotate, Scaling and ML Decision blocks are new additions to standard DDO-OFDM systems. Note the peculiar mapping of the I and Q signals from the Rotate block to the commutator, which is needed to realize component interleaving.

Fig. 2
Fig. 2

The received optical spectrum (top) with the components of the RF spectrum that are created upon photodetection (1-5).

Fig. 3
Fig. 3

Simulated (crosses) and analytical RF signal and noise levels (lines). Note that the RF noise level drops at higher frequencies. η = 1.0, OSNR = 13 dB, BL = BH = 0, BASE = 60 GHz.

Fig. 4
Fig. 4

Variation of Signal to Interference Noise Ratio (SINR) across the subcarrier band for a number of OSNRs.

Fig. 5
Fig. 5

Optimal angle of pairing versus the index of subcarrier pairing. The higher-frequency subcarriers have a 45-degree optimum. The label is OSNR.

Fig. 6
Fig. 6

Illustration of component interleaving on symbols that have been rotated by 45°. The color coding is significant as it shows how an output symbol’s position is determined by the positions of two input symbols. The output symbols X have been slightly displaced (for example, at the origin), to show that multiple symbols from the original constellations can map to a single point on the interleaved constellations. Nine constellation points are created for 45° rotation. For rotations of less than 45°, sixteen constellation points will be created.

Fig. 7
Fig. 7

Illustration scaling to produce constellations with similar-sized distributions.

Fig. 8
Fig. 8

Component de-interleaving. In this example, the inphase (real) values of a pair of symbols are used to create the upper new symbol: the quadrature (imaginary) values of two symbols are used to create the lower new symbol. The upper and lower new symbols are then passed to the upper and lower ML detectors, as shown in Fig. 1.

Fig. 9
Fig. 9

Maximum Likelihood (ML) Detection process in each decoder (upper and lower). This is applied to every received symbol. The Equivalent Thresholds (green) are not used in the ML process, but are included to illustrate that there is not a simple pair of straight-line thresholds that can be used.

Fig. 10
Fig. 10

Required OSNR for BER = 10−3 versus the ratio of carrier power to sideband power with and without pairing.

Equations (7)

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r 0 (t)=s(t)+A.cos(2π f 0 t)+ n h (t)+ n v (t)
s(t)=Re( k=0 N sc 1 X k e j2π( f 0 + B gap +kΔf)t )
y(t)=R( | s(t)+Acos( w c t)+ n v (t) | 2 + | n h (t) | 2 ).
G y (f)= 2 G s (f) A 2 4 [ δ(f f 0 )+δ(f+ f 0 ) ] {1} + G s (f) G s (f) {2} + G n (f) G n (f) {3} + 2 G n (f) A 2 4 [ δ(f f 0 )+δ(f+ f 0 ) ] {4} + 2 G s (f) G n (f) {5} +[DC, 2 f 0 component]
θ k opt ={ π/4 β k 3 tan 1 [ ( β k 2 1) ( β k 2 1) 2 β k 2 ] β k > 3
λ p k = SIN R p k ; λ q k = SIN R q k .
X p k =Re( a k e j θ k )+jRe( b k e j θ k ); X q k =Im( a k e j θ k )+jIm( b k e j θ k )

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