## Sensitivity improvement and carrier power reduction in direct-detection optical OFDM systems by subcarrier pairing |

Optics Express, Vol. 20, Issue 2, pp. 1635-1648 (2012)

http://dx.doi.org/10.1364/OE.20.001635

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### 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).

© 2012 OSA

## 1. Introduction

1. A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express **14**(6), 2079–2084 (2006). [CrossRef] [PubMed]

2. B. J. C. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “120 Gbit/s over 500-km using single-band polarization-multiplexed self-coherent optical OFDM,” J. Lightwave Technol. **28**(4), 328–335 (2010). [CrossRef]

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

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

2. B. J. C. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “120 Gbit/s over 500-km using single-band polarization-multiplexed self-coherent optical OFDM,” J. Lightwave Technol. **28**(4), 328–335 (2010). [CrossRef]

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

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

9. 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]

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]

9. 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]

*subcarrier pairing*, i.e., information is pre-coded across two subcarriers with unbalanced SINRs by using a complex exponential factor parameterized by a single angle and component interleaving. The angle can be optimally selected for the different subcarrier pairs. Since joint pre-coding is performed only across a pair of subcarriers, the complexity of joint maximum likelihood detection (MLD) is low.

## 2. System model

1. A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express **14**(6), 2079–2084 (2006). [CrossRef] [PubMed]

*B*+

_{gap}*B*/2. These waveforms drive a complex optical modulator to create the DDO-OFDM spectrum shown in the inset. This is transmitted over an amplified optical link, which adds ASE. The bandwidth of the ASE is limited by an optical bandpass filter. The photodetector causes intermixing of the carrier, ASE and subcarriers, as will be discussed below. A pair of microwave mixers down-convert the electrical spectrum so that the subcarriers lie either side of DC (the subcarrier at DC is not used for data transmission); this means that lower-rate Analog-to-Digital Converters (ADCs) can be used. The CP is stripped from the signal. An FFT acts as a matched filter for all of the subcarriers, producing a complex number for each subcarrier. Phase offsets are added to each subcarrier to equalize the phase distortion accumulated along the link, chiefly due to chromatic dispersion. In a typical DDO-OFDM system, a QAM demodulator follows the equalizer, slicing the complex signal to recover the data bits. This process is repeated for each OFDM symbol to give continuous data transmission. The equalizer is trained at the beginning of a simulation run by sending a data sequence known to the receiver under noiseless conditions and comparing the phases and magnitudes of the received subcarriers with their transmitted values.

_{sc}## 3. Electrical noise and interference spectrum

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

*N*is the number of subcarriers in the DDO-OFDM, occupying the bandwidth

_{sc}*B*. As illustrated at the top of Fig. 2 ,

_{sc}*B*is the guard band’s width between the optical carrier and the lowest frequency subcarrier, and

_{gap}*B*is the overall ASE noise bandwidth. Finally,

_{ASE}*B*and

_{L}*B*are the lower and upper excess noise bands. In the time domain, the received optical signal is given bywhere:

_{H}*n*(

_{h}*t*) and

*n*(

_{v}*t*) denote the ASE noise in the horizontal and vertical polarizations, which are assumed equal in power (unpolarized noise). We assume the optical signal

*s*(

*t*) and the optical carrier at frequency

*f*

_{0}are sent on the horizontal polarization. The signal

*s*(

*t*) represents the transmitted optical OFDM subcarrier band, i.e.where:

*X*are complex

_{k}*M*-QAM symbols with average energy

*E*and Δ

_{x}*f*=

*B*/

_{sc}*N*is the frequency spacing of the subcarriers.

_{sc}*r*

_{0}(

*t*) on a linear scale, denoted by

*G*(

_{ro}*f*).

*P*=

_{ca}*A*

^{2}/2 is the power of the optical carrier and

*P*= 2

_{s}*S*

_{0}

*B*is the total power in the OFDM subcarriers for continuous signals. For discrete signals, we define

_{sc}*P*= 2

_{sc}*S*

_{0}

*Δf*, so that we can write

*P*=

_{s}*N*. Finally,

_{sc}P_{sc}*η*=

*P*/

_{ca}*P*is the carrier-to-signal power ratio. We define OSNR in the standard way as the total optical signal power (

_{s}*P*+

_{ca}*P*, divided by the ASE noise power in both polarizations, falling within the standard reference bandwidth of 12.5-GHz (0.1 nm at 1550 nm). Using an optical filter and direct detection by a photodiode with responsivity

_{s})*R*, we obtain the down-converted electrical current

## 4. Electrical PSD and SINRs of DDO-OFDM

*δ*(

*f*) the Dirac function. The terms

*G*(

_{s}*f*) and

*G*(

_{n}*f*) =

*N*are the PSD of the OFDM signal

_{ASE}*s*(

*t*) and of the ASE noise in both polarizations, respectively. The above expression is valid under the assumption that both

*n*(

*t*) and

*s*(

*t*) are zero-mean Gaussian random processes with variances

*N*and

_{ASE}*S*

_{0}, respectively. This assumption is valid when the number of subcarriers is sufficiently large.

*G*(

_{s}*f*) accounting for the unwanted tones [5

**16**(2), 860–865 (2008). [CrossRef] [PubMed]

*G*(

_{n}*f*); {4} is noise that has been down converted by mixing with the carrier; and {5} comes from mixing of noise with the OFDM subcarriers. The sum of the terms {2}, {3}, {4} and {5} represents the noise and interference impairments. The DC component stems from the optical carrier and the unwanted tones, while the (2

*f*

_{0}) stems from the optical carrier. It is important to note that some of the resulting baseband components are generated from the negative frequency parts of the underlying double-sided PSDs. The electrical signal

*G*(

_{y}*t*) is further processed by a low pass filter (LPF) with cutoff frequency

*B*+

_{gap}*B*+

_{sc}*B*, and its DC component is removed. The corresponding filtered terms in Eq. (4) are shown in Fig. 2 on a linear scale by analytic computation of the continuous convolution operations. In practice, a spectrum analyzer in a simulation will operate on sampled signals and display sampled spectra with a given resolution bandwidth

_{H}*B*. The corresponding convolution operations are replaced by discrete convolutions of sampled spectra.

_{res}*one sided*PSD (where positive frequency PSDs in Fig. 1(b) are scaled by a factor two) is shown on a logarithmic scale. In this example, we consider a 60 Gbit/s optical OFDM signal using 4-QAM modulation with 1024 bits per OFDM symbols using

*N*= 512 subcarriers. The OFDM signal occupies

_{sc}*B*= 30 GHz bandwidth. A gap,

_{sc}*B*= 30 GHz, between the carrier and the subcarriers was used. The total ASE noise bandwidth is

_{gap}*B*= 60 GHz. The resolution bandwidth

_{ASE}*B*=

_{res}*Δf*/4 = 14.648 MHz. The optical power into the photodiode is 1 mW and the photodiode has a responsivity of 1 A/W with the RF power measured into a load of 1 Ω. The RF powers of the signals and noise all scale with the square of the optical power and responsivity, but linearly with the load resistance. Note that, because the resolution bandwidth is one-quarter of the subcarrier spacing, the indicated SINR (the difference between the red and black lines) is 6 dB more than the actual SINR that a subcarrier would experience. Thus, we would expect a SINR in the range 6 dB to 9 dB for 13-dB OSNR.

*B*= 30 GHz, the unwanted intermodulation tones can be ignored [1

_{gap}1. A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express **14**(6), 2079–2084 (2006). [CrossRef] [PubMed]

*,*

_{i}*i*= 1,…,

*N*, defined as the ratio of power of OFDM signal at the

_{sc}*i*-th subcarrier and the noise and interference power at the

*i*-th subcarrier, measured over a bandwidth equal to the subcarrier spacing. This is due to the noise and interference impairments shown in Fig. 2. The analytical results of Eq. (4) allow each SINR

*, to be computed without the need for Monte-Carlo simulations. The computed SINRs are shown in Fig. 4 for OSNR = 10, 13, 15 and 19 dB. The electrical SINR increases at higher frequencies, due the contributions of*

_{i}*ASE*×

*ASE*noise and

*ASE*×

*subcarrier*noise, which are both frequency dependent (see Fig. 2). For 10-dB OSNR, the increase is 4 dB: for 19-dB OSNR this reduces to 3.2 dB. This difference is due to the relative contribution of

*ASE*×

*ASE*noise. For high OSNRs,

*ASE*×

*ASE*noise is negligible and so contributes to the slope in SINR across the band only marginally.

## 5. DDO-OFDM with pairing of “good” and “bad” subcarriers

9. 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]

*p*,

_{k}*q*),

_{k}*k*= 1,…,

*N*/2} forming a

_{sc}*partition*of the

*N*subcarriers, where

_{sc}*k*is the index of pairs. According to [9

**57**(6), 3542–3566 (2011). [CrossRef]

**57**(6), 3542–3566 (2011). [CrossRef]

*S*= {(

*p*,

_{k}*q*) = (

_{k}*k*,

*N*–

_{sc}*k*+ 1),

*k*= 1,…,

*N*/2}. As a simple example, if the system had 6 overall subcarriers (

_{sc}*N*= 6), we would have three pairs of subcarriers. The first pair (

_{sc}*k*= 1), would include the 1

^{st}and the 6

^{th}subcarriers, i.e., (

*p*,

_{1}*q*) = (1, 6). The second pair (

_{1}*k*= 2), will include the 2

^{nd}and the 5

^{th}subcarriers, i.e., (

*p*,

_{2}*q*) = (2, 5). The last pairing (

_{2}*k*= 3) will be (

*p*,

_{3}*q*) = (3, 4).

_{3}*k*) of

*M*-QAM information symbols

*a*and

_{k}*b*(see Fig. 1) by multiplying by rotation factor

_{k}*θ*is the

_{k}*rotation angle*for the

*k*-th pair. The impact of the rotation angle on the error performance of MIMO systems has been discussed in [9

**57**(6), 3542–3566 (2011). [CrossRef]

*θ*was derived analytically for 4-QAM, to minimize the total error probability and is given bywhere

_{k}^{opt},*condition number*of the pair of subcarriers (

*p*,

_{k}*q*), and

_{k}*η*= 0.5. For higher OSNRs, there are fewer subcarrier pairs with optimal rotation angles

*θ*that are not 45°. Specifically, when OSNR = 7 and 19 dB, there are 54 and 6 subcarrier pairs whose condition number is greater than

_{k}^{opt}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]

*p*,

_{k}*q*) will acquire different SINRs with the difference in SINR dependent on the index of the pair,

_{k}*k*. In order to apply ML detection correctly, the constellations after component de-interleaving should have circularly symmetric spreads. This can be achieved by scaling each received symbol by the square-root of its expected SINR before component de-interleaving; that is, symbols with low SINRs are reduced in size relative to the symbols with higher SINRs. Figure 7 illustrates this process.

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]

*a*, if one channel loses one component, say

_{k}**44**(4), 1453–1467 (1998). [CrossRef]

## 6. Simulations of the required OSNR with and without pairing

^{−3}as a function of the carrier-to-signal power ratio,

*η*. These results were obtained using MATLAB® Monte-Carlo simulations of the receiver with the variance of the random electrical noise for each subcarrier set by the calculated SINR. To obtain each point, the OSNR was swept to obtain a plot of BER versus ONSR. Also included are points (⋄) obtained using a VPItransmissionMaker simulation, where optical noise is added before the photodiode, so the photodetection generates electrical noise with the expected spectrum. These points validate the MATLAB model’s results and confirm the quality of the Gaussian approximation of the interference terms. In the VPItransmissionMaker simulations, the rotation angle was fixed to 45°, which gives slightly suboptimal results.

## 7. Discussion and conclusions

*Rate*= 1 code), so does not adversely impact on the spectral efficiency of the system. The results are also applicable to any optical OFDM system where subcarriers with bad SINR can be paired with subcarriers of good SINRs.

13. J. M. Tang, P. M. Lane, and K. A. Shore, “High-speed transmission of adaptively modulated optical OFDM signals over multimode fibers using directly modulated DFBs,” J. Lightwave Technol. **24**(1), 429–441 (2006). [CrossRef]

*e.g.*BPSK, QPSK, 8-QAM, 16-QAM) depending on the SINR of a particular subcarrier. It is suitable when the SINRs vary by at much more than 3 dB, which is not the case in our situation. Adaptive Modulation also varies the transmission rate of the channel, which is generally inconvenient in most telecommunications applications. Another technique to cope with unequal SINRs is to vary the transmission powers of subcarriers to equalize the error rates across the subcarriers (‘Power Loading’ [14

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]

## Acknowledgments

## References and links

1. | A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express |

2. | B. J. C. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “120 Gbit/s over 500-km using single-band polarization-multiplexed self-coherent optical OFDM,” J. Lightwave Technol. |

3. | W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. |

4. | 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 |

5. | A. J. Lowery, “Amplified-spontaneous noise limit of optical OFDM lightwave systems,” Opt. Express |

6. | S. L. Jansen, I. Morita, and H. Tanaka, “Carrier-to-signal power in fiber-optic SSB-OFDM transmission systems” in |

7. | G. Raleigh and J. Cioffi, “Spatio-temporal coding for wireless communication,” IEEE Trans. Commun. |

8. | R. Knopp and G. Caire, “Power control schemes for TDD systems with multiple transmit and receive antennas,” in |

9. | S. K. Mohammed, E. Viterbo, Y. Hong, and A. Chockalingam, “MIMO precoding with X- and Y-codes,” IEEE Trans. Inf. Theory |

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 |

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 |

12. | G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory |

13. | J. M. Tang, P. M. Lane, and K. A. Shore, “High-speed transmission of adaptively modulated optical OFDM signals over multimode fibers using directly modulated DFBs,” J. Lightwave Technol. |

14. | C. S. Park and K. B. Lee, “Transmit power allocation for BER performance improvement in multicarrier systems,” IEEE Trans. Commun. |

15. | Q. Yang, W. Shieh, and Y. Ma, “Bit and power loading for coherent optical OFDM,” IEEE Photon. Technol. Lett. |

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. |

**OCIS Codes**

(060.4080) Fiber optics and optical communications : Modulation

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Subsystems for Optical Networks

**History**

Original Manuscript: September 28, 2011

Revised Manuscript: October 15, 2011

Manuscript Accepted: October 17, 2011

Published: January 11, 2012

**Virtual Issues**

European Conference on Optical Communication 2011 (2011) *Optics Express*

**Citation**

Yi Hong, Arthur J. Lowery, and Emanuele Viterbo, "Sensitivity improvement and carrier power reduction in direct-detection optical OFDM systems by subcarrier pairing," Opt. Express **20**, 1635-1648 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-1635

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### References

- A. J. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express14(6), 2079–2084 (2006). [CrossRef] [PubMed]
- B. J. C. Schmidt, Z. Zan, L. B. Du, and A. J. Lowery, “120 Gbit/s over 500-km using single-band polarization-multiplexed self-coherent optical OFDM,” J. Lightwave Technol.28(4), 328–335 (2010). [CrossRef]
- W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett.42(10), 587–588 (2006). [CrossRef]
- 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.
- A. J. Lowery, “Amplified-spontaneous noise limit of optical OFDM lightwave systems,” Opt. Express16(2), 860–865 (2008). [CrossRef] [PubMed]
- 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.
- G. Raleigh and J. Cioffi, “Spatio-temporal coding for wireless communication,” IEEE Trans. Commun.46(3), 357–366 (1998). [CrossRef]
- 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.
- S. K. Mohammed, E. Viterbo, Y. Hong, and A. Chockalingam, “MIMO precoding with X- and Y-codes,” IEEE Trans. Inf. Theory57(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. Theory44(4), 1453–1467 (1998). [CrossRef]
- 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.
- G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation,” IEEE Trans. Inf. Theory44(3), 927–946 (1998). [CrossRef]
- J. M. Tang, P. M. Lane, and K. A. Shore, “High-speed transmission of adaptively modulated optical OFDM signals over multimode fibers using directly modulated DFBs,” J. Lightwave Technol.24(1), 429–441 (2006). [CrossRef]
- 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]
- 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]
- 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]

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