## Theoretical and experimental evaluation of clipping and quantization noise for optical OFDM |

Optics Express, Vol. 19, Issue 18, pp. 17713-17728 (2011)

http://dx.doi.org/10.1364/OE.19.017713

Acrobat PDF (1154 KB)

### Abstract

Orthogonal frequency division multiplexing (OFDM) has recently gained substantial interest in high capacity optical fiber communications. Unlike wireless systems, optical OFDM systems are constrained by the limited resolution of the ultra high-speed digital-to-analog converters (DAC) and analog-to-digital converters (ADC). Additionally, the situation is exacerbated by the large peak-to-average power ratio (PAPR) inherent in OFDM signals. In this paper, we study the effects of clipping and quantization noise on the system performance. We analytically quantify the introduced distortion as a function of bit resolution and clipping ratio, both at the DAC and ADC. With this we provide a back-to-back signal-to-noise ratio analysis to predict the bit error rate of the system, assuming a fixed received optical power and ideal electrical-optical-electrical conversion. Simulation and experimental results are used to confirm the validity of the expressions.

© 2011 OSA

## 1. Introduction

1. B. Schmidt, A. Lowery, and J. Armstrong, “Experimental demonstration of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. **26**, 196–203 (2008). [CrossRef]

4. J. Armstrong, “OFDM for optical communcations,” J. Lightwave Technol. **27**, 189–204 (2009). [CrossRef]

5. Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express **17**, 17658–17668 (2009). [CrossRef] [PubMed]

12. R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “*Optical Fiber Communication Conference and Exposition (OFC)*,”(Los Angeles, CA, 2011).

5. Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express **17**, 17658–17668 (2009). [CrossRef] [PubMed]

10. Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. **16**, 1235–1244 (2010). [CrossRef]

6. N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-time 2.5 GS/s coherent optical receiver for 53.3-Gb/s sub-banded OFDM,” J. Lightwave Technol. **28**, 494–501 (2010). [CrossRef]

7. R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. **22**, 745–747 (2010). [CrossRef]

9. R. Giddings, X. Jin, E. Hugues-Salas, E. Giacoumidis, J. Wei, and J. Tang, “Experimental demonstration of a record high 11.25 Gb/s real-time optical OFDM transceiver supporting 25 km SMF end-to-end transmission in simple IMDD systems,” Opt. Express **18**, 5541–5555 (2010). [CrossRef] [PubMed]

12. R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “*Optical Fiber Communication Conference and Exposition (OFC)*,”(Los Angeles, CA, 2011).

5. Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express **17**, 17658–17668 (2009). [CrossRef] [PubMed]

10. Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. **16**, 1235–1244 (2010). [CrossRef]

13. D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circ. Syst. I **53**, 1741–1748 (2006). [CrossRef]

14. E. Vanin, “Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion,” Opt. Express **19**, 4280–4293 (2011). [CrossRef] [PubMed]

**17**, 17658–17668 (2009). [CrossRef] [PubMed]

10. Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. **16**, 1235–1244 (2010). [CrossRef]

16. Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “*Proc. of Intl. Conf. on Transparent Optical Networks*,” (Munich, Germany, 2010). [CrossRef]

14. E. Vanin, “Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion,” Opt. Express **19**, 4280–4293 (2011). [CrossRef] [PubMed]

1. B. Schmidt, A. Lowery, and J. Armstrong, “Experimental demonstration of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. **26**, 196–203 (2008). [CrossRef]

## 2. Optical OFDM

### 2.1. Transmitter

*s*[

*k*], which are chosen from a constellation like quadrature phase-shift keying (QPSK) or quadrature amplitude modulation (QAM). These are modulated using an inverse discrete Fourier transform (IDFT) of size

*K*, and extended cyclically to include a cyclic prefix (CP) of length

*N*

_{CP}, Not all inputs to the IDFT are used, which allows for band-edge protection, over-sampling, or inclusion of guard bands for direct detection (DD). The set of non-zero or active IDFT inputs is denoted as, In a hardware implementation, all baseband processing will be done in fixed-point format. We will neglect this here as we assume that the bit-resolution of the digital-to-analog converter (DAC) will be the dominant source of quantization error. This is reasonable for optical OFDM implementations, as a common fixed-point IDFT will have easily 8–12 bit precision [5

**17**, 17658–17668 (2009). [CrossRef] [PubMed]

**16**, 1235–1244 (2010). [CrossRef]

*v*

_{D}[

*n*] is the quantization error introduced by the DAC. The distortion or mean-squared error (MSE) introduced by the DAC is then, where we assume that the quantization noise is a (wide-sense) stationary process.

*x*[

_{q}*n*] can be interpreted as the IDFT of the noisy data symbols

*s*[

_{q}*k*], Since the IDFT is a linear transform, the noisy data symbols

*s*[

_{q}*k*] are simply where the

*ṽ*

_{D}[

*k*] are the discrete Fourier transform (DFT) of the quantization error We notice that the noisy data symbols

*s*[

_{q}*k*] extend beyond the set of active IDFT inputs

*S*.

_{A}*x*[

_{q}*n*], to a continuous signal,

*x*(

*t*). The operation can be mathematically represented as a discrete time signal driving a low-pass filter (LPF),

*g*

_{DAC}, where the sampling rate is

*B*= 1/

*T*, and the LPF passband needs to be chosen appropriately. The (complex) baseband signal is then upconverted to the carrier frequency,

_{s}*f*, In optical systems a laser will take the place of the oscillator, and the “carrier frequency”

_{c}*f*is usually expressed in terms of wavelength, e.g., 850 to 1550 nm in typical optical OFDM systems.

_{c}### 2.2. Coherent Receiver

*h*(

*τ*), while the receiver noise (optical and electrical) is modeled as an additive signal,

*v*

_{N}(

*t*), The signal is down converted using a local oscillator, Then sampled using the analog-to-digital converter (ADC), modeled using a LPF

*g*

_{ADC}, Again we will assume that the discrete signal will be quantized going through the ADC, we introduce the quantized baseband signal,

*N*

_{CP}samples are discarded and the discrete signal is converted to frequency domain via a DFT, for

*m*∈

*S*, and where the

_{A}*ṽ*[

_{N}*m*] represent the effect of the optical and electrical receiver noise [18]. The

*ṽ*[

_{A}*m*] are the DFT of the ADC quantization noise,

*v*[

_{A}*n*], as

*ṽ*[

_{D}*m*] is the DFT of the DAC noise. Finally, the channel coefficients

*H*[

*m*] contain the channel and all filter effects, where

*G*

_{DAC}(

*f*),

*H*(

*f*), and

*G*

_{ADC}(

*f*) are the Fourier transform of

*g*

_{DAC}(

*τ*),

*h*(

*τ*) and

*g*

_{ADC}(

*τ*) respectively.

## 3. Effect of Quantization Noise

### 3.1. Signal-to-Noise Ratio

*m*-th subcarrier as,

*ṽ*[

_{D}*m*] is weighted by the channel (and filter) coefficients

*H*[

*m*], while the ADC and receiver noise are not. We next evaluate the average noise power.

*N*

_{0}as the power of the optical and electrical receiver noise in the time domain (at the output of the ADC), and the relation to the frequency domain is as before. Finally the SNR on the

*m*-th subcarrier can be evaluated as,

### 3.2. Gaussian Approximation of Input

### 3.3. Calculating the Distortion

*q*bits, which corresponds to a uniform quantizer with

*M*= 2

*levels, as illustrated in Fig. 1. As we model the OFDM signal as zero-mean Gaussian, a mid-rise quantizer that is symmetric around zero is the best choice (although if implementation requires a mid-tread quantizer, the derivation is easily adapted).*

^{q}*x*[

*n*] are distributed as complex Gaussian random variables, with zero mean and variance

*N*as shown in Eqs. (23) and (24). Accordingly the real and imaginary part of each

_{A}E_{s}*x*[

*n*] are independent real Gaussian random variables, with half the variance,

*N*/2, each. We therefore limit our consideration to quantizing the real- and imaginary parts identically. With this we can simplify the quantization problem to that of two identical real Gaussian random variables,

_{A}E_{s}*t*is a real Gaussian random variable,

*t*is its quantized version, and

_{q}*f*(

*t*) is its probability density function (the second factor of two is for folding the positive/negative interval). While values of

*t*smaller than

*M*/2 · Δ will only incur a maximum quantization error of ±Δ/2, the clipping error for values larger than

*M*/2 · Δ is (theoretically) unbounded, The probability density function of a real Gaussian random variable with mean

*μ*= 0 and variance

*σ*

^{2}=

*N*/2 is

_{A}E_{s}*t*) is the Gaussian cumulative density function Using Eq. (29) to solve Eq. (26), Eq. (27) and inserting back into Eq. (25), the final result is

*M*= 2

*and the chosen step-size Δ, see also Fig. 1. When choosing the step-size proportional to the standard deviation of the input, see Eq. (31), the resulting distortion scales linearly with the second moment of the*

^{q}*x*[

*n*],

*N*, but is otherwise independent of this parameter. Looking at the “clipping ratio”, which is commonly defined as the ratio of the maximum to the average output power, we can express the clipping ratio as a function of the newly introduced scaling factor

_{A}E_{s}*γ*in Eq. (32). So when varying the proportionality constant

*γ*, we are effectively varying the clipping ratio (the factor 1/2 in the numerator is because the ratio is considered per real or imaginary part).

*M*from 2

^{3}= 8 to 2

^{8}= 256, and the clipping ratio from 0 to 12 dB. As the clipping ratio is defined proportional to the signal, any signal scaling is therefore accounted for when entering the DAC. We therefore arbitrarily assume that the symbol constellations are scaled as

*E*= 1/

_{s}*N*, this leads the to samples

_{A}*x*[

*n*] at the input of the DAC having unit power. Clearly there is an optimum tradeoff between quantization and clipping error that minimizes the distortion or MSE introduced by the DAC. In fact since the MSE scales only linearly with the value of the input power, the optimum clipping ratio depends only on the number of bits

*q*= log

_{2}

*M*.

## 4. Simulation of Coherent OFDM

### 4.1. Simulation Setup

**17**, 17658–17668 (2009). [CrossRef] [PubMed]

**16**, 1235–1244 (2010). [CrossRef]

*B*= 21.4 GHz.

*g*

_{DAC}(

*τ*) =

*g*

_{ADC}(

*τ*) =

*g*

_{LPF}(

*τ*); the filter frequency response is plotted in Fig. 3. This is deemed sufficient to model most effects of D/A and A/D conversion, like aliasing or filter flanks that extend outside the baseband bandwidth

*B*. The simulation corresponds to electrical back-to-back performance, and the channel

*h*(

*τ*) is simply a time delay. The additive noise power is set to

*N*

_{0}= 10

^{−4}. We consider a DFT size of

*K*= 128, to avoid the roll-off region of the filter we deactivate one eighth of the subcarriers, accordingly |

*S*| = 112. The CP has a length of

_{A}*N*

_{CP}= 8

### 4.2. SNR Analysis

*N*= 1; this is achieved by scaling the constellation symbols such that

_{A}E_{s}*E*= 1/

_{s}*N*. With this the SNR at the

_{A}*m*th subcarrier is (assuming |

*H*[

*m*]|

^{2}= 1), where we separate DAC and ADC error. Due to scaling the constellation, the time domain samples,

*x*[

*n*], are of unit power, allocating

*K*/

*N*= 0.58 dB amplification per subcarrier. We compare the predicted values with a numerical simulation, where we plot numerator and denominator separately.

_{A}*N*

_{0}leading to about 2 · 10

^{−4}≈ −37 dB. In case of limited DAC and ADC resolution, see Fig. 4(b), the error is simply doubled (3 dB increase), while at 8 bit the combined error is roughly 3 · 10

^{−4}≈ 35 dB. Although the assumed LPF in Fig. 3 is basically ideal within the used frequency band, its flanks can be observed in the DAC noise in Fig. 4(a). This will be more obvious in the experimental section where the used DAC has significant roll-off also within the OFDM signal band and Eq. (35) will have to be replaced with the more detailed Eq. (22) to account for this amplification and/or attenuation of the DAC noise.

### 4.3. BER Prediction

*B*= 21.4 GHz sampling rate and

*M*-ary modulation, the data rate accounting for the overhead caused by the CP and oversampling is, For QPSK, 16-QAM, and 64-QAM, the data rates correspond to 35.2, 70.5, and 105.7 Gb/s respectively. We plot simulation results and predictions based on inserting Eq. (35) into Eqs. (36)–(38) in Fig. 5. In comparison to the simulation results, we see a good fit at BERs above 10

^{−4}. This indicates that the clipping noise is approximately Gaussian up to about three standard deviations around the mean, but then the tail behavior is noticeably different. In any case the optimum clipping ratio in terms of MSE matches either exactly the one based on BER or is very close (although the actual BER can deviate somewhat).

## 5. Experimental Direct-Detected OFDM System

### 5.1. Experimental Setup

*K*= 1024; since we assumed coherent detected OFDM in the derivation, we insert sufficient guard bands to avoid intermodulation distortion (IMD) within the OFDM signal band (see, e.g., [1

1. B. Schmidt, A. Lowery, and J. Armstrong, “Experimental demonstration of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. **26**, 196–203 (2008). [CrossRef]

*S*| = 400; to generate a completely real discrete multi-tone (DMT) signal, we assign the subcarriers with negative indices the conjugate complex values of the subcarriers with positive indices. A bias of 6 dB is also applied to the signal after passing through the DAC, where 6 dB is the ratio of the bias power, relative to the total OFDM double-sideband power. This will effectively reduce the observed SNR at the receiver by about 6 dB, since this amount of optical power is not available for the OFDM signal.

_{A}*m*-th subcarrier as

*G*

_{DAC}[

*m*], the average signal power of the

*m*-th subcarrier at the input of the DAC is set to and

*α*is chosen such that This corresponds to

*N*= 1 when evaluating Eq. (31). Since the OFDM sideband is attenuated going through the DAC, it is amplified with a factor

_{A}E_{s}*α*/

*N*before entering the optical modulator and applying the bias, which keeps the transmitted optical power constant (and amplifies the DAC noise). The receiver noise figure is about

_{A}*N*

_{0}= 10

^{−3}, and the used sampling scope has 8 bit ADC resolution and a mostly ideal filter characteristic

*G*

_{ADC}(

*f*) ≈ 1.

*m*-th subcarrier is, where we see that although we achieved a uniform channel transfer function via pre-equalization, the noise values will vary across the FFT outputs and the contribution by the DAC noise is increased by

*α*/

*N*≈ 1 dB.

_{A}### 5.2. SNR Analysis

*m*| < 200, significant IMD of the OFDM band increases the noise level (which is not considered in the prediction). Although the DAC roll-off was precompensated and we achieve uniform spectral power within the OFDM band, the SNR across the modulated subcarriers is not constant, as the dominant DAC noise reflects the DAC roll-off. The match between prediction and simulation is not as close as in Fig. 4(a), which we attribute to unaccounted behavior of direct-detection, e.g., IMD between the OFDM band and parts of the DAC noise that extend into the guard band |

*m*| < 256.

^{3}OFDM symbols to estimate the noise level as in the simulation, we use less than a hundred in the experimental setup. We also notice that the measured DAC roll-off in Fig. 7 is not highly precise, as the precompensation does not achieve fully uniform power across the OFDM band. Generally though, the relative levels of noise are fairly accurate.

*m*, have better performance.

*N*

_{0}= 3 · 10

^{−3}. With this – including bias and oversampling – the SNR is receiver noise limited to below 24 dB. Based on this, the match in Fig. 9(b) is quite reasonable overall. Compared to Fig. 9(a) the DAC noise is smaller, so the IMD effects are also less present. This leads to a better match between simulation and prediction (which both assume ideal DAC behavior), where before there was a better match between simulation and experiment.

### 5.3. BER Results

## 6. Conclusion

## References and links

1. | B. Schmidt, A. Lowery, and J. Armstrong, “Experimental demonstration of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. |

2. | S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. |

3. | X. Jin, J. Tang, K. Qiu, and P. Spencer, “Statistical investigation of the transmission performance of adaptively modulated optical OFDM signals in multimode fiber links,” J. Lightwave Technol. |

4. | J. Armstrong, “OFDM for optical communcations,” J. Lightwave Technol. |

5. | Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express |

6. | N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-time 2.5 GS/s coherent optical receiver for 53.3-Gb/s sub-banded OFDM,” J. Lightwave Technol. |

7. | R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. |

8. | F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in “ |

9. | R. Giddings, X. Jin, E. Hugues-Salas, E. Giacoumidis, J. Wei, and J. Tang, “Experimental demonstration of a record high 11.25 Gb/s real-time optical OFDM transceiver supporting 25 km SMF end-to-end transmission in simple IMDD systems,” Opt. Express |

10. | Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. |

11. | B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “ |

12. | R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “ |

13. | D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circ. Syst. I |

14. | E. Vanin, “Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion,” Opt. Express |

15. | C. R. Berger, Y. Benlachtar, and R. I. Killey, “Optimum clipping for optical OFDM with limited resolution DAC/ADC,” in “ |

16. | Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “ |

17. | A. Papoulis and S. U. Pillai, |

18. | For simplicity we neglect the effect of the receive filters and ADC conversion on this noise term. |

19. | J. G. Proakis, |

**OCIS Codes**

(060.4080) Fiber optics and optical communications : Modulation

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: May 19, 2011

Revised Manuscript: June 30, 2011

Manuscript Accepted: July 15, 2011

Published: August 25, 2011

**Citation**

Christian R. Berger, Yannis Benlachtar, Robert I. Killey, and Peter A. Milder, "Theoretical and experimental evaluation of clipping and quantization noise for optical OFDM," Opt. Express **19**, 17713-17728 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17713

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### References

- B. Schmidt, A. Lowery, and J. Armstrong, “Experimental demonstration of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. 26, 196–203 (2008). [CrossRef]
- S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 1, 6–15 (2008). [CrossRef]
- X. Jin, J. Tang, K. Qiu, and P. Spencer, “Statistical investigation of the transmission performance of adaptively modulated optical OFDM signals in multimode fiber links,” J. Lightwave Technol. 18, 3216–3224 (2008). [CrossRef]
- J. Armstrong, “OFDM for optical communcations,” J. Lightwave Technol. 27, 189–204 (2009). [CrossRef]
- Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17, 17658–17668 (2009). [CrossRef] [PubMed]
- N. Kaneda, Q. Yang, X. Liu, S. Chandrasekhar, W. Shieh, and Y.-K. Chen, “Real-time 2.5 GS/s coherent optical receiver for 53.3-Gb/s sub-banded OFDM,” J. Lightwave Technol. 28, 494–501 (2010). [CrossRef]
- R. Giddings, E. Hugues-Salas, X. Jin, J. Wei, and J. Tang, “Experimental demonstration of real-time optical OFDM transmission at 7.5 Gb/s over 25-km SSMF using a 1-GHz RSOA,” IEEE Photon. Technol. Lett. 22, 745–747 (2010). [CrossRef]
- F. Buchali, R. Dischler, A. Klekamp, M. Bernhard, and Y. Ma, “Statistical transmission experiments using a real-time 12.1 Gb/s OFDM transmitter,” in “Optical Fiber Communication Conference and Exposition (OFC) ,”(San Diego, CA, 2010).
- R. Giddings, X. Jin, E. Hugues-Salas, E. Giacoumidis, J. Wei, and J. Tang, “Experimental demonstration of a record high 11.25 Gb/s real-time optical OFDM transceiver supporting 25 km SMF end-to-end transmission in simple IMDD systems,” Opt. Express 18, 5541–5555 (2010). [CrossRef] [PubMed]
- Y. Benlachtar, P. Watts, R. Bouziane, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, M. Glick, and R. Killey, “Real-time digital signal processing for the generation of optical orthogonal frequency-division-multiplexed signals,” IEEE J. Sel. Top. Quantum Electron. 16, 1235–1244 (2010). [CrossRef]
- B. Inan, O. Karakaya, P. Kainzmaier, S. Adhikari, S. Calabro, V. A. Sleiffer, N. Hanik, and S. L. Jansen, “Realization of a 23.9 Gb/s real time optical-OFDM transmitter with a 1024 point IFFT,” in “Optical Fiber Communication Conference and Exposition (OFC) ,”(Los Angeles, CA, 2011).
- R. Schmogrow, M. Winter, B. Nebendahl, D. Hillerkuss, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “101.5 Gbit/s real-time OFDM transmitter with 16QAM modulated sub-carriers,” in “Optical Fiber Communication Conference and Exposition (OFC) ,”(Los Angeles, CA, 2011).
- D. Dardari, “Joint clip and quantization effects characterization in OFDM receivers,” IEEE Trans. Circ. Syst. I 53, 1741–1748 (2006). [CrossRef]
- E. Vanin, “Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion,” Opt. Express 19, 4280–4293 (2011). [CrossRef] [PubMed]
- C. R. Berger, Y. Benlachtar, and R. I. Killey, “Optimum clipping for optical OFDM with limited resolution DAC/ADC,” in “Proc. OSA Advanced Photonics Congress ,”(Toronto, CA, 2011).
- Y. Benlachtar, R. Bouziane, R. Killey, C. Berger, P. Milder, R. Koutsoyannis, J. Hoe, M. Püschel, and M. Glick, “Optical OFDM in the data center,” in “Proc. of Intl. Conf. on Transparent Optical Networks ,” (Munich, Germany, 2010). [CrossRef]
- A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).
- For simplicity we neglect the effect of the receive filters and ADC conversion on this noise term.
- J. G. Proakis, Digital Communications , 4th ed. (McGraw-Hill, 2001).

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