## Bandpass sampling in heterodyne receivers for coherent optical access networks |

Optics Express, Vol. 20, Issue 28, pp. 29404-29412 (2012)

http://dx.doi.org/10.1364/OE.20.029404

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### Abstract

A novel digital receiver architecture for coherent heterodyne-detected optical signals is presented. It demonstrates the application of bandpass sampling in an optical communications context, to overcome the high sampling rate requirement of conventional receivers (more than twice the signal bandwidth). The concept is targeted for WDM coherent optical access networks, where applying heterodyne detection constitutes a promising approach to reducing optical hardware complexity. The validity of the concept is experimentally assessed in a 76 km WDM-PON scenario, where the developed DSP achieves a 50% ADC rate reduction with penalty-free operation.

© 2012 OSA

## 1. Introduction

*B*and IF centered on

*f*, the highest frequency component will be

_{c}*f*+

_{c}*B/*2, which sets the minimum analog bandwidth requirement for both the photoreceiver and ADC. (b) To satisfy the Shannon-Nyquist theorem [2], a high sampling rate (

*f*) is required at the ADC when conventional low-pass sampling is employed. This must be larger than twice the highest frequency component: 2(

_{s}*f*+

_{c}*B/*2).

*f*, arbitrarily close to the theoretical minimum (2

_{s}*B*) needed to accurately reconstruct the modulating baseband signal (a process termed bandpass sampling [3]). However, this requires careful selection of the carrier and sampling oscillator frequencies

*f*and

_{c}*f*, which in turn must be precise enough to avoid detrimental aliasing effects. This poses the question of whether such a scheme can be used in an optical coherent communication system, where fast (and relatively large) frequency fluctuations occur due to normalized laser linewidths that can typically be as high as

_{s}*Δv∙T*≈ 10

_{s}^{−3}(where

*Δv*is the linewidth and

*T*is the symbol period).

_{s}4. S. Dris, P. Bakopoulos, I. Lazarou, B. Schrenk, and H. Avramopoulos, “Low-Complexity DSP Using Undersampling for Heterodyne Receivers in Coherent Passive Optical Access Networks,” in *European Conference and Exhibition on Optical Communication*, OSA Technical Digest (online) (Optical Society of America, 2012), paper We.3.A.4.

*B*= 12 GSa/s, and is half the rate required when performing conventional low-pass sampling on the same signal at the Nyquist rate (2×(9.3+3) = 24.6 GSa/s). In addition, it represents a ~2.9-fold rate reduction (normalized to the symbol rate) compared to the recent implementation of Smolorz et al. [5], in the case of the 0.311 Gbaud heterodyne signals that was sampled at 3.7 GSa/s.

## 2. Principle of bandpass sampling

*f*< 2(

_{s}*f*/2

_{c}+B*)*. As long as these resulting replicas do not overlap, aliasing can be avoided, even if the Nyquist criterion is not adhered to. Moreover, a copy of the signal appears near the baseband; bandpass sampling can therefore be thought of as simultaneous digitization and frequency translation. This technique not only offers the potential for relaxing the sampling speed requirement of the ADC below that necessary with traditional low-pass Nyquist sampling; it can also reduce the amount of memory needed to capture a given time interval of a continuous signal, thus decreasing overall computational complexity. It should be noted, however, that even with bandpass sampling, the ADC’s analog bandwidth must still be high enough to accommodate the original signal (>

*f*+

_{c}*B*/2).

*f*lies within the interval [6],

_{s}*m*can be any positive integer that results in

*f*> 2

_{s}*B*, and determines the number of replications after sampling; in the illustrative example of Fig. 2, m = 4. Clearly the numerators in Eq. (1) are twice the lower (

*f*) and higher (

_{L}*f*) frequency limits of the original bandlimited signal:

_{U}*f*/

_{s}*B*, to the normalized highest frequency component,

*f*/

_{U}*B*. Dividing by

*B*and substituting Eq. (2) into Eq. (1), we can write:

*f*/

_{s}*B*for a given value of

*m*. Plotting this for values of

*m*= 1 to 3, we obtain the solid lines of Fig. 3 whose gradients are 2/(

*m*+1). Similarly, the upper limits for a range of values of

*m*are determined by the left-hand side of Eq. (3), and these are shown as dashed lines in the same plot. The resulting white ‘wedges’ correspond to the acceptable operating points where no aliasing occurs. The dotted line is the lower limit of conventional sampling (2

*f*), as determined by the Shannon-Nyquist theorem. Also evident from the graph is that rates below 2

_{U}*f*/

_{s}*B*are not allowed, as this is the absolute minimum given by the Shannon-Nyquist theorem.

*m*. The wedges of allowed sampling rates become much narrower, placing more stringent limits on the range of frequency uncertainty that can be tolerated without any significant aliasing occurring. The implication of all this is that the operating point must be chosen to be slightly above the theoretical minimum. How much above depends on the laser linewidth, as well as its long-term wavelength stability. It should be noted that similarly, the tolerance of the ADC clock, as well as its jitter would cause vertical movement of the operating point. However, modern ADCs have jitter specifications that are a tiny fraction of the baudrate of a typical optical communication system, so this uncertainty is negligible in practice.

## 3. Undersampling heterodyne receiver

*f*is first passed through an analog bandpass filter (BPF) to suppress out-of-band noise. This is a crucial step to avoid SNR degradation in the signal at the input of the ADC; the bandpass sampling process aggregates noise outside the band of interest and ‘folds’ it into the baseband, thus corrupting the resulting discrete signal. Even an ideal BPF, however, cannot mitigate the thermal noise from the subsequent sampling device; this noise power increases roughly by a factor corresponding to the amount of undersampling (

_{c}*m*+1) [7

7. R. G. Vaughan, N. L. Scott, and D. Rod White, “The theory of bandpass sampling,” IEEE Trans. Signal Process. **39**(9), 1973–1984 (1991). [CrossRef]

*r(t)*) residing on an IF carrier of ~9.3GHz, and oversampled at 50 GSa/s. With no pulse shaping, the bandwidth is approximately twice the baudrate (6 GHz). Figure 5(b) is the corresponding single-sided electrical spectrum. The red circles in Fig. 5(a) are the result of undersampling

*r(t)*at a rate of just

*f*= 1/

_{s}*T*= 12.5 GSa/s (derived from Eq. (1) with

_{s}*m*= 1), to yield the discrete-time signal

*r(nT*,

_{s})*f*=

_{c2}*f*-

_{c}*mf*= 9.3-12.5 = −3.2GHz (the negative sign simply means that the positive and negative image bands have been reversed, which is the case for odd values of

_{s}*m*).

*r(nT*is delayed by the filter delay Δ, and along with the output of the Hilbert filter forms the complex signal (Fig. 6(a) ),

_{s})*I*and

*Q*are the tributaries of the transmitted signal. The exponential term is essentially a complex rotation with the known carrier frequency (

*ω*= 2π

_{c2}*f*) that results from the frequency translation property of the bandpass sampling process. Rather than removing it at this stage, we first perform symbol clock recovery with the square timing algorithm. This reduces the sample rate from 1/

_{c2}*T*down to the symbol rate 1/

_{s}*T*, therefore saving computational resources in subsequent operations. The result is shown in the IQ plot of Fig. 6(b), where the rotating symbols can be seen as a ‘donut’ shape. The rotation due to the exponential term in Eq. (4) is then removed by complex multiplication, and this is evident in Fig. 6(c) where the only rotations left are due to the frequency mismatch between transmitter and LO lasers, as well as their combined linewidths. The final constellation of Fig. 6(d) is obtained after employing standard algorithms for frequency offset estimation [8

_{sym}8. A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photon. Technol. Lett. **19**(6), 366–368 (2007). [CrossRef]

## 4. Application in a coherent PON

*f*= 4.5 GHz, which was adequate for accommodating the signal bandwidth (±3 GHz for the main lobe). The Nyquist rate for low-pass sampling this signal was 15 GSa/s, corresponding to twice the highest frequency component in the received heterodyne signal: 2(

_{c}*f*+

_{c}*B*/2). To evaluate this signal, it was digitized in a 16 GHz real-time oscilloscope at 50 GSa/s (oversampled) and was demodulated offline using the standard, Nyquist approach. The BER performance was estimated over ~1.2∙10

^{6}bits (Fig. 8(a) ).

*B*, which sets a lower limit to the acceptable sampling rate

*f*2

_{s}>*B*. In our implementation the signal bandwidth was 6 GHz necessitating a sampling rate of at least 12 GHz. Given the 9.3 GHz IF, this indicated that the only acceptable operating area from Fig. 3 was the first wedge corresponding to

*m*= 1. From Eq. (1), the allowed sampling rate range is 12.3-12.6 GSa/s, thus allowing plenty of room for laser linewidth-induced frequency fluctuations (Fig. 11 ). A sampling rate of 12.5 GSa/s was chosen due to limitations of the available digitizer. Long-term wavelength stability was adequate for testing under laboratory conditions, whereas in a real ONU implementation a simple feedback loop would be required to control the LO wavelength within the allowed range.

## 5. Conclusion

## Acknowledgments

## References and links

1. | H. Rohde, S. Smolorz, J. S. Wey, and E. Gottwald, “Coherent Optical Access Networks,” in |

2. | C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng. |

3. | J. Proakis and D. Manolakis, |

4. | S. Dris, P. Bakopoulos, I. Lazarou, B. Schrenk, and H. Avramopoulos, “Low-Complexity DSP Using Undersampling for Heterodyne Receivers in Coherent Passive Optical Access Networks,” in |

5. | S. Smolorz, E. Gottwald, H. Rohde, D. Smith, and A. Poustie, “Demonstration of a Coherent UDWDM-PON with Real-Time Processing,” in |

6. | R. Lyons, |

7. | R. G. Vaughan, N. L. Scott, and D. Rod White, “The theory of bandpass sampling,” IEEE Trans. Signal Process. |

8. | A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photon. Technol. Lett. |

9. | E. Ip and J. M. Kahn, “Feedforward Carrier Recovery for Coherent Optical Communications,” J. Lightwave Technol. |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.1660) Fiber optics and optical communications : Coherent communications

(060.4250) Fiber optics and optical communications : Networks

(060.2840) Fiber optics and optical communications : Heterodyne

**ToC Category:**

Subsystems for Optical Networks

**History**

Original Manuscript: October 3, 2012

Revised Manuscript: November 16, 2012

Manuscript Accepted: November 21, 2012

Published: December 19, 2012

**Virtual Issues**

European Conference on Optical Communication 2012 (2012) *Optics Express*

**Citation**

Paraskevas Bakopoulos, Stefanos Dris, Bernhard Schrenk, Ioannis Lazarou, and Hercules Avramopoulos, "Bandpass sampling in heterodyne receivers for coherent optical access networks," Opt. Express **20**, 29404-29412 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-28-29404

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### References

- H. Rohde, S. Smolorz, J. S. Wey, and E. Gottwald, “Coherent Optical Access Networks,” in proceedings of Optical Fiber Communication Conference (OFC), OSA Technical Digest (Optical Society of America, 2011), paper OTuB1.
- C. E. Shannon, “Communication in the presence of noise,” Proc. Inst. Radio Eng.37, 10–21 (1949).
- J. Proakis and D. Manolakis, Digital Signal Processing, (Pearson Prentice Hall 2007).
- S. Dris, P. Bakopoulos, I. Lazarou, B. Schrenk, and H. Avramopoulos, “Low-Complexity DSP Using Undersampling for Heterodyne Receivers in Coherent Passive Optical Access Networks,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (online) (Optical Society of America, 2012), paper We.3.A.4.
- S. Smolorz, E. Gottwald, H. Rohde, D. Smith, and A. Poustie, “Demonstration of a Coherent UDWDM-PON with Real-Time Processing,” in proceedings of Optical Fiber Communication Conference (OFC), OSA Technical Digest (Optical Society of America, 2011), paper PDP4.
- R. Lyons, Understanding DSP, (Prentice Hall PTR 2001).
- R. G. Vaughan, N. L. Scott, and D. Rod White, “The theory of bandpass sampling,” IEEE Trans. Signal Process.39(9), 1973–1984 (1991). [CrossRef]
- A. Leven, N. Kaneda, U.-V. Koc, and Y.-K. Chen, “Frequency Estimation in Intradyne Reception,” IEEE Photon. Technol. Lett.19(6), 366–368 (2007). [CrossRef]
- E. Ip and J. M. Kahn, “Feedforward Carrier Recovery for Coherent Optical Communications,” J. Lightwave Technol.25,2675–2692 (2007).

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