Internet traffic is growing exponentially worldwide, driven by multimedia applications such as video sharing and point-to-point file transfers. By 2014, demand is expected to increase by 64 exabytes (or billion gigabytes) per month, equivalent to over three million years' worth of DVD-quality video.^{1} How to keep ever-greater volumes of data moving instantaneously from place to place without bottlenecks poses a challenge to the speed of both electrical and optical components. If the backbone networks were to fail, it would affect communication between continents and cities and consequently business, education, and other kinds of critical information sharing. Currently, keeping up the pace of data would require laying down more fiber to increase capacity. Yet according to the Shannon limit—a measure of the information transmission rate in the presence of noise—higher-order modulation formats are needed to accommodate the increased data traffic while keeping changes to the system configuration to a minimum in the interest of cost. On the receiver side, a local oscillator (LO) laser must be at the same frequency as the received signal to obtain the original intensity and phase information. But time-varying laser phase noise introduces distortions. Consequently, the LO laser should be locked to the received signal's phase to recover the transmitted signal phase.

Full information (i.e., the amplitude and phase) of the optical electric field can be preserved in digital coherent receivers. Accordingly, rather than using an optical phase-locked loop to lock the phase of the LO laser to the transmitter laser—which is sensitive to feedback delay in ultra-high-speed (e.g., 100Gbits/s) optical systems—an LO laser can run freely (i.e., require no extra control to adjust frequency and phase) where we are able to recover its dithering phase using a digital signal processing (DSP) phase-estimation algorithm. A conventional scheme^{2} has been proposed to raise received M-ary (the signal phase is chosen from M different phases) phase-shift-keying (PSK) signals to the Mth power for estimating the carrier phase. Unfortunately, such methods are susceptible to nonlinear phase unwrapping and to the block-length effect.^{3} The latter refers to the influence of the chosen memory length on the accuracy of the estimated carrier phase. A shorter filter length is preferred for tracking rapidly varying phase noise, and vice versa. Additional research is required to apply the Mth power to quadrature amplitude modulation (QAM) formats, such as those used for increasing channel capacity. To get around these problems, we propose using adaptive decision-aided phase estimation, which is capable of adjusting the filter weight based on the received signal information.

**Figure 1. **Structure of the adaptive decision-aided algorithm. r(k): Received signal. α and 1−α: Weights assigned to the previous and current phase reference. m,

: The decision of the received symbol and its conjugate. T: Symbol duration (the minimum time interval between condition changes of a signal). V(k+1): Phase reference.

To eliminate the block-length effect found in other phase-estimation algorithms and improve performance, we introduce a first-order adaptive filter to assign different weights α and 1−α to the previous and current phase reference. Figure 1 shows the structure of our algorithm. The received signal *r(k)* is fed into the adaptive decision-aided module to generate the phase reference *V(k+ 1)*, which is used to de-rotate the next signal *r(k+ 1)*. Known training data is sent to the receiver to acquire the characteristics of a given channel (the channel used to examine the algorithm), thus adjusting the weight α to optimize operation of the adaptive filter.

The weight α is chosen at each time *k* based on observations {*r*(*l*); 0≤*l*≤*k*}to minimize the conditional risk function *R(k)*. Minimizing *R(k)* for each sample of observations {*r*(*l*), 0≤ *l*≤*k*} in turn minimizes the average risk *E*[*R(k)*]. The optimal value of α at each time *k* is obtained by taking the first derivative of *R(k)*with respect to α, yielding α=*A(k)*/*B(k)*. Details are available elsewhere.^{3} Note that the numerator *A(k)* and denominator *B(k)* are formed recursively, thus requiring little memory and low computational complexity.

**Figure 2. **The trajectory of the filter gain

with ideal decision feedback in a simulated quadrature phase-shift-keying system (σ

_{p}^{2}=1×10

^{−3} rad

^{2}). γ

_{b}: Values of signal-to-noise ratio.

Figure 2 shows the trajectory of the filter gain α(*k*) versus different values of signal-to-noise ratio (SNR), γ_{b}. Simulation shows that starting from α(0)= 0, α(*k*) increases to a steady-state value between 0 and 1 as *k* increases. Thus, the gain 1−α(*k*) on the current input decreases from 1 at *k*=0 to a steady-state value less than 1. Figure 2 clearly shows that the higher the SNR, the smaller the value α(*k*), because the current input signal gives much more information on *V*(*k*+1) than the previous reference phase at high SNR.

**Table 1. **Linewidth per laser/symbol rate at 1dB penalty for different phase-estimation algorithms at BER=10−4. BER: Bit error rate. DA ML: Decision-aided maximum likelihood. L: Memory length. NLMS: Normalized least-mean square. QAM: Quadrature amplitude modulation.

Formats | DA ML | Adaptive DA | NLMS (*μ*=0.2) |
---|

Optimum *L* |

QPSK | 2.2 ×10^{−4} | 2.5×10^{−4} | 2.3×10^{−4} |

8 PSK | 3.0 × 10^{−5} | 4.1×10^{−5} | 3.8 ×10^{−5} |

16 PSK | 8.8 × 10^{−6} | 9.5×10^{−6} | 9.5×10^{−6} |

16 QAM | 2.5 × 10^{−5} | 2 ×10^{−5} | 1 ×10^{−5} |

Table 1 lists the maximum tolerance to laser linewidth leading to a 1−dB γ_{b} penalty at BER (bit error rate) = 10^{−4} for each modulation format. Clearly, the adaptive decision-aided (DA) algorithm improves laser linewidth tolerance in M-PSK systems. Also, our simulation results show that the algorithm performs consistently better in M-PSK modulation formats than DA maximum likelihood (ML) and normalized least-mean square (NLMS) algorithms.

In summary, we have proposed an adaptive decision-aided algorithm that does not suffer from the block-length effect. Moreover, it has a strong adaptive capability that enables it to recover the carrier phase effectively without knowledge of the statistics of the phase and additive noise, or any preset parameters. It can be applied in different modulation formats and has a better laser linewidth tolerance than DA ML and NLMS algorithms especially in M-PSK formats. For these reasons, the adaptive decision-aided algorithm is well-suited to reconfigurable networks. In the future, we will investigate and further optimize its performance in the presence of fiber nonlinearity and enhanced electrical phase noise.

Changyuan Yu, Pooi-Yuen Kam, Shaoliang Zhang

National University of Singapore

Singapore, Singapore

Changyuan Yu is currently an assistant professor in the Department of Electrical and Computer Engineering. He received his PhD in electrical engineering from the University of Southern California (2005). His research focuses on optical fiber communication systems. He has authored or co-authored over 100 research papers.

Pooi-Yuen Kam obtained his SB, SM, and PhD in electrical engineering from the Massachusetts Institute of Technology (1972, 1973, and 1976, respectively). Since 1978, he has been with the Department of Electrical and Computer Engineering, National University of Singapore, where he is now a professor. His research interests are in digital communication.

Shaoliang Zhang received his BEng in communication engineering from Beijing University of Posts and Telecommunications (2006). He is now pursuing a PhD in the Department of Electrical and Computer Engineering, National University of Singapore. His research focuses on digital signal processing for coherent optical communication systems.

Jian Chen

Nanjing University of Posts and Telecommunications

Nanjing, China

Jian Chen received his BS, MS, and PhD in electronic engineering from Southeast University, Nanjing, China (1988, 1990, and 1994, respectively). He is currently a professor. His research interests include coherent optical communication, visible light communication, and optical access networks.

References:

2. A. J. Viterbi, A. N. Viterbi, Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,

*IEEE Trans. Inf. Theory* 29, no. 4, pp. 543-551, 1983. doi:

10.1109/TIT.1983.10567133. S. Zhang, P. Y. Kam, C. Yu, J. Chen, Decision-aided carrier phase estimation for coherent optical communications,

*J. Lightw. Technol. 28*, no. 11, pp. 1597-1607, 2010. doi:

10.1109/JLT.2010.2048198