Feed-forward carrier phase recovery for offset-QAM Nyquist WDM transmission

Haoyuan Tang; Meng Xiang; Songnian Fu; Ming Tang; Perry Shum; Deming Liu

doi:10.1364/OE.23.006215

1. Introduction

As Internet traffic demands impose great challenges on current fiber-optical transmission, intense researches have been devoted to increasing the spectral efficiency (SE), in order to scale the fiber optical transmission capacity. The use of advanced modulation format is one of effective ways to improve SE [1–3]. 1-Tbit/s dual-carrier transmission over 320-km standard single-mode fiber (SSMF) is demonstrated using dual polarization (DP) 64-ary quadrature amplitude modulation (64-QAM) at 64 Gbaud [1]. However, the advantage of advanced modulation formats is weakened due to the high optical-signal-noise-ratio (OSNR) requirement and complex generation together with reception implementation. Alternatively, optically multiplexed multicarrier systems with channel spacing equal to symbol rate are currently received worldwide attentions [4–10]. From a view of implementation complexity, Nyquist wavelength division multiplexing (Nyquist WDM) may be an optimum alternative compared with orthogonal frequency-division multiplexing (OFDM) [4, 5]. However, the inter-channel interference (ICI) penalty is inevitable due to the narrow channel spacing in Nyquist WDM transmission. Offset quadrature amplitude modulation (OQAM) is recently proposed and investigated in optically Nyquist WDM superchannel to relax the stringent component requirements of transmitter-side (Tx) spectrum shaping and improve transmission performance [11,12]. Thanks to the half-symbol delay between in-phase and quadrature components, OQAM signal can be de-multiplexed at the receiver-side (Rx) without ICI even on the condition of severe spectral overlapping with adjacent channels [11–18]. However, different from QAM signal where phase noise leads to sole constellation rotation, phase noise results in additional crosstalk for OQAM [13, 15]. Therefore, OQAM imposes a strict requirement on laser linewidth, and generally a laser linewidth of several kHz is indispensable for achieving its benefit.

So far, many carrier phase recovery (CPR) algorithms [19–23] have been successfully proposed for QAM to improve the laser linewidth tolerance. Among them, the feed-forward blind phase search (BPS) and QPSK partitioning schemes are attractive because of good linewidth tolerance, compared with other feed-back phase lock loop schemes [19,22]. Normally, all those CPR schemes for QAM signal are implemented after adaptive channel equalization. However, as for OQAM signal, because of the additional crosstalk induced by phase noise, phase noise perturbs the adaptive channel equalization with rather low equivalent OSNR. As a result, laser linewidth with only 6 kHz is commonly used to avoid phase noise induced crosstalk [11, 12]. Recently, a CPR scheme incorporated into the adaptive channel equalization is proposed in a feedback manner [13], and its effectiveness is verified with 4-OQAM in long haul transmission [14]. Nonetheless, the linewidth tolerance of such scheme is limited by the feed-back delay. Moreover, training sequences for initialization are essential for the convergence process in order to achieve correct CPR operation.

In this paper, we carry out a semi-analytical investigation of additional crosstalk induced by phase noise in OQAM Nyquist WDM system and find that the CPR has to be implemented prior to the inter-symbol-interference (ISI) equalization. Then, to the best of our knowledge, a modified feed-forward blind phase search (M-BPS) CPR scheme for OQAM is proposed for the first time. The effectiveness of the proposed M-BPS scheme is verified under scenario of 5-channel PDM 4-OQAM/ 16-OQAM Nyquist WDM systems with a symbol rate of 28 Gbaud.

2. Phase noise induced crosstalk

Figure 1 shows the mathematical model of OQAM Nyquist WDM system. The optical field of Rx signal at the i-th channel can be represented as [11]:

E_{i} (t) = E_{0} \sum_{k = i - I}^{k = i + I} \sum_{n = - \infty}^{\infty} (a_{k, n} I_{k, i} (t - n T) + j b_{k, n} Q_{k, i} (t - n T)) e x p (j (ω_{k} - ω_{i}) n T + j ϕ_{k})

ω_{k}

and

ϕ_{k}

are the frequency and phase of the k-th carrier, respectively, where

ω_{k} - ω_{i} = 2 π (k - i) / T

,

ϕ_{k} - ϕ_{i} = (k - i) π / 2

. 2I + 1 indicates the number of channels.

h_{s} (t)

represents the pulse shape after signal generation, while

h_{s}^{*} (- t)

represents the impulse response of matched filter at the receiver side [11].

I_{k, i} (t)

and

Q_{k, i} (t)

represent the impulse response of the in-phase and quadrature tributaries of the k-th channel after the filter targeted to de-multiplex the i-th channel, and can be represented as [11]:

I_{k, i} (t) = \int_{- \infty}^{\infty} h_{s} (t - τ) e^{j (ω_{k} - ω_{i}) (t - τ)} h_{s}^{*} (- τ) d τ

Q_{k, i} (t) = \int_{- \infty}^{\infty} h_{s} (t - τ - \frac{T}{2}) e^{j (ω_{k} - ω_{i}) (t - τ)} h_{s}^{*} (- τ) d τ

By setting

t = m T

and

(m + 0.5) T

for the in-phase and quadrature tributaries in Eq. (1), respectively, we can obtain the even sample

R_{i, m}^{0}

and odd sample

R_{i, m}^{1}

for the i-th channel.

\begin{array}{l} R_{i, m}^{0} \propto (a_{i, m} I_{i, i} (0) + j b_{i, m} Q_{i, i} (0)) e x p (j ϕ_{i}) \\ + \sum_{n \neq m} (a_{i, n} I_{i, i} ((m - n) T) + j b_{i, n} Q_{i, i} ((m - n) T)) e x p (j ϕ_{i}) \\ + \sum_{k \neq i} \sum_{n} (a_{k, n} I_{k, i} ((m - n) T) + j b_{k, n} Q_{k, i} ((m - n) T)) e x p (j (k - i) π / 2) e x p (j ϕ_{i}) \end{array}

\begin{array}{l} R_{i, m}^{1} \propto (a_{i, m} I_{i, i} (0.5 T) + j b_{i, m} Q_{i, i} (0.5 T)) e x p (j ϕ_{i}) \\ + \sum_{n \neq m} (a_{i, n} I_{i, i} ((m - n + 0.5) T) + j b_{i, n} Q_{i, i} ((m - n + 0.5) T)) e x p (j ϕ_{i}) \\ + \sum_{k \neq i} \sum_{n} (a_{k, n} I_{k, i} ((m - n + 0.5) T) + j b_{k, n} Q_{k, i} ((m - n + 0.5) T)) e x p (j (k - i) π / 2) e x p (j ϕ_{i}) \end{array}

By combining the real part of

R_{i, m}^{0}

and the imaginary part of

R_{i, m}^{1}

, the recovered sample

R_{i, m}

can be represented as:

R_{i, m} = ℜ (R_{i, m}^{0}) + j ℑ (R_{i, m}^{1})

The first, second, and third terms of Eq. (4) and (5) represent the signal, ISI and ICI, respectively. From Eq. (4)–(6), we can see that both ICI and ISI for the specific symbol are related to phase noise

ϕ_{i}

. Here we define two normalized parameters, ICI to signal power ratio (CSPR) and ISI to signal power ratio (ISPR) to give a quantitative evaluation of ISI and ICI with respect to the phase noise

ϕ_{i}

.

C S P R = \sum_{k \neq i} \sum_{n} \frac{{| R_{i, m}^{k, n} |}^{2}}{{| a_{k, n} + j b_{k, n} |}^{2}} \times \frac{1}{| I_{i, i} (0) |^{2}}

I S P R = \sum_{n \neq m} \frac{{| R_{i, m}^{i, n} |}^{2}}{{| a_{i, n} + j b_{i, n} |}^{2}} \times \frac{1}{| I_{i, i} (0) |^{2}}

where

a_{k, n} + j b_{k, n}

represents the transmitted n-th symbol of the k-th channel,

{| I_{i, i} (0) |}^{2}

is a normalized factor during the calculation of CSPR and ISPR,

R_{i, m}^{k, n}

represents the crosstalk from the transmitted symbol

a_{k, n} + j b_{k, n}

into the targeted recovered sample

R_{i, m}

in i-th channel. Although

R_{i, m}^{k, n}

shares the same physical meaning for both QAM and OQAM signal, its mathematical representation is different, due to the fact the mathematical model of QAM and OQAM signal is different. The

R_{i, m}^{k, n}

for QAM signal is represented as:

R_{i, m}^{k, n} \propto (a_{k, n} + j b_{k, n}) I_{k, i} ((m - n) T) e x p (j ϕ_{k})

While the

R_{i, m}^{k, n}

for OQAM signal is represented as:

\begin{array}{l} R_{i, m}^{k, n} \propto ℜ {(a_{k, n} I_{k, i} ((m - n) T) + j b_{k, n} Q_{k, i} ((m - n) T)) e x p (j (k - i) π / 2) e x p (j ϕ_{i})} \\ + j ℑ {(a_{k, n} I_{k, i} ((m - n + 0.5) T) + j b_{k, n} Q_{k, i} ((m - n + 0.5) T)) e x p (j (k - i) π / 2) e x p (j ϕ_{i})} \end{array}

During the calculation, 5 channels with memory length of 1000 symbols for individual channel are taken into account. In addition, root-raised cosine (RRC) pulse shaping with a roll-off of 0.4 is used to minimize ISI during OQAM/QAM signal generation [11,15]. Then, the relationship between phase noise

ϕ_{i}

and CSPR, ISPR for different modulation formats can be calculated, respectively, as shown in Fig. 2. For QAM, ISPR is determined by the signal pulse shape, while CSPR is determined by the spectral overlapping with adjacent channels. As we can see that, CSPR and ISPR remain constant whatever

ϕ_{i}

varies for QAM signal, indicating of only constellation rotation by the phase noise. However, for OQAM signal, CSPR and ISPR show a parabolic relationship with phase noise

ϕ_{i}

and reach the maximum value when

ϕ_{i}

is equal to

π / 2

, indicating of the phase noise induced additional crosstalk. When

ϕ_{i}

is equal to 0, the CSPR becomes 0 even on condition of severe spectral overlapping with adjacent channels. At the same time, the ISPR reaches minimal value which is the same as that of QAM. Therefore, if the phase noise

ϕ_{i}

is properly compensated, the OQAM signal outperforms the QAM signal due to the low CSPR. Specifically, the calculated constellations after receiver-side coherent detection with a phase noise of

0^{0}

and

45^{0}

for 4-QAM and 4-OQAM are presented in Fig. 3. As we can see, clearer constellation is obtained for 4-OQAM on condition of totally compensated phase noise (

ϕ_{i} = 0^{0}

). However, the situation is worsened on condition of

ϕ_{i} = 45^{0}

, due to the phase noise induced crosstalk for 4-OQAM. It is well known that traditional feed-forward CPR algorithms of QAM signal, such as BPS and QPSK partition method, are commonly implemented after adaptive channel equalization. Adaptive channel equalization using either constant modulus algorithm (CMA) or multimodulus algorithms (MMA), is performed for QAM signal in order to realize both polarization de-multiplexing and ISI equalization. However, for OQAM signal, ISPR and CSPR are determined by phase noise and reach the maximum value, when the phase noise is

π / 2

. The large ISPR and CSPR indicate a sharp decrease of equivalent OSNR for the recovered sample

R_{i, m}

, which will perturb the ISI equalization during adaptive channel equalization, especially when the signal laser source has wide linewidth. Therefore, for OQAM signal, ISI equalization has to be set behind the CPR module. Moreover, CPR algorithms of QAM signal only take into account of constellation rotation in the presence of phase noise. As a result, CPR algorithms of QAM signal cannot simply apply to OQAM signal [14].Therefore, for OQAM signal, the CPR module is compulsory to both correct the constellation rotation and mitigate the phase-noised induced additional crosstalk. After a function separation of polarization de-multiplexing and ISI equalization, a new DSP flow with a linewidth-tolerant CPR scheme for OQAM signal can be anticipated.

Fig. 1 . Mathematical model of OQAM Nyquist WDM system.

Download Full Size | PDF

Fig. 2 Variation of ISPR and CSPR with respect to phase noise for QAM and OQAM signal, respectively.

Download Full Size | PDF

Fig. 3 Signal constellation comparison.

Download Full Size | PDF

3. M-BPS CPR

Here, we propose a modified blind phase search (M-BPS) CPR algorithm using even sampling symbols $R_{i, m}^{0}$ and odd sampling symbols $R_{i, m}^{1}$ normalized by the average power simultaneously, as shown in Fig. 4. $R_{i, m}^{0}$ and $R_{i, m}^{1}$ are firstly rotated by a number of B uniformly distributed test phases $ϕ_{b}$ with:

ϕ_{b} = \frac{b}{B} \cdot π, b = 1, 2 \cdot \cdot \cdot B

The recovered sample

R_{i, m, b}

is obtained according to:

R_{i, m, b} = ℜ {R_{i, m}^{0} \cdot \exp (- j ϕ_{b})} + j ℑ {R_{i, m}^{1} \cdot \exp (- j ϕ_{b})}

Then

R_{i, m, b}

is fed into a hard decision circuit and the squared distance to the closest constellation point is calculated in the complex plane:

{| d_{i, m, b} |}^{2} = {| R_{i, m, b} - d e c i s i o n (R_{i, m, b}) |}^{2}

In order to mitigate the additive noise, L consecutive input symbols with the same test phases are summed as follows:

e_{i, m, b} = \sum_{n = - f l o o r (\frac{L}{2}) + 1}^{n = c e l l (\frac{L}{2})} {| d_{i, m + n, b} |}^{2}

The desired phase angle for the m-th symbol is determined by

b_{i, m}^{d}

and represented by

ϕ_{Target}

.

b_{i, m}^{d} = {b | m i n (e_{i, m, b}), b = 1, 2 \cdot \cdot \cdot B}

ϕ_{T \arg et} = \frac{b_{i, m}^{d}}{B} \cdot π

After phase recovery with the desired phase angle, odd and even sampling symbols are reshaped by parallel-to-serial conversion. Therefore, we can obtain the T/2-spaced digital OQAM signal, which can be fed into the following T/2-spaced adaptive channel equalization based on a modified least-mean-square (M-LMS) algorithm for the ISI equalization [15]. In order to verify the assumption that the minimal squared distance leads to the completed phase noise compensation, numerical calculation of the relationship between the test phases and normalized squared distance, in case the phase noise is

ϕ_{i} = π / 6

, is conducted for 4-OQAM and 16-OQAM, respectively, as shown in Fig. 5. When the test angle is approaching the actual phase noise, there is a steep decrease in normalized squared distance and its minimum value is near the desired phase noise to be compensated.

Fig. 4 Block diagram of proposed M-BPS scheme for OQAM signal.

Download Full Size | PDF

Fig. 5 Relationship between test angle and normalized squared distance on the condition of phase noise $ϕ_{i} = π / 6$ .

Download Full Size | PDF

4. Results and discussion

The multi-carrier source is obtained from an optical comb generator (OCG) with channel spacing of 28 GHz. The date trains consist of 28 Gbit/s $2^{17}$ -1 pseudo-random binary sequences (PRBS) and differential coding is used to solve the phase ambiguity problem. These logic data are used to generate multi-level electrical signals and RRC digital finite-impulse-response (FIR) filter with a roll-off coefficient of 0.4 is applied. The equivalent frequency response of the driving amplifier and the modulator’s electronic interface is assumed to be shaped with 5th-order Bessel filter with a 3dB bandwidth of 0.75 times baud rate. For the purpose of OQAM signal generation, the quadrature component is delayed by half symbol duration with respect to the in-phase component. Then, 5 carriers are, respectively, introduced to 5 parallel modulators driven by these electrical signals. Polarization division multiplexing (PDM) is achieved through a delay of 180 symbols between two polarization tributaries. After polarization multiplexing, those modulated carriers are phase shifted by $Φ_{k} = (k - 3) \times Δ Φ (k = 1 \cdot \cdot \cdot 5)$ . Especially, $Δ Φ$ of $90^{0}$ is indispensable for optimal performance. At the receiver side, amplified spontaneous emission (ASE) noise loading is used to adjust the OSNR. Then, a 5th-order Bessel electronic filter with 3dB bandwidth of 0.75 times baud rate is used to emulate the Rx electrical bandwidth after the polarization-diverse and phase-diverse coherent detection. Finally, the received analog signals are sampled by 8-bit analogue-to-digital converters (ADCs) with two samples per symbol and fed into the offline digital signal processing (DSP) module. As shown in Fig. 6(b) a matched RRC FIR filter is firstly employed. Polarization de-multiplexing is then performed by four butterfly 1-tap T/2-spaced finite impulse-response (FIR) filters based on the standard constant modulus(CMA) algorithm [24], followed by frequency offset compensation (FOC) using the fast Fourier transform (FFT) method. Note that, the four butterfly 1-tap CMA based FIR filter can only be used for polarization de-multiplexing, not for PMD compensation. Afterwards, feed-forward CPR is implemented with our proposed algorithm. Next, adaptive ISI equalization is performed by 25-tap T/2-spaced FIR filters based on M-LMS algorithm [15]. Chromatic dispersion (CD) is not taken into account, due to the fact that it can be fully compensated by the static digital time/frequency domain filters. Meanwhile, signal polarizations are not maintained but randomly rotated after transmission. Thus, we use the lumped polarization model dispersion (PMD) model [24] to investigate its effect on the proposed CPR scheme, because PMD can lead to not only polarization crosstalk of PDM signal both also differential group delay (DGD)-induced ISI. Finally, bit errors are counted for transmission performance evaluation.

Fig. 6 (a) Simulation setup for OQAM Nyquist WDM system. (b) Receiver side DSP flow.

Download Full Size | PDF

4.1 Effect of phase angle resolution

The required number of test phase B is a significant parameter for the proposed M-BPS scheme and trade-off is expected between the system performance and implementation complexity. Figure 7 shows the required-OSNR penalty at BER = $10^{-3}$ relative to the theoretical limit with respect to test angles, given linewidth and duration product $Δ f * T_{S} = 2 e - 5$ . The performance starts to converge with increasing the number of test angles, indicating of less than 0.05 dB required-OSNR penalty fluctuations with respect to the steady-state value. Consequently, the number of test angles equal to 32 and 64 are the optimum choice for 4-OQAM and 16-OQAM, respectively, and fixed in our next investigation.

Fig. 7 M-BPS performance with respect to the number of test angles.

Download Full Size | PDF

4.2 Effect of PMD

In order to verify the capability of mitigation polarization crosstalk using one tap CMA [25], the Q-factor of received signal with respect to various azimuth and elevation rotation angles, on the condition of linewidth and duration product $Δ f * T_{S} = 2 e - 5$ , is shown in Fig. 8. We can conclude that, negligible performance penalty is observed when there exists polarization crosstalk. Note that the output signal from the 1-tap CMA based equalizer has to be T/2 spaced, which is different from the traditional CMA for QAM signal, where output signal is T spaced. Next, in order to investigate the performance of the proposed CPR scheme in the presence of DGD, the relationship between the Q-factor and the DGD for 4-OQAM and 16-OQAM signal, on the condition of $Δ f * T_{S} = 2 e - 5$ , is shown in Fig. 9. The maximum tolerable DGD for 16-OQAM signal is 6ps, given 1-dB Q-factor penalty. Considering the PMD coefficient of SSMF, the proposed CPR scheme is able to support more 1000km SSMF transmission.

Fig. 8 Relationship between Q-factor and azimuth/elevation rotation angles on the condition of $Δ f * T_{S} = 2 e - 5$ , (a) for 4-OQAM: OSNR = 14dB, (b) for 16-OQAM: OSNR = 21dB.

Download Full Size | PDF

Fig. 9 Relationship between Q-factor and DGD on condition of $Δ f * T_{S} = 2 e - 5$ (for 4-OQAM: OSNR = 14dB; for 16-OQAM: OSNR = 21dB).

Download Full Size | PDF

4.3 Effect of ISI equalization

As described in section 2, the CPR has to be implemented before ISI equalization, which may lead to a reduced equivalent OSNR. In our proposed DSP flow, M-LMS algorithm can offer effective equalizations for bandwidth-limited optical signal on mitigation the ISI impairments. The major sources of ISI for the used optical channel model include CD, PMD, filtering, and residual phase noise. In order to investigate the performance of the proposed CPR scheme in the presence of ISI, the relationship between required OSNR and the 3dB bandwidth of transmitter-side 5th-order Bessel electronic filter for 4-OQAM and 16-OQAM on the condition of various linewidth are shown in Fig. 10. Considering RRC filter with roll-off coefficient of 0.4, the spectrum bandwidth of the received electrical OQAM signal is limited to less than 19.6GHz due to the fact of 28Gbaud symbol rate. As shown in Fig. 10, both cases suffer from performance deterioration when the transmitter-side 3dB bandwidth is under 19.6 GHz. If we further reduce the 3dB bandwidth of transmitter-side electronic filter to the half symbol rate of 14 GHz, severe ISI occurs. Consequently, the performance penalty for 4-OQAM are 0.23 dB and 0.25 dB for $Δ f * T_{S} = 1 e - 6$ and $Δ f * T_{S} = 5 e - 5$ , respectively; the performance penalty for 16-OQAM are 0.28 dB and 0.46 dB for $Δ f * T_{S} = 1 e - 6$ and $Δ f * T_{S} = 2 e - 5$ , respectively. As we can see, our proposed CPR scheme still functions well in the presence of ISI. Next, the optimization of number of taps for the M-LMS based equalizer is investigated. Generally, the optimum number of taps is mainly determined by the impulse response of the in-phase $I_{i, i} (t)$ and quadrature tributaries $Q_{i, i} (t)$ of the i-th channel after wavelength division de-multiplexing. Figure 11(a) shows the relationship between the Q-factor and the number of taps on condition of different laser linewidths, in case the OSNR of 16-OQAM signal is 21dB. When the number of taps is more than 7, there exists negligible performance penalty for the used equalizer. Furthermore, we can observe that the laser linewidth has almost no effect on the optimum number of taps. Next, considering the PMD-induced ISI, we investigate the relationship between Q-factor and number of taps in the presence of various DGD on condition of $Δ f * T_{S} = 2 e - 5$ , in case the OSNR of 16-OQAM signal is 21dB. As shown in Fig. 11(b), within the range of tolerable DGD, the DGD shows negligible influence on the optimum number of taps for the used equalizer. Therefore, 25-tap modified-LMS is enough to mitigate the ISI.

Fig. 10 Relationship between required OSNR and transmitter-side 3dB bandwidth for (a) 4-OQAM, (b) 16-OQAM.

Download Full Size | PDF

Fig. 11 Relationship between Q-factor and number of taps for16-OQAM signal, with respect to (a) different laser linewidths, (b) DGD on the condition of $Δ f * T_{S} = 2 e - 5$ .

Download Full Size | PDF

4.4 Phase noise tolerance

Then, the optimization of block size for our proposed M-BPS scheme is investigated. Generally, the optimal block size is determined by a trade-off between amplified spontaneous emission (ASE) noise and laser linewidth induced phase noise. Large block size is helpful to average the ASE noise, while small block size is preferred to avoid the de-correlation of phase noise within the block, along with the reduction of complementation complexity. The relationship between required-OSNR at BER = $10^{-3}$ and block size is presented in Fig. 12 with different $Δ f * T_{S}$ for 4-OQAM and 16-OQAM, respectively. As we can see, large block size is preferred with narrow laser linewidth while small block size is preferred with wide laser linewidth. Moreover, the optimal block size can be also obtained with different laser linewidth. For example, the optimal block size of 30 can be obtained for 4-OQAM given $Δ f * T_{S}$ equal to $2 \times 10^{-4}$ . Under the optimal block size, the tolerance against phase noise for our proposed M-BPS scheme is investigated and the required-OSNR penalty at BER = $10^{-3}$ with different $Δ f * T_{S}$ is shown in Fig. 13. As we can see that, the maximum tolerable $Δ f * T_{S}$ for 4-OQAM and 16-OQAM are $6.5 \times 10^{-4}$ and $1.1 \times 10^{-4}$ , respectively, given 1-dB required-OSNR penalty. Assuming a symbol rate of 28 Gbaud, the tolerable linewidths are 18.2 MHz and 3.08 MHz for 4-OQAM and 16-OQAM, respectively.

Fig. 12 Required OSNR vs the block size under different $Δ f * T_{S}$ .

Download Full Size | PDF

Fig. 13 Required OSNR penalty against the linewidth and symbol duration product $Δ f * T_{S}$ .

Download Full Size | PDF

Conclusion

We carry out a semi-analytical investigation on the phase-noise induced additional crosstalk during OQAM Nyquist WDM transmission. Our investigations shows that the CPR of OQAM signal has to be implemented prior to the ISI equalization, because of phase noise induced additional crosstalk. After a function separation of polarization de-multiplexing and ISI equalization, we propose a new DSP flow with a linewidth-tolerant blind feed-forward CPR scheme for OQAM signal. The proposed M-BPS scheme can greatly relax the strict requirement on the laser linewidth, and a tolerance of linewidth and symbol duration products of $1.1 \times 10^{-4}$ and $6.5 \times 10^{-4}$ is secured for 16-OQAM and 4-OQAM, respectively, given 1-dB required-OSNR penalty at BER = $10^{-3}$ .

Acknowledgments

This work was supported by National Natural Science Foundation of China (61275069, 61331010) and National Key Scientific Instrument and Equipment Development Project (No. 2013YQ16048702).

References and links

1. F. Buchali, K. Schuh, L. Schmalen, W. Idler, E. Lach, and A. Leven, “1-Tbit/s dual-carrier DP 64QAM transmission at 64Gbaud with 40% overhead soft-FEC over 320km SSMF,” Optical Fiber Communication Conference (2013), paper OTh4E.3. [CrossRef]

2. J. Yu, X. Zhou, Y. K. Huang, S. Gupta, M. F. Huang, T. Wang, and P. Magill, “112.8-Gb/s PM-RZ-64QAM optical signal generation and transmission on a 12.5 GHz WDM grid,” Optical Fiber Communication Conference (2010), paper OThM1. [CrossRef]

3. X. Zhou, J. Yu, M.-F. Huang, Y. Shao, T. Wang, L. Nelson, P. Magill, M. Birk, P. I. Borel, D. W. Peckham, R. Lingle Jr, and B. Zhu, “64-Tb/s, 8 b/s/Hz, PDM-36QAM transmission over 320 km using both pre- and post-transmission digital signal processing,” J. Lightwave Technol. 29(4), 571–577 (2011). [CrossRef]

4. R. Schmogrow, R. Bouziane, M. Meyer, and P. A. Milder, “Real-Time Digital Nyquist-WDM and OFDM Signal Generation: Spectral Efficiency Versus DSP Complexity,” European Conference on Optical Communications (2012), paper Mo.2.A. [CrossRef]

5. G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist-WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22(15), 1129–1131 (2010). [CrossRef]

6. A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. 17(2), 504–506 (2005). [CrossRef]

7. G. Bosco, V. Curri, A. Carena, P. Poggiolini, and F. Forghieri, “On the performance of Nyquist-WDM terabit superchannels based on PM-BPSK, PM-QPSK, PM-8QAM or PM-16QAM subcarriers,” J. Lightwave Technol. 29(1), 53–61 (2011). [CrossRef]

8. X. Zhou, L. E. Nelson, P. Magill, R. Isaac, B. Zhu, D. W. Peckham, P. I. Borel, and K. Carlson, “PDM-Nyquist-32QAM for 450-Gb/s Per-channel WDM transmission on the 50 GHz ITU-T grid,” J. Lightwave Technol. 30(4), 553–559 (2012). [CrossRef]

9. R. Schmogrow, M. Winter, M. Meyer, D. Hillerkuss, S. Wolf, B. Baeuerle, A. Ludwig, B. Nebendahl, S. Ben-Ezra, J. Meyer, M. Dreschmann, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “Real-time Nyquist pulse generation beyond 100 Gbit/s and its relation to OFDM,” Opt. Express 20(1), 317–337 (2012). [CrossRef] [PubMed]

10. J. Wang, C. Xie, and Z. Pan, “Generation of spectrally efficient Nyquist-WDM QPSK signals using DSP techniques at transmitter,” Optical Fiber Communication Conference (2012), paper OM3H.5. [CrossRef]

11. J. Zhao and A. D. Ellis, “Offset-QAM based coherent WDM for spectral efficiency enhancement,” Opt. Express 19(15), 14617–14631 (2011). [CrossRef] [PubMed]

12. M. Xiang, S. Fu, M. Tang, H. Tang, P. Shum, and D. Liu, “Nyquist WDM superchannel using offset-16QAM and receiver-side digital spectral shaping,” Opt. Express 22(14), 17448–17457 (2014). [CrossRef] [PubMed]

13. J. Fickers, A. Ghazisaeidi, M. Salsi, and F. Horlin, “Multicarrier offsetQAM modulations for coherent optical communication systems,” Optical Fiber Communication Conference (2014), paper M2A.5. [CrossRef]

14. J. Fickers, A. Ghazisaeidi, M. Salsi, G. Charlet, P. Emplit, and F. Horlin, “Multicarrier Offset-QAM for Long-Haul Coherent Optical Communications,” J. Lightwave Technol. 30(11), 1664–1676 (2014).

15. S. Randel, A. Sierra, X. Liu, and S. Chandrasekhar, “Study of Multicarrier Offset-QAM for Spectrally Efficient Coherent Optical Communications,” European Conference on Optical Communications (2011), paper Th.11.A.1. [CrossRef]

16. S. Randel, S. Corteselli, S. Chandrasekhar, A. Sierra, X. Liu, P. Winzer, T. Ellermeyer, J. Lutz, and R. Schmid, “Generation of 224-gb/s multicarrier offset-QAM using a real-time transmitter,” Optical Fiber Communication Conference (2012), paper OM2H.2.

17. Z. Li, T. Jiang, H. Li, X. Zhang, C. Li, C. Li, R. Hu, M. Luo, X. Zhang, X. Xiao, Q. Yang, and S. Yu, “Experimental demonstration of 110-Gb/s unsynchronized band-multiplexed superchannel coherent optical OFDM/OQAM system,” Opt. Express 21(19), 21924–21931 (2013). [CrossRef] [PubMed]

18. F. Horlin, J. Fickers, P. Emplit, A. Bourdoux, and J. Louveaux, “Dual-polarization OFDM-OQAM for communications over optical fibers with coherent detection,” Opt. Express 21(5), 6409–6421 (2013). [CrossRef] [PubMed]

19. T. Pfau, S. Hoffmann, and R. Noe, “Hardware-efficient coherent digital receiver concept with feed forward carrier recovery for M-QAM constellations,” J. Lightwave Technol. 27(8), 989–999 (2009). [CrossRef]

20. T. Pfau and R. Noe, “Phase-noise-tolerant two-stage carrier recovery concept for higher order QAM formats,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1210–1216 (2010). [CrossRef]

21. X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receivers with M-QAM modulation format,” IEEE Photon. Technol. Lett. 22(14), 1051–1053 (2010). [CrossRef]

22. H. Louchet, K. Kuzmin, and A. Richter, “Improved DSP algorithms for coherent 16-QAM transmission,” European Conference on Optical Communications (2008), paper Tu.1.E.6. [CrossRef]

23. D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightwave Technol. 24(1), 12–21 (2006). [CrossRef]

24. C. Xie and L. Moller, “The accuracy assessment of different polarization mode dispersion models,” Opt. Fiber Technol. 12(2), 101–109 (2006). [CrossRef]

25. T. F. Detwiler, A. J. Stark, and Y. T. Hsueh, “Offset QPSK receiver implementation in 112Gb/ s coherent optical networks,” European Conference on Optical Communications (2010), paper P3.24.

Feed-forward carrier phase recovery for offset-QAM Nyquist WDM transmission

Abstract

1. Introduction

2. Phase noise induced crosstalk

3. M-BPS CPR

4. Results and discussion

4.1 Effect of phase angle resolution

4.2 Effect of PMD

4.3 Effect of ISI equalization

4.4 Phase noise tolerance

Conclusion

Acknowledgments

References and links

Cited By

Figures (13)

Equations (16)

Optics Express