Modulation-format-independent blind phase search algorithm for coherent optical square M-QAM systems

Xian Zhou; Kangping Zhong; Yuliang Gao; Chao Lu; Alan Pak Tao Lau; Keping Long

doi:10.1364/OE.22.024044

1. Introduction

To satisfy the ever-increasing demand for communication bandwidth, we have witnessed tremendous improvements in high-speed optical transmission systems over the past few years [1, 2]. Advanced modulation formats, such as M-ary quadrature amplitude modulation (M-QAM) (4-QAM, 16-QAM, 64-QAM, etc.), are indispensable to achieve the high transmission capacity. For a target modulation format, the special digital signal processing (DSP) technologies should be employed to compensate the transmission impairments. In this case, the signal modulation format is required to be known and fixed. Recently, however, elastic optical network (EON) [3, 4] is proposed to reduce the bandwidth wastage caused by the granularity mismatch between the client layer and the physical layer and to better match emerging dynamic and heterogeneous network traffic patterns. EON is expected to maximize overall efficiency by using flexible transmission systems with adaptive baud rate, bandwidth, and modulation format. Therefore, one of key challenges for DSP algorithms is the need to be independent or transparent to modulation format [5].

In this article, we mainly focus on developing modulation-format-independent (MFI) DSP for carrier phase estimation(CPE). As one of key DSP units, tremendous studies have been done on CPE, such as Viterbi-Viterbi phase estimation (VVPE) for quadrature phase shift keying (QPSK) [6], QPSK partitioning method for 16-QAM [7], blind phase search (BPS) for M-QAM [8], superscalar parallelization based CPE for M-QAM [9], and some multi-stages hybrid CPE techniques [10–14], etc. It is not difficult to realize that a priori knowledge of the modulation format is necessary to these CPE algorithms. In our previous work of [15], a universal phase-lock-loop based CPE (U-CPE-PLL) was proposed as a MFI algorithm. However, U-CPE-PLL still has two weaknesses: 1) the feedback loop causes a tradeoff between the linewidth tolerance capability and the speed requirement of hardware, and 2) a convergence process is required to achieve the right phase estimation. Therefore, in this paper we propose a MFI-BPS algorithm which not only is totally implemented in a feed-forward manner, but also maintains the known excellent linewidth tolerance feature of BPS. The effectiveness and performance of the proposed MFI-BPS algorithm are analyzed and demonstrated in simulations and on 224 Gbit/s polarization multiplexing 16-QAM (PM-16QAM) experiments.

2. Operation principle of MFI-BPS algorithm

It is well-known that the traditional BPS algorithm [8] can achieve nearly optimal linewidth tolerance for arbitrary M-QAM but is not transparent to modulation format since a decision unit is required to provide the reference signal for Euclidean distance calculation. To achieve MFI, our proposed symmetric BPS (S-BPS) algorithm [16] is employed here, in which a common phase error detection (PED) can be applied to all M-QAM (M = 2²ⁿ, n = 1, 2…) formats without decision, followed by another blind searching process in the initial state to determine a parameter N_CA of S-BPS without a prior knowledge of the modulation format, which can be regarded as a modulation format recognition (MFR) process. In the following, we will introduce our proposed MFI-BPS in detail.

2.1 Symmetric BPS algorithm for square M-QAM

Fig. 1 shows the block diagram of the S-BPS CPE algorithm. The input symbol-rate sample r(k) is rotated by test phase angles $φ_{b}$ ,

z (k, b) = r (k) \cdot \exp (j φ_{b}), [φ_{b} = \frac{b}{B} \cdot \frac{π}{2} - \frac{π}{4}, b = 1, 2, ..., B]

where B denotes the number of the test phase angles for CPE. Then, the real and imaginary part of the rotated sample z(k,b) – I(k,b) and – Q(k,b) are fed into a constellation aggregation (CA) module instead of a decision unit given by,

{\begin{cases} I (k, b, i) = a b s (I (k, b, i - 1)) - \frac{D}{2^{i - 1}} \\ Q (k, b, i) = a b s (Q (k, b, i - 1)) - \frac{D}{2^{i - 1}} \end{cases}, i = 1, ..., N_{C A}

where abs(.) stands for returning the absolute value of the input. The parameters N_CA denotes the number of iteration calculation in CA and D represents a “center distance” of the constellation in one quadrant. Note that D will be unchanged with modulation format for power-normalized signals.

Fig. 1 Block diagram of the S-BPS algorithm.

Download Full Size | PDF

Based on the symmetry of square M-QAM (M = 2²ⁿ, n = 1, 2…) signals, the constellation points will be collected together in CA. Without phase error impairments, I(k,b,N_CA) and Q(k,b,N_CA) should converged to zero at N_CA = n, thus $a b s (I (k, b, N_{C A}))$ and $a b s (Q (k, b, N_{C A}))$ have their minimum values while the right test phase angle is taken. Next, in order to smooth out additive white Gaussian noise (AWGN) influences on PED, we take the average of $a b s (I (k, b, N_{C A}))$ and $a b s (Q (k, b, N_{C A}))$ of 2L consecutive samples rotated by the same test phase angle b, i.e.

S (k, b) = \sum_{p = k - L + 1}^{k + L} (a b s (I (p, b, N_{C A})) + a b s (Q (p, b, N_{C A})))

Figure 2 depicts the measured S(k,b) (N_CA = n) as a function of phase compensation error for 4-QAM, 16-QAM, 64-QAM and 256-QAM respectively, where S(k,b) is normalized by its minimum value to display. It can be seen that S has its minimum value when phase error is zero. So the optimal test phase angle for the k^th sample can be determined by finding the minimum value of S, and the estimated carrier phase error for compensation is given by

\tilde{θ} (k) = unwrap (φ_{\hat{b}})

where

\hat{b}

is the index of the minimum value of

S (k, b)

\hat{b} = \underset{b = 1, 2, \dots, B}{a r g \min} (S (k, b))

and unwarp[.] stands for the conventional phase unwrapping.

Fig. 2 Normalized S(k,b) as a function of phase compensation error (N_CA = n, n = log₂(M)/2).

Download Full Size | PDF

In S-BPS, PED is a common process for the square M-QAM constellations and correct phase error can be estimated as long as N_CA = n, n = log₂(M)/2. But conversely, a wrong N_CA will result in phase estimation failure. Therefore, a blind searching process for modulation format recognition (MFR) is required to determined N_CA before the phase error estimation.

2.2 Modulation format recognition process

It is worth noting that the common phase error detector in S-BPS has a unique characteristic, i.e. the detection process for the signal with a high-order modulation format will traverse the detection processes of the signals with relatively low modulation order, as illustrated in Fig. 3. Here, the signal constellations for the detailed PED process are given by taking 4-QAM, 16-QAM and 64-QAM as examples, and no phase noise impact are assumed for clarity.

Fig. 3 Signal distribution changes with constellation aggregation for 4-QAM, 16-QAM and 64-QAM modulation formats.

Download Full Size | PDF

Based on this feature, the maximum possible modulation level (denoted as M_max) in the flexible transmission is set to be the detection object in PED initially (called as “full-order detection (FOD)”), and the intermediate results within the detector are also recorded so as to search the correct N_CA for a unknown modulation format. The detailed computational process of FOD is depicted in Fig. 4.

Fig. 4 The block diagram of full-order detection (FOD).

Download Full Size | PDF

Considering to the effect of AWGN, the outputs of each step of FOD with the same test phase angle, i.e. abs(I(k, b, N_CA) and abs(Q(k, b, N_CA) where N_CA = 1, 2, …, log₂(M_max)/2, are summed up in 2L₁ consecutive samples,

S_{F O D} (k, b, N_{C A}) = \sum_{p = k - L_{1} + 1}^{k + L_{1}} (a b s (I (p, b, N_{C A})) + a b s (Q (p, b, N_{C A})))

where L₁ denotes the half length of the summing window for MFR, which is purposely differentiated from a similar parameter-L of CPE so as to analyze independently in a convenient manner. For the same reason, B₁ is here used to denote the number of test phase angles in FOD, i.e. b = 1, 2, ..., B₁. Assuming that M_max = 64, different modulation signals go through the FOD, and their corresponding S_FOD (N_CA = 1, 2 and 3 respectively) as a function of carrier phase error are shown in Fig. 5.

Fig. 5 Normalized S_FOD as a function of carrier phase error at N_CA = 1, 2 and 3 respectively for (a) 4-QAM, (b) 16-QAM and (c) 64-QAM signals.

Download Full Size | PDF

It can be seen from Fig. 5, the normalized S_FOD changes dramatically with the correct N_CA (i.e. N_CA = 1 for 4-QAM, N_CA = 2 for 16-QAM, and N_CA = 3 for 64-QAM) while S_FOD is quite insensitive to the b for the wrong N_CA. In this case, the difference of the normalized S_FOD between its maximum and minimum values can be used for MFR. Since the relatively high computation complexity will be induced by additional normalization process for S_FOD, we study the difference ratio

D i f f (N_{C A}) = \underset{b = 1, 2, ..., B_{1}}{\max (S_{F O D} (k, b, N_{C A}))} / \underset{b = 1, 2, ..., B_{1}}{\min (S_{F O D} (k, b, N_{C A}))}

Then, the correct N_CA can be determined by searching the index that maximize Diff, i.e,

{\hat{N}}_{C A} = \underset{N_{C A} = 1, \dots, \log_{2} (M_{\max}) / 2}{\arg \max} D i f f (N_{C A})

Figure 6 shows each step Diff for different input signal modulation format. It can be seen that the maximum of Diff is a good indicator of the modulation format. Note that in order to reflect this phenomenon clearly, only a fixed phase error is considered in Fig. 6, so a long enough summing window of 2L₁ can be taken to average the effect of AWGN. However, the peak value will be influenced by both AWGN and laser phase noise in practice. In order to avoid being submerged, parameter design for MFI-BPS are very important for MFR, which will be investigated and analyzed in the following simulation and experimental studies.

Fig. 6 Diff of each step based on different input signals: 4-QAM, 16-QAM and 64-QAM respectively.

Download Full Size | PDF

3. Simulation results and discussion

Numerical simulations are conducted to analyze the impact of key parameters in MFR and evaluate the performance of the proposed MFI-BPS algorithm comprehensively. Here, 256-QAM is assumed as the modulation format with highest possible order in the transmission. In our simulations, more than 5000 tests for each point are used to calculate the correct probability of MFR and a total of 10⁶ symbols are used to obtain the bit error ratio (BER). To avoid the 4-fold phase ambiguity in those square QAM signals, the first two bits of each symbol are assigned to perform differential coding [17]. Before entering to the carrier phase estimator, the influences of laser linewidth and AWGN will be imposed on the modulated signal, where the phase noise is typically modeled as a Wiener process [18], and the Gaussian noise effect is reflected by using the energy per bit to noise spectral density ratio - E_b/N₀ [19].

For an unknown modulation format, the valid phase estimation in MFI-BPS depends on the correctness of the prior MFR. So first we investigate the influence of the summing window length 2L₁ on the recognition accuracy (see Fig. 7). Here, the number of test angles B₁ in FOD is always set to 64 for getting an enough phase resolution, so as to focus our attention on the effect of 2L₁. For each modulation format, two E_b/N₀ are considered, in which the smaller one corresponds to the “ASE-noise limitation” to achieve BER = 1 × 10⁻³, and two typical sizes of phase noise are considered, i.e.,△f·T_s = 7.14 × 10⁻⁶, △f·T_s = 7.14 × 10⁻⁵, where △f denotes the sum linewidth of the transmitter and receiver lasers (corresponding to 200kHz and 2MHz at 28 Gbaud respectively), T_s is the symbol period. It can be seen from Fig. 7, the accuracy is improved with the increase of 2L₁ at beginning. Until breaking the premise that the almost same phase errors are kept in the symbols of a summing window, increasing 2L₁ will not be useful and may cause a reduction in accuracy. This phenomenon is more obvious to the high-level formats, because they are more vulnerable to laser linewidth. However, there is a exception, i.e. 256-QAM. As shown in Fig. 7(b), it presents a better recognition performance than 64-QAM. This results from the noise-induced fluctuation to Diff(i) more than Diff(j) when i>j. If noise cannot be suppressed well, this phenomenon will exactly help to improve the recognition accuracy for the maximum-level modulation format, namely 256-QAM in our simulation.

Fig. 7 Correct probability of MFR as a function of the summing window length 2L₁ with different linewidth and E_b/N₀ (a) for 4-QAM and16-QAM, (b) for 64-QAM and 256-QAM.

Download Full Size | PDF

As emphasized before, the correct MFR is the essential condition for subsequent CPE. But from above simulation results, increasing 2L₁ is not enough to guarantee the recognition correctness completely for all the formats, because of the limitation of laser linewidth. In this case, another characteristic should be utilized, which is that the modulation format will be kept the same over a long period. Therefore, the multiple FODs can be used to calculate Diff respectively and corresponding Diff in each step are summed up to average the noise out and obtain a more accurate Diff for MFR. Then, Eq. (8) can be replaced by

{\hat{N}}_{C A} = \underset{N_{C A} = 1, \dots, \log_{2} (M_{\max}) / 2}{\arg \max} (\sum_{}^{m} D i f f (N_{C A}))

where m denotes the number of Diff for averaging_. Fig. 8(a)-8(b) illustrate the correct probability of MFR as a function of the summing window length 2L₁ from m = 1 to m = 5 for 16-QAM and 64-QAM respectively, where E_b/N₀ @10⁻³BER and △f·T_s = 7.14 × 10⁻⁵ are taken. It can be seem that there is a obvious accuracy improvement with the increasing of m, which illustrates the effect of AWGN is further suppressed effectively. Since increasing m is immune to the constraint of laser linewidth, the risk of wrong recognition can be avoid completely by using a large enough m value.

Fig. 8 Correct probability of MFR as a function of the summing window length 2L₁ with the sum of different number of Diff, (a) for 16-QAM, (b) for 64-QAM.

Download Full Size | PDF

Next, we investigate another critical parameter B₁ in the MFR process. E_b/N₀ @10⁻³ BER and △f·T_s = 7.14 × 10⁻⁵ are also considered in this simulation, and the AWGN influence is suppressed by 2L₁ = 40 and m = 5. Figure 9 shows the correct probability of MFR as a function of B₁ for 4-QAM, 16-QAM, 64-QAM and 256-QAM respectively. It can be seen that there is increasing requirement on the phase resolution for the higher order modulation format, except for 256-QAM. This exception also results from that N_CA being estimated to be log₂(M_max)/2 has the highest wrong probability, which is exactly to improve the recognition performance of 256-QAM (corresponding to M_max in our simulation) as explained above. As shown in Fig. 9, the recognition correctness can be guaranteed as long as B₁≥16 for all the formats. Comparing to the blind phase estimation (referred to [8, 16]), there is a lower requirement for test phase angle resolution in MFR. In this case, the part of phase rotated results in MFR can be fully reused in following CPE. So there is not extra computational cost on multiplication by the introduction of MFR. Furthermore, MFR will be stopped as long as signal modulation format is identified, which also make that MFR-induced power consumption can be ignored.

Fig. 9 Correct probability of MFR as a function of the number of test phase angles B₁.

Download Full Size | PDF

After successful MFR, the linewidth-induced phase impairment will be estimated, and the performance characteristics of phase error estimation will be consistent with that of the original S-BPS algorithm. Therefore, the parameter influences of 2L and B can be referred to our previous work of [16]. Here, we provide more comprehensive comparison results in BER performances for 4-QAM, 16-QAM, 64-QAM and 256-QAM respectively, as depicted in Fig. 10. The theoretical optimum results are given as a reference, which is calculated by [19]

Fig. 10 BER as a function of E_b/N₀ for 4-QAM, 16-QAM, 64-QAM and 256-QAM by using the proposed MFI-BPS algorithm.

Download Full Size | PDF

B E R = \frac{2}{\log_{2} M} (1 - \frac{1}{\sqrt{M}}) e r f c [\sqrt{\frac{3 \log_{2} M}{2 (M - 1)} \frac{E_{b}}{N_{0}}}]

In term of the phase estimation, B is set to 32 for 4-QAM and 16-QAM, and set to 64 for 64-QAM and 256-QAM respectively. Optimum values of 2L are used to deal with different conditions in this simulation, but for △f·T_s = 0, 2L = 1000.

4. Experimental results for 224 Gbit/s PM-16QAM system

In the section, MFR and BER performances of the proposed MFI-BPS algorithm are further experimentally assessed in a 224 Gbit/s polarization multiplexing 16-QAM (PM-16QAM) system, as shown in Fig. 11(a).

Fig. 11 (a) Experimental setup for 224Gbit/s PM-16-QAM system, (b) offline DSP. EDFA: erbium doped fiber amplifier; OBPF: optical bandpass filter; PC: polarization controller; PBS: polarization beam splitter; PBC: polarization beam combiner.

Download Full Size | PDF

In the transmitter, four copies of 28 Gbit/s binary pseudo-random bit sequence (PRBS) of length 2¹⁵-1 are obtained by a bit pattern generator, which are further attenuated, relatively delayed and combined to generate two four-level signals. Then they are used to drive an integrated LiNbO₃ Mach-Zehnder IQ modulator so as to generate a single polarization 16-QAM signal. Here, an external cavity laser (ECL) with 100 kHz linewidth is used. Then the single polarization 16-QAM signal is fed into a polarization multiplexer, which is split and recombined in orthogonal polarizations after delaying one of the split signals to de-correlate it from another split signal. Variable amounts of amplified spontaneous emission (ASE) noise from a broadband source are added to adjust the optical signal-to-noise ratio (OSNR). The OSNR is measured by using the measurement function of an optical spectrum analyzer with a noise reference bandwidth of 0.1 nm. The received optical signal is amplified, filtered and divided into two arbitrary orthogonal polarization states. Then, both states of polarization are mapped from the optical field into four electrical signals by utilizing the passive quadrature hybrid with balanced detectors. Here, the local oscillator (LO) has a nominal linewidth of 100 kHz. Next, the four electrical signals are digitized by 80 GSa/s analog-to-digital converters (ADC) by using two real-time oscilloscopes with 32GHz electrical bandwidth.

Figure 11(b) shows offline signal processing blocks. Firstly, a fourth order digital low-pass Bessel filter with 21 GHz bandwidth is used to eliminate the noise outside of the band. Then samples are processed with orthogonalization for IQ imbalance compensation [20] and down-sampled to 56 GSa/s. After timing recovery by using digital square and filter algorithm [21], four 13-taps fractionally-spaced (T_s/2) adaptive filters arranged in butterfly structure and optimized by the standard constant modulus algorithm (CMA) algorithm [22] are employed to polarization de-multiplexing, chromatic-dispersion (CD) and polarization mode dispersion (PMD) mitigation. Next, carrier frequency offset between transmitter laser and LO is compensated by using the method of [23], and the carrier phase is recovered by using the proposed MFI-BPS and the traditional BPS [8] respectively for comparison. Finally, the BER are measured by bit error counting after symbol decisions.

In MFI-BPS, the first MFR is very crucial to guarantee the CPE correctness. According to above analysis results, the recognition precision is closely related to two design parameters −2L₁ and m. Furthermore, during the length limitation on 2L_1, the recognition correctness can be ensured by increasing m. In order to validate these conclusions in the experiment, the correct probability of MFR as a function of 2L₁ and m at OSNR = 22.3 dB is shown in Fig. 12. Here, the 256-QAM is also assumed as the highest-order format possible in the FOD and B₁ is set to 32. For observation in high-precision, the correct probabilities over 99.5% are distinguished with different colors. It can be seen that only increasing 2L₁ is not enough to avoid the risk of incorrect MFR, due to the dual influences of AWGN and laser phase noise. However, as expected, the residual failure probability can be completely eliminated by increasing m, and there are many combination of 2L₁ and m that can reach the desired MFR accuracy, in which the least 136 samples are required while m = 17, 2L₁ = 8. In order to improve MFR stability and reserve the correct S_FOD in FOD for subsequent phase estimation conveniently, 2L₁ is set equal to 2L, i.e. 70, and m is set to 10 for all the following experimental results.

Fig. 12 Correct probability of MFR as a function of 2L₁ and m at OSNR = 22.3 dB.

Download Full Size | PDF

Since the standard BPS algorithm can achieve the optimal tolerance for laser linewidth, the BER performance of MFI-BPS is investigated and compared to the traditional BPS algorithm in Fig. 13. The theoretical optimum results are also displayed as a reference, which can be calculated according Eq. (10) and OSNR = $\frac{E_{b}}{N_{0}} \cdot \frac{R_{b}}{2 B_{r e f}}$ (R_b is the total bit rate and B_ref = 12.5e9 Hz). In term of the traditional BPS, the precondition of unknown modulation format is not considered. For fair comparison, the parameter settings are the same in the two algorithms, namely B = 32, 2L = 70. It can be seen that based on successful MFR, the linewidth-induced phase impairment is estimated and compensated effectively by using the proposed MFI-BPS algorithm, and the experimental results demonstrate that MFI-BPS can achieve nearly the same linewidth tolerance as the standard BPS algorithm.

Fig. 13 BER performance as a function of OSNR with MFI-BPS and standard BPS algorithm.

Download Full Size | PDF

5. Conclusion

In this paper, we proposed a MFI-BPS CPE algorithm for square M-QAM coherent optical systems. The modulation format can be determined first by using constellation aggregation and a blind search method in the feedforward manner before CPE. Simulation and experimental results show that when the noise suppression window length is restricted by laser linewidth, the MFR correctness can be guaranteed by taking multiple estimates of the full-order detection (FOD) metric for averaging. In addition, the strong phase noise compensation capability is preserved by using the proposed MFI-BPS algorithm, which can achieve nearly the same linewidth tolerance of the standard BPS algorithm.

Acknowledgment

This study is supported by the National Basic Research Program of China (2012CB315905), the National Natural Science Foundation of China (61401020 and 61302064), and Hong Kong Scholars Program (XJ2013026). The authors would also like to acknowledge the support of the Hong Kong Government General Research Fund (GRF) under project number PolyU 152079/14E.

References and links

1. T. J. Xia, G. Wellbrock, A. Tanaka, M. Huang, E. Ip, D. Qian, Y. Huang, S. Zhang, Y. Zhang, P. Ji, Y. Aono, S. Murakami, and T. Tajima, “High Capacity Field Trials of 40.5 Tb/s for LH Distance of 1,822 km and 54.2 Tb/s for Regional Distance of 634 km,” in Proc. OFC (2013), Paper PDP5A.4. [CrossRef]

2. J. Cai, H. Zhang, H. G. Batshon, M. Mazurczyk, O. Sinkin, Y. Sun, A. Pilipetskii, and D. Foursa, “Transmission over 9,100 km with a Capacity of 49.3 Tb/s Using Variable Spectral Efficiency 16 QAM Based Coded Modulation,” in Proc. OFC (2014), Paper Th5B.4. [CrossRef]

3. M. Jinno, B. Kozicki, H. Takara, A. Watanabe, Y. Sone, T. Tanaka, and A. Hirano, “Distance-adaptive spectrum resource allocation in spectrum-sliced elastic optical path network,” IEEE Commun. Mag. 48(8), 138–145 (2010). [CrossRef]

4. O. Gerstel, M. Jinno, A. Lord, and S. J. B. Yoo, “Elastic optical networking: a new dawn for the optical layer?” IEEE Commun. Mag. 50(2), 12–20 (2012). [CrossRef]

5. A. P. T. Lau, Y. Gao, Q. Sui, D. Wang, Q. Zhuge, M. Morsy-Osman, M. Chagnon, X. Xu, C. Lu, and D. V. Plant, “Advanced DSP Techniques Enabling High Spectral Efficiency and Flexible Transmissions: Toward elastic optical networks,” IEEE Signal Process. Mag. 31(2), 82–92 (2014). [CrossRef]

6. A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef]

7. I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photon. Technol. Lett. 22(9), 631–633 (2010). [CrossRef]

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

9. K. Piyawanno, M. Kuschnerov, B. Spinnler, and B. Lankl, “Low complexity carrier recovery for coherent QAM using superscalar parallelization,” in Proc. ECOC (2010), Paper. We.7.A.3, 2010. [CrossRef]

10. K. P. Zhong, J. H. Ke, Y. Gao, J. C. Cartledge, A. P. T. Lau, and C. Lu, “Carrier phase estimation for DP-16 QAM Using QPSK partitioning and quasi-multiplier-free algorithms,” in Proc. OFC (2014), paper W4K.2. C.

11. 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]

12. Y. L. Gao, A. P. T. Lau, S. Y. Yan, and C. Lu, “Low-complexity and phase noise tolerant carrier phase estimation for dual-polarization 16-QAM systems,” Opt. Express 19(22), 21717–21729 (2011). [CrossRef] [PubMed]

13. K. P. Zhong, J. H. Ke, Y. Gao, and J. C. Cartledge, “Linewidth-tolerant and low-complexity two-stage carrier phase estimation based on modified QPSK partitioning for dual-polarization 16-QAM systems,” J. Lightwave Technol. 31(1), 50–57 (2013). [CrossRef]

14. Q. Zhuge, M. Morsy-Osman, X. Xu, M. E. Mousa-Pasandi, M. Chagnon, Z. A. El-Sahn, and D. V. Plant, “Pilot-aided carrier phase recovery for M-QAM using superscalar parallelization based PLL,” Opt. Express 20(17), 19599–19609 (2012). [CrossRef] [PubMed]

15. Y. L. Gao, A. P. T. Lau, and C. Lu, “Modulation-format-independent carrier phase estimation for square M-QAM systems,” IEEE Photon. Technol. Lett. 25(11), 1073–1076 (2013). [CrossRef]

16. X. Zhou, C. Lu, A. P. T. Lau, and K. P. Long, “Low-complexity carrier phase recovery for square M-QAM based on S-BPS algorithm,” IEEE Photon. Technol. Lett. 26(18), 1863–1866 (2014). [CrossRef]

17. W. Weber, “Differential encoding for multiple amplitude and phase shift keying systems,” IEEE Trans. Commun. 26(3), 385–391 (1978). [CrossRef]

18. M. Tur, B. Moslehi, and J. W. Goodman, “Theory of laser phase noise in recirculating fiber-optic delay lines,” J. Lightwave Technol. 3(1), 20–31 (1985). [CrossRef]

19. J. D. Proakis and M. Salehi, Digital Communications, McGraw-Hill, 2008.

20. I. Fatadin, S. J. Savory, and D. Ives, “Compensation of quadrature imbalance in an optical QPSK coherent receiver,” IEEE Photon. Technol. Lett. 20(20), 1733–1735 (2008). [CrossRef]

21. H. Meyr, M. Moeneclaey, and S. Fechtel, Digital Communication Receivers. (John Wiley, New York, 1997).

22. D. Godard, “Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” IEEE Trans. Commun. 28(11), 1867–1875 (1980). [CrossRef]

23. M. Selmi, Y. Jaouen, and P. Ciblat, “Accurate digital frequency offset estimator for coherent PolMux QAM transmission systems,” in Proc. ECOC (2009), paper P3.08.

Modulation-format-independent blind phase search algorithm for coherent optical square M-QAM systems

Abstract

1. Introduction

2. Operation principle of MFI-BPS algorithm

2.1 Symmetric BPS algorithm for square M-QAM

2.2 Modulation format recognition process

3. Simulation results and discussion

4. Experimental results for 224 Gbit/s PM-16QAM system

5. Conclusion

Acknowledgment

References and links

Cited By

Figures (13)

Equations (10)

Optics Express