Feed-forward frequency offset estimation for 32-QAM optical coherent detection

Fei Xiao; Jianing Lu; Songnian Fu; Chenhui Xie; Ming Tang; Jinwen Tian; Deming Liu

doi:10.1364/OE.25.008828

1. Introduction

To satisfy ever-increasing bandwidth requirement, M-ary quadrature amplitude modulation (M-QAM) formats together with coherent detection and digital signal processing (DSP) have attracted worldwide attentions to build up spectral-efficient fiber optical transmission system [1–4]. Dual-polarization quadrature phase-shift keying (DP-QPSK) format has been commercially available for 100G transmission system [5]. For the 400G system, DP-16-QAM is a promising candidate and has also drawn extensive studies [6]. Then, higher order QAM will be taken into account for future higher capacity and higher spectral efficiency (SE) fiber optical transmission. 32-QAM signals can carry 5 bits per symbol, which enable the SE up to 10 b/s/Hz with polarization division multiplexing (PDM) technique [7]. Meanwhile, 32-QAM has better tolerance of additive white Gaussian noise (AWGN) and laser linewidth in comparison with 64-QAM [8]. Therefore, 32-QAM has potentials to be used in next generation fiber optical transmission for achieving high SE [7, 9–12]. As for optical coherent detection, frequency offset (FO) between the local oscillator (LO) and the laser source acting as transmission carrier is one of most important impairments which forces the phase of signals to vary fast over time. Therefore, FO needs to be compensated before carrier phase estimation (CPE) by block M^th power [13] or blind phase search (BPS) algorithm [14], because those CPE algorithms are designed without considering the FO effect. Several non-decision-aided (NDA) FO estimation (FOE) schemes operated in a feed-forward manner have been proposed for real-time implementation [15–19]. The differential FOE (Diff-FOE) for M-ary phase shift keying (M-PSK) format can estimate the FO by computing the phase increment between two adjacent samples raised to the M^th power for modulation removal [15]. Diff-FOE can be used for 16-QAM using QPSK partition technique, which takes a block size of more than 10000 symbols to achieve the FOE function [16]. For higher order QAM, Diff-FOE is no longer suitable. Fast Fourier transform based FOE (FFT-FOE) scheme is a periodogram method, where the maximization of the discrete-frequency spectrum of the fourth-power received samples can be acquired with the help of FFT [17, 18]. FFT-FOE has very fast FO acquisition time, only requiring hundreds of symbols. Although FFT-FOE is derived for M-PSK format, it can still be applied to both 16-QAM and 64-QAM by taking the phase order M of 4 into account [18]. Meanwhile, it is well known that the computation complexity of FFT increases fast with respect to the block size used for FFT (FFT size). Considering both the computation complexity and FOE resolution, we must choose an optimal FFT size during real-time implementation such as 512 symbols [18] and 528 symbols [19] for 16-QAM. However, when the FFT-FOE scheme is applied to 32-QAM, whose constellation points are not strictly rectangular distribution like 16-QAM and 64-QAM, the discrete-frequency spectrum suffers from severe distortions if the FFT size is still hundreds of symbols. This is mainly due to the lack of four points at four corners of 32-QAM constellation. As a result, FFT-FOE fails to realize correct FOE for 32-QAM within a reasonable FFT size (such as 512 symbols) [18, 19]. Alternatively, some feed-back FOE schemes such as optical phase lock loop (OPLL) using the recovered carrier phases [12, 20] or training-symbol assisted scheme [21, 22] have been applied to 32-QAM transmission experiments. However, for real-time implementation, feed-forward FOE algorithms are always preferred due to the possible hardware parallelization and pipelining implementation [16]. To the best of our knowledge, no feed-forward and NDA FOE has been demonstrated for 32-QAM format so far.

In this paper, we propose a feed-forward and NDA FOE for 32-QAM. The points of inner QPSK ring is selected and amplified in digital domain after adaptive equalization. Then the intensity peak of its spectrum can be easily identified by FFT technique. We call this QPSK-selection assisted FFT-FOE. The QPSK-selection assisted FFT-FOE is suitable for 32-QAM while keeping the advantages of traditional FFT-FOE including both fast FO acquisition time and wide FOE range of [-symbol rate/8, + symbol rate/8]. The performance is numerically and experimentally verified under the scenario of back-to-back (B2B) transmission with 10 Gbaud dual polarization (DP)-32-QAM signals.

2. Operation principle of QPSK selection scheme

At the coherent receiver side, a canonical model of the received signal in X or Y polarization after ideal analog-to-digital conversion (ADC), clock recovery and retiming, chromatic dispersion compensation, polarization division de-multiplexing, and polarization-mode dispersion (PMD) compensation can be written as [19]

r (k) = m (k) \exp (j (Δ ω k + θ (k))) + n (k), k = 0, 1, 2, \dots

m (k)

is the k^th data symbol.

Δ ω = 2 π Δ f T

is the angular frequency offset where T is the symbol period. The

θ (k)

is the laser phase noise modeled as a Wiener process.

n (k)

stands for the AWGN. For the traditional FFT-FOE, the frequency estimation

Δ \hat{f}

is given under the condition of the maximization of the periodogram

r^{4} (k)

as

Δ \hat{f} = \frac{1}{4} \arg \max_{| Δ \hat{f} | < 1 / 2 T} | \sum_{k = 0}^{N - 1} r^{4} (k) e^{- j 2 π Δ \hat{f} T k} |

where

\arg \max_{| Δ \hat{f} | < 1 / 2 T} (.)

means the operation of searching the

Δ \hat{f}

within the range of

[- 1 / 2 T, + 1 / 2 T]

, when the function (.) value is maximized. Equation (2) leads to a computationally intensity peak search in the periodogram of

r^{4} (k)

. The peak search can be implemented by FFT technique [23]. Figures 1(a)-1(d) show the constellations of QPSK, 16-QAM, 32-QAM, and 64-QAM, respectively. If

m (k)

is a QPSK signal, it has been remarked that

m^{4} (k)

is constant and independent of the data stream. This is because that the modulation phases of QPSK constellation points are

[- \frac{3}{4} π, - \frac{1}{4} π, + \frac{1}{4} π, + \frac{3}{4} π]

which can be removal by raising the

r (k)

to its 4th power. Consequently, FFT-FOE can be used to estimate the FO based on

r^{4} (k)

[18]. If

m (k)

is 16-QAM or 64-QAM modulated,

m^{4} (k)

is not constant anymore. However, the fourth-order constellation of 16-QAM or 64-QAM is non-circular, i.e.

E [m^{4} (k)] \neq 0

. In particular, two properties of constellations of 16-QAM or 64-QAM, as shown in Figs. 1(b) and 1(d), respectively, make contributions to find the maximum value in the discrete spectrum using FFT:

Fig. 1 Constellations of (a) QPSK, (b) 16-QAM, (c) 32-QAM, (d) 64-QAM.

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(1) On the diagonal line with slope equal to + 1 or −1, there are 2/4 rings of 16/64-QAM constellation points which follow the QPSK distribution (red points in Figs. 1(b) and 1(d)). The modulation phase of these points can be removed by 4th power method. In particular, there are four points at four corners in the constellation of 16(64)-QAM, which have the maximum amplitude of all the points. According to Eq. (2), these points have most important contributions to search the intensity peak in spectrum, leading to the successful identification of FFT-FOE.
(2) The residual constellation points distribute symmetrically on both sides of the diagonal line. Then, the intensity peak in spectrum will suffer from little disturbance and can be still easily found using FFT.

Therefore, traditional FFT-FOE can be effectively applied to 16-QAM and 64-QAM signals. However, there happens a lack of four points at four corners of the 32-QAM constellation. Although 32-QAM points are still symmetric, the intensity peak of FFT-FOE technique suffered from severe distortions unless much longer FFT size is applied, indicating of huge computation complexity. Here, we propose QPSK-selection assisted FFT-FOE scheme for 32-QAM signals. The block diagram for QPSK-selection assisted FFT-FOE scheme is shown in Fig. 2. The incoming 32-QAM symbols are first normalized by its average power. Then, there are 5 rings with amplitudes of 0.3156, 0.7057, 0.9468, 1.1379, and 1.3012. It has been mentioned that those points, which are QPSK distributed, are helpful to search the intensity peak. Therefore, we select the inner QPSK ring (the points with amplitude $\leq (0.3156 + 0.7057) / 2$ ) and their amplitudes of those points are digitally amplified up to a relatively large value of 1.5, which is a little larger than the amplitude of the external ring (1.3012). This process is shown in Figs. 3(a) and 3(b) (under the condition of SNR = 24 dB) and Figs. 3(c) and 3(d) (under the condition of SNR = 21 dB). After selecting and digitally amplifying the inner QPSK ring, the intensity peak of FO suffered will be enhanced in the spectrum. When the symbol rate is 10 Gbaud, FO is set to be 0.35 GHz with a FFT size of 512 symbols. Figures 4(a)-4(b) and Figs. 4(c)-4(d) show the power spectrum of $r^{4} (k)$ before/after QPSK selection under conditions of SNR = 24 dB and SNR = 21 dB, respectively. We can observe that, when traditional FFT-FOE is applied to 32-QAM, lots of interference peaks occur in the spectrum, which causes the intensity peak challenging to find. However, with the help of proposed QPSK selection technique, the intensity peak becomes obviously with the substantial contributions of the inner QPSK ring. Please note that the amplitude of 1.5 is enough for the purpose of peak searching. If the amplified amplitude is too large, we find that the spectrum will become messy under the condition of SNR less than 17 dB. This phenomenon is due to the error occurrence during the selection of the inner QPSK ring, when there is severe AWGN. After the selection and digital amplification, the estimated $Δ F_{e s t}$ is obtained by FFT, and the FO can be compensated using the term of $\exp (- j 2 π Δ F_{e s t} k T_{s})$ accordingly.

Fig. 2 Block diagram of QPSK-selection assisted FFT-FOE scheme.

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Fig. 3 Constellations of received 32-QAM signals $r (k)$ (a) before selection and digital amplification of the inner QPSK ring, SNR = 24 dB, (b) after selection and digital amplification of the inner QPSK ring, SNR = 24 dB, (c) before selection and digital amplification of the inner QPSK ring, SNR = 21 dB, (d) after selection and digital amplification of the inner QPSK ring, SNR = 21 dB. The symbol rate is 10G Baud, FO is set to 0.35GHz.

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Fig. 4 4th power spectrum of received 32-QAM signals $r^{4} (k)$ using (a) traditional FFT-FOE, SNR = 24 dB, (b) QPSK-selection assisted FFT-FOE, SNR = 24 dB, (c) traditional FFT-FOE, SNR = 21 dB, (d) QPSK-selection assisted FFT-FOE, SNR = 21 dB. The symbol rate is 10G Baud, FO is set to 0.35GHz.

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3. Simulations results

As shown in Fig. 5(a), we carry out numerical simulations for 10 Gbaud 32-QAM signals to investigate the performance of our proposed FOE scheme, under condition of B2B transmission. Traditional FFT-FOE is also done for the purpose of comparison. Different values of $Δ f$ are set and AWGN is loaded to vary the SNR. Please note that in our simulation, other impairments induced by timing clock error, chromatic dispersion, polarization mode dispersion and phase noise are assumed to be completely compensated, in order to focus our attention on the FOE. It is well known that FFT-FOE has a frequency estimation resolution limited by the FFT size to $\frac{symbol rate}{4 \times FFT size}$ . Therefore, if the $Δ F_{e s t}$ in a certain simulation is beyond the range of $[Δ f - \frac{symbol rate}{4 \times FFT size \times 2}, Δ f + \frac{symbol rate}{4 \times FFT size \times 2}]$ , we can judge that an error occurs at this time or vice versa. At each $Δ f$ and SNR, the error probability is obtained over $1 \times 10^{7}$ independent runs for different FOEs, in order to guarantee the reliability of performance evaluation. Figures 5(b)-5(d) show the FOE error probability as a function of SNR with various FFT sizes in the case of $Δ f$ = 0 GHz, $Δ f$ = 0.35 GHz, $Δ f$ = 1 GHz, respectively. When the FFT size is 512, the error probability using traditional FFT-FOE is totally intolerant (basically more than 50%) with respect to the $Δ f$ in all SNRs. However, our proposed FOE scheme can realize error-free FOE above SNR = 17.5 dB with a FFT size of only 512 symbols. When SNR is below 17.5 dB, there occurs error for our proposed FOE scheme, due to wrong selection of the inner QPSK ring under the condition of low SNR. Moreover, we can observe that the error probability with FFT size of 1024 is smaller than that with FFT size of 512 symbols under the condition of the SNR lower than 17 dB, indicating of that longer FFT size is helpful to mitigate the selection mistake. Furthermore, we find that the error probability of traditional FFT-FOE is relatively low with a FFT size of 1024 and the condition of $Δ f$ = 0 GHz. However, when $Δ f$ becomes larger, the error probability also increases substantially. This phenomenon is due to the fact that the 4th power operation is nonlinear. For traditional FFT-FOE, the larger $Δ f$ is, the more severe the phase change between the symbols is. Such phase variations are amplified during the 4th power operation. Therefore, the FFT-FOE is challenging to estimate a wider FO of 32-QAM. But for the QPSK-selection assisted FFT-FOE, the function of FOE is guaranteed by the digital amplification of inner QPSK ring. The BER curve of 32-QAM together with the theoretical calculation [24] as the reference are shown in Fig. 6. We can observe that, at the 20% FEC threshold of BER = 2 × 10⁻²,our proposed QPSK-selection assisted FFT-FOE shows a SNR penalty of only 1.6 dB with respect to the theoretical one. The penalty is due to the differential coding and limited FOE resolution, and it can be fully compensated by the subsequent module of carrier phase estimation (CPE). However, for traditional FFT-FOE, due to its very high error probability for 32-QAM, the BER is always intolerant, indicating of the transmission interruption. The performance of QPSK-selection assisted FFT-FOE with respect to various $Δ f$ is also investigated under conditions of SNR of 24 dB, 21 dB, and 18 dB, as shown in Fig. 7(a). Again, the QPSK-selection assisted FFT-FOE is unbiased within the range of [-symbol rate/8, + symbol rate/8], i.e. [-1.25 GHz, + 1.25 GHz] for 10 Gbaud 32-QAM signals. Figure 7(b) shows the FOE error of QPSK-selection assisted FFT-FOE under various SNRs. Please note that our proposed QPSK-selection assisted FFT-FOE is a kind of scanning method with a resolution the same as all FFT-based algorithms, such as FFT methods for chromatic dispersion estimation [25, 26] and traditional FFT-FOE [18]. When the estimation value is located near the real value within the resolution, the FOE error is cyclical with respect to the FO changes, as shown in Fig. 7(b).

Fig. 5 (a) Simulation setup. FOE error probability as a function of SNR under the condition of (b) $Δ f$ = 0 GHz, (c) $Δ f$ = 0.35 GHz and (d) $Δ f$ = 1 GHz.

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Fig. 6 Theoretical BER calculation as a function of SNR.

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Fig. 7 (a) Performance of QPSK-selection assisted FFT-FOE under various SNRs. (b) FOE error of QPSK-selection assisted FFT-FOE under various SNRs.

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4. Experimental results

Next, we carry out experimental verification to further investigate the performance of our proposed FOE scheme for 10 Gbaud DP-32-QAM signals. Figure 8(a) shows the experimental setup. An external cavity laser (ECL) with 100-kHz linewidth is used as transmitter source. The arbitrary waveform generator (AWG, Tektronix 7122C) provides 10 Gbaud binary electrical signals for both in-phase and quadrature arms of the modulator. Then, the signal is polarization division multiplexed with 140ns optical delay between two polarization tributaries. Under the B2B measurements, the variable optical attenuator (VOA) and Erbium doped fiber amplifier (EDFA) are deployed to adjust the optical SNR (OSNR) of the received signal. At the receiver side, another ECL with ~100 kHz linewidth is used as the LO to realize coherent detection. It should be mentioned that the central wavelength of the LO can be adjusted at the receiver side to deliberately set the FO. The OSNR of signal is monitored by optical spectrum analyzer (OSA). Finally, the detected electrical signals are digitized and captured by a 50 GSa/s digital sampling oscilloscope (Tektronix, DPO73304D) for offline processing. The offline DSP flow is also shown in Fig. 8. Firstly, samples are processed with orthogonalization for IQ imbalance compensation [27] and down-sampling to 2 samples per symbol. The timing recovery consists of two parts. One is the clock recovery module using classic digital filter and square algorithm [28]. The other part is time frame synchronization. In our frame structure, training symbols at the frame beginning are used for the purpose of frame synchronization and pre-convergence. In particular, frame synchronization is realized by two identical patterns consecutively and the timing metric calculation of the received signals, which is known as the Schmidt & Cox algorithm [29]. After timing recovery, four 15-taps fractionally-spaced (Ts/2) finite impulse-response (FIR) filters arranged in butterfly structure are employed for the purpose of polarization division de-multiplexing and differential group delay (DGD) mitigation. Those FIR filters are first adapted by the standard constant modulus algorithm (CMA) for pre-convergence. Then, the equalization is realized by switching CMA to radius-directed equalization (RDE) algorithm. The FOE is implemented by either QPSK-selection assisted FFT-FOE or traditional FFT-FOE. The following CPE is operated using BPS before signal de-mapping and decoding. Bit error ratio (BER) counting is finally preformed for performance evaluation. Figure 8(b) shows the frame structure in the experiment which is designed for investigating the FOE function. The specific frame consists of a frame head, 2048 QPSK symbols, and 2¹⁵-1 32-QAM data sequence. The frame head is used for timing recovery and providing the marginfor the convergence of CMA algorithm. The 2048 QPSK symbols are used to calculate the FO $Δ F_{e s t - Q P S K}$ using traditional FFT-FOE as the criterion to evaluate the FOE for the following 32-QAM signal. In practice, laser frequency drifts over time at a range of MHz/s, due to aging or temperature variation, and might also experience sudden frequency jumps due to mechanical disturbances to the laser cavity [19]. However, the FO is stable in a certain experiment within tens of thousands of symbols in our frame structure as the symbol rate is as high as 10 Gbaud. Therefore, we can use the $Δ F_{e s t - Q P S K}$ from the front QPSK signals as the evaluation criterion. Please note that the $Δ F_{e s t - Q P S K}$ using 2048 QPSK symbols also has a resolution of $\frac{symbol rate}{4 \times FFT size}$ . Therefore, if $Δ F_{e s t}$ from 32-QAM is beyond the range of $[Δ F_{e s t - Q P S K} - \frac{symbol rate}{4 \times FFT size \times 2} + \frac{symbol rate}{4 \times 2048 \times 2}, Δ F_{e s t - Q P S K} + \frac{symbol rate}{4 \times FFT size \times 2} - \frac{symbol rate}{4 \times 2048 \times 2}]$ , we can judge that an error occurs or vice versa. In such QPSK sequence, the last 512 QPSK symbols are also employed as training symbols for traditional FFT-FOE. As for the pre-generated 32-QAM sequence, FOE is implemented under sliding-window manner where the window of FFT size slides over 20000 times at each OSNR and per polarization. Then the error probability of FOE is calculated to support the BER performance for various FOE methods. Finally, we are able to compare the performance between QPSK selection scheme and traditional FFT-FOE.

Fig. 8 (a) Experimental setup and DSP flow for 10 Gbaud DP-32-QAM system. OBPF: optical band-width pass filter, PC: polarization controller, PBS: polarization beam splitter, PBC: polarization beam combiner, ASE: amplified spontaneous emission. (b) Frame structure.

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Figures 9(a)-9(b) show the error probability of FOE with respect to the OSNRs, when the FOs are set to 0 GHz and 1 GHz, respectively. It can be seen that lots of error occurs using traditional FFT-FOE with a FFT size of either 512 or 1024. In particular, traditional FFT-FOE fails to function correctly, when the FO is set to 1 GHz. For our proposed FOE scheme, there occurs no error when the OSNR is higher than 14.1 dB with a FFT size of only 512 symbols. Experimental distributions of the FOE are shown in Figs. 10(a)-10(f), when the FO is set to be 0 GHz and 1GHz under conditions of various OSNRs, respectively. We can observe that, when the OSNRs are 16.7 dB and 19.6 dB, the FOE values always concentrate on the FO setting. Even under the condition of low OSNR of 13.0 dB, the FOE fluctuation of our proposed scheme is few. However, there occur lots of errors using traditional FFT-FOE. Figure 11 shows BER performance as a function of OSNR using three FOE methods, including traditional FFT-FOE, QPSK training symbol assisted FFT-FOE, and QPSK-selection assisted FFT-FOE, with a FFT size of 512 symbols. The BER curve using QPSK training symbols assisted FFT-FOE is used as a reference to evaluate the performances of traditional FFT-FOE and our proposed FOE scheme. We can see that for traditional FFT-FOE, due to its very high error probability for 32-QAM, the BER is always intolerant, indicating that high FOE error probability will result in transmission interruption. However, each value of our proposed FOE is the same as the FOE value obtained from QPSK training symbols assisted FFT-FOE method when the OSNR is higher than 14.1 dB, under the condition of the same FFT size. Therefore, no BER difference can be observed over OSNR range from 14.1 dB to 30 dB for both traditional QPSK training symbols assisted FFT-FOE and our proposed FOE scheme. When the OSNR is less than 14.1 dB, FOE error happens for QPSK-selection assisted FFT-FOE, due to the wrong selection of the inner QPSK ring. However, the BER performance is still better than that using traditional FFT-FOE, indicating of the robust operation for our proposed FOE technique. On the other hand, there are two attractive advantages of our QPSK-selection assisted FFT-FOE in comparison with traditional FFT-FOE with help of QPSK training symbols. First, for 32-QAM format, blind FOE can be operated without QPSK training symbols. Secondly, even if the FO varies fast, our proposed feed-forward FOE scheme can track the FO using a block-by-block method or a sliding-window way. However, FOE tracking is impossible for QPSK training symbols assisted FFT-FOE. Finally, we can observe that the correct estimation range of proposed FOE scheme covers the OSNR range where the 20% FEC threshold of $BER = 2 \times 10^{- 2}$ is satisfied. Therefore, our proposed FOE scheme is very suitable for state-of-art fiber optical 32-QAM transmission.

Fig. 9 FOE error probability and BER with respect to various OSNRs, (a) FO = 0 GHz, (b) FO = 1 GHz.

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Fig. 10 Experimental distributions of FOE at (a) OSNR = 13.0 dB, FO = 0 GHz; (b) OSNR = 16.7 dB, FO = 0 GHz; (c) OSNR = 19.6 dB, FO = 0 GHz; (d) OSNR = 13.0 dB, FO = 1 GHz; (e) OSNR = 16.7 dB, FO = 1 GHz; (f) OSNR = 19.6 dB, FO = 1 GHz. QS-FFT-FOE: QPSK-selection assisted FFT-FOE.

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Fig. 11 BER performance as a function of OSNR, (a) FO 0 GHz, (b) FO is 1 GHz. QT-FFT-FOE: QPSK training symbol assisted FFT-FOE, QS-FFT-FOE: QPSK-selection assisted FFT-FOE.

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5. Computation complexity analysis

Complexity of DSP algorithm is critical for practical applications. For traditional FFT-FOE algorithm, it takes $2 N l o g_{2} N + 10 N + 2$ real multipliers, $3 N l o g_{2} N + 5 N$ real adders and $N$ comparators for a FFT size of $N$ symbols [19, 30]. For our proposed QPSK-selection assisted FFT-FOE, it takes additional calculations beside the complexity of traditional FFT-FOE algorithm. For selection and amplifying operations of the QPSK ring, it takes (1) 2 real multipliers and 1 real adder to calculate the amplitude of each symbol; (2) 1 comparator to compare the amplitude of each symbol and the threshold to select the QPSK ring; (3) 2 real multipliers to amplify the amplitude (in both I and Q tributaries) of each symbol belongs to the QPSK ring. The complexities of both two FOE algorithms are summarized in Table 1. Compared with traditional FFT-FOE, the complexity of QPSK-selection assisted FFT-FOE increases with only additional 14% real multipliers and 3% real adders when FFT size is 512. However, as shown in both simulation and experimental results, traditional FFT-FOE with a FFT size of 512 symbols cannot function well for 32-QAM. Therefore, the complexity increment of QPSK-selection assisted FFT-FOE is reasonable.

Table 1. Complexity comparison of two methods

View Table

6. Conclusions

We propose a feed-forward and NDA FOE scheme for 32-QAM using QPSK selection technique, after we identify the beneficial effect of QPSK-distributed constellation points for searching the intensity peak in the discrete-frequency spectrum of fourth-power received symbols. The proposed FOE technique can be applied to 32-QAM while kept the advantages of fast FO acquisition time and FOE range of [-symbol rate/8, + symbol rate/8]. Simulation results show that no FOE error occurs with a FFT size of only 512 symbols, when the signal-to-noise ratio (SNR) is above 17.5 dB. However, the error probability of traditional FFT-FOE scheme is always intolerant. Meanwhile, the proposed FOE scheme functions well for 10 Gbaud DP-32-QAM signal to reach 20% FEC threshold of $BER = 2 \times 10^{- 2}$ , under scenario of B2B transmission.

Funding

National Natural Science Foundation of China (61575071, 61711530043); National Key Research and Development Program of China (2016YFE0121300); Open Fund (2016OCTN-01) of State Key Laboratory of Optical Communication Technologies and Networks, Wuhan Research Institute of Posts &Telecommunications.

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	Algorithm	Real multipliers	Real adders	Comparators
1	traditional FFT-FOE	$2 N l o g_{2} N + 10 N + 2$	$3 N l o g_{2} N + 5 N$	$N$
2	QPSK-selection assisted FFT-FOE	$2 N l o g_{2} N + 14 N + 2$	$3 N l o g_{2} N + 6 N$	$2 N$

Feed-forward frequency offset estimation for 32-QAM optical coherent detection

Abstract

1. Introduction

2. Operation principle of QPSK selection scheme

3. Simulations results

4. Experimental results

5. Computation complexity analysis

6. Conclusions

Funding

References and links

Cited By

Figures (11)

Tables (1)

Equations (2)

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