Abstract

We propose a novel direct detection (DD) scheme for polarization division multiplexed (PDM) single sideband (SSB) signals with two orthogonal carriers located at the opposite sides. Polarization diversity is realized with a pair of optical filters that are used to suppress the unwanted orthogonal carrier component. A PDM-SSB DD receiver is thus constructed without polarization de-rotation. The intra-polarization signal-signal beat interference (SSBI) can be mitigated by Kramers-Kronig detection or iterative SSBI cancellation. For inter-polarization SSBI mitigation, we propose a joint iterative SSBI cancellation method. The proposed PDM-SSB DD scheme is validated with a principle experiment of 40Gbaud PDM-SSB 16-ary quadrature amplitude modulation (16-QAM) signals. After 80km standard single-mode fiber (SSMF) transmission, the bit-error rates (BERs) achieve 20% hard-decision forward error correction (HD-FEC) threshold of 1.5 × 10−2. The performance of iterative SSBI cancellation, Kramers-Kronig detection, and joint iterative SSBI cancellation are evaluated for PDM-SSB signals with different carrier-to-signal ratios (CSPRs) through numerical simulations. Moreover, a multi-input-multi-output (MIMO) equalization scheme is proposed and validated with numerical simulation, which can suppress the linear inter-polarization crosstalk and relax the sharpness requirement of optical filter edges.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Coherent detection dominates in long haul transmission systems due to its good performance and high spectral efficiency. In recent years, with the growing demand for high speed transmission in data center inter-connections and metro networks, direct detection (DD) has attracted extensive attentions. Coherent receivers require complex hardware including local oscillator (LO), two 90° optical hybrids, four balanced photodiodes (PDs) and four analogue-to-digital converters (ADCs) to enable polarization- and phase-diversity detection. In contrast, DD systems only need one single-ended PD and one ADC for each polarization in the receiver, which have the advantages of low cost and easy integration. Therefore, DD is currently more favorable in short reach transmission and some metro applications [1–3].

The transmission distance of conventional intensity modulation (IM) DD systems is severely limited by the chromatic dispersion (CD) induced power fading effect [4]. In contrast, single sideband (SSB) modulation with DD can avoid the power fading effect and simultaneously achieve high spectral efficiency (SE) by removing one of the sideband. To make full use of the bandwidth of the digital-to-analogue converter (DAC), optical carrier [5-6] or digital virtual carrier [7–9] based SSB schemes are proposed, leading to similar SE and data rate as that of single-polarization coherent systems. A disadvantage of SSB is signal-signal beat interference (SSBI) caused by the square-law detection of PD. So far, several digital linearization methods have been proposed [10–12], which regard the SSBI term as a perturbation and subtract it from the received waveform. In addition to these methods, the Kramers-Kronig (KK) detection [13] has shown its superiority to reconstruct the complex optical field of the SSB signal from its amplitude waveform given that the minimum phase condition is satisfied.

Polarization division multiplexing (PDM) can double both the SE and the system capacity. For PDM coherent detection, the state of polarization (SOP) of the LO at the receiver can be well aligned and equally split to reconstruct the replica of both polarization signals. In comparison, the optical carrier in SSB DD systems, which plays the equivalent role of the LO, is added at the transmitter and undergoes random polarization rotation in the fiber link. In PDM-SSB DD systems, it is thus no longer practical to equally split the carrier using a single polarization beam splitter (PBS) without active polarization control [14-15]. Here we name the random carrier splitting phenomenon in PDM-SSB DD systems as carrier fading, which is different from the power fading effect in IM-DD systems. To overcome the carrier fading problem, one attempt is to utilize an optical filter followed by a Faraday rotation mirror to generate orthogonal polarized carriers [16]. In [17], an additional balanced-PD and 3 × 2 multi-input-multi-output (MIMO) equalization is employed to make the system performance a weak function of the carrier SOP. Furthermore, Stokes vector receiver (SVR) combined with KK detection is designed to achieve four-dimension detection [15, 18–20], which is theoretically capable to detect all the SOP of the carrier by de-rotation in Stokes space [21]. However, the hardware complexity of a SVR is almost identical with a full coherent receiver except for the LO. Another approach is adding the optical carriers on the opposite sides of the PDM signal. In doing so, a PBS with 4 × 4 MIMO equalization is experimentally demonstrated to detect PDM signals [14]. Alternatively, with SSBI separated by guard band equal to the signal bandwidth, two optical filters can be utilized for polarization de-multiplexing of the partially frequency-overlapped PDM signal [22].

In this work, we propose a novel PDM-SSB DD scheme based on completely frequency-overlapped SSB signals of X and Y polarizations. At the transmitter, the carriers of both polarizations are added at the opposite sides of the signals. At the receiver side, a pair of optical filters are employed to remove the unwanted orthogonal carrier for polarization de-multiplexing. With digital SSBI mitigation, the PDM-SSB DD scheme requires only small guard bands between the SSB signals and their respective carriers. To verify this scheme, we experimentally demonstrate 40Gbaud PDM 16-ary quadrature amplitude modulation (16-QAM) signal transmission over 80km standard single-mode fiber (SSMF) with bit-error rates (BERs) below 20% hard-decision forward error correction (HD-FEC) threshold of 1.5 × 10−2 [23]. The gross bit rate is 320Gb/s, and the net bit rate is 261.3Gb/s considering both frame redundancy and the 20% HD-FEC overhead. In our experiment, the SSBI is compensated by either the KK detection or our proposed joint iterative SSBI cancellation method. There is no polarization de-rotation in our experiment. The performance of iterative SSBI cancellation, KK detection, and joint iterative SSBI cancellation are further investigated numerically for PDM-SSB signals with different carrier-to-signal ratios (CSPR). Moreover, to meet the requirement of practical applications, a MIMO equalization is investigated in simulation to mitigate the residual linear inter-polarization crosstalk, considering the impact of the roll-off of the optical filter edges and the guard bands between the SSB signals and their respective carriers.

The remainder of the paper is organized as follows. In Section 2, the principle of the optical filter based PDM-SSB DD scheme is introduced with a detailed analysis of SSBI impairments. Section 3 presents a principle transmission experiment of 320Gb/s PDM-SSB 16-QAM signals. Section 4 compares the performance of three SSBI cancellation methods through numerical simulations. Section 5 presents the MIMO equalization based residual linear inter-polarization crosstalk suppression. Finally, the conclusions are drawn in Section 6.

2. Principle of the optical filter based PDM-SSB DD scheme

The PDM-SSB signals are generated with two orthogonally offset carriers on the opposite sides of the SSB signals. Figure 1(a)-1(c) present three alternative schemes to generate the carriers: the bias generated carrier, the digital carrier, and the optical carrier scheme, respectively. In Fig. 1(a), the signal is up-converted and the modulator is biased above the null point to generate the carrier component, which wastes half of the DAC bandwidth. Another approach is driving the optical modulator biased at null point with a baseband QAM signal and add a shifted digital tone as the carrier, which can utilize the full bandwidth of DAC. The drawback of the digital carrier method is the residual image tone generation [7–9] and requirement of high DAC resolution. In addition to digital carrier generation, optical frequency comb generator (OFCG) could be used to obtain both SSB signal and the phase locked optical carrier. However, the OFCG has increased cost and hardware complexity, which might show its advantage in WDM scenarios. In our experiment, we choose the third scheme but with independent optical carriers since it is easier to be implemented. The dual polarization (DP) modulator based digital virtual carrier generation scheme would be studied in a future work.

 

Fig. 1 (a) Bias induced carrier generation scheme. (b) Digital virtual carrier generation scheme. (c) Optical carrier generation scheme. (d) Reception principle of the optical filter based PDM DD scheme. ECL: external cavity laser; OFCG: optical frequency comb generator; SP: single polarization; Mod.: modulator; PBC: polarization beam combiner; AWG: arbitrary waveform generator; DP: dual polarization; PM-OC: polarization-maintaining optical coupler; OBPF: optical band-pass filter; Pol.: polarization.

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Figure 1(d) shows the reception principle of the optical filter based PDM-SSB DD scheme. The received signal is firstly divided into two copies for dual-polarization detection. After optical band-pass filters (OBPFs) with steep edges, the unwanted component from the orthogonal carrier can be suppressed. Here we define the extinction ratio (ER) α as a relative amount of the unwanted carrier power before and after OBPF. After square-law detection of PD, the output photo-currents (I1 and I2) of the two reception branches can be written as Eq. (1) and Eq. (2). Here Cx and Cy are the optical carrier of each polarization, while Sx and Sy are the SSB signal of each polarization, respectively. Re{·} denotes the real part, and () is the conjugation operation. The 1st and the 2nd terms on the right side of Eq. (1) and Eq. (2) are the beat of the carrier of each polarization, which are direct current (DC) terms and can be removed. The 3rd term is the desired linear term, and the 4th term is the residual linear inter-polarization crosstalk, which depends on the edge roll-off of the OBPF. The 5th and the 6th terms are the intra-polarization SSBI and inter-polarization SSBI, respectively.

I1=|Sx+Cx|2+|Sy+Cy/α|2=|Cx|2+|Cy/α|2+2Re{SxCx}+2Re{SyCy}/α+|Sx|2+|Sy|2.
I2=|Sx+Cx/α|2+|Sy+Cy|2=|Cy|2+|Cx/α|2+2Re{SyCy}+2Re{SxCx}/α+|Sx|2+|Sy|2.

If the edge roll-off of the OBPF or the guard band between the signal and the carrier is large enough, the unwanted carrier can be mostly removed. We can thus obtain Eq. (3) and Eq. (4) from Eq. (1) and Eq. (2) by adopting α+. In Eq. (3) and Eq. (4), the linear inter-polarization crosstalk can be neglected, while intra- and inter-polarization SSBI become the primary impairments.

I1=|Cx+Sx|2+|Sy|2=|Cx|2+2Re{SxCx}+|Sx|2+|Sy|2.
I2=|Sx|2+|Cy+Sy|2=|Cy|2+2Re{SyCy}+|Sy|2+|Sx|2.

To mitigate intra- and inter-polarization SSBI, we present and compare three kinds of methods that include iterative SSBI cancellation, Kramers-Kronig detection, and joint iterative SSBI cancellation. In general, the intra-polarization SSBI term can be regarded as a perturbation and reconstructed from the received photocurrent. Figure 2(a) shows the iterative SSBI cancellation method. Here rx/yin(t) represents the received signal. H() is Hilbert transform.rx/yout(t) is the output signal of each polarization after SSBI cancellation. The SSBI term is digitally estimated as |rx/yin(t)+jH(rx/yin(t))|2, which assumes the received waveform to be the linear beating between the signal and the carrier. However, the real SSBI is included in the received waveform. Therefore, it would be beneficial to introduce iterations to improve the precision of SSBI estimation.

 

Fig. 2 DSP flows of (a) Iterative SSBI cancellation; (b) Kramers-Kronig detection; (c) Joint iterative SSBI cancellation.

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Another method of SSBI mitigation is the well-known Kramers-Kronig detection, which is based on the fact that the natural logarithm of the intensity and the phase of the optical field are Hilbert transform of each other. As shown in Fig. 2(b), the amplitude of the optical field is firstly recovered by square root operation. Then the phase of the optical field can be reconstructed by taking the Hilbert transform of the logarithm of the amplitude. Finally, the complex optical field is recovered by the multiplication of the amplitude and the phase.

However, since the information of the other polarization signal is not known, both iterative SSBI cancellation and Kramers-Kronig detection can only deal with intra-polarization SSBI. To further suppress the inter-polarization SSBI, we propose the joint iterative SSBI cancellation as shown in Fig. 2(c). In this method, the received signal of two branches are jointly processed after synchronization. To be specific, the intra-polarization SSBI is reconstructed from the waveform of the same polarization, and the inter-polarization SSBI is estimated from the waveform of other polarization, respectively. Similar to the single-polarization SSB case, iterations could also be introduced to help improve the precision of both intra- and inter-polarization SSBI estimation in the PDM scenario. Here we choose 4 iterations for both iterative SSBI cancellation and joint iterative SSBI cancellation to achieve convergence. The performance of the above three methods are compared for PDM-SSB signals with different CSPRs in Section 4.

3. 320Gb/s 16-QAM PDM DD transmission experiment

In this section, to validate our proposed PDM-SSB DD scheme, we experimentally demonstrate 40Gbaud PDM-SSB 16-QAM signal transmission with direct detection. The SSBI is compensated by either KK detection or the proposed joint iterative SSBI cancellation method.

3.1 Experimental setup and DSP stack

The experimental setup is shown in Fig. 3. At the transmitter, an external cavity laser (ECL) with ~100kHz linewidth is utilized as the light source. The arbitrary waveform generator (AWG) (Keysight M8195A) operating at 64GSa/s generates a 40Gbaud baseband Nyquist 16-QAM signal, which drives the single-polarization (SP) IQ modulator biased at the null point to modulate the light from ECL1 (at 1549.99nm). Then the signal is split into two branches for PDM emulation. To be specific, one branch is delayed by 160-symbols for de-correlation, and the other is attenuated to balance the signal power. ECL2 (at 1550.20nm) and ECL3 (at 1549.78nm) are used as the optical carrier of each polarization, respectively. The polarization-maintaining erbium-doped fiber amplifier (PM-EDFA) is employed to adjust the CSPR. Then the signals of two polarizations are combined together through the PBC. Before 80km SSMF transmission, an EDFA is used to optimize the launch power. Note that such generating scheme is easy to be implemented for demonstration as only one modulator is required to emulate PDM-SSB signals. If two modulators are used to generate PDM-SSB signals, the digital virtual carrier or the bias generated optical carrier can be adopted without the requirement of ECL2 and ECL3.

 

Fig. 3 Experimental setup. AWG: arbitrary waveform generator; ECL: external cavity laser; Mod.: modulator; PM-EDFA: polarization-maintaining erbium-doped fiber amplifier; OC: optical coupler; PBC: polarization beam combiner; SSMF: standard single-mode fiber; OBPF: optical band-pass filter; PD: photodiode; EA: electrical amplifier; DSO: digital storage oscilloscope.

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At the receiver side, the fiber loss is firstly compensated by EDFA. The received signal is divided into two copies for X and Y polarization detection, respectively. In our experiment, one tunable OBPF is used to emulate the simultaneous reception of each polarization signal by suppressing the unwanted carrier. To be specific, we adjust the center frequency of the OBPF to suppress the optical carrier on Y polarization for X polarization detection, and then the optical carrier on X polarization for Y polarization detection. The edge roll-off of the OBPF (Yenista Optics XTM-50/U) is about 800dB/nm. The filtered signal of each polarization is detected by one single-ended PD and subsequently amplified by one electrical amplifier (EA) both with 50GHz bandwidth. The electrical signals are sampled by a real-time digital storage oscilloscope (Keysight DSA-X 96204Q) operating at 160GSa/s to perform offline digital signal processing (DSP).

The diagram of the DSP is shown in Fig. 4(a) and 4(b). At the transmitter, the bit stream is mapped to 16-QAM first. After 8 times up-sampling, the signal is digitally shaped using root raise cosine (RRC) filter with a roll-off factor of 0.01. The CD is pre-compensated at the transmitter. Before sending to the AWG, the baseband signal is 5 times down-sampled. At the receiver, the signal is firstly re-sampled to 4 samples per symbol (SPS). Since the bandwidth of the transceiver in our experiment is large enough compared with the signal bandwidth, we do not apply pre-emphasis before SSBI compensation. In practical systems with limited bandwidth, pre-emphasis should be applied prior to the SSBI compensation, which can help improve the estimation precision of SSBI. The SSBI of each polarization is separately overcome with KK detection or compensated together by the joint iterative SSBI cancellation method. It should be noted that to perform joint iterative SSBI cancellation, the signals of X/Y polarizations are separately detected and then digitally synchronized before being simultaneously sent into the algorithm flow as shown in Fig. 2(c). After SSBI compensation, the signal is down-converted by the subcarrier with the frequency of FC=0.65×FS (FS is the signal symbol rate) and filtered by a matched RRC filter. After synchronization, two-point resampling is performed. Then the residual frequency offset between the optical carrier and the signal is estimated by obtaining the maximum of |FFT(r4(t))|. After carrier frequency recovery, the signals of two polarizations are separately equalized with a Ts/2 (Ts means the symbol time period) spaced training sequence based time domain equalization. The equalizer taps are updated by the recursive least square (RLS) algorithm based on the training sequences. The FIR filter is subsequently used to equalize the following data symbols as shown in Fig. 4(c). The phase correction is performed in two steps: (1) Coarse phase tracking using the uniformly distributed pilots. (2) Accurate recovery based on the blind phase search (BPS) algorithm [24]. Note that both the carrier frequency recovery and the phase correction stage can be removed if the digital virtual carrier or the optical comb carrier generation scheme is adopted. Figure 4(c) depicts the frame structure of the baseband Nyquist signal. The preamble includes two 64-symbol synchronization sequences and four 128-symbol training sequences. 50800 data symbols are transmitted after the preamble. For coarse phase estimation, we uniformly insert 2 pilots for each block of 254 data symbols.

 

Fig. 4 (a) Transmitter side DSP. (b) Receiver side DSP; (c) Frame structure of transmitted signal. RRC: root raise cosine, Pre CD comp.: chromatic dispersion pre-compensation.

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3.2 Experimental results

Figure 5(a) shows the optical spectra before and after the PBC at the transmitter with 0.02nm resolution. The PDM signal occupies ~40GHz optical bandwidth, and 6GHz guard band is set between the signal and the carrier for each polarization. Figure 5(b) displays the transmitted and the received spectra. The extinction ratio of the unwanted carrier before/after OBPF is approximately 40dB, which guarantees the validation of Eq. (3) and Eq. (4). Figure 5(c) shows the profile of the transmission spectrum of the OBPF in our experiment, which has sharp enough edges.

 

Fig. 5 (a) Optical spectra at the transmitter. (b) Transmitted and received optical spectra. (c) Optical spectrum of the OBPF in our experiment. The resolution is set as 0.02nm.

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In our proposed PDM-SSB DD scheme, the carrier-to-signal power ratio (CSPR) is defined as the total power proportion between the carriers and the SSB signals of two polarizations, which is shown in Eq. (5).

CSPR(dB)=10log10Pxcarrier+PycarrierPxsignal+Pysignal.

It should be noted that a higher CSPR would result in smaller effective optical signal-to-noise ratio (OSNR) after transmission, while a lower CSPR would increase the influence of both intra- and inter-polarization SSBI. Based on the above considerations, the CSPR is optimized as 12dB in our experiment. Figure 6(a) plots the measured BERs of X/Y polarizations as a function of total launch power after 80km SSMF transmission. For simplicity, we use ‘SSBI-C = 0’, ‘KK’, and ‘SSBI-C = 2’ to represent the scenarios without SSBI cancellation, with KK detection, and with joint iterative SSBI cancellation, respectively. The total launch power for two polarizations is optimized as 12dBm. With the help of KK detection, the BERs of X/Y polarizations can be reduced from 1.78 × 10−2 and 1.83 × 10−2 to 1.05 × 10−2 and 1.12 × 10−2, respectively. Better results can be achieved if the joint iterative SSBI cancellation is applied, which decreases the BERs of X/Y polarizations to 5.3 × 10−3 and 5.6 × 10−3, respectively. Figure 6(b)-6(g) displays the typical constellations of X/Y polarizations with/without SSBI compensation (including KK detection or joint SSBI cancellation) at 12dBm launch power after 80km transmission. Since SSBI compensation is carried out in the DSP, the comparison is performed without changing system configuration. We can find that the constellation points become more concentrated with KK detection, and further convergence can be observed with joint iterative SSBI cancellation.

 

Fig. 6 (a) Measured BERs of X/Y polarization versus total launch power after 80km SSMF transmission. SSBI-C = 0: without SSBI compensation; KK: with KK detection; SSBI-C = 2: with joint iterative SSBI cancellation. (b)&(c) Typical constellations of X/Y polarizations without SSBI compensation at 12dBm launch power. (d)&(e) Typical constellations of X/Y polarization with KK detection at 12dBm launch power. (f)&(g) Typical constellations of X/Y polarizations with joint iterative SSBI cancellation. Pol.: polarization; w/o: without; w/: with.

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Figure 7(a) shows the measured BERs versus OSNR for PDM/single polarization (SP) signal with/without SSBI compensation at back-to-back (BTB) scenario, respectively. Both the power of the carriers and the SSB signals are included in the OSNR definition. For PDM signals without any SSBI compensation (purple and magenta curves), there is an error floor above 1.0 × 10−2. For intra-polarization SSBI compensation, the required OSNR of PDM signals with KK detection (red and orange curves) is 45.1dB at the BER of 1.0 × 10−2. Furthermore, for both intra- and inter-polarization SSBI compensation, joint iterative SSBI cancellation (navy and blue curves) has an additional ~7.9dB OSNR sensitivity improvement at the BER of 1.0 × 10−2. On the other hand, SP signal suffers only intra-polarization SSBI, while PDM signal suffers both intra- and inter- polarization SSBI. Therefore, it is fair to compare the OSNR sensitivity values between SP signal with KK detection (brown and dark yellow curves) and PDM signal with joint iterative SSBI cancellation (navy and blue curves). At the BER of 1.0 × 10−2, such a PDM induced OSNR penalty is measured as ~4.5dB, which includes a 3dB inherent penalty. Figure 7(b)-7(g) displays the typical constellations of PDM/SP signal without SSBI compensation, with KK detection, and with joint SSBI cancellation at BTB, respectively. The comparison between Fig. 7(b)-7(c) and Fig. 7(d)-7(e) shows the impact of intra-polarization SSBI, while the comparison between Fig. 7(d)-7(e) and Fig. 7(f)-7(g) presents the impact of the inter-polarization SSBI.

 

Fig. 7 (a) Measured BERs versus OSNR for PDM/SP signal at BTB scenario, respectively. SSBI-C = 0: without SSBI compensation; KK: with KK detection; SSBI = 2: with joint iterative SSBI cancellation. (b)&(c) Typical constellations of X/Y polarizations without SSBI compensation for PDM signals. (d)&(e) Typical constellations of X/Y polarizations with KK detection for PDM signals. (f)&(g) Typical constellations of X/Y polarizations with joint iterative SSBI cancellation. The OSNR are all fixed as 52dB. Pol.: polarization; SP: single polarization; w/o: without; w/: with.

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4. Simulation evaluation of SSBI cancellation methods

In this section, we carry out numerical simulations at BTB scenario using commercial software VPItransmissionMakerTM 9.1. The performance of iterative SSBI cancellation, KK detection, and the joint iterative SSBI cancellation are compared for PDM-SSB signals with different CSPR values. In our simulation, the DAC and ADC have infinite resolution. The PDs are ideal without dark currrent, thermal noise and shot noise. According to the assumption of Eq. (3) and Eq. (4), the OBPF is modeled as an ideal rectangular filter to focus on SSBI cancellation. The other parameters are kept the same as those in our experiment.

Figure 8(a) shows the simulated BERs as a function of OSNR for PDM-SSB signals with different CSPR values at BTB scenario. Note that ‘SSBI-C = 0’, ‘SSBI-C = 1’, ‘SSBI-C = 2’, and ‘KK’ represent the scenarios without SSBI cancellation, with iterative SSBI cancellation, with joint iterative SSBI cancellation, and with KK detection, respectively. In the low OSNR region, the OSNR sensitivity curves are shifted proportional to the CSPR since the power of carrier is involved in the OSNR definition. However, in the high OSNR region, the curve with lower CSPR has a higher BER floor because the influence of SSBI is relatively larger. For intra-polarization SSBI mitigation, the iterative SSBI cancellation and the KK detection show similar improvement. Moreover, the joint iterative SSBI cancellation exhibits the best performance, which almost removes the BER floor by handling both intra- and inter-polarization SSBI. Figure 8(b)-8(e) displays typical constellations of 10dB CSPR signal at 45dB OSNR without SSBI cancellation, with iterative SSBI cancellation, with KK detection, and with joint iterative SSBI cancellation, respectively. The performance of three SSBI mitigation methods can be confirmed from the aggregation degree of the constellation points.

 

Fig. 8 (a) Simulated BERs versus OSNR for PDM-SSB signals with different CSPRs at BTB. SSBI-C = 0: without SSBI cancellation; SSBI-C = 1: with iterative SSBI cancellation; SSBI-C = 2, with joint iterative SSBI cancellation; KK, with KK detection. (b)-(e) Typical constellations of a 10dB CSPR signal at 45dB OSNR without SSBI cancellation, with iterative SSBI cancellation, with KK detection, and with joint iterative SSBI cancellation, respectively.

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5. MIMO equalization based residual filtering linear crosstalk mitigation

In our experiment, one OBPF with a steep edge roll-off of 800dB/nm is employed to achieve polarization de-multiplexing. However, such optical filter is too expensive for practical applications. Therefore, it is important to evaluate the impact of OBPF edge roll-off on system performance. As shown in Eq. (1) and Eq. (2) in Section 2, if the edge roll-off of the OBPF is not large enough, the residual linear inter-polarization term would become more serious, which is proportional to the reciprocal of ER (1/α).

To eliminate the residual linear inter-polarization crosstalk, we replace the single-input-single-output (SISO) equalization in the receiver side DSP by a MIMO equalization as in Fig. 9(a). The structure is modified from the 2 × 2 butterfly-structured adaptive FIR filter in Jones space with conjugation operation (the red block) added for the cross-polarization terms, which is consistent with the 4th term in Eq. (1) and Eq. (2). The reason for the conjugation operation can also be understood as that the signal of each polarization are on the opposite sides of the carrier during PD detection. Furthermore, in order to obtain the 2 × 2 channel response matrix, the training sequences are accordingly modified to four pairs of time-interleaved patterns across the two polarizations. Here tx and ty are both 128-symbol Chu-sequences, and ‘0’ stands for a 128-symbol zeros sequence.

 

Fig. 9 (a) DSP flow of the modified MIMO equalization. Conj(·): conjugation operation; RLS: recursive least square algorithm. (b) Simulated BERs versus OSNR of a 12dB CSPR signal with 4th-order Gaussian OBPF at BTB. (c)-(f) Typical constellations of a 12dB CSPR signal at 45dB OSNR without SSBI cancellation, with KK detection, with joint iterative SSBI cancellation, and with both joint SSBI cancellation and MIMO equalization, respectively.

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t1=(tx0),t2=(0ty),tx=ty.

Based on the above analysis, we study the improvement of MIMO equalization in numerical simulations. Different from Section 4, the OBPF is modeled as Gaussian filter with different orders to emulate the real filter with non-ideal edges. As a reference, the OBPF in our experiment can be modeled as a 4th-order Gaussian filter. Figure 9(b) shows the simulated BERs versus OSNR for a PDM-SSB signal with a 12dB CSPR. A 4th-order Gaussian OBPF is used at BTB scenario. The BER floor is completely removed with the help of MIMO equalization. Figure 9(c)-9(f) displays the corresponding constellations at a 45dB OSNR value without SSBI cancellation, with KK detection, with joint iterative SSBI cancellation, and with joint SSBI cancellation/MIMO equalization, respectively.

In Fig. 10(a), we investigate the requirement of OBPF orders for a PDM-SSB signal with a 12dB CSPR signal at BTB scenario. The guard band is fixed as 6GHz. The joint iterative SSBI cancellation is utilized. The ideal rectangular OBPF (black curve) can be compared as a reference, which does not suffer residual linear inter-polarization crosstalk. Without MIMO equalization, a 4th-order Gaussian OBPF will lead to an OSNR penalty of ~2.2dB at 20% HD-FEC threshold. However, if MIMO equalization is applied, a 2nd-order Gaussian OBPF only incurs an OSNR penalty about 2.6dB. Moreover, once a 5th-order OBPF is employed in the experiment setup, the residua linear inter-polarization crosstalk can be neglected and there is no need to use MIMO equalization.

 

Fig. 10 (a) Simulated BERs versus OSNR with different OBPF orders with/without MIMO equalization at BTB. (b) Simulated BERs versus OSNR with different guard bands with/without MIMO equalization at BTB. w/o: without; w/: with.

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Figure 10(b) shows the simulated BERs versus OSNR with different guard bandwidths with/without MIMO equalization at BTB scenario. The OBPF is fixed as a 4th-order Gaussian filter. Without MIMO equalization, a 6GHz guard band is required to reduce the BER floor. In contrast, a 3GHz guard band with MIMO equalization even outperforms a 6GHz guard band without MIMO equalization.

6. Conclusion

We propose and demonstrate a PDM-SSB DD scheme with orthogonal offset carriers located at the opposite sides of X/Y polarizations. Polarization separation is realized by removing the unwanted carrier component with a pair of optical filters, which acts as a polarization rotation-invariant receiver. The proposed scheme is validated by an experiment of 40Gbaud PDM-SSB 16-QAM signal transmitting over 80km SSMF. The SSBI impairment is mitigated by KK detection or the proposed joint iterative SSBI cancellation. As the joint iterative SSBI cancellation can compensate for both intra- and inter-polarization SSBI, it shows better performance compared with KK detection, which is confirmed in both experiment and numerical simulations. A MIMO equalization is further proposed to suppress the residual linear inter-polarization crosstalk. The simulation results indicate that it is possible to employ optical filter with more smooth edges or smaller guard band if MIMO equalization is applied. Our work shows the feasibility of the optical filter based PDM-SSB DD scheme in practical short-reach and metro applications.

Funding

National Natural Science Foundation of China (No. 61475004 and No. 61535002).

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4. D. Che, Q. Hu, and W. Shieh, “Linearization of direct detection optical channels using self-coherent subsystems,” J. Lightwave Technol. 34(2), 516–524 (2016). [CrossRef]  

5. Y. Zhu, K. Zou, Z. Chen, and F. Zhang, “224Gb/s optical carrier-assisted Nyquist 16-QAM half-cycle single-sideband direct detection transmission over 160km SSMF,” J. Lightwave Technol. 35(9), 1557–1565 (2017). [CrossRef]  

6. X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard single-mode fiber using Kramers-Kronig detection,” Proc. Optical Fiber Communication Conference, Paper Th5B.6 (2017).

7. W. Peng, X. Wu, V. R. Arbab, K. Feng, B. Shamee, L. C. Christen, J. Yang, and A. E. Willner, “Theoretical and experimental investigations of direct-detected RF-tone assisted optical OFDM systems,” J. Lightwave Technol. 27(10), 1332–1339 (2009). [CrossRef]  

8. T. M. F. Alves, L. M. M. Mendes, and A. V. T. Cartaxo, “High granularity multiband OFDM virtual carrier-assisted direct-detection metro networks,” J. Lightwave Technol. 33(1), 42–54 (2015). [CrossRef]  

9. S. T. Le, K. Schuh, M. Chagnon, F. Buchali, R. Dischler, V. Aref, H. Buelow, and K. M. Engenhardt, “1.72Tb/s virtual-carrier assisted direct-detection transmission over 200km,” J. Lightwave Technol. 36(6), 1347–1353 (2018). [CrossRef]  

10. W. R. Peng, X. Wu, K. M. Feng, V. R. Arbab, B. Shamee, J. Y. Yang, L. C. Christen, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation technique,” Opt. Express 17(11), 9099–9111 (2009). [CrossRef]   [PubMed]  

11. K. Zou, Y. Zhu, F. Zhang, and Z. Chen, “Spectrally efficient terabit optical transmission with Nyquist 64-QAM half-cycle subcarrier modulation and direct detection,” Opt. Lett. 41(12), 2767–2770 (2016). [CrossRef]   [PubMed]  

12. Z. Li, M. Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. Thomsen, P. Bayvel, and R. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35(10), 1887–1893 (2017). [CrossRef]  

13. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-kronig coherent receiver,” Optica 3(11), 1220–1227 (2016). [CrossRef]  

14. D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightwave Technol. 28(4), 484–493 (2010). [CrossRef]  

15. D. Che, C. Sun, and W. Shieh, “Direct detection of the optical field beyond single polarization mode,” Opt. Express 26(3), 3368–3380 (2018). [CrossRef]   [PubMed]  

16. W. Peng, K. Feng, and A. E. Willner, “Direct-detected polarization division multiplexed OFDM systems with self-polarization diversity,” Proc. LEOS, paper. MH3(2008). [CrossRef]  

17. M. Nazarathy and A. Agmon, “Doubling direct-detection data rate by polarization multiplexing of 16-QAM without active polarization control,” Opt. Express 21(26), 31998–32012 (2013). [CrossRef]   [PubMed]  

18. T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480 Gb/s direct detection over 80km SSMF enabled by Stokes vector Kramers Kronig transceiver,” Opt. Express 25(26), 33534–33542 (2017). [CrossRef]  

19. D. Che, C. Sun, and W. Shieh, “Single-channel 480-Gb/s direct detection of POL-MUX IQ signal using single-sideband Stokes vector receiver,” Proc. Optical Fiber Communication Conference, Tu2C.7 (2018). [CrossRef]  

20. C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers-Kronig receiver,” J. Lightwave Technol. 35(24), 5418–5424 (2017). [CrossRef]  

21. D. Che, A. Li, X. Chen, Q. Hu, Y. Wang, and W. Shieh, “Stokes Vector Direct Detection for Linear Complex Optical Channels,” J. Lightwave Technol. 33(3), 678–684 (2015). [CrossRef]  

22. A. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photonics Technol. Lett. 22(7), 468–470 (2010). [CrossRef]  

23. R. Ryf, S. Randel, N. K. Fontaine, M. Montoliu, E. Burrows, S. Chandrasekhar, A. H. Gnauck, C. Xie, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Gruner-Nielsen, R. V. Jensen, and R. Lingle, “32-bit/s/Hz spectral efficiency WDM transmission over 177-km few-mode fiber,” Proc. Optical Fiber Communication Conference, PDP5A.1(2013).

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

References

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  1. G. N. Liu, L. Zhang, T. Zuo, and Q. Zhang, “IM/DD transmission techniques for emerging 5G fronthaul, DCI and metro applications,” J. Lightwave Technol. 36(2), 560–567 (2018).
    [Crossref]
  2. K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Lightwave Technol. 36(2), 377–400 (2018).
    [Crossref]
  3. J. Shi, J. Zhang, Y. Zhou, Y. Wang, N. Chi, and J. Yu, “Transmission performance comparison for 100-Gb/s PAM-4, CAP-16, and DFT-S OFDM with direct detection,” J. Lightwave Technol. 35(23), 5127–5133 (2017).
    [Crossref]
  4. D. Che, Q. Hu, and W. Shieh, “Linearization of direct detection optical channels using self-coherent subsystems,” J. Lightwave Technol. 34(2), 516–524 (2016).
    [Crossref]
  5. Y. Zhu, K. Zou, Z. Chen, and F. Zhang, “224Gb/s optical carrier-assisted Nyquist 16-QAM half-cycle single-sideband direct detection transmission over 160km SSMF,” J. Lightwave Technol. 35(9), 1557–1565 (2017).
    [Crossref]
  6. X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard single-mode fiber using Kramers-Kronig detection,” Proc. Optical Fiber Communication Conference, Paper Th5B.6 (2017).
  7. W. Peng, X. Wu, V. R. Arbab, K. Feng, B. Shamee, L. C. Christen, J. Yang, and A. E. Willner, “Theoretical and experimental investigations of direct-detected RF-tone assisted optical OFDM systems,” J. Lightwave Technol. 27(10), 1332–1339 (2009).
    [Crossref]
  8. T. M. F. Alves, L. M. M. Mendes, and A. V. T. Cartaxo, “High granularity multiband OFDM virtual carrier-assisted direct-detection metro networks,” J. Lightwave Technol. 33(1), 42–54 (2015).
    [Crossref]
  9. S. T. Le, K. Schuh, M. Chagnon, F. Buchali, R. Dischler, V. Aref, H. Buelow, and K. M. Engenhardt, “1.72Tb/s virtual-carrier assisted direct-detection transmission over 200km,” J. Lightwave Technol. 36(6), 1347–1353 (2018).
    [Crossref]
  10. W. R. Peng, X. Wu, K. M. Feng, V. R. Arbab, B. Shamee, J. Y. Yang, L. C. Christen, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation technique,” Opt. Express 17(11), 9099–9111 (2009).
    [Crossref] [PubMed]
  11. K. Zou, Y. Zhu, F. Zhang, and Z. Chen, “Spectrally efficient terabit optical transmission with Nyquist 64-QAM half-cycle subcarrier modulation and direct detection,” Opt. Lett. 41(12), 2767–2770 (2016).
    [Crossref] [PubMed]
  12. Z. Li, M. Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. Thomsen, P. Bayvel, and R. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35(10), 1887–1893 (2017).
    [Crossref]
  13. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-kronig coherent receiver,” Optica 3(11), 1220–1227 (2016).
    [Crossref]
  14. D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightwave Technol. 28(4), 484–493 (2010).
    [Crossref]
  15. D. Che, C. Sun, and W. Shieh, “Direct detection of the optical field beyond single polarization mode,” Opt. Express 26(3), 3368–3380 (2018).
    [Crossref] [PubMed]
  16. W. Peng, K. Feng, and A. E. Willner, “Direct-detected polarization division multiplexed OFDM systems with self-polarization diversity,” Proc. LEOS, paper. MH3(2008).
    [Crossref]
  17. M. Nazarathy and A. Agmon, “Doubling direct-detection data rate by polarization multiplexing of 16-QAM without active polarization control,” Opt. Express 21(26), 31998–32012 (2013).
    [Crossref] [PubMed]
  18. T. M. Hoang, M. Y. S. Sowailem, Q. Zhuge, Z. Xing, M. Morsy-Osman, E. El-Fiky, S. Fan, M. Xiang, and D. V. Plant, “Single wavelength 480 Gb/s direct detection over 80km SSMF enabled by Stokes vector Kramers Kronig transceiver,” Opt. Express 25(26), 33534–33542 (2017).
    [Crossref]
  19. D. Che, C. Sun, and W. Shieh, “Single-channel 480-Gb/s direct detection of POL-MUX IQ signal using single-sideband Stokes vector receiver,” Proc. Optical Fiber Communication Conference, Tu2C.7 (2018).
    [Crossref]
  20. C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers-Kronig receiver,” J. Lightwave Technol. 35(24), 5418–5424 (2017).
    [Crossref]
  21. D. Che, A. Li, X. Chen, Q. Hu, Y. Wang, and W. Shieh, “Stokes Vector Direct Detection for Linear Complex Optical Channels,” J. Lightwave Technol. 33(3), 678–684 (2015).
    [Crossref]
  22. A. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photonics Technol. Lett. 22(7), 468–470 (2010).
    [Crossref]
  23. R. Ryf, S. Randel, N. K. Fontaine, M. Montoliu, E. Burrows, S. Chandrasekhar, A. H. Gnauck, C. Xie, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Gruner-Nielsen, R. V. Jensen, and R. Lingle, “32-bit/s/Hz spectral efficiency WDM transmission over 177-km few-mode fiber,” Proc. Optical Fiber Communication Conference, PDP5A.1(2013).
  24. X. Zhou, “An improved feed-forward carrier recovery algorithm for coherent receiver with M-QAM modulation format,” IEEE Photonics Technol. Lett. 22(14), 1051–1053 (2010).
    [Crossref]

2018 (4)

2017 (5)

2016 (3)

2015 (2)

2013 (1)

2010 (3)

A. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photonics Technol. Lett. 22(7), 468–470 (2010).
[Crossref]

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

D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightwave Technol. 28(4), 484–493 (2010).
[Crossref]

2009 (2)

Agmon, A.

Alves, T. M. F.

Amin, A. A.

A. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photonics Technol. Lett. 22(7), 468–470 (2010).
[Crossref]

Antonelli, C.

Arbab, V. R.

Aref, V.

Bayvel, P.

Buchali, F.

Buelow, H.

Cartaxo, A. V. T.

Chagnon, M.

Chandrasekhar, S.

Che, D.

Chen, X.

Chen, Z.

Chi, N.

Chi, S.

Christen, L. C.

Cvijetic, N.

Dischler, R.

El-Fiky, E.

Engenhardt, K. M.

Erkilinç, M.

Fan, S.

Feng, K.

Feng, K. M.

Galdino, L.

Hoang, T. M.

Hu, J.

Hu, Q.

Huo, J.

Killey, R.

Lau, A. P. T.

Le, S. T.

Li, A.

Li, Z.

Liu, G. N.

Lu, C.

Mecozzi, A.

Mendes, L. M. M.

Morita, I.

A. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photonics Technol. Lett. 22(7), 468–470 (2010).
[Crossref]

Morsy-Osman, M.

Nazarathy, M.

Peng, W.

Peng, W. R.

Plant, D. V.

Qian, D.

Schuh, K.

Shamee, B.

Shi, J.

Shi, K.

Shieh, W.

Shtaif, M.

Sillekens, E.

Sowailem, M. Y. S.

Sun, C.

Takahashi, H.

A. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photonics Technol. Lett. 22(7), 468–470 (2010).
[Crossref]

Tanaka, H.

A. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photonics Technol. Lett. 22(7), 468–470 (2010).
[Crossref]

Thomsen, B.

Wang, T.

Wang, Y.

Willner, A. E.

Winzer, P. J.

Wu, X.

Xiang, M.

Xing, Z.

Yang, J.

Yang, J. Y.

Yu, C.

Yu, J.

Zhang, F.

Zhang, J.

Zhang, L.

Zhang, Q.

Zhong, K.

Zhou, X.

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Lightwave Technol. 36(2), 377–400 (2018).
[Crossref]

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

Zhou, Y.

Zhu, Y.

Zhuge, Q.

Zou, K.

Zuo, T.

IEEE Photonics Technol. Lett. (2)

A. A. Amin, H. Takahashi, I. Morita, and H. Tanaka, “100-Gb/s direct-detection OFDM transmission on independent polarization tributaries,” IEEE Photonics Technol. Lett. 22(7), 468–470 (2010).
[Crossref]

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

J. Lightwave Technol. (12)

G. N. Liu, L. Zhang, T. Zuo, and Q. Zhang, “IM/DD transmission techniques for emerging 5G fronthaul, DCI and metro applications,” J. Lightwave Technol. 36(2), 560–567 (2018).
[Crossref]

K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Lightwave Technol. 36(2), 377–400 (2018).
[Crossref]

J. Shi, J. Zhang, Y. Zhou, Y. Wang, N. Chi, and J. Yu, “Transmission performance comparison for 100-Gb/s PAM-4, CAP-16, and DFT-S OFDM with direct detection,” J. Lightwave Technol. 35(23), 5127–5133 (2017).
[Crossref]

D. Che, Q. Hu, and W. Shieh, “Linearization of direct detection optical channels using self-coherent subsystems,” J. Lightwave Technol. 34(2), 516–524 (2016).
[Crossref]

Y. Zhu, K. Zou, Z. Chen, and F. Zhang, “224Gb/s optical carrier-assisted Nyquist 16-QAM half-cycle single-sideband direct detection transmission over 160km SSMF,” J. Lightwave Technol. 35(9), 1557–1565 (2017).
[Crossref]

W. Peng, X. Wu, V. R. Arbab, K. Feng, B. Shamee, L. C. Christen, J. Yang, and A. E. Willner, “Theoretical and experimental investigations of direct-detected RF-tone assisted optical OFDM systems,” J. Lightwave Technol. 27(10), 1332–1339 (2009).
[Crossref]

T. M. F. Alves, L. M. M. Mendes, and A. V. T. Cartaxo, “High granularity multiband OFDM virtual carrier-assisted direct-detection metro networks,” J. Lightwave Technol. 33(1), 42–54 (2015).
[Crossref]

S. T. Le, K. Schuh, M. Chagnon, F. Buchali, R. Dischler, V. Aref, H. Buelow, and K. M. Engenhardt, “1.72Tb/s virtual-carrier assisted direct-detection transmission over 200km,” J. Lightwave Technol. 36(6), 1347–1353 (2018).
[Crossref]

Z. Li, M. Erkılınç, K. Shi, E. Sillekens, L. Galdino, B. Thomsen, P. Bayvel, and R. Killey, “SSBI mitigation and the Kramers-Kronig scheme in single-sideband direct-detection transmission with receiver-based electronic dispersion compensation,” J. Lightwave Technol. 35(10), 1887–1893 (2017).
[Crossref]

D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightwave Technol. 28(4), 484–493 (2010).
[Crossref]

C. Antonelli, A. Mecozzi, M. Shtaif, X. Chen, S. Chandrasekhar, and P. J. Winzer, “Polarization multiplexing with the Kramers-Kronig receiver,” J. Lightwave Technol. 35(24), 5418–5424 (2017).
[Crossref]

D. Che, A. Li, X. Chen, Q. Hu, Y. Wang, and W. Shieh, “Stokes Vector Direct Detection for Linear Complex Optical Channels,” J. Lightwave Technol. 33(3), 678–684 (2015).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Optica (1)

Other (4)

W. Peng, K. Feng, and A. E. Willner, “Direct-detected polarization division multiplexed OFDM systems with self-polarization diversity,” Proc. LEOS, paper. MH3(2008).
[Crossref]

D. Che, C. Sun, and W. Shieh, “Single-channel 480-Gb/s direct detection of POL-MUX IQ signal using single-sideband Stokes vector receiver,” Proc. Optical Fiber Communication Conference, Tu2C.7 (2018).
[Crossref]

X. Chen, C. Antonelli, S. Chandrasekhar, G. Raybon, J. Sinsky, A. Mecozzi, M. Shtaif, and P. Winzer, “218-Gb/s single-wavelength, single-polarization, single-photodiode transmission over 125-km of standard single-mode fiber using Kramers-Kronig detection,” Proc. Optical Fiber Communication Conference, Paper Th5B.6 (2017).

R. Ryf, S. Randel, N. K. Fontaine, M. Montoliu, E. Burrows, S. Chandrasekhar, A. H. Gnauck, C. Xie, R. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Gruner-Nielsen, R. V. Jensen, and R. Lingle, “32-bit/s/Hz spectral efficiency WDM transmission over 177-km few-mode fiber,” Proc. Optical Fiber Communication Conference, PDP5A.1(2013).

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Figures (10)

Fig. 1
Fig. 1 (a) Bias induced carrier generation scheme. (b) Digital virtual carrier generation scheme. (c) Optical carrier generation scheme. (d) Reception principle of the optical filter based PDM DD scheme. ECL: external cavity laser; OFCG: optical frequency comb generator; SP: single polarization; Mod.: modulator; PBC: polarization beam combiner; AWG: arbitrary waveform generator; DP: dual polarization; PM-OC: polarization-maintaining optical coupler; OBPF: optical band-pass filter; Pol.: polarization.
Fig. 2
Fig. 2 DSP flows of (a) Iterative SSBI cancellation; (b) Kramers-Kronig detection; (c) Joint iterative SSBI cancellation.
Fig. 3
Fig. 3 Experimental setup. AWG: arbitrary waveform generator; ECL: external cavity laser; Mod.: modulator; PM-EDFA: polarization-maintaining erbium-doped fiber amplifier; OC: optical coupler; PBC: polarization beam combiner; SSMF: standard single-mode fiber; OBPF: optical band-pass filter; PD: photodiode; EA: electrical amplifier; DSO: digital storage oscilloscope.
Fig. 4
Fig. 4 (a) Transmitter side DSP. (b) Receiver side DSP; (c) Frame structure of transmitted signal. RRC: root raise cosine, Pre CD comp.: chromatic dispersion pre-compensation.
Fig. 5
Fig. 5 (a) Optical spectra at the transmitter. (b) Transmitted and received optical spectra. (c) Optical spectrum of the OBPF in our experiment. The resolution is set as 0.02nm.
Fig. 6
Fig. 6 (a) Measured BERs of X/Y polarization versus total launch power after 80km SSMF transmission. SSBI-C = 0: without SSBI compensation; KK: with KK detection; SSBI-C = 2: with joint iterative SSBI cancellation. (b)&(c) Typical constellations of X/Y polarizations without SSBI compensation at 12dBm launch power. (d)&(e) Typical constellations of X/Y polarization with KK detection at 12dBm launch power. (f)&(g) Typical constellations of X/Y polarizations with joint iterative SSBI cancellation. Pol.: polarization; w/o: without; w/: with.
Fig. 7
Fig. 7 (a) Measured BERs versus OSNR for PDM/SP signal at BTB scenario, respectively. SSBI-C = 0: without SSBI compensation; KK: with KK detection; SSBI = 2: with joint iterative SSBI cancellation. (b)&(c) Typical constellations of X/Y polarizations without SSBI compensation for PDM signals. (d)&(e) Typical constellations of X/Y polarizations with KK detection for PDM signals. (f)&(g) Typical constellations of X/Y polarizations with joint iterative SSBI cancellation. The OSNR are all fixed as 52dB. Pol.: polarization; SP: single polarization; w/o: without; w/: with.
Fig. 8
Fig. 8 (a) Simulated BERs versus OSNR for PDM-SSB signals with different CSPRs at BTB. SSBI-C = 0: without SSBI cancellation; SSBI-C = 1: with iterative SSBI cancellation; SSBI-C = 2, with joint iterative SSBI cancellation; KK, with KK detection. (b)-(e) Typical constellations of a 10dB CSPR signal at 45dB OSNR without SSBI cancellation, with iterative SSBI cancellation, with KK detection, and with joint iterative SSBI cancellation, respectively.
Fig. 9
Fig. 9 (a) DSP flow of the modified MIMO equalization. Conj(·): conjugation operation; RLS: recursive least square algorithm. (b) Simulated BERs versus OSNR of a 12dB CSPR signal with 4th-order Gaussian OBPF at BTB. (c)-(f) Typical constellations of a 12dB CSPR signal at 45dB OSNR without SSBI cancellation, with KK detection, with joint iterative SSBI cancellation, and with both joint SSBI cancellation and MIMO equalization, respectively.
Fig. 10
Fig. 10 (a) Simulated BERs versus OSNR with different OBPF orders with/without MIMO equalization at BTB. (b) Simulated BERs versus OSNR with different guard bands with/without MIMO equalization at BTB. w/o: without; w/: with.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

I 1 = | S x + C x | 2 + | S y + C y /α | 2 = | C x | 2 + | C y /α | 2 +2Re{ S x C x }+ 2Re{ S y C y }/α + | S x | 2 + | S y | 2 .
I 2 = | S x + C x /α | 2 + | S y + C y | 2 = | C y | 2 + | C x /α | 2 + 2Re{ S y C y }+2Re{ S x C x }/α + | S x | 2 + | S y | 2 .
I 1 = | C x + S x | 2 + | S y | 2 = | C x | 2 +2Re{ S x C x }+ | S x | 2 + | S y | 2 .
I 2 = | S x | 2 + | C y + S y | 2 = | C y | 2 +2Re{ S y C y }+ | S y | 2 + | S x | 2 .
CSPR( dB )=10 log 10 P xcarrier + P ycarrier P xsignal + P ysignal .
t 1 =( t x 0 ), t 2 =( 0 t y ), t x = t y .

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