Open Access
Add to BibSonomy
Abstract
Low-cost, spectrally efficient self-coherent detection capable of optical field recovery is desired for inter-data center connections and metro networks. In this work, a simplified symmetric carrier assisted differential detection (S-CADD) receiver structure is proposed, which removes the single-ended photodiode branch and saves one ADC in standard asymmetric CADD (A-CADD) receivers. To compensate for the signal-signal beating (SSBI) impairment, a low-complexity iterative SSBI mitigation algorithm is put forward as well. The computational complexity is reduced by moving equalization, de-modulation and modulation out of each iteration. Based on single-carrier twin-single sideband (SSB) pulse- and quadrature-amplitude modulation (PAM and QAM) signals, the OSNR sensitivity with different carrier-to-signal power ratios (CSPRs) at back-to-back (BTB) scenario, the bit-error rates (BER) performance after 1000km fiber transmission, and the received optical power sensitivity at BTB are theoretically and numerically compared for both S-CADD and A-CADD receivers, respectively.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Driven by 4K/8K high-definition video, augmented/virtual reality (AR/VR), cloud computing, and other broadband services in 5G era, high-speed transmission solution attracts increasing attentions for data-center interconnections and metro networks. Although coherent detection has the advantages of superior sensitivity, high spectral efficiency (SE), and capability of linear optical field recovery [1], the requirement of narrow-linewidth local oscillator (LO) lasers with wavelength alignment remains a barrier for its application in such cost-sensitive scenarios [2–3]. On the other hand, intensity modulation with direct detection (IM-DD) is more promising for short-reach link, due to its simplicity and low-cost [4]. However, as the transmission distance increases, the fiber dispersion induced phase variations on the conjugate sidebands of IM signal would turn into amplitude distortion after the square-law detection of photodiode, and thus the available bandwidth is limited by the frequency selective power fading effect [5]. Therefore, as a compromise, a category of self-coherent schemes has been widely discussed.
So far, tremendous efforts have been made to improve the transmission distance and SE of self-coherent schemes [6–19]. In [6], a block-wise phase switch (BPS) scheme is proposed to achieve fading-free detection. In order to obtain both the in-phase and quadrature components of the optical field, π/2 phase shift is applied on the signal or the optical carrier of the two consecutive blocks, leading to only 50% electrical SE with respect to single polarization coherent detection. Based on one-symbol delay, single carrier interleaved direct detection (SCI-DD) scheme is reported [7,8]. 1/2 or 1/3 time blocks should be left unmodulated for signal-carrier beating, indicating up to 67% electrical SE of coherent detection. By introducing the dimension of polarization, Stokes vector receiver (SVR) is able to acquire up to 3-dimensional information including intensity of both polarization and the inter-polarization phase [9,10]. Meanwhile, single sideband (SSB) signaling is also a good candidate with digital linearization algorithms such as Kramers-Kronig (KK) relation [11] or iterative signal-signal beat interference (SSBI) mitigation [12–14]. However, the electrical SE is still halved, since it is inherently a kind of self-heterodyne detection. Although twin-SSB [15,16] and two-sided KK transceiver [17] are designed to double the electrical SE later, the usage of optical filters with sharp edge roll-off at the receiver prevents its practical application.
Recently, a novel carrier assisted differential detection (CADD) receiver is put forward as self-homodyne detection [18,19]. Complex-valued double-sideband (DSB) orthogonal frequency division multiplexing (OFDM) signal is detected without using optical filter, and similar electrical SE as single polarization coherent detection can be approached by reducing the guard band. Different from the conventional differential detection, CADD deals with the linear signal-carrier beating term, and thus transmission impairments can be effectively compensated at the receiver. However, to construct the asymmetric CADD (A-CADD) receiver in [18,19], one 90° optical hybrid, one single-ended photodiode (SPD), and a pair of balanced PDs (BPD) are needed, which is relatively complex. Also, since the receiver structure is not symmetric between the SPD and hybrid branch, additional delay and amplitude mismatch should be taken into consideration for practical implementation.
In this work, we propose a simplified symmetric CADD (S-CADD) receiver structure and its corresponding optical field recovery approach. A low-complexity iterative SSBI mitigation algorithm is also designed, which does not include equalization, demodulation and modulation stages in each iteration. Based on single-carrier twin-SSB pulse- and quadrature-amplitude modulation (PAM and QAM) signals, the proposed S-CADD receiver and simplified iterative SSBI mitigation algorithm are validated and compared with conventional scheme through simulation in three scenarios: (1) OSNR sensitivity with different carrier-to-signal power ratios (CSPRs) at back-to-back (BTB) case, (2) BER performance after 1000km fiber transmission, and (3) received optical power sensitivity with various CSPRs at BTB. Corresponding theoretical analysis is also provided to confirm the results. The simulation results indicate that S-CADD receiver exhibits better performance at low CSPR, and has better power sensitivity than A-CADD receiver.
The rest of the paper is organized as follows. In Section 2, the structure and reception principle of A-CADD and S-CADD transceivers are introduced, respectively. The proposed simplified iterative SSBI mitigation algorithm is also presented. Section 3 shows the simulation results and provides corresponding explanations in three scenarios. Finally, conclusions are drawn in Section 4.
2. Principle of S-CADD receiver and simplified iterative SSBI mitigation
2.1 Principle of S-CADD receiver
First of all, we introduce the structure and reception principle of A-CADD and S-CADD receivers as shown in Figs. 1(a)–1(d). Specifically, Fig. 1(a) shows the structure of A-CADD reported in [18], while Fig. 1(b) shows its equivalent version by replacing 90° optical hybrid with 3×3 coupler [20]. The proposed S-CADD receiver and its equivalent structure, are displayed in Figs. 1(c)–1(d), respectively, where the upper SPD detection branch is removed.
Fig. 1. Structures of A-CADD and S-CADD receivers. (a) A-CADD receiver with 90° hybrid; (b) A-CADD receiver with 3×3 coupler; (c) S-CADD receiver with 90° hybrid; (d) S-CADD receiver with 3×3 coupler.
The principle of A-CADD receiver in Fig. 1(a) can be briefly stated as follows. C and $S(t )$ denote the optical carrier and the complex-valued DSB signal, respectively. Then the input signal of the A-CADD receiver can be expressed as $C + S(t )$. After PD detection, the waveforms captured by ADC1/2/3 are given as:
Here the splitting ratios of 1×2 couplers and 90° hybrid are considered. Re{·} and Im{·} represent the real and imaginary part operation, respectively. After linear combination, the signal can be calculated as:
On the right side of Eq. (2), the 1st and 2nd terms are the linear carrier-signal beating terms with inter-symbol interference (ISI), and the 3rd and 4th terms are the SSBI impairments. After SSBI compensation, the residual ISI can be eliminated by time-domain equalization or frequency-domain transfer function as in Eq. (3).
Here FFT{·} and IFFT{·} denotes the fast Fourier transform and inverse fast Fourier transform, respectively. ${H_{\textrm{A - CADD}}}(f )= 1 - {e^{ - j2\pi f\tau }}$ is the transfer function of A-CADD receiver.
Different from A-CADD receiver, the optical field recovery of S-CADD receiver in Fig. 1(c) only needs to combine the photocurrent outputs of the hybrid branch, which are similar as in Eq. (1b) and Eq. (1c).
Note that since one 1×2 optical coupler and the SPD is saved, the amplitude coefficient in Eq. (4) is increased to 1/2. Then delay $\tau ^{\prime}$ can be applied to the waveform ${R_2}(t )$ as:
By subtracting the conjugation of Eq. (5) from Eq. (4), the desired beating terms together with ISI and SSBI impairments can be acquired.
Similarly, the target signal can be finally obtained with the help of transfer function as:
Here ${H_{\textrm{S - CADD}}}(f )= 1 - {e^{ - j2\pi f \cdot 2\tau ^{\prime}}}$ is the transfer function of S-CADD receiver. In contrast to A-CADD receiver, S-CADD receiver would not be affected by the additional delay of 1×2 coupler after optical delay line as well as amplitude mismatch, owing to its symmetric structure. Also, S-CADD receiver can achieve lower optimal CSPR and better power sensitivity, which will be shown in Section 3 and Appendix A. Besides, according to Eq. (7), when $\tau = 2\tau ^{\prime}$ is satisfied, S-CADD receiver would share the same transfer function as A-CADD scheme, leading to the same available passband for transmission. It should be noted that the delay and subtraction operation in Eqs. (4)–(6) can be realized by analog circuits, and thus the requirement of sampling rate can be relaxed. Furthermore, 3×3 coupler based structure in Fig. 1(d) can achieve signal reception as well. The detailed derivation is given in Appendix A.
2.2 Simplified iterative SSBI mitigation
For both A-CADD and S-CADD receivers, SSBI is the main source of performance limitation. Taking A-CADD receiver for example, Fig. 2(a) depicts the iterative SSBI mitigation method proposed in [18]. In each iteration, the ISI is suppressed by multiplying the inverse transfer function and equalization. The influence of SSBI and noise is removed after symbol decision. Then the SSBI can be reconstructed with the ‘clean’ symbols according to the formula of ${S^ \ast }({t - \tau } )S(t )- {|{S({t - \tau } )} |^2}$. For S-CADD receiver, the formula should be modified as ${S^ \ast }({t - \tau^{\prime}} )S(t )- {S^ \ast }({t - \tau^{\prime}} )S({t - 2\tau^{\prime}} )$. Finally, iterations are introduced to improve the precision of SSBI estimation. However, the computational complexity is too high, since both receiver- and transmitter-side digital signal processing (DSP) are involved in the loop. For signals after fiber transmission, the dispersion compensation and inverse dispersion emulation would further increase the complexity.
Fig. 2. (a) Conventional iterative SSBI mitigation algorithm in [18]; (b) proposed simplified iterative SSBI mitigation algorithm.
Here we put forward a simplified iterative SSBI mitigation algorithm as shown in Fig. 2(b). Firstly, the SSBI can be rewritten as $[{S(t )- S({t - \tau } )} ]\cdot {S^ \ast }({t - \tau } )$. In each iteration, the term $S(t )- S({t - \tau } )$ can be estimated after subtracting SSBI from the input waveform. After passing the inverse transfer function, the term ${S^ \ast }({t - \tau } )$ is emulated by delay and conjugation operation. Therefore, the SSBI is easily reconstructed by the product of the above two terms. In doing so, the receiver-side dispersion compensation, equalization and demodulation are moved out of the loop, and re-modulation is avoided, making the complexity greatly reduced. Note that in the simplified iteration SSBI mitigation algorithm, the singularities at f=0, ±1/τ should be removed by either setting zeros in the frequency domain or convoluting with window filter in the time domain, in order to avoid vibration. The simplified SSBI mitigation algorithm is still valid for S-CADD receiver, once the SSBI is emulation in the form of $[{S(t )- S({t - 2\tau^{\prime}} )} ]\cdot {S^ \ast }({t - \tau^{\prime}} )$. Specifically, $S(t )- S({t - 2\tau^{\prime}} )$ and ${S^ \ast }({t - \tau^{\prime}} )$ can be obtained before and after inverse transfer function, respectively.
2.3 DSP stacks of single-carrier signal in A-CADD and S-CADD system
In general, OFDM signal is more suitable for CADD receiver, due to its ability of entropy loading [21] against the uneven transfer function. On the other hand, the feasibility of single-carrier modulated signal has not been demonstrated in CADD system. Here we will evaluate the performance of Nyquist-shaped twin-SSB PAM/QAM signals, respectively. As shown in Fig. 3(a), to generate twin-SSB PAM signal, two independent bit streams are mapped into PAM-$\sqrt M $ format for left/right sideband (LSB/RSB), respectively. Here the baud rate is set as $2B$, therefore the aggregate bit rate is $2B{\log _2}M$ ($= 2 \times 2B \times {\log _2}\sqrt M $). To construct rectangular-like spectra, the symbol sequences are digitally shaped with root raised cosine (RRC) filter. Since PAM signal is real-valued, one of the conjugated sidebands can be removed by Hilbert filter. After up-conversion for guard band insertion, LSB and RSB are combined. The optical carrier can be added by adjusting the bias of modulator. For twin-SSB QAM signal generation, as shown in Fig. 3(b) two M-QAM symbol sequences are employed at baud rate of B. The total bit rate can be also calculated as $2B{\log _2}M$ ($= 2 \times B \times {\log _2}M$). After pulse shaping, the two sidebands are shifted to the left and right, respectively. In comparison, it is found that given the same total bit rate, the twin-SSB PAM/QAM signals occupy the same bandwidth, indicating the same electrical SE of ∼${\log _2}M$.
Fig. 3. Transmitter-side DSP for (a) twin-SSB PAM signal; (b) twin-SSB QAM signal; Receiver-side DSP for (c) twin-SSB PAM signal; (d) twin-SSB QAM signal. Tx: transmitter-side; Rx: receiver-side; RSB: right sideband; LSB: left sideband; RRC: root raised cosine.
At the receiver, as shown in Fig. 3(c) and Fig. 3(d), both twin-SSB PAM and QAM signals are firstly filtered by the inverse transfer function to flatten the spectra. For twin-SSB PAM signal, the target sideband is down-converted with the edge of spectrum next to zero frequency. Then the unwanted sideband is removed with Hilbert filter. After extracting the real part and match RRC filter shaping, the signal is finally recovered. Differently, for twin-SSB QAM signal reception, the desired sideband is down-converted with the center of spectrum to zero frequency. Afterwards, matched RRC filter is enough for signal recovery as a low-pass filter. According to the transmitter- and receiver-side DSP, CADD can deal with twin-SSB PAM/QAM signals without using optical filter, and the electrical SE and capacity is doubled from KK receiver.
3. Results and discussion
3.1 Simulation setup
The performance of S-CADD receiver structure and simplified iterative SSBI mitigation algorithm are verified and compared numerically by co-simulation of MATLAB and VPItransmissionMaker. Figure 4 shows the simulation setup, in which transmitter- and receiver-side DSP are performed in MATLAB, and the fiber, optical and electrical devices are modelled in VPI. For fair comparison, 60 Gbaud twin-SSB PAM-4 and 30 Gbaud twin-SSB 16-QAM signals are employed to achieve the same bit rate of 240Gb/s, respectively. At the head of each frame, a 1024-symbol sequence is used for synchronization and equalization, 220 total bits are transmitted for BER calculation. The roll-off of the RRC filter is set as 0.01. Note that in order to share the same transfer function, the time delay $\tau $ and $\tau ^{\prime}$ for A-CADD and S-CADD receivers are 25ps and 12.5ps, respectively. Generally, the enhanced region of transfer function can be calculated as $[{{1 \mathord{\left/ {\vphantom {1 {6\tau }}} \right.} {6\tau }},{5 \mathord{\left/ {\vphantom {5 {6\tau }}} \right.} {6\tau }}} ]$ and $[{{1 \mathord{\left/ {\vphantom {1 {12\tau^{\prime}}}} \right.} {12\tau^{\prime}}},{5 \mathord{\left/ {\vphantom {5 {12\tau^{\prime}}}} \right.} {12\tau^{\prime}}}} ]$ for A-CADD and S-CADD receivers, respectively, which corresponds to [6.67GHz, 33.33GHz] in this case. Then the subcarrier factor k and k’ in Fig. 3(a) and Fig. 3(b) are set as 0.083(=20/60-0.25) and 0.667(=20/30) for PAM and QAM signals, respectively. In this way, twin-SSB PAM-4 and twin-SSB 16-QAM signals are both up-converted to the center frequency of 20GHz with almost the same guard band, and the enhanced region of the transfer function is fully used.
Fig. 4. Simulation setup. DAC: digital-to-analog convertor; ADC: analog-to-digital convertor; IQ Mod.: IQ modulator; SSMF: standard single-mode fiber; AWGN: additive white Gaussian noise.
At the transmitter, the optical carrier is added according to the CSPR, where both sidebands are included in the definition of signal power. At the transmitter, laser source is centered at 1550nm, and the IQ modulator is used for twin-SSB signal modulation, which is biased above the null point according to the target CSPR. The dispersion parameter of SSMF is set as 17ps/nm/km. The nonlinear coefficient is set as zero to focus on the influence of fiber dispersion. After transmission, optical additive white Gaussian noise (AWGN) is mixed with signal for OSNR sensitivity measurement.
At the receiver, A-CADD/S-CADD receivers in Figs. 1(a)–1(d) are switched for comparison. There is no additional insertion loss for optical couplers and 90° hybrid. The PDs are modeled with responsivity of 0.7A/W, dark current of 3×10−9 A, and thermal noise of 10−11 A/Hz1/2, respectively. Shot noise contributes to the PD noise as well.
3.2 OSNR sensitivity at BTB
We first compare the performance of conventional and proposed simplified iterative SSBI mitigation algorithms as a function of iterations. Note that in this subsection, in order to test OSNR sensitivity, PD is modelled ideal without any noise. Figures 5(a)–5(b) plot the bit-error rate (BER) versus number of iterations for twin-SSB PAM-4 and 16-QAM signals detected by S-CADD receiver with 90° hybrid [Fig. 1(c)] at BTB, respectively. The CSPR and OSNR are fixed as 8dB and 32dB, respectively. Here iteration 0 means without SSBI compensation. As the number of iterations increases, BER with conventional algorithm shrinks slightly faster than the simplified iterative SSBI mitigation. When the number of iterations is larger than 5, the performance gets saturated for both algorithms, and similar BER is achieved. Therefore, the iteration is set as 5 in the following simulations.
Fig. 5. BER versus number of iterations for (a) twin-SSB PAM signal and (b) twin-SSB QAM signal detected by S-CADD receiver with 90° hybrid at BTB, respectively. (i)∼(vi) Typical eye-diagrams/constellations without/with SSBI mitigation. Prop.: proposed simplified iterative SSBI mitigation; Conv.: conventional iterative SSBI mitigation.
Then we evaluate the SSBI compensation performance for twin-SSB PAM-4/16-QAM signals with different SSBI compensation methods at BTB, respectively. The CSPR-value in Figs. 6(a)–6(d) and Figs. 7(a)–7(d) is also changed to vary the influence of SSBI. We can find that: (1) Without SSBI compensation, the BER is still ∼1×10−2 with low-CSPR although the OSNR is large enough. With the help of conventional/proposed iterative SSBI mitigation, the error floor can be successfully reduced. (2) At low CSPR-values, the performance of proposed iterative algorithm is worse than the conventional one, because the residual SSBI is involved in the reconstruction process. When the CSPR is larger than 10dB, the BER with proposed iterative algorithm is similar or even slightly better than the conventional algorithm. The reason is that ‘clean’ symbols are used to reconstruct the SSBI in the conventional algorithm, and the noise-signal beating contribution is not fully emulated. (3) Since the optical carrier is included in the definition of signal power in OSNR, the OSNR sensitivity curves move to the right as the CSPR-value increases. For 8dB CSPR, there is still error floor after applying iterative SSBI mitigation, where wrong symbol recognition is occurred with large SSBI.
Fig. 6. Simulated OSNR sensitivity of twin-SSB PAM-4 signal for (a) A-CADD receiver with 90° hybrid; (b) A-CADD receiver with 3×3 coupler; (c) S-CADD receiver with 90° hybrid; (d) S-CADD receiver with 3×3 coupler at different CSPR at BTB, respectively. w/o: without SSBI compensation; w/ prop.: with proposed simplified iterative SSBI mitigation; w/ conv.: with conventional iterative SSBI mitigation.
Fig. 7. Simulated OSNR sensitivity of twin-SSB 16-QAM signal for (a) A-CADD receiver with 90° hybrid; (b) A-CADD receiver with 3×3 coupler; (c) S-CADD receiver with 90° hybrid; (d) S-CADD receiver with 3×3 coupler at different CSPR at BTB, respectively. w/o: without SSBI compensation; w/ prop.: with proposed simplified iterative SSBI mitigation; w/ conv.: with conventional iterative SSBI mitigation.
Figures 8(a)–8(b) shows the simulated BER versus OSNR of twin-SSB PAM-4/16-QAM signal with different CADD receivers, respectively. The proposed SSBI mitigation is applied for all the curves for fair comparison. At low CSPR-values, the influence of SSBI is more severe with A-CADD receivers than S-CADD receivers. Therefore, the S-CADD receivers can support lower optimal CSPR for transmission at BTB. On the other hand, as the CSPR increases, the curves of four receiver structures get closer, indicating the same OSNR sensitivity. The theoretical derivation is provided in Appendix A.
Fig. 8. Simulated OSNR sensitivity of (a) twin-SSB PAM-4; (b) twin-SSB 16-QAM signal with different CADD receivers, respectively.
3.3 Transmission performance
In this subsection, we demonstrate that both A-CADD and S-CADD receivers are capable of receiver-side chromatic dispersion compensation (CDC), which allows more flexible application scenarios. Since IQ modulator is used at the transmitter, pre-CDC is used as a reference.
Figure 9 and Fig. 10 display the 1000km SSMF transmission performance of twin-SSB PAM-4/16-QAM signals with different CADD receivers, respectively. It is found that: (1) For the same OSNR, BER performance is degraded by SSBI impairment at low CSPR, and limited by true signal-to-noise ratio at high CSPR. Due to the feature of smaller SSBI, S-CADD receivers can achieve lower optimal CSPR and better BER. (2) At low CSPR values, the residual SSBI would cause further distortion with post-CDC, resulting in worse performance than pre-CDC. However, comparable performance is observed with post- and pre-CDC, once the SSBI is successfully suppressed. (3) Although twin-SSB PAM-4 and twin-SSB 16-QAM signals exhibit the same bandwidth, fiber dispersion brings more severe ISI for twin-SSB PAM-4 signal, owing to its halved symbol duration.
Fig. 9. BER versus CSPR for twin-SSB PAM-4 signal with (a) A-CADD receiver with 90° hybrid; (b) A-CADD receiver with 3×3 coupler; (c) S-CADD receiver with 90° hybrid; (d) S-CADD receiver with 3×3 coupler after 1000 km SSMF transmission, respectively. CDC: chromatic dispersion compensation.
Fig. 10. BER versus CSPR for twin-SSB 16-QAM signal with (a) A-CADD receiver with 90° hybrid; (b) A-CADD receiver with 3×3 coupler; (c) S-CADD receiver with 90° hybrid; (d) S-CADD receiver with 3×3 coupler after 1000 km SSMF transmission, respectively. CDC: chromatic dispersion compensation.
3.4 Received power sensitivity at BTB
Furthermore, the received power sensitivities with four CADD receivers are compared for twin-SSB PAM-4/16-QAM signals as in Fig. 11 and Fig. 12, respectively. Here optical noise is not added to focus on the influence of PD noise. For all cases, the sensitivity of CADD receivers can be sorted from the most to the least sensitive as follows: S-CADD with 3×3 coupler, S-CADD with 90° hybrid, A-CADD with 3×3 coupler, A-CADD with 90° hybrid. Specifically, at 8dB CSPR, A-CADD receiver has >2.7dB power sensitivity penalty compared with S-CADD receivers, which is mainly caused by SSBI impairment. When the CSPR gets larger, the error floor of the A-CADD receiver disappears, and the power sensitivity penalty gradually decreases to ∼0.8dB. Similar phenomenon can be observed for both twin-SSB PAM-4 and twin-SSB 16-QAM signals. The sensitivity difference between four CADD receivers mainly comes from thermal noise of PDs, which is also proved theoretically in Appendix A.
Fig. 11. Simulated received power sensitivity for twin-SSB PAM-4 signal with different CADD receivers at BTB, respectively. (a) CSPR=8 dB; (b) CSPR=10 dB; (c) CSPR=12 dB; (d) CSPR=14 dB. ROP: received optical power. w/: with.
Fig. 12. Simulated received power sensitivity for twin-SSB 16-QAM signal with different CADD receivers at BTB, respectively. (a) CSPR=8 dB; (b) CSPR=10 dB; (c) CSPR=12 dB; (d) CSPR=14 dB. ROP: received optical power. w/: with.
4. Conclusion
In summary, we propose a simplified S-CADD receiver for complex-valued DSB signal reception, which does not require the SPD branch and reduces one ADC in standard A-CADD receiver. A simplified iterative SSBI mitigation algorithm is also put forward. The computational complexity is greatly reduced by moving equalization, de-modulation and modulation out of each iteration. The feasibility of single-carrier twin-SSB PAM-4 and twin-SSB 16-QAM signals is verified for both A-CADD and S-CADD receivers, respectively. Through numerical simulation, we first show that S-CADD receiver can achieve lower optimal CSPR both at BTB and after 1000km fiber transmission. Secondly, the capability of flexible receiver-side dispersion compensation is demonstrated for CADD receivers. Moreover, S-CADD receivers exhibit better power sensitivity than the standard structures at BTB. The simulation results coincide with theoretical derivation. We believe that the S-CADD receiver can provide a low-cost and spectrally efficient solution for inter-data center connections and metro networks.
A. Appendix
A.1. SNR of A-CADD receiver with 90° hybrid
The SNR of A-CADD receiver with 90° hybrid in the presence of PD noise only is deduced as follows. As shown in Fig. 1(a), the output photocurrents after square-law detection of PD can be written as:
Here ${n_{e0}}$∼${n_{e4}}$ denote PD noises of each PD. Then the waveforms are combined as:
If the SSBI term is fully compensated, the SNR can be calculated as:
Here $H(f )= 1 - \exp ({ - j2\pi f\tau } )$ is the transfer function. Since ${n_{e0}}$∼${n_{e4}}$ are independent and identically distributed (i.i.d.) random variables, the variance of noises can be statistically added.
To obtain the SNR in the presence of optical noise only, we should set the PD noises to zeros and substitute $S(t )$ with $S(t )+ {n_{opt}}(t )$. Then Eq. (9) can be re-written as:
After SSBI mitigation and inverse transfer function for ISI elimination, the SNR is
Here ${P_{S(t )}}$ and ${P_{{n_{opt}}}}$ denote the power of signal and optical noise, while ${B_{ref}}$ and ${B_S}$ are the 0.1nm reference bandwidth and signal bandwidth in the OSNR definition, respectively.
A.2. SNR of A-CADD receiver with 3×3 coupler
The SNR of A-CADD receiver with 3×3 coupler in the presence of PD noise only is deduced as follows. As shown in Fig. 1(b), the output photocurrents can be obtained as:
Then the waveforms are combined as:
If the SSBI term is fully compensated, the SNR can be calculated as:
The SNR in the presence of optical noise only can be obtained by setting the PD noise to zeros and substituting $S(t )$ with $S(t )+ {n_{opt}}(t )$. Then the combined waveform is:
After SSBI mitigation and inverse transfer function for ISI elimination, the SNR is
A.3. SNR of S-CADD receiver with 90° hybrid
The SNR of S-CADD receiver with 90° hybrid in the presence of PD noise only is deduced as follows. The output photocurrents in Fig. 1(c) are the same as Eq. (8b) and Eq. (8c), except for changing the coefficient from ${1 \mathord{\left/ {\vphantom {1 {2\sqrt 2 }}} \right.} {2\sqrt 2 }}$ to 1/2. Then the waveforms are combined as:
If the SSBI term is fully compensated, the SNR can be calculated as:
Note that here $H(f )= 1 - \exp ({ - j2\pi f2\tau^{\prime}} )= 1 - \exp ({ - j2\pi f\tau } )$, if $\tau = 2\tau ^{\prime}$ is satisfied.
To obtain the SNR in the presence of optical noise only, we should set the PD noise to zeros and substitute $S(t )$ with $S(t )+ {n_{opt}}(t )$. Then the combined waveform can be re-written as:
After SSBI mitigation and inverse transfer function for ISI elimination, the SNR is
A.4. SNR of S-CADD receiver with 3×3 coupler
The SNR of S-CADD receiver with coupler in the presence of PD noise only is deduced as follows. The output photocurrents in Fig. 1(d) are the same as Eqs. (13b)–(13d), except for changing coefficient from ${1 \mathord{\left/ {\vphantom {1 {2\sqrt 2 }}} \right.} {2\sqrt 2 }}$ to 1/2. Then the waveforms are combined as:
If the SSBI term is fully compensated, the SNR can be calculated as:
To obtain the SNR in the presence of optical noise only, we should set the PD noise to zeros and substitute $S(t )$ with $S(t )+ {n_{opt}}(t )$. Then the combined waveform can be re-written as:
After SSBI mitigation and inverse transfer function for ISI elimination, the SNR is
By comparing Eq. (10), Eq. (15), Eq. (19), and Eq. (23), the received power sensitivity can be sorted from the most sensitive to least sensitive as: S-CADD receiver with 3×3 coupler, S-CADD receiver with 90° hybrid, A-CADD receiver with 3×3 coupler, A-CADD receiver with 90° hybrid. On the other hand, all the structures have the same OSNR sensitivity, if SSBI is perfectly compensated.
Funding
National Key Research and Development Program of China (2018YFB1800904); National Natural Science Foundation of China (61431009).
Acknowledgments
We thank Zhongwei Tan, Xiaoke Ruan, and Lei Zhang for valuable discussion.
Disclosures
The authors declare no conflicts of interest.
References
1. K. Kikuchi, “Fundamentals of coherent optical fiber communications,” J. Lightwave Technol. 34(1), 157–179 (2016). [CrossRef]
2. M. Morsy-Osman, M. Sowailem, E. El-Fiky, T. Goodwill, T. Hoang, S. Lessard, and D. Plant, “DSP-free ‘coherent-lite’ transceiver for next generation single wavelength optical intra-datacenter interconnects,” Opt. Express 26(7), 8890–8903 (2018). [CrossRef]
3. T. Gui, X. Wang, M. Tang, Y. Yu, Y. Lu, and L. Li, “Real-Time Demonstration of 600 Gb/s DP-64QAM Self-Homodyne Coherent Bi-Direction Transmission with Un-Cooled DFB Laser,” Proc. Optical Fiber Communication Conference, paper Th4C.3 (2020).
4. 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]
5. 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]
6. X. Chen, A. Li, D. Che, Q. Hu, Y. Wang, J. He, and W. Shieh, “Block-wise phase switching for double-sideband direct detected optical OFDM signals,” Opt. Express 21(11), 13436–13441 (2013). [CrossRef]
7. X. Chen, D. Che, A. Li, J. He, and W. Shieh, “Signal-carrier interleaved optical OFDM for direct detection optical communication,” Opt. Express 21(26), 32501–32507 (2013). [CrossRef]
8. D. Che, X. Chen, J. He, A. Li, and W. Shieh, “102.4-Gb/s single-polarization direct-detection reception using signal carrier interleaved optical OFDM,” Proc. Optical Fiber Communication Conf., Paper Tu3G.7 (2014).
9. M. Chagnon, M. Morsy-Osman, D. Patel, V. Veerasubramanian, A. Samani, and D. Plant, “Digital Signal Processing for Dual-Polarization Intensity and Inter-polarization Phase Modulation Formats Using Stokes Detection,” J. Lightwave Technol. 34(1), 188–195 (2016). [CrossRef]
10. D. Che, C. Sun, and W. Shieh, “Maximizing the spectral efficiency of Stokes vector receiver with optical field recovery,” Opt. Express 26(22), 28976–28981 (2018). [CrossRef]
11. A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-kronig coherent receiver,” Optica 3(11), 1220–1227 (2016). [CrossRef]
12. 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]
13. 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]
14. 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 200 km,” J. Lightwave Technol. 36(6), 1347–1353 (2018). [CrossRef]
15. L. Zhang, T. Zuo, Q. Zhang, E. Zhou, G. N. Liu, and X. Xu, “Transmission of 112-Gb/s DMT over 80-km SMF by Twin-SSB Technique,” in Proc. Eur. Conf. Opt. Commun., Paper 0373 (2015).
16. Y. Zhu, X. Ruan, K. Zou, and F. Zhang, “Beyond 200G Direct Detection Transmission with Nyquist Asymmetric Twin-SSB Signal at C-Band,” J. Lightwave Technol. 35(17), 3629–3636 (2017). [CrossRef]
17. C. Antonelli, A. Mecozzi, and M. Shtaif, “Kramers Kronig PAM transceiver and two-sided polarization-multiplexed Kramers Kronig transceiver,” J. Lightwave Technol. 36(2), 468–475 (2018). [CrossRef]
18. W. Shieh, C. Sun, and H. Ji, “Carrier-assisted differential detection,” Light: Sci. Appl. 9(1), 18 (2020). [CrossRef]
19. C. Sun, T. Ji, H. Ji, Z. Xu, and W. Shieh, “Experimental Demonstration of Complex-valued DSB Signal Field Recovery via Direct Detection,” IEEE Photonics Technol. Lett. 32(10), 1 (2020). [CrossRef]
20. C. Xie, P. J. Winzer, G. Raybon, A. H. Gnauck, B. Zhu, T. Geisler, and B. Edvold, “Colorless coherent receiver using 3 ( 3 coupler hybrids and single-ended detection,” Opt. Express 20(2), 1164–1171 (2012). [CrossRef]
21. D. Che and W. Shieh, “Approaching the Capacity of Colored-SNR Optical Channels by Multicarrier Entropy Loading,” J. Lightwave Technol. 36(1), 68–78 (2018). [CrossRef]
