1. Introduction

In optical communications, physical dimensions of electromagnetic light-wave or the transmission medium such as time, polarization, frequency, mode, and space are fully exploited to increase the channel capacity and enhance the optical network flexibility. Another degree of freedom, the power domain can also be utilized for multiplexing. In the recent 5G wireless system, the power domain type non-orthogonal multiple access (NOMA) technique [1,2] is adopted for multiple access, which superimposes signals from multiple users in the power domain at the base station and adopts the successive interference cancellation (SIC) for signal separation at the user equipment. The NOMA technique allows multiple users to access the frequency resource at the same time, which improves the spectral efficiency and fairness. The NOMA scheme also finds applications in visible light communications [3,4] or elastic passive optical networks [5,6]. Noticeably, the power domain multiplexing technique can be implemented in coherent optical systems to resolve the wavelength conflict or facilitate network flexibility by optically combining two independent polarization-multiplexed quadrature phase-shift keying (PM-QPSK) signals with certain power ratio, which is called as optical overlap technique [7]. The single-carrier signal, as the basic signal format for optical overlap, instead of orthogonal frequency division multiplexing (OFDM) signal format, has the advantage that timing synchronization is not required. Implementing the power multiplexing in the optical domain has the flexibility and advantage that the power ratio of the two channels can be differentiated at the transmitter part or at the intermediate router node. Noted power levels are usually controlled at the transmitter part in the NOMA scheme, via either digital signal generation or optical components.

Although the signal overlap technique can resolve the wavelength conflict, the optical overlap of independent channels on the same frequency grid can be treated as in-band crosstalk [8], which may induce severe impact, especially to the high-order modulation formats. In order to realize efficient signal overlapping with satisfactory system performance, several works have been proposed on realizing the spectral overlap of QPSK signals. In [9], two polarization-multiplexed differential QPSK (PM-DQPSK) signals with balanced power levels were optically combined on the common channel to realize optical physical-layer network coding and they were separated and decoded properly using appropriate digital signal processing (DSP) algorithms. The prefix and the suffix of each channel were required for channel estimation so as to facilitate the signal re-construction and interference subtraction. Besides, there have been several works on the performance of ultra-dense wavelength division multiplexing (WDM) system, in which channel spacing was narrowed to close or even smaller than the channel’s baud rate, causing the spectrum overlap [10,11]. The partial spectrum overlap from adjacent WDM channels resulted in crosstalk and led to the increased optical-to-noise ratio (OSNR) requirement. In [7], the optical overlap of two independent PM-QPSK signals with a certain power ratio encoded with low-density parity-check (LDPC) was first experimentally demonstrated. Furthermore, the system performance of the two overlapped QPSK signals was analyzed, by numerical simulations, with respect to the net bit rate, transmission distance, the symbol rate, and the relevant networking applications, showing the benefits, in terms of spectrum usage, reach and blocking probability [12,13].

Nyquist shaping of the PM-QPSK signal is considered as it can further increase the spectrum efficiency, occupying minimal bandwidth close to the signal’s baud rate. In [14], we have experimentally demonstrated that two Nyquist-PM-QPSK signals could be optically combined with a certain power ratio for common transmission and got individual recovery properly from the overlapped signal, via successive interference cancellation. In [15], we have analyzed the bit error rate (BER) performance of two Nyquist-PM-QPSK signals with different baud rates, via simulation, in which one channel occupied two frequency slots and the other one only occupied one frequency slot. In this paper, we further characterize various system parameters, including time offset, polarization rotation, frequency offset, signal-to-interference ratio, etc., which determine such adjacent channel interference performance, and further optimize the channel power ratio when two optical channels, each carrying a Nyquist shaped and polarization multiplexed quadrature phase-shift keying (Nyquist-PM-QPSK) signal are being multiplexed with optical spectral overlap. Besides, we experimentally demonstrate the BER performance of the two overlapped noisy Nyquist-PM-QPSK channels for back to back (BTB) and 100-km single-mode fiber (SMF) transmission, with optimized channel power ratio. The impact from time offset on channel interference is also experimentally verified.

The rest of the paper is organized as follows. Section 2 illustrates the operation principle of the proposed optical signal overlap technique in detail. Section 3 demonstrates the simulation results of the overlapped system under different interfering conditions. Section 4 presents the experimental results. Finally, Section 5 summarizes the paper.

2. Operation principle

Figure 1 illustrates two possible application examples of optical overlap technique in elastic optical networks. Figure 1(a) shows the application of optical overlap technique at the intermediate node C. Two independent channels, denoted by their transmitted information data s_d and s_w, are sent from their respective source nodes A and B. Possible wavelength conflict occurs since two channels occupy the same spectrum resource. At intermediate node C, the optical power difference between s_d and s_w is carefully adjusted to form the composite overlapped signal s_o for common C-D link transmission. The dominant channel s_d is set to have relatively higher power than the weak channel s_w before being optically combined, via an optical coupler. Then, the overlapped signal s_o is split along D-E and D-F fiber links for further transmission to their respective destination nodes E and F. At either receiver side, both s_d and s_w can be recovered from the overlapped signal s_o. Figure 1(b) shows another possible application in the 1 + 1 protection network, in which the optical overlap is implemented at the transmitter node. Two optical channels s_d and s_w are generated at source node A, having their own working paths A-E-C and A-F-D, respectively. For the protection path, the overlapped signal s_o combined from s_d and s_w works as the back-up signal for the common link A-B-C transmission. At destination C and D, both s_d and s_w can be separated and extracted from the back-up signal s_o. The demodulation procedures and the related DSP algorithms are explained in detail as follows.

 

Fig. 1. Network scenario: (a) the overlap technique to resolve the wavelength conflict issue; (b) the optical overlap technique applied in the 1 + 1 protection network.

Download Full Size | PDF

2.1 Optical overlap of s_d and s_w

At node C in Fig. 1(a), before optical combination, the OSNRs corresponding to s_d and s_w are defined as

Herein, $OSNR_w^{\prime}$ is defined as the power ratio between the attenuated s_w and ASE noise with the assumption of perfect cancellation of s_d. In the demodulation, the signal s_d suffers strong interference from s_w and the ASE noise. From Eq. (6), proper demodulation of s_d requires large power attenuation to s_w, corresponding to small $\alpha $ or large CPR. From Eq. (7), the recovery of s_w is dependent on the effective interference mitigation of s_d and small attenuation, namely large $\alpha $ or small CPR. Thus, SIR or CPR should be optimized to guarantee proper recovery for both signals. The optimal power ratio implies the power attenuation before the optical overlap.

2.2 s_d and s_w demodulation

At the destination node, the overlapped signal s_o is coherently received as

The SIC scheme is applied to remove S_d from S_o to recover S_w. Suppose that ${\hat{S}_d}$ is the decoded signal with forward error correction (FEC) and with the Nyquist shaped reconstruction. The interference cancellation is performed as follows

3. Numerical simulation

In this section, we performed the simulations to analyze the performance of the overlapped system. Firstly, we evaluated the BER performance considering several interfering factors, the relative time offset, polarization rotation, and frequency offset. Secondly, we implemented the optical overlap at the transmitter side, in which two Nyquist-PM-QPSK signals were optically superimposed to form the overlapped signal s_o with additional ASE noise. The BER performance, the OSNR penalty, and the optimal SIR were analyzed under different system parameters. Thirdly, we optically overlapped two noisy Nyquist-PM-QPSK channels and demonstrated the BER performance of s_d and s_w as well as the optimized CPR with respect to OSNR_d and OSNR_w.

In the simulation, two independent Nyquist-PM-QPSK channels were generated, namely s_d and s_w. The baud rate was set to 10-GBd. The roll-off factor for Nyquist filtering was 0.2 and the length of Nyquist filter was set to 128 symbols. The oversampling ratio was set to 16 to emulate the analog waveform. The electrical signals were modulated onto the optical domain via IQ modulator with two independent 100-kHz linewidth lasers. The respective optical powers, P_d of s_d was set at 0dBm and P_w of s_w was varied by a VOA. Then, s_d and s_w were optically combined together. At the receiver side, s_o was acquired by coherent detection, where another 100-kHz linewidth laser was used as the local oscillator (LO). The acquired signal s_o was filtered by a 5^th order Bessel filter and was re-sampled to 2 samples per symbol. The algorithms for demodulating the single-carrier QPSK signal were employed for individual recovery.

3.1 Time offset

The inset in Fig. 2(a) shows the eye diagram of the Nyquist shaped QPSK signal within one symbol period. The signal waveform varied in amplitude. From the eye diagram, the signal waveform reached the maximum value when the time offset was equal to the half symbol period (1/10 GBaud), which resulted in the maximum interference. Different time offsets would result in variable interference even under the fixed power ratio for optical overlap. We have performed the simulation to verify it. In the simulation, SIR was set to 7.3 dB, where P_d and P_w were 0 dBm and −7.3 dBm, respectively. The Nyquist signals s_d and s_w were up-sampled to 16-fold to emulate the analog signal waveform and added together with various sample offsets to emulate the different time delays. After optical overlapping, the OSNR_o of s_o was set to 19dB with additional white Gaussian noise. The polarization states of two signals were aligned.

 

Fig. 2. Simulation: (a) (b) (c) the calculated Q² of s_d and s_w versus time offset, polarization rotation and frequency offset; (d) the calculated BER of s_d and s_w versus SIR, (I) (II) constellation diagrams of s_d and s_w at SIR of 5.6 dB in case 1; (III) (IV) constellation diagrams of s_d and s_w at SIR of 6 dB in case 1; (V) (VI) constellation diagrams of s_d and s_w at 9-dB SIR in case 2.

Download Full Size | PDF

As shown in Fig. 2(a), the calculated Q² varied periodically with respect to time delay. We could see that timing offset had obvious influence on s_d but just a slight effect to s_w. In the demodulation of s_d, the interference from s_w became the maximum when the timing offset was equal to the half symbol period. As a result, the Q² factor of s_d dropped from 10.8 dB to 8.1 dB. However, the time delay had little effect on s_w, since the interference signal s_d was subtracted. The Q² of s_w fluctuated within the range of 10.1∼10.6 dB. It could be noticed that timing synchronization was not strictly required in the recovery of s_d and s_w.

3.2 Polarization rotation

Since the polarization of light-wave would rotate during the propagation in fiber, the relative polarization rotation between s_d and s_w might induce variable interference. The inset in Fig. 2(b) shows the projections of s_w along s_d in orthogonal polarization directions for the cases of aligned polarization and relative 45-degree polarization rotation. The projection of s_w along s_d could increase to $\sqrt 2 $ at 45-degree rotation, resulting in the maximum interference. In the simulation, the polarization rotation of s_w was set to 0∼180 degree while the polarization of s_d was fixed. The two parameters SIR and OSNR_o were set to 7.3 dB and 19 dB, respectively. Two signals were timing synchronized. As shown in Fig. 2(b), the Q² factor of s_d changed periodically as a function of the rotation angle with a period of 90 degree. When the rotation angle was 45 degree, the interference reached the maximum value. Meanwhile, the Q² value of s_d was the worst, dropped from 11.3 dB to 8.3 dB. For s_w, the Q² also changed periodically with 90 degree as a period, dropping from 10.6 dB to 10.3 dB. It could be explained that when the interference increased to the maximum value, the channel estimation for s_d tended to be improper, resulting in imperfect interference cancellation. However, the impairment effect was small, since the Q² values of s_w fluctuated within a small range.

3.3 Frequency offset

We have also analyzed the effect of frequency offset on mutual interference since the laser source would have a wavelength drift in a real system. In the simulation, channel s_w was set to have a frequency offset relative to s_d. Two parameters, OSNR_o and SIR were set to 19 dB and 7.3 dB. At the receiver end, the LO was aligned with the central frequency of s_d.

Figure 2(c) shows the Q² of s_d and s_w as a function of frequency offset. The Q² values of s_d dropped from 10.9 dB to 10.3 dB within the range from - 2.5∼2.5 GHz, which was caused by the extra phase change induced by the frequency offset. Beyond 2.5-GHz frequency offset, the performance of s_d improved since the large frequency offset of s_w resulted in small interference on s_d. The frequency offset had a small impact on s_d. But for s_w, the Q² decreased from 10.5dB to 7.5dB up within the range from −5∼5 GHz. Noted that the mismatch of central carrier of s_w and LO led to the bad performance of s_w.

3.4 SIR

To analyze the signal interference, the BER results of s_d and s_w were calculated by varying SIR without additional ASE noise in different interfering conditions, as shown in Fig. 2(d). In case 1, the interfering conditions were that two signals were timing synchronized and polarization aligned. In case 2, the time offset was set to be half of the symbol period and the polarization rotation difference was 45 degree. In case 1, it could be noticed that the BER of s_d and s_w dropped sharply when the SIR was beyond 5.9 dB. When the SIR was below 5.9 dB, it cannot guarantee successful and stable recovery of either s_d or s_w. As the SIR further increased beyond 6 dB, both s_d and s_w had BER below 10⁻⁴. From Fig. 2(d) (III), the constellation diagram of s_d became four circles since the timing and polarization were aligned. In the NOMA case, it is known that the superposition of two QPSK signals digitally can obtain standard 16 quadrature amplitude modulation (16QAM) signals with the optimal power ratio 6dB [4,6]. In this simulation, for the optical overlap scheme in case 1, the SIR value around 5.9 dB was the critical point to separate s_d and s_w. As shown in Fig. 2(d) (I) and 2(d) (II), both s_d and s_w could not be recovered properly at SIR of 5.6 dB, due to the strong interference causing the crossing and overlapping of s_o in the four quadrants.

In case 2, the BER performance of s_d improved obviously within the range from 5.5 to 10 dB in SIR. The BER of s_w changed slightly during the range of 10⁻⁵∼10⁻⁴. In case 2, the signal waveforms of s_d and s_w changed without the same tendency due to the mismatched timing and polarization. There was no critical point present in the SIR. Thus, the constellation diagram of s_d in Fig. 2(d) (V) was similar to a noisy QPSK signal with no existence of critical point in SIR.

3.5 Signal overlap

We have analyzed the influence of time offset and polarization rotations on the Q² performance of s_d and s_w. In this section, we will show the overlapped system performance under different interfering conditions compared with that of Nyquist shaped and polarization multiplexed 16 quadrature amplitude modulation (Nyquist-PM-16QAM). In the simulation, different values of SIR were tested for optimization. After optical overlap s_d and s_w, ASE noise was added to vary the OSNR_o values.

The BER of the overlapped signal s_o is defined as the average of pre-FEC BERs of the recovered s_d and s_w. The BER performance of the overlapped s_o could be optimized by SIR, which is the optimal SIR to realize the minimal BER of s_o. In Fig. 3(a), the BER results versus OSNR_o are shown for signal s_o in case 1 and case 2, compared with that of Nyquist-PM-16QAM. The respective BERs of s_d and s_w are also presented in the figure. For case 1 and case 2, the required OSNR_o values at BER of 3.8×10⁻³ were about 15.9 dB and 17.5 dB, respectively. The high OSNR requirement is reasonable and fair since the overlap method results in a two-fold bitrate and higher modulation format, equivalent to 16QAM. At the FEC threshold, about 1-dB and 2.6-dB OSNR penalties could be observed for two cases, compared with that of 10-GBaud Nyquist-PM-16QAM. The OSNR penalty is caused by the interference and incoherence of two optical signals.

 

Fig. 3. Simulation: (a) BER of s_o, s_d and s_w as functions of OSNR_o under case 1 and case 2 as well as the BER of Nyquist-PM-16QAM; (b) the optimal SIR versus OSNR_o.

Download Full Size | PDF

Figure 3(b) shows the optimal SIR. In case 1, the optimal SIR was around 7 dB. However, we should increase the SIR under the strong interfering condition as in case 2. Before optical combination, if the time offset and polarization states of two channels are unknown, we can combine the two channels with the optimal SIR in case 2 to guarantee successful demodulation of s_d and s_w. If we can ensure the timing synchronization and the aligned polarization state at the transmitter side, the SIR can be set to 7 dB to achieve the optimal BER performance with the acceptable the OSNR penalty, as low as 1dB.

3.6 Noisy channel overlap

We extend to apply the optical overlap technique to two noisy channels at the intermediate router node. To analyze the mutual channel interference, ASE noises in both channels are considered. The parameter CPR is a more direct and reasonable parameter for the optical overlapping of two channels. In the simulation, the signal s_d and s_w were added with ASE noises to vary OSNR_d and OSNR_w. The dominant channel power, the sum of P_d and P_Nd was set to 0 dBm. The weak channel power, the sum of P_w and P_Nw was varied by a VOA (equal to –CPR dBm). Different values of CPR, OSNR_d and OSNR_w were tested. We analyzed the relationship between CPR and BER performance under the strong interfering condition with half of the symbol period time offset and the relative 45 degree polarization rotation. We have also shown the optimized CPR values to get the minimal BERs of s_d and s_w.

Figures 4(a) and 4(b) show the simulation results, the contour lines of BERs (with log operation) of s_d and s_w, with respect to OSNR_d and OSNR_w, respectively. For s_d, the BER performance improved as OSNR_d increased obviously. The BER of s_d improved slowly as OSNR_w increased since CPR was the dominant factor. For s_w, the BER performance improved when OSNR_d and OSNR_w increased. For s_w, the total ASE noise from the two channels was the dominant factor. For the fixed OSNR_w, the BER of s_w improved with respect to OSNR_d, due to the quick decrease of the noise component P_Nd and slow increase of CPR.

 

Fig. 4. Simulation: (a) and (b) contour lines of BERs of s_d and s_w as functions of OSNR_d and OSNR_w, respectively; (c) contour lines of optimal CPR as a function of OSNR_d and OSNR_w.

Download Full Size | PDF

As shown in Fig. 4(c), the optimal CPR values with respect to OSNR_d and OSNR_w fell in the range of 7∼9.5 dB. For the fixed OSNR_d, optimal CPR increased as the OSNR_w increased. When the OSNR_w increased, the signal power P_w relatively increased for the fixed sum of P_w and P_Nw. The P_w in s_w had stronger interference effect than the ASE noise P_Nw on s_d, resulting in the larger optimal CPR. For the fixed OSNR_w, CPR increased slowly when OSNR_d increased since the noise power P_Nd decreased. The simulation results provided the optimal CPR for noisy channel overlapping with the knowledge of two channels’ OSNR values.

4. Experimental results

4.1 Experiment for signal overlap system

In this section, we set up the experiment for the overlapped system, in which two optical Nyquist-PM-QPSK signals were overlapped with additional ASE noise before the receiver side. As shown in Fig. 5(a), the Nyquist QPSK signal was generated by MATLAB offline, whose roll factor was set to 0.2 and the oversampling ratio was set to 2. The length of Nyquist finite impulse response (FIR) was set to 128 symbols. The I and Q components of the Nyquist-QPSK signals loaded to the arbitrary waveform generator (AWG) operating at 12-Gsample/s, after two analog low pass filters (LPFs) were sent to the optical IQ modulator. Thus, the baud rate of the Nyquist QPSK signal was 6 GBaud. Via the IQ modulator, the electrical signal was modulated onto an optical carrier generated by an external cavity laser (ECL) working at 1550.06-nm with 100-kHz linewidth. After that, the Nyquist-PM-QPSK symbols were generated by a polarization splitter, a piece of polarization maintaining fiber in one polarization branch for decorrelation and another polarization combiner. After that, the optical Nyquist-PM-QPSK signal was split into two branches and de-correlated by a piece of 10-km SMF, aiming to generate two optical signals, namely s_d and s_w. The power ratio between s_d and s_w was carefully adjusted by attenuating P_w of s_w via a variable optical attenuator (VOA), before being combined via an optical coupler, to form the overlapped signal s_o. The ASE noise was introduced to emulate diverse OSNRs of s_o. At the receiver side, 1% power of s_o was tapped off for OSNR measurement by an optical spectrum analyzer (OSA). The rest signal s_o after 0.8-nm bandwidth optical bandpass filter (OBPF) was detected by a coherent receiver with another 100-kHz linewidth ECL as the LO. The electrical symbols were sampled and stored by a 50-Gsample/s real-time digital storage oscilloscope (DSO). The insets in Fig. 5 represent the constellations of s_d, s_w and s_o with phase noise compensation before and after optical overlap, respectively. Noted that the constellation of s_o was not similar to that of 16-QAM due to the incoherence between s_d and s_w.

 

Fig. 5. Experimental setup for the signal overlap system, the insets (I) (II) (III) show the phase noise compensated constellations of s_d, s_w and s_o, respectively.

Download Full Size | PDF

We investigated the BER performance of the overlapped system versus diverse SIR, OSNR_o, and OSNR_w^’, respectively, as in Figs. 6(a)–6(d). Figure 6(c) illustrates the BER performances of s_d, s_w and s_o versus different SIR when OSNR_o was set at 17 dB. The BER of s_d increased with the increase of SIR, while the BER of s_w had opposite changing tendency except for the first point. The minimal BER of s_o could be found when the SIR was set at 8.3 dB. Since the BER of s_o represented the mean value of pre-FEC BERs of the recovered s_d and s_w, 8.3 dB was the optimized value of SIR. It was worthy to notice that both s_d and s_w cannot be recovered correctly with the SIR as low as 5.3-dB due to the strong mutual interference. Besides, the BER curves in Fig. 6(c) were not smooth, since the polarization state may vary during the power attenuation processing and the transmission in fiber.

 

Fig. 6. Experimental results: (a) calculated BER of s_o, s_d, s_w and 16QAM as a function of OSNR_o; (b) the optimal SIR as a function of OSNR_o; (c) calculated BER of s_o, s_d and s_w versus SIR at OSNR_o of 17 dB; (d) calculated BER versus OSNR_w^’ for cases of recovered s_w and only QPSK for transmission.

Download Full Size | PDF

Figure 6(a) illustrates the BER performances of s_d, s_w and s_o versus different OSNR_o, when the SIRs were set at the optimal values (i.e., 8.3 dB for 17-dB OSNR_o). As shown in Fig. 6(a), the required OSNR_o for the overlapped system to reach the BER threshold at 3.8×10⁻³ was about 15.7 dB, indicating an OSNR penalty of about 1.3 dB compared to the case employing the 6-GBaud Nyquist-PM-16QAM. The OSNR penalty was caused by the proposed optical overlap scheme. As shown in Fig. 6(b), the optimal SIR varied with change of the OSNR_o. Noted that the SIR became stable as the OSNR_o increased beyond 14 dB. Figure 6(d) depicts the BER performance of s_w versus different OSNR_w^’ defined in Eq. (7), when the SIR was set at its optimal value. As shown in Fig. 6(d), an OSNR penalty about 1.2-dB could be observed for s_w compared to the case when only 6-GBaud Nyquist-PM-QPSK was transmitted (labeled as “QPSK”). It indicated the effectiveness of proper recovery and the interference cancellation of s_d. This experiment demonstrated the optical overlap scheme applied at the transmitter side, without a strict requirement of timing synchronization or the knowledge of the relative polarization state. All of the experimental results verified that two signals s_d and s_w could be successfully separated and properly recovered from the overlapped signal s_o with a certain SIR.

4.2 Experiment for noisy channel overlap

Given the feasible application of the optical overlap technique in an elastic optical network (e.g. at its intermediate transmission node), we set up another experiment for the optically overlapped system of two noisy channels as in Fig. 7, in which s_d and s_w experienced different ASE noises. The experimental setup in Fig. 7 was similar to that in Fig. 5(a) except for the transmission part. In the transmission part, two independent ASE noises were added to the upper and lower branches to vary OSNR_d and OSNR_w of s_d and s_w, respectively. Then, 10% power of the channel was tapped off for OSNR measurement, before two 100-GHz bandwidth OBPFs followed to remove the out of band noise. In the lower branch, its channel power (the sum of P_w and P_Nw) attenuated by a VOA, was optically overlapped with the upper branch channel for both BTB and 100-km SMF transmission.

 

Fig. 7. Experimental setup for the optical overlap of two noisy channels.

Download Full Size | PDF

In the second experiment, we investigated the relationship among OSNR_d, OSNR_w and the optimal CPR, where the CPR was tested within the range of 5.5∼10dB with a step of 0.5 dB. Figures 8(a)–8(b) show the respective BER results of s_d and s_w under the optimal CPRs for BTB transmission. The BERs of s_d and s_w were dependent on both OSNR_d and OSNR_w. As for s_d, it could achieve below the BER threshold of 3.8×10⁻³ (i.e., −2.4 in log₁₀ (•)), when OSNR_d was above 18dB. Even when OSNR_d was below 18dB, BER of s_d could still reach the required BER at high OSNR_w values. Figure 8(e) shows the optimal CPR versus OSNR_d and OSNR_w. It can be noticed that the optimal CPR increased as OSNR_d and OSNR_w increased. And OSNR_w had a more obvious effect on the change of the optimal CPR than OSNR_d, which agreed with the simulation results.

 

Fig. 8. Experimental results: (a) (b) contour lines of BERs for signal s_d and s_w as functions of OSNR_d and OSNR_w for the BTB system; (c) (d) contour lines of BERs for signal s_d and s_w as functions of OSNR_d and OSNR_w for the 100-km transmission; (e) contour lines of optimal CPR as a function of OSNR_d and OSNR_w for BTB system; (f) Q² of s_d and s_w versus to optical delay at OSNR_d of 18 dB and OSNR_w of 15 dB in BTB system, the insets (I) (II) constellations of s_d and s_w at the delay of 60 ps, (III) (IV) constellations of s_d and s_w at the delay of 160 ps.

Download Full Size | PDF

Figures 8(c)–8(d) show the contour lines of BER results of s_d and s_w with respect to OSNR_d and OSNR_w after 100-km transmission, under the optimized CPR set according to Fig. 8(e). Both s_d and s_w can be successfully recovered from the overlapped signal s_o. For s_d, the BER results were better than those of the BTB system within the OSNR_d range of 16∼18dB and 21∼22dB. For s_w, the BER results were worse than those of the BTB system. Noticeably, although the optimized CPR values in BTB system might not be the optimal CPR for transmission system due to the possible change in the interfering conditions, time offset or polarization state between s_d and s_w, such optimal CPR values for BTB transmission can be a valuable power ratio guidance for noisy channel overlapping.

Besides the optimal CPR, we also analyzed the interfering effect of time offset between two noisy channels. In the experimental system shown in Fig. (7), we put an optical delay line in the s_w branch to emulate different time delays. The range of the optical delay line was 0∼160 ps close to one symbol period 167 ps (i.e., 1/6GBd). Figure 8(f) shows Q² performance of s_d and s_w as well as the fitting curves, with the OSNR_d and OSNR_w being set to 18 dB and 15 dB, respectively. The Q² values of s_d had 2.5dB decrease due to the impact of time delay on channel interference. For s_w, the Q² value changed a little around 8.5dB with small fluctuations. The insets in Figs. 8(a)–8(d) show the constellations of recovered s_d and s_w at 60-ps and 160-ps delay. Noted that the constellation of s_d at 160-ps delay consisted of four circles. It was the case when the two signals s_d and s_w were almost timing aligned. The constellation of s_d at 60-ps delay was similar to the noisy QPSK signal because the two overlapped channels were not timing synchronized. The experimental results and constellation diagrams matched the results obtained from the simulation in section 3.1 and 3.4. In the NOMA scheme, the digitally overlapped signal got 16QAM constellation for two users or 64QAM constellation for three users with QPSK as the basic signal for each user. However, in the optical overlap scheme, the constellation diagram of the overlapped signal was not like 16QAM constellation, due to the incoherent of two channels, caused by the time offset, polarization rotation, frequency offset and phase noise.

5. Summary

In this paper, we have performed numerical simulations and experiments to analyze the performance of two Nyquist-PM-QPSK channels under optical overlap, considering various system parameters. In the simulations, we have analyzed the impact of time offset, polarization rotation, frequency offset, SIR and ASE noise on mutual interference. The OSNR penalties of the overlapped system were found to be 1 dB and 2.6 dB under two conditions, compared to those of the Nyquist-PM-16QAM. As for noisy channel overlap, the CPRs were optimized and analyzed with respect to OSNR_d and OSNR_w. In the first experiment, we have demonstrated the signal recovery of two Nyquist-PM-QPSK signals, with complete spectral overlap, at a total bit rate of 48-Gb/s with 1.3-dB OSNR penalty observed. In the experiment of optical overlap of two noisy channels, the BER performances of s_d and s_w were demonstrated under the optimal CPRs with respect to OSNR_d and OSNR_w. Using the optimal CPRs of BTB system as reference, both s_d and s_w can be separated and recovered from the overlapped signal s_o after 100-km transmission. The interfering effect of time offset had been verified via experiment, resulting in a 2.5-dB decrease of Q² of s_d and a little fluctuation in Q² of s_w.