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Abstract
For weakly coupled mode-division multiplexed (MDM) transmission systems, we design and implement optical coherent receiver prototypes with real-time multiple-input multiple-output (MIMO) digital signal processing to equalize two degenerate linearly polarized modes with dual polarization. Using field programmable gate array circuits, we implement real-value 8 × 2 MIMO adaptive equalization with externally separated phase compensators based on the least mean square algorithm, which enables not only training equalization but also fast carrier-phase tracking. With the optical coherent MIMO receiver prototype, we demonstrate real-time weakly coupled 10 × MDM wavelength-division multiplexed dual-polarization quadrature phase shift keying transmission over 48-km few-mode fibers. This report shows a record number of multiplexed spatial modes, namely, 10 modes with dual polarization, in real-time MDM transmission experiments.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
To overcome the fundamental limitation of transmission capacity in standard single-mode fibers, the mode-division multiplexing (MDM) technique in few-mode fibers (FMFs) is a promising candidate [1,2]. Different optical signals can be transmitted over different linearly polarized (LP) modes in FMFs, increasing the transmission capacity in proportion to the number of transmission modes. There have been many reports on several-hundred-Tbit/s MDM transmission demonstrations [3–6] and large-scale MDM transmission experiments with 45 modes [7].
In MDM systems, the most critical issue is that different modes are mixed during FMF transmission, resulting in signal crosstalk. The mode couplings can be compensated for by introducing multiple-input multiple-output (MIMO) digital signal processing (DSP) in optical receivers. For large-scale MDM systems with many multiplexed modes, this approach suffers the huge MIMO complexity increases in proportion to the square of the mode number. For instance, 10 × MDM systems with dual polarization require real-value 40 × 40 MIMO whose complexity reaches approximately 100 times as large as that of the real-value 4 × 4 MIMO introduced in conventional single-mode coherent receivers. Unfortunately, MIMO DSP has been performed offline in almost all MDM transmission experiments reported so far. Considering the practical deployment of MDM systems, real-time MIMO DSP implementation is indispensable. With real-time MIMO DSP, only 3 or 4 × MDM transmission experiments have been reported [8,9].
Using FMFs with large difference between effective refractive indices [10,11] and selective mode multiplexers [12,13], the couplings between different LP modes can be suppressed. Unless the couplings from different LP modes are not significantly large in FMF transmission, the MIMO size can be drastically reduced because we can use only the real-value 8 × 8 MIMO to equalize two degenerate LP modes and dual polarization. Although specially designed FMFs and optical devices are required to suppress mode couplings, real-time MIMO implementation is practical. This is called the weakly coupled MDM approach [14], and 400-Tbit/s 10 × MDM transmission experiments have recently been demonstrated even with offline MIMO DSP [4,6].
In this paper, we report an experimental demonstration of weakly coupled 10 × MDM wavelength-division multiplexed (WDM) transmission over 48-km FMFs using real-time MIMO coherent receivers. We implement real-time MIMO DSP to equalize two degenerate LP modes with dual polarization. Based on field programmable gate array (FPGA) circuits, we implement real-value 8 × 2 MIMO DSP. One of the features of our real-time MIMO DSP is adaptive control based on the training-aided least mean square (LMS) algorithm, in which the singularity problem [15] is perfectly avoidable even in MDM systems. Another is carrier-phase compensation parts externally separated from the MIMO part to improve the carrier-phase tracking speed [16]. Using optical coherent receivers with real-time MIMO DSP, so-called real-time coherent MIMO receivers, we experimentally demonstrate the real-time weakly coupled 10 × MDM transmission of three-channel WDM dual-polarization (DP) quadrature phase shift keying (QPSK) optical signals over 48-km FMFs. We have already reported real-time MDM/WDM transmission experiments [17]. In this paper, the design and fabrication of our real-time MIMO DSP are described in detail, and numerical results for the performance evaluation of our designed MIMO DSP are included.
The paper is structured as follows. Section 2 shows the configuration and design of our prototype real-time MIMO coherent receiver. In Section 3, the simulated results are shown. The aims of the simulation are to evaluate the impact of the singular problem by increasing the number of spatial tributaries and to evaluate the carrier-phase tracking performance of MIMO with external phase compensators. Section 4 describes an experimental demonstration of the real-time 10 × MDM WDM transmission experiments. Section 5 presents the conclusions.
2. Optical real-time MIMO coherent receiver
We designed and fabricated an optical MIMO receiver to equalize two degenerate LP modes with polarization tributaries. Figure 1(a) shows the configuration of our coherent MIMO receiver. It was assumed that 10 × MDM DP-QPSK 18-subcarrier-modulated signals were received. The signal bandwidth was 12 GHz, and the baudrate of one subcarrier was 625 Mbaud. The signal bitrate per mode without FEC overhead was 45 Gbit/s. By demultiplexing one subcarrier, we can reduce the required sampling rate of the following analog-to-digital convertors (ADCs). First, the received MDM signals were spatially demultiplexed into two degenerate modes, e.g., LP11a and LP11b. In our receiver, we used a mode demultiplexer based on multiple phase plates [12]. We can precisely and arbitrarily obtain desired spatial amplitude and phase patterns by repeated phase modulation and diffraction in multiple phase plates with free-space propagation Two demultiplexed signals were simultaneously received by two integrated coherent receivers with polarization and phase diversity. A tunable laser with a linewidth of 5 kHz was used as a local oscillator (LO). By tuning the LO frequency, only the desired subcarrier was demultiplexed. The received electrical signals passed through a low-pass filter (LPF) with a cutoff frequency of 450 MHz to suppress the sampling aliases, and they were digitized by two 4-channel 10-bit ADCs, which were connected to two Xilinx Virtex-7 FPGA evaluation boards (VC707) via FPGA mezzanine card (FMC) interfaces. The ADC sampling rate was 1.25 GSample/s, namely, 2 sample/symbol. The FPGA clock rate was 312.5 MHz, and the sampled sequences were parallelized into four tributaries. In the boards, filtering to suppress amplified spontaneous emitted (ASE) noise and frequency offset compensation were implemented based on an overlapped fast Fourier transformation (FFT) with a block size of 1024. To compensate for the frequency offset, we detected a pilot tone inserted within each subcarrier. The power ratio of the pilot tone to the signal was -10 dB, and the excess power of the inserted pilot tones was quite negligible. After downsampling to 1 sample/symbol, the eight-channel samples with eight-bit resolution were transferred to another Xilinx Virtex-7 FPGA evaluation board (VC7215) with FMC-SMA conversion boards. The transfer rate in the SMA cable was 6.25 Gbit/s. In the second board (VC7215), adaptive MIMO equalization and bit error ratio (BER) measurements were implemented. The FPGA clock rate was 156.25 MHz, and each channel deserialized into four tributaries. The appearance of the real-time DSP circuits is shown in Fig. 1(b).
Fig. 1. (a) Configuration and (b) appearance of implemented real-time MIMO coherent receiver prototype.
The configuration of the implemented real-value 8 × 2 MIMO is shown in Fig. 2. The entries of the MIMO consist of finite impulse response (FIR) filters, and then the tap coefficients are adaptively controlled based on the LMS algorithm. Note that carrier-phase compensators based on single tap were separated from the MIMO part, improving the carrier-phase tracking performance [16]. The tap coefficients of the MIMO and phase compensators were simultaneously updated. The eight real-value sequences (two LP modes × dual pol. × I and Q) r1(k), r2(k), ···, r8(k) (k is discrete time) coming from previous FPGA VC707 boards deserialized with a degree of parallelism P because the DSP clock is typically much slower than the signal baudrate. In our implementation, the 625 Mbaud samples were parallelized into four tributaries, P = 4, because the DSP clock rate was 156.25 MHz. They were blocked with K consecutive samples, and then the p-th (p = 0, 1, ···, P – 1) deserialized tributary was stored in K × 1 vectors as described by
By using two real-value samples (single LP mode × single pol. × I and Q) v1(κ) and v2(κ), a complex-value sample w(κ) was obtained as
where w(κ) corresponds to one spatial tributary (mode a or b, polarization x or y). Next, the phase comparators based on single tap, p(κ) and q(κ), were performed. The equalized sample z(κ) was eventually obtained as described by For adaptive control, the tap coefficients of the MIMO and the phase comparators, cmi (κ), p(κ), and q(κ), were updated by using the LMS algorithm. Note that they were simultaneously updated in the single feedback loop using the following equations [16],Note that the update was done once in P consecutive samples due to the parallelism architecture, although it was done sample-by-sample in the offline DSP case [18]. The parallelism with P induces delay of P-sample duration in adaptive control. In addition, the pipeline delay is inevitable due to the flip-flops in the real-time implementation. The pipeline delays in the MIMO and two phase comparators are indicated by δM, δp, and δq in Eqs. (7), respectively. The total delay in the feedback control is calculated by multiplying the degree of parallelism and the pipeline delay, P·δM, P·δp, and P·δq. Since delay makes the feedback control unstable, we need to reduce the feedback delays as much as possible. In particular, it is required to suppress the delays for the phase compensators, δp and δq, to track the fast fluctuation of the carrier phase in optical coherent detection. In our implementation, the pipeline delays δp and δq were reduced by the duration of the five deserialized samples, i.e., the total delay of the 20-sample duration. Since spatial couplings such as polarization/mode couplings are slowly varied, a relatively large delay for MIMO control is allowable. In our real-time DSP, the pipeline delay δM was 45 deserialized samples.
The adaptive equalization started with the training mode by using known training samples as the references d(κ). After the equalization errors were sufficiently suppressed, it switched to the decision directed mode, in which the decision samples were used as the references. Since each spatial tributary has a different training sequence, only the desired spatial tributary can be distinguished by using the training sequence. Training-aided equalization makes it possible to completely avoid the singularity problem, in which undesired spatial tributaries might be decoded in blind equalization [15].
After completing the MIMO adaptive equalization, bits were decoded by decision of the equalized samples, and then the BER was calculated. The resulting BERs and equalized samples were transferred to a PC. In this work, the aim is to confirm real-time operation of MIMO to equalize two degenerate LP modes. In our implementation, only two streams corresponding to I and Q components were decoded because the MIMO was limited to a 8 × 2 size due to restriction of the logic sell size of the FPGA boards that we used. Using multiple cutting-edge FPGA boards, we can implement 8 × 8 MIMO to equalize two degenerate LP modes including dual polarization.
3. Numerical performance evaluation of our designed MIMO
In this section, we show numerical results to evaluate the performance of our designed MIMO. The aims are to investigate (1) how much the singularity problem impacts MDM systems and (2) how much the carrier-phase tracking performance is improved by separating carrier-phase compensators from the MIMO part even in the presence of feedback delay. As explained in Section 2, our real-time MIMO is adaptively controlled based on the training-aided LMS algorithm. In conventional single-mode DP-QPSK systems, blind equalization based on the constant modulus algorithm (CMA) is usually introduced because of robustness against phase noise. Since this algorithm cannot distinguish equalized tributaries, undesired spatial tributaries might be decoded, especially when the mode-dependent loss (MDL) increases. This is known as the singularity problem. In subsection 3.1, we note that the singularity problem becomes more serious in MDM systems. In our real-time MIMO based on the LMS algorithm, the singularity problem can be completely avoided. Carrier-phase recovery is also achieved, but the fast tracking speed is required for optical coherent reception with large phase noise. As mentioned previously, in our implementation, the carrier-phase compensators are separated from the MIMO part, improving the carrier-phase tracking performance. In subsection 3.2, we show the numerical performance evaluation of the MIMO with external phase compensators considering feedback delay in adaptive control.
3.1 Numerical investigation of the singularity problem in MDM systems
The simulation model is shown in Fig. 3. In the transmitter, streams of pseudorandom integer values (0, 1, 2, or 3) are generated based on the Mersenne twister [19] with a length of 1,000, and then they are mapped into the gray-coded QPSK format. The obtained QPSK symbols are parallelized into 2N channels, expressed as a 2N-dimensional complex-value vector x = [x1, x2, ···, x2N]T. After upsampling to 2 sample/symbol and rectangular Nyquist shaping, the samples are linearly modulated to N × MDM signals with dual polarization. The electrical fields of the MDM signals are expressed as a complex-value vector E = [E1, E2, ···, E2N]T. The signals are transmitted over an optical channel based on an MDL emulator, which is described by the 2N × 2N matrix H, as mentioned later. The signals after the MDL channel, HE, suffer from 2N-dimensional additive white Gaussian noise (AWGN) vector n. The SNR value for each spatial channel is set to 10 dB. They are received by N × parallelized polarization diversity coherent receivers. The received samples are filtered by Nyquist shaping and then equalized by a half-symbol-spaced complex-value 2N × 2N MIMO. The MIMO taps are adaptively controlled by the CMA and the modified CMA [20]. In the modified CMA, the 2N × 2N MIMO is decomposed into 2N × 1 multiple-input single-output (MISO) equalizers, and the tap coefficients are sequentially updated from the first MISO. The initial taps of the i-th MISO are determined to satisfy the orthogonality with estimated taps of the previous MISO. Therefore, the modified CMA scheme has higher tolerance for the singularity problem. After the CMA-based MIMO equalization, 2N channels of the equalized samples are obtained as expressed by y = [y1, y2, ···, y2N]T. Finally, we confirm whether singularity could occur. We calculate the cross correlation between the complex amplitudes of xi and yj, and the channel xi giving the maximum correlation value is recognized as the equalized channel. The singularity occurs when the same channels are multiplexed from the different decoded channel yi. By our Monte Carlo simulation with 10,000 realizations, the occurrence probability of the singular problem is calculated.
The optical channel H is modeled as follows [21]. It is decomposed into H = VΛUH, where UH indicates the Hermite conjugation of a matrix U. In this simulation, V and U are random and independent 2N × 2N unitary matrixes given by using the procedure described in [22]. Λ is a 2N × 2N diagonal matrix presenting MDL, and the 2N diagonal entries Λi are determined as [23]
Figure 4 shows the calculated occurrence probability of the singularity problem as a function of the mode number N. Closed blue squares, closed red triangles, and closed green circles indicate the results in the CMA case with MDL = 0, 3, and 6 dB, respectively. In the single-mode dual-polarization system, we can see the possibility of 0.6% even in the absence of MDL. This is because the CMA failed to keep the orthogonality between polarizations during the update of the MIMO taps [15]. As the MDL value increases, the probability of the singularity problem also increases because the orthogonality between spatial channels degrades due to the MDL [25]. In the weakly coupled MDM system, which corresponds to the two-mode system, the CMA is not completely practical since the singularity problem can occur with a probability of higher than 40% even in the absence of MDL.
The calculated occurrence probability in the modified CMA case is also plotted in the same figure. Open blue squares, open red triangles, and open green circles show the results in the case with MDL = 0, 3, and 6 dB, respectively. The probability decreases because the modified CMA constrains the orthogonality between equalized channels. Although the singularity problem is negligibly small in the single-mode system, as reported in [20], it becomes more serious in the MDM system. In the weakly coupled MDM system, the singularity problem can occur with a probability higher than 0.1% even in the absence of MDL. As the MDL increases, the probability of the singularity problem also increases, which is the same trend as in the CMA case. Thus, blind MIMO equalization based on the CMA and the modified CMA is not suitable for highly reliable MDM systems. On the other hand, we implemented MIMO adaptive equalization based on the LMS algorithm, as mentioned in the previous section. This is completely avoidable for the singularity problem.
3.2 Numerical evaluation of the carrier-phase tracking performance of our designed MIMO with external phase compensators
As previously reported [16], the carrier-phase tracking performance can be improved by separating phase compensators from the MIMO part, but the feedback delay has never been considered in the performance evaluation. In this subsection, we numerically evaluate the carrier-phase tracking performance of our designed MIMO in the presence of feedback delays. In our simulation, carrier-phase tracking for the single-mode single-polarization QPSK signals is evaluated, since the aim is to numerically clarify the tracking performance not for polarization variation but for carrier-phase fluctuation.
The simulation model is shown in Fig. 5. Bit streams based on repetition pseudorandom bit sequences (PRBSs) with periods of 215–1 are mapped into QPSK symbols through 1:2 deserialization. After upsampling to 2 sample/symbol, rectangular Nyquist shaping is performed. With the QPSK samples, a CW light with a linewidth δf/2 is linearly modulated at the signal baudrate B. The optical signals suffer from AWGN, and then they are received by coherent detection with an LO whose linewidth is δf/2. The two received streams r1(k) and r2(k), which correspond to real and imaginary parts, are rectangular-shaped filtered with a bandwidth of 1.1 × B to suppress out-band AWGN. The received samples are blocked with a size K and deserialized with a degree P. In this case, the clock rate of DSP, fDSP, is expressed by fDSP = B/P. The first tributary of the deserialized samples, u(κ) = [u1(κ), u2(κ)]T, is the equalized real-value 2 × 2 MIMO [c1(κ), c2(κ)], followed by external phase comparators p(κ) and q(κ). In the simulation, the MIMO adaptive equalization is almost the same as our implemented MIMO, as mentioned in the previous section, but the MIMO size is real-value 2 × 2. Finally, the BER is calculated based on the equalized samples after the MIMO. It is assumed that the pipeline delays δM, δp, and δq for the MIMO and phase comparator parts are identical, i.e., δ = δM = δp = δq, and the degree of parallelism P and pipeline delays δ are varied.
We simulated the dependence of the BER values on the SNR values, and then the SNR values required for BERs smaller than 1 × 10−2 were extracted. The results are shown in the upper part of Fig. 6(a). The horizontal axis shows the linewidth normalized by the signal baudrate, δf/B. Closed circles, open circles, closed triangles, open triangles, closed squares, open squares, and closed diamonds indicate the numerical results in cases with total delays P·δ of 4, 8, 16, 32, 64, 128, and 256, respectively. We can see that the penalty becomes larger as the normalized linewidth δf/B and the total delay P·δ increase. For comparison, the lower part of the figure shows the results obtained with the conventional MIMO without external phase comparators. We find that our designed MIMO is more tolerant of phase noise and delay, compared with the conventional scheme. To make the advantages clear, Fig. 6(b) shows the required SNR as a function of δf/B normalized by the inverse of the total delay, δf·P·δ/B, which is equivalent to the linewidth normalized by the DSP bandwidth including delay, δf·δ/fDSP. The definitions of markers are the same as those in Fig. 6(a). Note that the calculated results degenerate into the same curve. In our MIMO with external phase compensators, we find that the SNR penalty is negligible for δf·δ/fDSP smaller than 2 × 10−4. In the conventional scheme, it is suppressed for δf·δ/fDSP < 4 × 10−3. The results suggest that our designed MIMO improves the phase tracking performance by approximately five times even in the presence of feedback delay. As shown in Fig. 6(b), the required SNR values are determined by the normalized linewidth δf·δ/fDSP. Note that it does not depend on the signal baudrate B in the real-time DSP, whereas it depends on B in the offline DSP [16]. In this work, the performance of our designed MIMO was evaluated for the QPSK format. It is expected that the requirement for the spectral linewidth and calculation delay becomes much harder for high-order QAM formats because the phase margin becomes much smaller than that of the QPSK case.
Fig. 6. Calculated required SNR values for BERs smaller than 1 × 10−2 as a function of the linewidth δf normalized by the (a) signal baudrate B and (b) DSP bandwidth fDSP/δ.
4. Real-time 10 × MDM WDM transmission experiment
With the real-time MIMO receiver prototype mentioned in Section 2, we demonstrated a real-time weakly coupled 10 × MDM transmission experiment of WDM DP-QPSK signals over a 48-km FMF. Figure 7(a) shows the experimental setup, which was almost the same as that of our previous offline experiments [4,6]. The center channel was generated from a tunable laser with a spectral linewidth of approximately 5 kHz and modulated by an optical IQ modulator (IQM), which was driven by two electrical streams (I and Q components) generated from an arbitrary waveform generator (AWG) at a sampling rate of 25 GSample/s. The baseband signal was the QPSK format with 18 subcarriers at 625 Mbaud. The signal bandwidth was 12 GHz. After polarization multiplexing and wavelength multiplexing with a frequency spacing of 12.5 GHz, we obtained three-channel WDM DP-QPSK signals. The power spectra of the single-channel and WDM signals are shown by dashed line and solid line in Fig. 7(b), respectively. It is shown that the three WDM channels were ultradensely aligned. The WDM signals were split into ten copies, which were given by a relative delay of approximately 200 ns for signal decorrelation. By mode multiplexing the 10 delayed copies, the 10 × MDM signals were generated. In our experiment, a mode multiplexer based on multiple phase plates [14] was used. A FMF for the transmission was designed to suppress couplings between the different LP modes. It had a step index type profile with large differences (> 6 × 10−4) of the effective refractive indices between adjacent LP modes [11]. After the MDM transmission over the 48-km FMF, the MDM/WDM signals were received by the real-time coherent MIMO receiver prototype. In the experiment, the 48-km FMF was coiled around a fiber bobbin whose diameter was approximately 200 mm. Both edges of the fiber were fusion-spliced at the output port of the mode multiplexer and the input port of the mode demultiplexer in the real-time MIMO receiver.
Fig. 7. (a) Experimental setup for real-time weakly coupled 10 × MDM WDM transmission over 48-km FMF. (b) The power spectra of the DP-QPSK signals before and after wavelength multiplexing.
First, we experimentally evaluated the mode coupling characteristics in the weakly coupled 10 × MDM transmission. The experimental setup for measuring the mode coupling characteristics is shown in Fig. 8. DP-QPSK optical signals at 32 Gbaud were launched into one input port of the mode multiplexer, and then only one mode was excited in the FMF. All the output powers from the mode demultiplexer were measured. The measurement wavelength was 1550 nm. Table 1(a) shows the measured mode coupling values in a set of the mode multiplexer and demultiplexer. Since any coupling within degenerate modes and polarizations can be compensated by MIMO equalization, couplings between LP modes dominate the transmission performance. We found that the mode coupling was sufficiently suppressed, and the maximum value was -18.9 dB in the coupling between LP01 and LP11a/LP11b. Table 1(b) indicates the measured values of mode couplings in the whole MDM transmission, which was composed of the 48-km FMF, the mode multiplexer, and the mode demultiplexer. Although the mode couplings were enhanced by the 48-km FMF transmission, they were kept smaller than -15 dB. The total values of mode couplings from all input modes, namely, mode crosstalk, are calculated to be -10.8 dB, -10.4 dB, -10.4 dB, -9.5 dB, -9.5 dB, -8.6 dB, -11.1 dB, -11.1 dB, -10.7 dB, and -10.7 dB in LP01, LP11a, LP11b, LP21a, LP21b, LP02, LP31a, LP31b, LP12a, and LP12b, respectively. Even in the presence of the calculated magnitudes of the mode crosstalk, it is expected that the BER could be kept smaller than 1 × 10−2 for the QPSK format.
Fig. 8. Experimental setup for measuring the mode coupling characteristics of the 48-km FMF with a set of the mode multiplexer and demultiplexer.
Table 1. Measured mode coupling values between different modes in a set of the mode multiplexer and demultiplexer (a) without and (b) with the 48-km FMF.
Next, we measured the BER characteristics of the single-mode single-channel signals in the back-to-back configuration without any mode multiplexing. The measured BERs of the x and y polarization tributaries of the center subcarrier are plotted as closed circles and open circles in Fig. 9, respectively. Closed triangles, open triangles, closed squares, and open squares are those of edge subcarriers at the shortest and longest wavelengths. The error floor around a BER of 10−4 was found. The BER performance for the shortest wavelength subcarrier was slightly better than that of other subcarriers. Figure 10 shows the subcarrier dependence of the average BER values for dual polarization tributaries when the OSNR was 25 dB. Open circles and closed circles indicate the results of x and y polarization, respectively. BERs smaller than 10−3 for all subcarriers were achieved, although we found some dependency on the subcarrier. This dependency is due to the bandwidth characteristic of the AWG used for optical IQ modulation. We evaluated the tolerance of our scheme for the frequency offset. When the frequency offset was varied by tuning the LO frequency, the BERs of the center subcarrier were measured at OSNR = 20 dB. The measured results are indicated in Fig. 11. The BER was slightly degraded for the frequency offset larger than 40 MHz. This is due to the cut-off frequency of LPFs before ADCs.
Finally, we measured the BER values of 10 × MDM signals after 48-km FMF transmission. In the single-channel case, the measured BERs of all 10 modes and all 18 subcarriers are shown in Fig. 12. Closed circles and open circles indicate the results of the x and y polarization tributaries, respectively. The insets are the constellation maps of the center subcarriers. Although the BERs deteriorated with the mode crosstalk, they were kept smaller than 2.7 × 10−2, which corresponds to the BER threshold for 20%-overhead FEC [26]. In the WDM case, the average BER values of the center and both edge subcarriers are plotted as open circles in Fig. 13. Closed circles show the results in the single-channel case. We observed smaller BERs than the FEC threshold even in the WDM cases, although some degradation due to wavelength multiplexing was found. In the experiments, a transmission capacity of 375 Gbit/s per WDM channel was achieved assuming 20%-overhead FEC. These results show the feasibility of real-time weakly coupled MDM transmission.
Fig. 12. Measured BERs of all subcarriers after 48-km 10-MFs in the single channel case. Inset: constellation maps of the center subcarriers.
Fig. 13. Average BERs of the center and both edge subcarriers. Open circles: the WDM case; closed circles: the single-channel case.
5. Conclusion
We showed a real-time optical coherent MIMO receiver prototype with FPGA implementation for equalizing two degenerate LP modes. Our implemented MIMO was adaptively controlled based on the training-aided LMS algorithm to avoid the singularity problem. To improve the carrier-phase tracking performance, the external phase compensator was separated from the MIMO part. By numerical simulations, we evaluated how much the singularity problem impacts MDM systems and clarify the necessity of the training-aided LMS algorithm for MIMO adaptive control. In addition, our numerical results showed that the external phase compensators improve the carrier-phase tracking performance by approximately five times. With the receiver prototype, we demonstrated the first real-time weakly coupled MDM transmission of 3-WDM 10-MDM DP-QPSK signals over a 48-km FMF.
Funding
Ministry of Internal Affairs and Communications (JPMI00316, SCOPE #171507001); National Institute of Information and Communications Technology; Japan Society for the Promotion of Science (KAKENHI Grant Number 18H03231).
Acknowledgements
Some of the research results were achieved by the Ministry of Internal Affairs and Communications (MIC), Research and Development of Innovative Optical Network Technology for a Novel Social Infrastructure (JPMI00316) (Technological Theme II : OCEANS), the MIC SCOPE #171507001, and the Japan Society for the Promotion of Science KAKENHI Grant Number 18H03231. This work is partially supported by the National Institute of Information and Communications Technology (NICT), Japan.
Disclosures
The authors declare no conflicts of interest.
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