In this paper, the feasibility of space division multiplexing for optical wireless fronthaul systems is experimentally demonstrated by implementing high speed MIMO-OFDM/OQAM radio signals over 20km 7-core fiber and 0.4m wireless link. Moreover, the impact of optical inter-core crosstalk in multicore fibers on the proposed MIMO-OFDM/OQAM radio over fiber system is experimentally evaluated in both SISO and MIMO configurations for comparison. The experimental results show that the inter-core crosstalk tolerance of the proposed radio over fiber system can be relaxed to −10 dB by using the proposed MIMO-OFDM/OQAM processing. These results could guide high density multicore fiber design to support a large number of antenna modules and a higher density of radio-access points for potential applications in 5G cellular system.
© 2016 Optical Society of America
To meet the rapid growth of mobile data caused by the prosperous mobile applications, the 5th generation (5G) mobile communication network that offers super high capacity (1000 times compared to long term evolution (LTE) networks) is indispensable . Radio over fiber (RoF) is an attractive technique for 5G cellular system and has gained more and more attentions  due to its centralized signal processing and network management, simple remote antenna unit (RAU) and low-cost implementation . To further increase the capacity, high spectral efficiency modulation format, massive multiple-input multiple-out (MIMO) and carrier aggregation techniques are about to be properly considered for 5G cellular system . For example, orthogonal frequency division multiplexing (OFDM) has been widely used in current RoF systems [4, 5] as a high spectral efficiency technology. However, the requirement of cyclic prefix (CP) and the low side lobes of the rectangular pulse shape spectrum in OFDM modulation induces the loss of spectral efficiency and vulnerability to inter carrier interference (ICI). As an alternative, OFDM using offset quadrature amplitude modulation (OQAM) is a sort of filter bank multicarrier (FBMC) technique, where the bank of prototype filters is used for pulse shaping . In OFDM/OQAM system, the filters can achieve a higher side lobe suppression ratio, which is very attractive for reducing electrical sub-band frequency interference in carrier aggregation . Moreover, by using well designed pulse shapes that satisfying the perfect reconstruction conditions, OFDM/OQAM can achieve smaller ICI without using CP and result in the increased spectral efficiency .
In addition, massive MIMO has been identified as a promising and disruptive air interface technology to significantly improve the capacity and flexibility through spatial multiplexing in 5G cellular system [1, 9]. To support a large amount of antennas in RAUs, multidimensional division multiplexing techniques in fiber are highly desired for low-cost implementation, for instance, 2 × 2 MIMO RoF using polarization division multiplex (PDM) has been investigated , and a 397 Mb/s 16-QAM OFDM-MIMO signal over wavelength division multiplexed passive optical network (WDM-PON) system has also been demonstrated in . Moreover, space-division multiplexing (SDM) based on multi-core fiber (MCF) or multi-mode fiber (MMF) has proved its great merit in overcoming the barrier from capacity limit of single mode fiber [11, 12] and has enormous advantages such as compactness and spatial parallelism to realize massive MIMO. However, the inter-core and inter-mode crosstalk are critical issues and need to be carefully concerned in fiber fabrication [13, 14]. Recently, the impact of different crosstalk levels in 150m 4-core fibers is evaluated using full-standard 2 × 2 MIMO LTE-A RoF transmission . However, the impact of crosstalk is experimentally emulated just by using two optical SMF couplers and variable optical attenuators in , and no wireless MIMO transmission and wireless multipath effects are considered in the evaluation. Therefore, it is highly desired to investigate the impact and tolerance of inter-core crosstalk in radio over multi-core fiber system for guiding high density multicore fiber design to support a higher density of radio-access points in 5G cellular system.
In this paper, we demonstrate a MIMO-OFDM/OQAM radio over 20km 7-core MCF and 0.4m wireless link based on space division multiplexing in fiber and wireless MIMO techniques. The transmission performance of MIMO-OFDM and MIMO-OFDM/OQAM over 7-core MCF is firstly compared. Moreover, the impact of optical inter-core crosstalk in 7-core fibers on the proposed MIMO-OFDM/OQAM radio over fiber system is experimentally evaluated in both SISO and MIMO configurations for comparison. The experimental and simulation results prove that the tolerance of inter-core crosstalk in this radio over 7-core MCF system could be relaxed to −10 dB by using MIMO-OFDM/OQAM processing, resulting in the increase of core density in MCF which could support a higher density of radio-access modules in the future massive MIMO RoF system.
2. Principle of OFDM/OQAM and MIMO composite channel estimation
Figure 1 illustrates the principle of DFT-based MIMO-OFDM/OQAM system . For each channel, a data stream is first mapped into a block of M × N K-QAM format matrix, where M is the IFFT points and N represents the total symbol numbers in this block and K is the QAM order. Subsequently, the real and imaginary part of this matrix are separated and the imaginary part is delayed by half symbol period. After inserting preambles for channel estimation, the phase of each point is shifted by (m + n-2) × π/2, where m is the index of subcarrier and n is the index of symbol. After M-points IFFT, each symbol is filtered by a bank of FIR shaping filters. At last, a P/S converter is used to generate the baseband continuous-time OFDM/OQAM signal, which can be expressed as:17]. is the additional phase term for .
In OFDM modulator, the used rectangular pulse shaping filter has sharp edges in the time domain but causes long trails in the frequency domain, resulting in spectral leakage. Moreover, the additional CP is required to resist ICI. However, in OFDM/OQAM modulator, the pulse shaping filter is, for example, root raised cosine filter or IOTA filter , and they could offer higher side lobe suppression ratio and no CP is needed. In our experiment, the root raised cosine filter with the length of 4 times of symbol length and roll-off factor of 1 is used for pulse shaping. Figure 2 shows the electrical spectra of OFDM signal and OFDM/OQAM signal. It could be clearly observed that the side lobe suppression ratio of OFDM/OQAM signal is about 35 dB higher than conventional OFDM signal.
At the receiver side, after synchronization, serial to parallel (S/P) conversion, FIR filters and M-points FFT module, the received signal is transformed to the frequency domain and the demodulated signal could be derived as:8]. The interference from can be written as Im,n . Assuming that the channel response is slowly changing in both time and frequency domain, the channel response can be regarded as constant in the first neighbor area, that is, . Under these assumptions, the zero-force (ZF) equalizer could be used to implement the channel estimation and equalization . After one tap equalization, the real field orthogonality could be maintained and then the obtained offset QAM signals could be transformed into QAM signals by delaying half symbol period and combining back to the complex form again.
In radio over multicore fiber system, when considering the inter-core crosstalk and taking 2 × 2 channels for example, the frequency domain channel model could be expressed as:
For 2 × 2 hybrid MCF optical and wireless MIMO channels as shown in Fig. 1, the frequency domain channel model can be described as:
At last, we can obtain the recovered signals as shown in Eq. (7). Symbol represents the taking-real-operation, and the interferences between transmitted symbols could be eliminated due to the real field orthogonality.
3. Experimental and simulation setup and results
3.1 Experimental investigation of OFDM and OFDM/OQAM based MCF RoF system
The experimental setup for three groups of 2 × 2 MIMO-OFDM/OQAM signals over multi-core fiber system is shown in Fig. 3, for a demonstration purpose. MIMO-OFDM and MIMO-OFDM/OQAM are both tested for comparison in our experiment. At the central office (CO), a 10 GSa/s arbitrary waveform generator (AWG, TekAWG7122B) is performed to generate two-channel RF OFDM/OQAM signals. For each channel, a data stream with a pseudo-random bit sequence (PRBS) length of 215-1 is mapped onto 192 16-QAM subcarriers and the used IFFT points are 256. For MIMO-OFDM case, each OFDM frame consists of 100 data symbols, of which 3 data symbols are used for time synchronization and MIMO channel estimation, and the cyclic prefix is 1/10 of the IFFT length. For MIMO-OFDM/OQAM case, each OFDM/OQAM also has 100 data symbols, of which 8 data symbols are adopted to facilitate time synchronization and full-loaded preambles based MIMO channel estimation. The generated two channel signals are then up converted to 2.2 GHz radio frequency in the AWG. The two RF OFDM/OQAM signals are used to modulate a 100kHz-linewidth continuous-wave (CW) laser (λ = 1550nm) by two Mach-Zehnder modulators (MZMs) respectively. After two erbium-doped fiber amplifiers (EDFAs), these two optical OFDM/OQAM signals are split into 3 groups by 4 power splitters, and 2 optical time delay modules are used to decorrelate the 3 groups of 2 × 2 MIMO-OFDM/OQAM signals. At last, the generated 3 groups of 2 × 2 MIMO-OFDM/OQAM optical signals are coupled into a 7-core MCF by the low loss and low crosstalk fan-in devices [18, 19]. The used 7-core MCF has low crosstalk characteristics by employing the trench assisted index profile whose cross section view is inserted in Fig. 3. 6 outer cores are chosen for the 3 groups of optical MIMO-OFDM/OQAM signals, as shown in the inset of Fig. 3. The rest core could be used for the controlling and management of RoF system purpose. All the cores have the inter-core crosstalk below −40 dB between each other. In each group, the generated 2 × 2 MIMO optical signals has a net rate of 4.42 Gb/s () with 600 MHz () bandwidth and 7.36 bits/s/Hz spectral efficiency for 2 × 2 MIMO-OFDM/OQAM case and 4.24 Gb/s () with 600 MHz () bandwidth and 7.06 bits/s/Hz spectral efficiency for 2 × 2 MIMO-OFDM case.
After 20 km 7-core MCF propagation, the optical OFDM/OQAM signals are divided by the fan-out device, and each group of 2 × 2 MIMO-OFDM/OQAM signals are received by two 10 GHz bandwidth photodiode (PD) and the generated RF signals are then fed into the antennas after two low noise amplifiers (LNA) with 27 dB gain. After air transmission, these two wireless signals are detected by two receiver antennas and then captured by a 25 GSa/s digital sampling oscilloscope (DSO, Tektronix DPO72504DX). Offline signal demodulation is then performed by a DSP-based receiver consisting of resampling, synchronization, MIMO channel estimation, data mapping, and BER counting. In our experiment, 7 × 105 bits are calculated for BER counting.
Figure 4(a) shows the measured BER performance in terms of received optical power in the PD for both 2 × 2 MIMO-OFDM/OQAM and MIMO-OFDM with 20 km MCF and 0.4 m wireless link (wi wl). It can be clearly observed that the receiver’s sensitivity at the forward-error correction (FEC) limit (BER of 3.8 × 10−3) is achieved at −7.6 dBm and −7.75 dBm for MIMO-OFDM and MIMO-OFDM/OQAM signals, respectively, and negligible power penalty (around 0.15 dB) is observed. It means that compared to MIMO-OFDM, MIMO-OFDM/OQAM RoF signals have similar BER performance even without the help of CP [20, 21], and has the potential to be used in 5G cellular system. The received constellations of one group of 2 × 2 MIMO-OFDM/OQAM and MIMO-OFDM signals are indicated in the insets of Fig. 4(a). The little EVM performance difference between two channels in each group could be attributed to the different performances of optical and electrical components in two channels.
Figure 4(b) shows the comparative BER performance of three groups of 2 × 2 MIMO-OFDM/OQAM signals over 20 km MCF with 0.4 m wireless link (wi wl). As mentioned above, the inter-core crosstalk of all the used 6 outer cores are below −40 dB, so it can be observed that in Fig. 4(b) the measured three groups of 2 × 2 MIMO-OFDM/OQAM signals has similar BER performance and negligible power penalty (0.5 dB) is induced by both the internal crosstalk and external crosstalk.
3.2 Impact of inter-core crosstalk of MCF on MIMO-OFDM/OQAM RoF system
To investigate the impact and tolerance of inter-core crosstalk of MCF in the proposed MIMO-OFDM/OQAM RoF system, the used MCF is tapered by Fujikura FSM-100P + splicer’s programmable tapering control with arc discharge technique , and the experimental evaluation setup is shown in Fig. 5. After the taper processing, the core pitch is reduced and the inter-core crosstalk is increased. We measure the inter-core crosstalk as follows. We launch the optical signal into one core, after multicore fiber transmission, we measure its output power and the adjacent cores’ output power. Then we can calculate the crosstalk. The crosstalk is the ratio of other core’s output power to the launched core’s output power. The transmission loss of the input core and the crosstalk from the input core to the other cores can be obtained. The measurement of the transmission loss and the crosstalk of the rest cores have the same procedure. At last, we can get a form of transmission loss and crosstalk between each cores. It should be noted that when more than two signals are transmitted in the MCF, the total crosstalk is the summation of each adjacent core’s crosstalk . Due to the channel number limitation of the used AWG (TekAWG7122B), and for the proof-of-concept-purpose, the inter-core crosstalk in 2 × 2 MIMO transmission system is evaluated and analyzed in our experiment. One group of 4.42 Gb/s 2 × 2 MIMO-OFDM/OQAM RoF without wireless transmission in Section 3.1 is chose for this evaluation. We believe that this inter-core crosstalk tolerance investigation in 2x2 MIMO transmission system could illustrate the inter-core crosstalk tolerance when more than two cores are used, because the proposed 2x2 MIMO channel estimation algorithm could be easily extended to N × N MIMO channel estimation algorithm for crosstalk cancellation. We measured the whole crosstalk and select several pairs of cores whose mean inter-core crosstalk are −32.05 dB, −21.75 dB, −13.5 dB, −10.58 dB, −6.35 dB respectively under different tapering waist and the transition length. Both SISO and MIMO configurations are investigated for comparison. There are some differences between the SISO configuration in our experiment and the traditional SISO system. In the traditional SISO system, there is only one core used for data transmission and no crosstalk occurs. In our experimental transmission with SISO configuration, two independent signals are transmitted in two cores under a certain inter-core crosstalk respectively, and each signal is demodulated separately without MIMO processing algorithm. Moreover, in the MIMO transmission system, inter-crosstalk also occurs but MIMO processing algorithm as described in Section 2 is used to effectively estimate the channel transfer matrix and eliminate the interferences. In this test, all the experimental parameters are kept the same as described in Section 3.1.
Figure 6(a) illustrates the BER performance versus inter-core crosstalk in both SISO and MIMO configurations without wireless transmission. These two BER curves are all tested at the received optical power of −7 dBm. As shown in Fig. 6(a), when the inter-core crosstalk is increased, both SISO and MIMO configuration suffer from BER performance degradation. Nonetheless, when the inter-core crosstalk is lower than −13.5 dB, the SISO configuration outperforms the MIMO configuration. This could be attributed to that when the inter-core crosstalk is very low, the channel noise dominates the crosstalk. In the transmission with SISO configuration, the transmitted signal only suffers from the channel noise. However, in the transmission with MIMO configuration, the channel noise is regarded as the crosstalk, and the calculated MIMO channel response is inaccurate. Therefore, the performance of the SISO configuration outperforms that of the MIMO configuration. When the inter-core crosstalk increases and becomes higher than −13.5 dB, the crosstalk is still regarded as channel noise in SISO configuration, resulting in the degradation of OSNR actually. While in the transmission with MIMO configuration, the increased crosstalk is useful for MIMO channel transfer matrix reconstruction and more accurate signals could be achieved by the MIMO processing algorithm compared with the SISO configuration. However, when the inter-core crosstalk increases further, the optical beat interference (OBI) will significantly degrade the BER performance in both SISO and MIMO configurations. Taking the transmission performance and core density of MCF into account, the tolerance of the inter-core crosstalk of the proposed MIMO-OFDM/OQAM RoF system is −10 dB. Figure 6(b) shows the measured BER performance versus received optical power in both SISO and MIMO configurations at different levels of inter-core crosstalk. When the inter-core crosstalk is −32.05 dB, the SISO configuration obviously has a better BER performance. When the inter-core crosstalk is increased to −6.35 dB, the error floor is obtained in SISO configuration, but error free transmission is still achieved in MIMO configuration. However, 1.3 dB power penalty is observed between −13.5 dB and −6.35 dB inter-core crosstalk in MIMO configuration.
To verify the above findings of inter-core crosstalk tolerance, we have simulated this MIMO-OFDM/OQAM RoF systems without wireless links using the multicore fiber nonlinear propagation model [24, 25] based on Matlab and VPI transmission Maker 9.0, taking the crosstalk’s random behavior into account. In our simulation, MIMO-OFDM/OQAM parameters are kept the same as used in the experiment, and both SISO and MIMO configurations are evaluated. Figure 7(a) shows the BER performance versus inter-core crosstalk at the received power of −19 dBm for both MIMO and SISO configurations in the evaluation. The trends of these two curves are similar to the experimental one, and the performance of MIMO configuration has become better than the performance of SISO configuration when the inter-core crosstalk is higher than −24 dB. Similar to the experimental results, when the inter-core crosstalk is −10 dB, we cannot get the BER below the FEC limit in SISO configuration, but error free transmission is still achieved in MIMO configuration, as shown in Fig. 7(b). It could be clearly observed that the simulation results in Fig. 7 and the experimental results in Fig. 6 support the same conclusion that the tolerance of inter-core crosstalk could be effectively relaxed by using the proposed full-loaded preambles based MIMO channel estimation algorithm.
To further investigate the impact of inter-core crosstalk on the proposed MIMO-OFDM/OQAM signals over MCF system, the BER performance of 2 × 2 MIMO-OFDM/OQAM RoF system are measured with and without wireless transmission for comparison under inter-core crosstalk of −32.05 dB, −13.5 dB and −6.35 dB as shown in Fig. 8. It could be clearly observed that about 2~3 dB power penalty induced by the wireless transmission in each case could be attributed to the increased cross interference, multipath effect and lower signal to noise ratio (SNR). That means the inter-core crosstalk in MCF and cross interference effect in wireless MIMO link can be effectively compensated by the proposed full-loaded preambles based MIMO channel estimation algorithm.
As discussed above, the tolerance of the inter-core crosstalk in MCF could be relaxed to −10 dB per 20km in the proposed MIMO-OFDM/OQAM signals over MCF system. That means the multicore fiber with a large plurality of cores (for example 36-cores MCF in ) could be adopted to support a large number of antenna modules and a higher density of radio-access points for potential applications in 5G cellular system.
We have experimentally demonstrated a spectral efficient and high speed MIMO-OFDM/OQAM radio over fiber system by combining 7-core MCF-based space division multiplexing and wireless MIMO techniques. MIMO-OFDM/OQAM RoF system is proved to have similar BER performance compared to MIMO-OFDM RoF system in our experiment, while with higher spectral efficiency. Moreover, the impact of optical inter-core crosstalk in 7-core fibers on the 4.42 Gb/s 2 × 2 MIMO-OFDM/OQAM RoF system is experimentally evaluated in both SISO and MIMO configurations for comparison. By using the proposed full-loaded preambles based MIMO channel estimation algorithm, the tolerance of inter-core crosstalk could be relaxed to −10 dB per 20km. These results have potential application in guiding high density multicore fiber design to support a higher density of radio-access points in 5G cellular system.
The corresponding author Lei Deng thanks the support of the National “863” Program of China (No. 2015AA016904) and the National Nature Science Foundation of China (NSFC) (No. 61307091, 61331010, and 61205063). The co-corresponding author Ming Tang also thanks the support of the Program for New Century Excellent Talents in University (NCET-13-0235).
References and links
1. J. G. Andrews, S. Buzzi, W. Choi, S. Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be,” IEEE J. Sel. Areas Comm. 32(6), 1065–1082 (2014). [CrossRef]
2. D. Wake, A. Nkansah, and N. J. Gomes, “Radio over fiber link design for next generation wireless systems,” J. Lightwave Technol. 28(16), 2456–2464 (2010). [CrossRef]
3. L. Chen, Y. Shao, X. Lei, H. Wen, and S. Wen, “A novel radio-over-fiber system with wavelength reuse for upstream data connection,” IEEE Photonics Technol. Lett. 19(6), 387–389 (2007). [CrossRef] [PubMed]
4. L. Deng, X. Pang, Y. Zhao, M. B. Othman, J. B. Jensen, D. Zibar, X. Yu, D. Liu, and I. T. Monroy, “2x2 MIMO-OFDM Gigabit fiber-wireless access system based on polarization division multiplexed WDM-PON,” Opt. Express 20(4), 4369–4375 (2012). [CrossRef] [PubMed]
5. S. E. Alavi, I. S. Amiri, M. Khalily, N. Fisal, A. S. M. Supa’at, H. Ahmad, and S. M. Idrus, “W-Band OFDM for radio-over-fiber direct-detection link enabled by frequency nonupling optical up-conversion,” IEEE Photonics J. 6(6), 1–7 (2014). [CrossRef]
6. Z. Li, T. Jiang, H. Li, X. Zhang, C. Li, C. Li, R. Hu, M. Luo, X. Zhang, X. Xiao, Q. Yang, and S. Yu, “Experimental demonstration of 110-Gb/s unsynchronized band-multiplexed superchannel coherent optical OFDM/OQAM system,” Opt. Express 21(19), 21924–21931 (2013). [CrossRef] [PubMed]
7. C. Li, X. Zhang, H. Li, C. Li, M. Lou, Z. Li, J. Xu, and S. Yu, “Experimental demonstration of 429.96Gb/s OFDM/OQAM-64QAM over 400km SSMF transmission within a 50GHz grid,” IEEE Photonics J. 6(4), 1–8 (2014).
8. C. Lélé, J. P. Javaudin, R. Legouable, A. Skrzypczak, and P. Siohan, “Channel estimation methods for preamble‐based OFDM/OQAM modulations,” Eur. Trans. Telecommun. 19(7), 741–750 (2008). [CrossRef]
9. P. Demestichas, A. Georgakopoulos, D. Karvounas, K. Tsagkaris, V. Stavroulaki, J. Lu, C. Xiong, and J. Yao, “5G on the Horizon: key challenges for the radio-access network,” IEEE Veh. Technol. Mag. 8(3), 47–53 (2013). [CrossRef]
10. M. B. Othman, L. Deng, X. Pang, J. Caminos, W. Kozuch, K. Prince, X. Yu, J. B. Jensen, and I. T. Monroy, “MIMO-OFDM WDM PON with DM-VCSEL for femtocells application,” Opt. Express 19(26), B537–B542 (2011). [CrossRef] [PubMed]
11. G. S. Gordon, M. J. Crisp, R. V. Penty, T. D. Wilkinson, and I. H. White, “Feasibility demonstration of a mode-division multiplexed MIMO-enabled radio-over-fiber distributed antenna system,” J. Lightwave Technol. 32(20), 3521–3528 (2014). [CrossRef]
12. M. Morant, A. Macho, and R. Llorente, “On the suitability of multicore fiber for LTE-advanced MIMO optical fronthaul systems,” J. Lightwave Technol. 34(2), 676–682 (2016). [CrossRef]
13. T. Sakamoto, T. Mori, M. Wada, T. Yamamoto, and F. Yamamoto, “Coupled multicore fiber design with low intercore differential mode delay for high-density space division multiplexing,” J. Lightwave Technol. 33(6), 1175–1181 (2015). [CrossRef]
15. A. Macho, M. Morant, and R. Llorente, “Experimental analysis of multicore crosstalk impact on MIMO LTE-a radio-over-fibre optical systems,” in Proceedings of IEEE International Conference on Communication Workshop (IEEE, 2015), pp. 329–333. [CrossRef]
16. X. Fang, Y. Xu, Z. Chen, and F. Zhang, “Frequency-domain channel estimation for polarization-division-multiplexed CO-OFDM/OQAM systems,” J. Lightwave Technol. 33(13), 2743–2750 (2015). [CrossRef]
17. P. Siohan, C. Siclet, and N. Lacaille, “Analysis and design of OFDM/OQAM systems based on filter bank theory,” IEEE T. Signal Process. 50(5), 1170–1183 (2002).
18. B. Li, Z. Feng, M. Tang, Z. Xu, S. Fu, Q. Wu, L. Deng, W. Tong, S. Liu, and P. P. Shum, “Experimental demonstration of large capacity WSDM optical access network with multicore fibers and advanced modulation formats,” Opt. Express 23(9), 10997–11006 (2015). [CrossRef] [PubMed]
19. Z. Feng, B. Li, M. Tang, L. Gan, R. Wang, R. Lin, Z. Xu, S. Fu, L. Deng, W. Tong, S. Long, L. Zhang, H. Zhou, R. Zhang, S. Liu, and P. P. Shum, “Multicore-fiber-enabled WSDM optical access network with centralized carrier delivery and RSOA-based adaptive modulation,” IEEE Photonics J. 7(4), 1–9 (2015). [CrossRef]
20. C. Lélé, P. Siohan, and R. Legouable, “2 dB better than CP-OFDM with OFDM/OQAM for preamble-based channel estimation,” in Proceedings of IEEE International Conference on Communications (IEEE, 2008), pp. 1302–1306. [CrossRef]
22. L. Gan, R. Wang, D. Liu, L. Duan, S. Liu, S. Fu, B. Li, Z. Feng, H. Wei, W. Tong, P. Shum, and M. Tang, “Spatial-division multiplexed Mach-Zehnder interferometers in heterogeneous multicore fiber for multi-parameter measurement,” IEEE Photonics J. 8(1), 1–8 (2016). [CrossRef]
23. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, “Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber,” Opt. Express 19(17), 16576–16592 (2011). [CrossRef] [PubMed]
24. B. Li, L. Gan, S. Fu, Z. Xu, M. Tang, W. Tong, and P. Shum, “The role of effective area in the design of weakly coupled MCF: optimization guidance and OSNR improvement,” IEEE J. Sel. Top Quantum. 22(2), 1–7 (2016). [CrossRef]
25. R. Luis, B. Puttnam, A. Cartaxo, W. Klaus, J. Mendinueta, Y. Awaji, N. Wada, T. Nakanishi, T. Hayashi, and T. Sasaki, “Time and modulation frequency dependence of crosstalk in homogeneous multi-core fibers,” J. Lightwave Technol. 34(2), 441–447 (2016). [CrossRef]
26. J. Sakaguchi, W. Klaus, J. M. Delgado Mendinueta, B. J. Puttnam, R. S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, and T. Kobayashi, “Realizing a 36-core, 3-mode fiber with 108 spatial channels,” in Optical Fiber Communication Conference, 2015 OSA Technical Digest Series (Optical Society of America, 2015), paper Th5C–2. [CrossRef]