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Modulation format conversion employing coherent optical superposition |
Optics Express, Vol. 20, Issue 26, pp. B322-B330 (2012)
http://dx.doi.org/10.1364/OE.20.00B322
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– Abstract
1. Introduction
2. Operation principle
3. Experimental set-up
4. Experimental results
5. Discussion
6. Conclusion
– References and links
– Abstract
1. Introduction
2. Operation principle
3. Experimental set-up
4. Experimental results
5. Discussion
6. Conclusion
– References and links
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Abstract
We propose and experimentally study the passive coherent optical addition of complex modulation format signals through the use of a delay line interferometer followed by a temporal gate to increase the encoded bits per symbol and consequently, the spectral efficiency of an incident signal. Modulation format conversion and packet compression are demonstrated as two possible application examples. A variety of modulation formats can be accommodated, whereas higher compression factors can be achieved through the use of a cascade of delay line interferometers.
© 2012 OSA
1. Introduction
Next-generation communication systems are expected to exploit complex modulation formats, wavelength and modulation format agile transponders, as well as dense photonic integration, to deliver sufficient capacity [1–4] and flexibility to meet user requirements.
X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3 × 485-Gb/s WDM transmission over 4800 km of ULAF and 12 × 100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” OFC-NFOEC, paper PDPC2 (2010).
Differential binary phase shift keying (D-BPSK) and more recently polarization-multiplexed quadrature phase shift keying (PM-QPSK) signals have begun to replace the previous industry standard of intensity-modulated on-off keying (OOK) signals. Indeed, the complex phase (and amplitude) encoded formats can carry several bits of information in a single transmitted symbol, allowing for higher spectral efficiencies, but are associated with more stringent optical signal to noise ratio (OSNR) requirements, meaning that the power budgets of transmission links (especially those comprising several amplification stages) must be carefully designed. In this context, different modulation formats may be selectively employed depending on the network demands and may even coexist in the same optical link. Thus, a means for converting signals from one format to another might be very beneficial and doing it using optics rather than electronics might be advantageous, since higher repetition rates and multi-channel operation can be accommodated.
All-optical format conversion can be performed using a number of techniques and the majority of them exploit nonlinear effects [5–7]. In the linear approach, two independent and wavelength shifted to a common carrier signals are coherently superposed in time to increase the bit per symbol and, thus, the overall spectral efficiency (SE). However, this technique imposes challenging carrier recovery extraction and phase locking requirements for the two signals.
K. Mishina, S. Kitagawa, and A. Maruta, “All-optical modulation format conversion from on-off-keying to multiple-level phase-shift-keying based on nonlinearity in optical fiber,” Opt. Express 15(13), 8444–8453 (2007). [CrossRef] [PubMed]
A simpler solution relies on coherently superposing in time the same information-carrying symbol with a delayed replica and can be easily achieved using a delay line interferometer (DLI) [8–10]. Unfortunately though directly deployment in this manner results in redundancy of information and thus no overall increase in SE.
In this paper, we extend the concept of passive superposition further and use an electro-optic gate to eliminate the redundant information in order to allow a real increase in the number of bits per symbol and an overall improvement in spectral efficiency [11,12]. Two different application examples are experimentally demonstrated to: (a) increase the SE of a 50 GHz channel by a factor of 4; and (b) temporally compress in time 128-symbol packets carrying either BPSK or QPSK signals, causing them to occupy only half of their original duration. Practical limitations of the scheme in terms of transmission distance and the associated laser linewidth requirements are also numerically investigated.
F. Parmigiani, J. Kakande, L. M. Jones, P. Petropoulos, and D. J. Richardson, “Temporal multiplexing of complex modulation formats facilitated by their coherent optical superposition,” European Conference and Exhibition on Optical Communication (ECEOC) Amsterdam, The Netherlands, June 16, 2012 (2010).
2. Operation principle
Figure 1
shows the operational principle of the passive coherent optical superposition scheme using a delay line interferometer, when a BPSK signal is considered at its input. The BPSK signal is split into two paths via the first 3dB coupler of the DLI; one of the two paths is delayed by m- bits related to the other, where m is an integer number, and shifted in phase by π/2 or any multiple (2n + 1) π/2, where n is an integer number, using a phase shifter (PS). The two signals are then coherently added together in the second 3dB coupler of the DLI and converted into a QPSK signal. The corresponding phase mapping between the input and output signals is summarized in Table 1
.
Table 1 Phase combination of two BPSK signals (Si1 and Si2) and converted QPSK signal (So).
| Arg(Si1) | Arg(Si2) | Arg(So) |
|---|---|---|
| 0 | π/2 | π/4 |
| π | π/2 | 3π/4 |
| 0 | 3π/2 | 7π/4 |
| π | 3π/2 | 5π/4 |
The scheme can be easily generalized to accommodate a variety of modulation formats asshown in Fig. 2(a)
, where the generic case of a phase and/or amplitude encoded signal with repetition rate 1/ΔΤ and the relative phase of its symbol denoted as ϕk (k = 1, 2, …) is considered at the input of each of the DLIs shown. The DLI includes a fixed delay of m ΔΤ, a PS and a variable optical attenuator (VOA), which are set depending on the specific application under consideration (format conversion or packet compression for example as it will be discussed below) and on the particular initial complex modulation format. The coherent addition of the electric fields allows to temporally compress the information carried by the original signal by doubling its number of bits per symbol, without broadening the spectral content of the signal.
Fig. 2 (a) Generalized passive coherent optical superposition operation principle using DLIs and time gating functions. (b) Extension to higher spectral efficiencies, higher compression factors and more complex modulation formats.
However, as the same signal is added to its delayed copy in the DLI, redundant information is also generated, which needs to be removed to truly achieve SE improvement. This can be easily understood through Fig. 2(a), where one can observe that bit ϕ2 of Signal1 is contained in both symbols (ϕ1 + ϕ2) and (ϕ2 + ϕ3) at the output of the DLI. Same discussion applies for the bit ϕii of Signal2. The removal of this redundant information can be performed using a rectangular time-gating function with a period that is double that of the time delay between the two arms in the DLI (mΔT), see Fig. 2(a). In this way, the new signal has the same information content as the original one, but occupies half of its space in time. This empty space can be then filled in by a different signal, properly time-interleaved and wavelength-shifted to a common carrier, as shown in Fig. 2(a), to effectively increase the SE and, thus, the overall transmission capacity.
Furthermore, if multiple DLIs with appropriately adjusted delays are used in series, as shown in Fig. 2(b), more complex modulation formats can be achieved. In this case, one single time-gating switch at the very end of the system can be used, with a period doubled ascompared to the sum of the various time delays between the two arms in the corresponding DLIs. Multiple signals can then be added in the empty spaces to achieve the maximum SE, just as in the early discussion.
Note that since the data is rearranged in time as a function of the DLI delay, the data will need to be pre-coded in order for the transmitted information to be retained.
Figure 3
shows some examples of numerical constellation diagrams, starting with a BPSK signal (1 bit per symbol) and finishing with a 256 QAM signal (8 bits/symbol), achieving in principle an overall SE improvement of 8. The numerical simulations were carried out using VPI Transmission Maker 8.0. Table 2
shows some examples of the phase shift and attenuation values required to enable various format conversions. Note that to achieve a correct 256 quadrature amplitude modulation (QAM), the symbols of the original 16 QAM signals are not equally spaced in the constellation diagram. If the signal is the result of multiple coherent additions, this simply implies that the attenuation value for the DLI used to format convert the quadrature phase shift keying (QPSK) signal into a 16QAM signal has to be changed from 6dB to 12dB in Table 2. .
Fig. 3 Some example of simulated constellation diagrams to re-code the original BPSK signal (a) to QPSK (b) 16QAM (c) and 256QAM (d) signals, respectively.
Table 2 Phase shift and attenuation values in the DLI to achieve various complex modulation formats.
| Initial Signal | Final Signal | Phase Shift [rad] | Attenuation [dB] |
|---|---|---|---|
| BPSK | QPSK | (2n + 1)π/2 | 0 |
| QPSK | 16QAM | nπ/2 | 6 |
| 16QAM | 256QAM | nπ/2 | 6 |
Finally, according to the specific delay used in the DLI, different applications of this temporal compressor can be envisaged. For example, the use of a few bits delay leads to symbol-by-symbol remodulation of the signal, while if a delay comparable to hundreds of bits is set, a packet compression scheme (through format conversion) can be implemented. Both examples are discussed in detail in the following sections.
3. Experimental set-up
Figure 4
shows the experimental set-up of the passive coherent optical superposition scheme. A narrow-linewidth (<1 kHz) continuous wave (CW) laser at a central wavelength of 1557.4nm was modulated to obtain a 10 Gbaud non-return-to-zero BPSK (or QPSK) 231−1 pseudorandom bit sequence (PRBS). The signal was then fed to the DLI, described in the previous section, to compose a QPSK (or 16QAM) signal at the output. For the format conversion experiment, a free-space 400ps DLI was used (4 bits delay at 10 Gbaud). For the packet compression experiment a fiberized DLI was used incorporating a few meters of single mode fiber to achieve ΔT = 12.8 ns (128 symbols at 10 Gbaud) delay between the two arms. An electronic feedback control was implemented to stabilize the system from perturbations induced mainly by thermal drifts. It comprised part of the original CW signal propagating in the opposite direction to the modulated signal through the DLI, an optical detector (~1MHz) and a proportional integral (PI) controller to control the piezo-electric transducer (PZT) based fiber stretcher in one of the two arms of the DLI. A synchronously driven amplitude modulator with repetition rate of 2ΔT was used to provide the rectangular time-gating function. Furthermore, to emulate the effect of a second independent signal, the multiplexed and gated signal was split in two, one portion was delayed relative to the next and had its carrier frequency shifted by 30MHz using an acousto-optic modulator (AOM) in order to decorrelate it from the other one, and then the two portions of the signal were recombined together. At the output of the system, the signals were characterized in terms of eye diagrams using a digital communication analyzer (DCA), and constellation diagrams using a homodyne coherent optical receiver.
4. Experimental results
The eye and constellation diagrams at various points of the format converter scheme are shown in Fig. 5
and Fig. 6
, when the input signals were BPSK (Fig. 5(a), 5(b) and 5(c)) and QPSK (Fig. 6(a), 6(b) and 6(c)), respectively. The error vector magnitude (EVM) of the original BPSK signal had a root mean square (rms) of 6.9%, see Fig. 5(a). After temporal multiplexing to QPSK and time gating the EVM became 7.1% rms, see Fig. 5(b). It is worth pointing out that the eye diagrams in Fig. 5(a) and Fig. 5(b) contain the same information, with the gated signal occupying half of the time slot available. The clearance of the redundant information is also visible as a cloud of points corresponding to zero amplitude in the constellation diagram in Fig. 5(b). This empty space can then be occupied by a second independent signal to effectively double the SE of the original signals. Figure 5(c) shows the eye and constellation diagrams when a second signal at essentially the same carrier frequency was temporally aligned and added to the empty slot. Clean and open eyes can be seen with a small beating due to the non-optimal temporal gating function used in the particular experiment. This is reflected in an increase of the EVM of the overall multiplexed QPSK signals, which became 9.5% rms.
Fig. 5 Eye diagrams and constellation diagrams at various points of the format converter for BPSK as input signals. Scale: 100ps/div.
Fig. 6 Eye diagrams and constellation diagrams at various points of the format converter for QPSK as input signals. Scale: 100ps/div.
Similar measurements were taken for an initial QPSK signal with EVM of 6.9% rms, see Fig. 6(a). After temporal multiplexing to 16QAM and time gating the EVM became 7.3% rms, see Fig. 6(b). Again, Fig. 6(a) and Fig. 6(b) contain the same information, with the gated signal occupying only half of the time slot available. Figure 6(c) shows the eye and constellation diagrams when a second signal was temporally aligned and added to the empty slot. It is worth noting that even in this case, the signal was originally generated by a BPSK transmitter followed by a DLI-based format converter, highlighting how cascading two DLIs, the second one with double the delay as compared to the first one, followed by a single time gatingswitch, is possible to directly go from BPSK to 16QAM. In this case, the same information occupied ¼ of the original time and the SE was efficiently increased by a factor of 4.
Figure 7
shows bit-error ratio (BER) measurements of the various format converted signals (taken at the output of the DLI) as compared to the original one, using an optically pre-amplified coherent receiver. A power penalty of about 3dB is observed going from BPSK to QPSK and of about 9dB from QPSK to 16QAM for BER = 10−3 in good agreement with the theoretical predictions reported in [13].
By simply increasing the time delay in the DLI a packet compression scheme was implemented and similar measurements to the previous case were taken. Figure 8(a)
and Fig. 8(c) show the eye and constellation diagrams of the initial BPSK and QPSK signals, respectively. The EVM values are the same as the previous case and only reported for completeness. Figure 8(b) and Fig. 8(d) show the newly generated and properly gated QPSK and 16QAM signals. Again, the same information is held in half of the available time slot.
Fig. 8 Eye diagrams and constellation diagrams at various points of the packet compression scheme for BPSK and QPSK as input signals. Scale: 2ns/div.
By observing the DCA traces, it is evident that the time gating response at low frequencies compromises slightly the performance of the system. Indeed, EVM values of 8.9% rms and 10.8% rms were recorded for the QPSK and 16QAM signals, respectively.
5. Discussion
The performance of the scheme was numerically assessed for signals that had undergone transmission over different fiber lengths, as well as for different initial laser linewidths. For these studies BPSK to QPSK format conversion at 10Gbaud was considered.
As the signal propagates through a non-compensated transmission link it accumulates dispersion and temporally broadens. Normally, this dispersion can be compensated for at the receiver, often using electronic dispersion compensation technologies. The above scheme however, is nonlinear in nature and therefore any accumulated dispersion prior to the device cannot be perfectly compensated for. In fact, we expect to observe a penalty in the presence of dispersion due to the loss of some signal information during the temporal gating. As such, for ideal operation any dispersion should be compensated for prior to the format converter scheme. The impact of dispersion is studied by calculating the EVM of a signal after the proposed scheme for various amounts of dispersion. Figure 9(a)
, top, shows how the signal EVM values vary as a function of the transmission length for various values of the delay in the DLI. A dispersion of 16ps/nm/km is assumed for the single mode fibre (SMF) used to emulate transmission. As shown, the performance depends drastically on the time delay used in the DLI, relative to the extent of pulse broadening due to dispersion. For long delays (such as 4096 bits), many of the temporally broadened pulses can still fit within the gating window, and therefore are minimally affected by the gating process. However, as the delay decreases, more and more of the pulses extend out of the gating window, hence an increased penalty is clearly visible. The maximum transmission distances for various DLI delays to achieve a 20% rms EVM are reported in Table 3
.
Fig. 9 (a) Simulated EVM values versus transmission length prior the proposed scheme for different DLI delays (switch time windows). (b) Simulated EVM values as a function of laser linewidth for different values of DLI delays.
Table 3 Maximum reach for various delays to achieve EVM ~20%rms.
| Delay [bits] | Transmission Length [km] |
|---|---|
| 1 | 25 |
| 4 | 75 |
| 8 | 100 |
| 32 | 600 |
| 128 | 3000 |
| 4096 | 105000 |
Since the scheme is based on coherent signal superposition, the impact of laser linewidth on the performance of the system was also investigated. In this case, as expected, the longer the delay, the more stringent the requirements on laser coherence, see Fig. 9(b).
As such a compromise may have to be made between dispersion tolerance and linewidth requirements, which respond in a complementary manner to increasing delay.
6. Conclusion
We have proposed and experimentally demonstrated two applications, in which passive coherent superposition of data bits has been combined with time gating to eliminate redundant information and thus effectively increase the overall spectral efficiency. The experiments demonstrated all-optical format conversion and packet compression respectively with, up to four times SE improvement (by cascading two DLIs together). Note that various conversions can be envisaged simply by adjusting the DLI parameters and higher SE can be achieved by adding DLIs to achieve any higher order modulation formats. Practical limitations of the scheme have been numerically studied.
Acknowledgments
Dr. F. Parmigiani gratefully acknowledges the support from the Royal Academy of Engineering/EPSRC through a University Research Fellowship. This work is supported by the EPSRC grant EP/I01196X: Transforming the Future Internet: The Photonics Hyperhighway.
References and links
X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3 × 485-Gb/s WDM transmission over 4800 km of ULAF and 12 × 100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” OFC-NFOEC, paper PDPC2 (2010). | |
X. Zhou, L. E. Nelson, R. Isaac, P. D. Magill, B. Zhu, D. W. Peckham, P. Borel, and K. Carlson, “4000km transmission of 50GHz spaced, 10x494.85-Gb/s hybrid 32-64QAM using cascaded equalization and training-assisted phase recovery,” OFC-NFOEC, paper PDP5C.6 (2012). | |
P. J. Winzer, A. H. Gnauck, S. Chandrasekhar, S. Draving, J. Evangelista, and B. Zhu, “Generation and 1,200-km transmission of 448-Gb/s ETDM 56-Gbaud PDM 16-QAM using a single I/Q modulator,” ECOC 2010, Torino, Italy, paper PDP 2.2 (2010). | |
Y. -K. Huang, E. Ip, M. -F. Huang, B. Zhu, P. N. Ji, Y. Shao, D. W. Peckham, R. Lingle., Jr, Y. Aono, T. Tajima, and T. Wang, “10×456-Gb/s DP-16QAM transmission over 8×100 km of ULAF using coherent detection with a 30-GHz analog-to-digital converter,” OECC 2010, Japan, paper PDP3 (2010). | |
K. Mishina, S. Kitagawa, and A. Maruta, “All-optical modulation format conversion from on-off-keying to multiple-level phase-shift-keying based on nonlinearity in optical fiber,” Opt. Express 15(13), 8444–8453 (2007). [CrossRef] [PubMed] | |
G. W. Lu, E. Tipsuwannakul, T. Miyazaki, C. Lundström, M. Karlsson, and P. Andrekson, “Format conversion of optical multilevel signals using FWM-based optical phase erasure,” J. Lightwave Technol. 29(16), 2460–2466 (2011). [CrossRef] | |
C. Su, Y. Yikai, L. Yi, L. Leng, X. Tian, X. X. Xinyu, and Y. Tian, “All-optical format conversion from NRZ to BPSK using a single saturated SOA,” IEEE Photon. Technol. Lett. 18(22), 2368–2370 (2006). | |
J. Kakande, A. Bogris, R. Slavík, F. Parmigiani, D. Syvridis, P. Petropoulos, and D. J .Richardson, “First demonstration of all-optical QPSK signal regeneration in a novel multi-format phase sensitive amplifier,” ECOC 2010, Torino, Italy, PD 3.3 (2010). | |
H. Kishikawa, P. Seddighian, N. Goto, S. Yanagiya, and L. R. Chen, “All-optical modulation format conversion from binary to quadrature phase-shift keying using delay line interferometer, ” Photonics Conference (PHO), 513 - 514 (2011). | |
M. Sköld, H. Sunnerud, M. Westlund, and P. A. Andrekson, “Simultaneous waveform and bit-error-rate measurements of 66 GBd PDM-16-QAM signals,” ECOC PD Th.13.B.3 (2011). | |
F. Parmigiani, J. Kakande, L. M. Jones, P. Petropoulos, and D. J. Richardson, “Packet compression of complex modulation formats based on coherent optical superposition,” International Conference on Transparent Optical Networks (ICTON 2012) Warwick UK (2012). | |
F. Parmigiani, J. Kakande, L. M. Jones, P. Petropoulos, and D. J. Richardson, “Temporal multiplexing of complex modulation formats facilitated by their coherent optical superposition,” European Conference and Exhibition on Optical Communication (ECEOC) Amsterdam, The Netherlands, June 16, 2012 (2010). | |
K. Kikuchi, “Coherent detection of phase-shift keying signals using digital carrier-phase estimation,” OFC (2006). |
OCIS Codes
(060.4230) Fiber optics and optical communications : Multiplexing
(230.1360) Optical devices : Beam splitters
(230.2090) Optical devices : Electro-optical devices
ToC Category:
Waveguide and Optoelectronic Devices
History
Original Manuscript: October 4, 2012
Revised Manuscript: November 6, 2012
Manuscript Accepted: November 6, 2012
Published: November 29, 2012
Virtual Issues
European Conference on Optical Communication 2012 (2012) Optics Express
Citation
Francesca Parmigiani, Liam Jones, Joseph Kakande, Periklis Petropoulos, and David J. Richardson, "Modulation format conversion employing coherent optical superposition," Opt. Express 20, B322-B330 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-26-B322
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References
- X. Liu, S. Chandrasekhar, P. J. Winzer, B. Zhu, D. W. Peckham, S. Draving, J. Evangelista, N. Hoffman, C. J. Youn, Y. H. Kwon, and E. S. Nam, “3 × 485-Gb/s WDM transmission over 4800 km of ULAF and 12 × 100-GHz WSSs using CO-OFDM and single coherent detection with 80-GS/s ADCs,” OFC-NFOEC, paper PDPC2 (2010).
- X. Zhou, L. E. Nelson, R. Isaac, P. D. Magill, B. Zhu, D. W. Peckham, P. Borel, and K. Carlson, “4000km transmission of 50GHz spaced, 10x494.85-Gb/s hybrid 32-64QAM using cascaded equalization and training-assisted phase recovery,” OFC-NFOEC, paper PDP5C.6 (2012).
- P. J. Winzer, A. H. Gnauck, S. Chandrasekhar, S. Draving, J. Evangelista, and B. Zhu, “Generation and 1,200-km transmission of 448-Gb/s ETDM 56-Gbaud PDM 16-QAM using a single I/Q modulator,” ECOC 2010, Torino, Italy, paper PDP 2.2 (2010).
- Y. -K. Huang, E. Ip, M. -F. Huang, B. Zhu, P. N. Ji, Y. Shao, D. W. Peckham, R. Lingle., Jr, Y. Aono, T. Tajima, and T. Wang, “10×456-Gb/s DP-16QAM transmission over 8×100 km of ULAF using coherent detection with a 30-GHz analog-to-digital converter,” OECC 2010, Japan, paper PDP3 (2010).
- K. Mishina, S. Kitagawa, and A. Maruta, “All-optical modulation format conversion from on-off-keying to multiple-level phase-shift-keying based on nonlinearity in optical fiber,” Opt. Express15(13), 8444–8453 (2007). [CrossRef] [PubMed]
- G. W. Lu, E. Tipsuwannakul, T. Miyazaki, C. Lundström, M. Karlsson, and P. Andrekson, “Format conversion of optical multilevel signals using FWM-based optical phase erasure,” J. Lightwave Technol.29(16), 2460–2466 (2011). [CrossRef]
- C. Su, Y. Yikai, L. Yi, L. Leng, X. Tian, X. X. Xinyu, and Y. Tian, “All-optical format conversion from NRZ to BPSK using a single saturated SOA,” IEEE Photon. Technol. Lett.18(22), 2368–2370 (2006).
- J. Kakande, A. Bogris, R. Slavík, F. Parmigiani, D. Syvridis, P. Petropoulos, and D. J .Richardson, “First demonstration of all-optical QPSK signal regeneration in a novel multi-format phase sensitive amplifier,” ECOC 2010, Torino, Italy, PD 3.3 (2010).
- H. Kishikawa, P. Seddighian, N. Goto, S. Yanagiya, and L. R. Chen, “All-optical modulation format conversion from binary to quadrature phase-shift keying using delay line interferometer, ” Photonics Conference (PHO), 513 - 514 (2011).
- M. Sköld, H. Sunnerud, M. Westlund, and P. A. Andrekson, “Simultaneous waveform and bit-error-rate measurements of 66 GBd PDM-16-QAM signals,” ECOC PD Th.13.B.3 (2011).
- F. Parmigiani, J. Kakande, L. M. Jones, P. Petropoulos, and D. J. Richardson, “Packet compression of complex modulation formats based on coherent optical superposition,” International Conference on Transparent Optical Networks (ICTON 2012) Warwick UK (2012).
- F. Parmigiani, J. Kakande, L. M. Jones, P. Petropoulos, and D. J. Richardson, “Temporal multiplexing of complex modulation formats facilitated by their coherent optical superposition,” European Conference and Exhibition on Optical Communication (ECEOC) Amsterdam, The Netherlands, June 16, 2012 (2010).
- K. Kikuchi, “Coherent detection of phase-shift keying signals using digital carrier-phase estimation,” OFC (2006).
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