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Abstract
In this paper, a phase-sensitive amplifier (PSA)-based two dimensional (2D)-to-one dimensional (1D) constellation reforming system is proposed and analyzed in detail. The proposed system theoretically realizes seven kinds of 10 GBaud quadrature amplitude modulation (QAM)-to-pulse amplitude modulation (PAM) conversions, including quadrature phase shift keying-to-PAM4 and 8QAM-to-PAM8 conversions. The constellation reforming system consists of a constellation squeezing PSA and a multi-level vector moving PSA. The operating principle and formula derivations of constellation squeezing and vector moving processes are fully explained, including the PSA transfer characteristics and PSA gain axis angle analytical solutions. When implementing QAM-to-PAM conversions, the constellations, spectra, eye diagrams, error vector magnitudes and bit error ratio (BER) performances of the QAM and PAM signals are measured. For 8QAM-to-PAM8 conversion, with the input OSNR of 25 dB and 30 dB, at the BER of 10−3, the converted PAM8 shows the receiver OSNR of 38.9 dB and 35.2 dB, respectively. The proposed and verified 2D-to-1D constellation reforming system builds an optical bridge connecting long-haul and short-reach networks, which can be employed in the format conversion, high-order format signal generation and shaping, and flexible information aggregation/de-aggregation.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The Internet of Everything era forces the forward development of optical communication networks [1], and the continuous growth of the type and quantity of information interaction leads to the continuous evolution of optical network architecture and capacity. To undertake huge amount of businesses, according to the perspective of transmission distance, current optical networks can be divided into transoceanic networks, backbone networks, metro networks, converged access networks and data center optical interconnections, etc. [2] Focus on the transmission links, various measures are adopted on multiplexing techniques (M), bandwidth (B), and spectral efficiency (SE) to enlarge the transmission capacity (C), which has the relationship of $C = 2M \cdot B \cdot SE$ [3,4]. Some auxiliary enhancement methods are also studied to improve the optical transmission distance and capacity, such as low-noise amplification [5,6], constellation shaping [7,8], on-chip devices [9,10], and artificial intelligence-driven optical transmission [11–13]. Current practical optical transmission scenarios consists of two dimensional (2D) modulation-coherent detection and one dimensional (1D) modulation-direct detection (DD). For 2D-coherent detection scenario, the schemes of $200G/\lambda$ dual polarization 8-ary quadrature amplitude modulation (DP-8QAM) [14] and $200G/\lambda$ DP-16QAM [15] are mature and have been applied in some long-haul transmission scenarios. For 1D-DD scenario, $400G/\lambda$ four-level pulse amplitude modulation (PAM4) scheme has been selected as the standard plan for short-reach transmission scenario [16]. Combining the above status, the multi-dimensional modulations and various optical network types will coexist and evolve forward for a long time. Therefore, the realization of flexible optical interconnection between multi-dimensional modulations is a key solution to solve the issues such as links blocking, resource management, and electronic bottlenecks caused by the coexistence of various optical networks [17].
The optical format conversion techniques build an optical bridge to connect various optical networks employing different languages and it can be structured into three types: one-to-one conversion, aggregation, and de-aggregation, which are with rich application prospects. Though the optical format conversion technique has the above applications, it also has the issues of complicated system, high cost, and few functions, because the immature industrialization of optical signal processing technique. With the deepening of research and continuous integration with other fields, we believe that the optical format conversion technique will settle these issues gradually. In recent years, the industry has focused its attention on the interconnections between modulations of different dimensions which are with more practical value, especially the interconnections between 2D and 1D modulations. For aggregation techniques, usually several low-order 1D modulation signals are combined into one high-order 2D modulation signal, such as 2 $\times$ on-off keying signal (OOK)-to-quadrature phase shift keying (QPSK) [18], and 4 $\times$ OOK-to-16QAM [19] aggregations. De-aggregation techniques achieve the opposite work, such as 16QAM-to-2 $\times$ unnatural PAM4 (uPAM4) [20,21], 64QAM-to-2 $\times$ uPAM8 [22,23], and 9QAM-to-2 $\times$ PAM3 [24] de-aggregations. The one-to-one optical conversion consists of both 1D-to-2D and 2D-to-1D conversions, and attracts more research attention recent years for its intuitive and direct function. The 1D-to-2D conversion schemes which have been proposed contain PAM4-to-QPSK [25] and PAM8-to-8PSK [26] conversions. Focus on the 2D-to-1D conversion techniques, [27] proposed a QPSK-to-uPAM4 conversion scheme with full-quadrature regeneration capacity, [28,29] firstly realized QPSK-to-PAM4 conversion employing three-wave mixing-based phase rotation and bias addition, and [30] proposed a QPSK-to-PAM4 conversion scheme with eye diagram shaping function. Although the existed 2D-to-1D conversion schemes have their advantages and extra processing functions, they all cannot expand the schemes into higher-order formats, which is an urgent requirement for 2D-to-1D conversion.
In this paper, a 2D-to-1D constellation reforming scheme is proposed and fully analyzed. The reforming system theoretically realizes QAM-to-PAM conversions by employing a constellation squeezing PSA and a constellation shifting PSA, and the eye diagrams of converted PAM signals are editable by rotating the constellation squeezing PSA gain axis. The 10 GBaud QPSK and 8QAM signals are injected into the proposed system and converted into 10 GBaud OOK/PAM3/PAM4 and PAM5/PAM6/PAM8 signals, respectively. Seven kinds of QAM-to-PAM conversions are implemented and analyzed with their constellations, eye diagrams, error vector magnitudes (EVMs), and bit error ratios (BERs). The theoretical derivations and system transfer characteristics of the constellation squeezing and shifting processes are given and depicted. With the input optical signal-to-noise ratio (OSNR) of 15dB and 25dB, at the BER of ${10^{\textrm { - }3}},$ the PAM4 signal converted from QPSK shows the receiver OSNR of 29dB and 20.2dB, respectively. With the input OSNR of 25dB and 30dB, at the BER of ${10^{\textrm { - }3}},$ the PAM8 signal converted from 8QAM shows the receiver OSNR of 38.9dB and 35.2dB, respectively. The 2D-to-1D constellation reforming function can be applied in vast signal processing and practical transmission scenarios, such as format conversion, signal flexible generation, and optical gateway.
2. Operating principle
The 2D-to-1D constellation reforming system is represented in Fig. 1, one of its typical and important application scenarios is bridging the long-haul and short-reach optical transmission networks, that is, to realize QAM-to-PAM conversions. Besides implementing the QAM-to-PAM conversions between the same modulation order, such as QPSK-to-PAM4 and 8QAM-to-PAM8 conversions, it also can convert QAM signals into the PAMs with different modulation orders, such as QPSK-to-OOK, QPSK-to-PAM3, 8QAM-to-PAM5, and 8QAM-to-PAM6, which enriches the system potential applications. The reforming system proposed in this manuscript is applied for QAM signals in one channel, which is a basic model. The advanced modulation and multiplexing technologies [31–33] are essential and crucial for the future optical transmission. The PSA-based optical processing system for advanced modulation signals with various multiplexing technologies attracts much attention [34–36] and will be our future important research direction. The input QAM signals are modified by the PSA-based constellation squeezing and vector moving parts, the detailed processing principle and theoretical derivations are introduced in the following subsections.
2.1 Constellation squeezing
The constellation squeezing process is realized by injecting QAM signals into one degenerate two-level PSA with the setup and spectrum shown in Fig. 2(a) and (b). The thought of two-level PSA squeezing function is proposed by [37], while it did not give the analytical solution of the PSA gain axis angle. By rotating the PSA gain axis, PSA maps the input signal constellation points onto the gain axis and make them distinguishable in amplitude. Figure 2(c) depicts the squeezing processes of a two-level PSA modifing one input vector signal with uniform amplitude level and full-phase information, the ${\theta _1},$ ${\theta _2},$ and ${\theta _3}$ are example PSA gain axis angles which are defined as the angles between PSA gain axes and in-phase axis. We can observe that the squeezed vectors has the shape of almost straight line and along the PSA gain axis, comparing with input vectors.
The theoretical principle of constellation squeezing processing can be derived from the degenerate two-level PSA equations. When the input signal (S1) and two pumps (P1, P2) occur four-wave mixing (FWM) effect in the high nonlinear fiber (HNLF) of PSA, the equation between the output and input signals can be expressed as [38]:
Fig. 1. 2D-to-1D constellation reforming function concept graph. Cons., constellation; Co. access, converged access.
Fig. 2. Constellation squeezing process concept graph. Att. axes, attenuation axes; ${\theta _1},$ ${\theta _2},$ and ${\theta _3}$ are example PSA gain axis angles.
From the PSA gain expression, the PSA gain axis angle ${\theta _{gain}}$ can be obtained:
The angle between the two-level PSA attenuation axis and gain axis equals $\pi /2.$ From Eq. (5) and (6), we can see that the PSA gain axis can be rotated by changing the relative phase among input signal carrier and pumps, which can be employed to flexibly edit the eye diagrams of converted PAM signals. The constellation points of input QAM signals can be mapped onto the PSA gain axis and distinguishable in amplitude through the constellation squeezing PSA.
2.2 Multi-level vector moving
When the constellation points of input vectors are mapped onto the PSA gain axes through constellation squeezing process, a multi-level vector moving processing is demanded to translate them from amplitude distinguishable into power distinguishable. A non-degenerate PSA-based vector moving structure is employed here as shown in Fig. 3(a) and (b), the input signal (S2), pumps (P0, P1) are launched into a HNLF to occur FWM effect. The PSA-based binary phase shift keying (BPSK)-to-OOK conversion system was proposed in [39], and [30] provided it the concept of vector moving. In this paper, the PSA-based vector moving function is expanded to be suitable for multi-level vectors, whose moving process is depicted in Fig. 3(c).
The operating principle of PSA-based vector moving is to add coherent constant vectors on the input vectors, and according to [38], the transfer function of non-degenerate PSA is:
We can observe from Eq. (8) that if ${\delta _2}$ equals a fixed value, the FWM process can be viewed as adding a coherent constant vector on the input vector and implementing the vector moving function. Both the constellation squeezing and vector moving parts require ${\delta _1}$ and ${\delta _2}$ to be fixed values to implement corresponding processing functions. The fixed ${\delta _1}$ and ${\delta _2}$ require that input signal carriers and pumps to be coherent, which can be realized by employing optical combs technique, such as the Mach-Zehnder modulator (MZM)-based optical combs generation scheme [40]. Besides the coherence generation, the coherence maintain is also a critical problem in the practical implementation, because the coherence between signal carrier and pumps may be affected by the link defects or unequal optical paths before the waves are injected into the HNLF. The environmental impact on coherence is necessary to be taken seriously, precise system tuning and an active phase-locking loop should be designed in the practical implementation, or the on-chip scheme is another effective approach to settle this issue.
2.3 QAM reforming scheme
The QAM signals constellation reforming schemes are depicted in Fig. 4, and this paper performs seven kinds of conversions for QPSK and 8QAM signals. The input QAM signals are processed by the constellation squeezing and vector moving parts. Because the QPSK and 8QAM constellations are symmetrical along the $45^\circ$ axis, the constellation squeezing PSA gain axis has an effective processing angle range of $\left ( {0^\circ \sim 45^\circ } \right ).$ The constellation squeezing process determines the final formats of converted signals, because the PSA gain axis angle effects the squeezed signal constellation shape.
As shown in Fig. 4, when the PSA gain axis angles are $0^\circ ,$ $27^\circ ,$ and $45^\circ ,$ the input QPSK is squeezed into BPSK, uPAM4, and uPAM3 signals, respectively. After the vector moving process, the BPSK, uPAM4, and uPAM3 signals are converted into OOK, PAM4, and PAM3 signals, respectively. For 8QAM signal, when the PSA gain axis angles are $0^\circ ,$ $22.5^\circ ,$ $32.5^\circ ,$ and $45^\circ ,$ the input 8QAM is squeezed into uPAM5, uPAM6, uPAM8, and uPAM5 signals, respectively. After the vector moving process, the uPAM5, uPAM6, uPAM8, and uPAM5 signals are converted into PAM5, PAM6, PAM8, and PAM5 signals, respectively. The corresponding relations of the QPSK and 8QAM conversions are shown in Tables 1 and 2. When the QAM signals are converted into the PAM formats with different modulation order, some points of the QAM constellation overlap with others. From the constellation reforming scheme, we can see that the eye diagrams of output PAM signals are editable by rotating the constellation squeezing PSA gain axis. The eye diagram editable PAM is a promising research direction and recently has some applications in optical access scenario to improve the aggregated capacity [41,42], the receiver power budget [43], and receiver sensitivity [44] in passive optical networks. The selected angles of the PSA gain axes are just examples, not a requirement. After the processing of constellation squeezing and vector moving, the input QAM signals are converted into PAM signals as required.
Table 1. Corresponding relations of QPSK conversions.a
Table 2. Corresponding relations of 8QAM conversions.a
3. Verifications & discussions
The constellation reforming scheme is verified by simulations which are based on the software of VPItransmissionMaker with the system setup shown in Fig. 5. The reforming system contains five main parts: phase-locked waves generation, QAM generation, constellation squeezing PSA, vector moving PSA, and signal receiver. A continuous wave (CW) laser (frequency: 193.2 THz, power: 100 mW) is selected to be the seed laser and launched into a MZM (push-push mode, ${V_{\pi - RF}}\textrm { = }{V_{\pi - \textrm {DC}}}:$ 8.8 volt, ${V_{DC}}:$ 0 volt). The MZM is driven by a radio frequency (RF) signal (${V_{peak}}:$ 5 volt, frequency: 50 GHz) to generate a series of phase locked waves which are employed as the signal carrier and PSA pumps. The generated phase-locked waves are filtered by a programmable filter to adjust their power and relative phase. A CW laser (frequency: 193.2 THz) is selected as the signal carrier and modulated by an IQ modulator to generate QAM signals. 20 Gbps and 30 Gbps pseudo random bit sequences (PRBSs) are employed to drive the IQ modulator to generate 10 GBaud QPSK and 8QAM signals, respectively. Before injected into the system, the QAM signals are coupled with an amplified spontaneous emission noise (ASE) resource to control its input OSNR. The constellation squeezing PSA is composed of an optical coupler, a HNLF (length: 550 m, nonlinear coefficient: 13.2 ${W^{ - 1}}k{m^{ - 1}}$), and an optical band-pass filter (BPF) (center frequency: 193.2 THz, bandwidth: 20 GHz). The input signals of constellation squeezing PSA contains QAM signals (frequency: 193.2 THz, 0.6 mW), pump1 (frequency: 193.15 THz, 60 mW), and pump2 (frequency: 193.25 THz, 60 mW). The vector moving PSA is composed of an optical coupler, a HNLF (length: 400 m, nonlinear coefficient: 13.2 ${W^{ - 1}}k{m^{ - 1}}$), and a BPF (center frequency: 193.2 THz, bandwidth: 20 GHz). Its input signals contains squeezed uPAM signals (frequency: 193.2 THz, 0.6 mW), pump0 (frequency: 193.1 THz, 30 mW), and pump1 (frequency: 193.15 THz, 60 mW).The system output signals are coupled with an ASE noise to adjust the receiver OSNR before signal detections. The constellations, spectra, eye diagrams, EVMs, BERs of the input and output signals are depicted and calculated to indicate the whole system performances. The constellations, spectra, eye diagrams, EVMs are measured with ${2^{11}}\textrm { = }2048$ QAM signal symbols, the BERs are estimated with ${2^{14}}\textrm { = 16384}$ QAM signal symbols.
3.1 PSA transfer characteristics
The phase and power gain transfer characteristics of constellation squeezing and vector moving PSAs are measured to examine the PSA features. A CW laser (frequency: 193.2 THz, 0.8 mW) with uniform power and modulated phase information of $\left ( { - 0.5\pi \sim 2.5\pi } \right )$ is launched into the constellation squeezing PSA. With these parameters, the constellation squeezing PSA has the condition of ${m_1} \approx 1$ in Eq. (2), which means the PSA has a nearly optimal two-level phase-squeezing feature. As shown in Fig. 6(a), the circular constellation of input optical vector is squeezed into a linear shape and consistent with the PSA gain axis angle. The constellations are depicted after power normalizing, as are the constellations and eye diagrams of QAM conversions. The phase and power transfer characteristics of the constellation squeezing PSAs with the gain axis angles of $0^\circ ,$ $30^\circ ,$ $60^\circ ,$ $90^\circ ,$ and $135^\circ$ are illustrated in Fig. 6(b)-(f), respectively. When the PSA gain axis angle ${\theta _{gain}}\textrm { = }0^\circ ,$ the PSA power gain versus input phase transfer function has a period of $\pi ,$ the maximum power gain occurs when the input phase ${\varphi _{mn1}} = n\pi$ and the minimum power gain occurs when the input phase ${\varphi _{mn1}} = \pi /2 + n\pi ,$ which is consistent with ${G_1} = 2{\left | {{\mu _1}} \right |^2}\left ( {1 + \cos 2{\varphi _{mn1}}} \right ).$ The output phase versus input phase transfer function shows a visible shape of "two-level step", the input phase ${\varphi _{mn1}}$ with the range of $\left ( { - \pi /2 + 2n\pi \sim \pi /2 + 2n\pi } \right )$ is squeezed into $2n\pi ,$ and the input phase with the range of $\left ( {\pi /2 + 2n\pi \sim 3\pi /2 + 2n\pi } \right )$ is squeezed into $\left ( {2n + 1} \right )\pi ,$ which are consistent with Eq. (3). The PSAs with other gain axes show similar power gain and phase transfer characteristics and have corresponding shifted curves because of the different gain axis angles. Figure 6 indicates that the degenerate PSA can implement the constellation squeezing processing and can be flexibly editable by adjusting the relative phase among input signal carrier and pumps.
Fig. 5. Constellation reforming system setup.CW, continuous wave; PF, programmable filter; IQ, IQ modulator; BPF, optical band-pass filter.
Fig. 6. (a) Constellations of constellation squeezing process; (b)-(f), power gain and phase transfer characteristics of constellation squeezing PSA.
A CW laser (frequency: 193.2 THz) with the power of $\left ( {0.5{\kern 1pt} {\kern 1pt} {\kern 1pt} mW,{\kern 1pt} {\kern 1pt} {\kern 1pt} 1.5{\kern 1pt} {\kern 1pt} {\kern 1pt} mW,{\kern 1pt} {\kern 1pt} {\kern 1pt} 2.5{\kern 1pt} {\kern 1pt} {\kern 1pt} mW,{\kern 1pt} {\kern 1pt} {\kern 1pt} 3.5{\kern 1pt} {\kern 1pt} {\kern 1pt} mW{\kern 1pt} } \right )$ and modulated phase information of $\left ( { - 0.75\pi \sim 2.75\pi } \right )$ is launched into the vector moving PSA with the ${\delta _\textrm {2}}\textrm { = 2}n\pi .$ From the constellations in Fig. 7(a), we can see that the input optical vectors have circular constellations, and they are moved to the right side of the in-phase axis, which means the vectors power are distinguishable through vector moving processing. The power gain and phase transfer characteristics of the vector moving PSA are depicted in Fig. 7(b) and (c). The input optical vector with power of 3.5 mW meets the condition of ${m_2} \approx 1,$ which makes the PSA has the maximum power gain of 5.6 dB, the minimum power gain of -41.9 dB, and shows a period of $2\pi .$ The vector moving PSA here shows a power gain transfer characteristic which is consistent with the equation ${G_2} = 2{\left | {{\mu _2}} \right |^2}\left ( {1 + \cos {\varphi _{mn2}}} \right ).$ The optical vector with ${m_2} \approx 1$ also shows nearly optimal phase transfer function of $\varphi _{mn2}^{out} = \arctan \left ( {\frac {{\sin {\varphi _{mn2}}}}{{1 + \cos {\varphi _{mn2}}}}} \right ),$ which can be derived from Eq. (9). The power gain versus input phase and output phase versus input phase curves indicate the non-degenerate PSA is able to complete the vector moving work and conversions from uPAM signals to PAM signals.
Fig. 7. (a) Constellations of vector moving process; (b) and (c), power gain and phase transfer characteristics of vector moving PSA.
3.2 Conversion performances
The 10 GBaud QPSK and 8QAM signals are launched into the constellation reforming system to perform the system format conversion function. The constellations and eye diagrams of QPSK reforming processing are shown in Fig. 8, the 10 GBaud QPSK has the input OSNR of 20 dB, the constellation squeezing PSA has the gain axis angles of $0^\circ ,$ $27^\circ ,$ and $45^\circ .$ Comparing Fig. 8(a) with Fig. 8(b)-(d), the constellation squeezing PSA maps the QPSK constellation points onto the gain axes and converts the input QPSK into BPSK, uPAM4, and uPAM3. This processing makes the input signal distinguishable in amplitude. Comparing the Fig. 8(b)-(d) with Fig. 8(f)-(h), we can see that the uPAM signals are converted into PAM signals by the vector moving PSA. Because the constellation points of the squeezed uPAM4 signal are nearly evenly arranged in amplitude, the converted PAM4 signal eye diagram is not evenly spaced in power. The power ratio of the converted PAM signals is editable by rotating the constellation squeezing PSA gain axis. Within the PSA gain axis angle effective range of $\left ( {0^\circ \sim 45^\circ } \right ),$ the constellation reforming system realizes QPSK-to-PAM conversions.
Fig. 8. Constellations, spectrum, and eye diagrams of QPSK conversions. PAM-$x^\circ$ is the converted PAM signal with PSA gain axis angle of $x^\circ .$
In order to analyze the system performances in detail, more quantitative analyses are performed and shown in Fig. 9. The relationship between the power ratio of PAM signal and PSA gain axis is an interesting point, so we sweep the constellation squeezing PSA gain axis angle with the range of $\left ( {0^\circ \sim 45^\circ } \right )$ to observe the change path of PAM signal power ratio. The PAM signal power ratio is defined as the ratio of the middle eye power and total power. As shown in Fig. 9(a), with the gain axis angle sweeps from $0^\circ$ to $45^\circ ,$ the PAM signal power ratio changes from 100% to 0%, which results that the format conversion changes from QPSK-to-OOK to QPSK-to-PAM4, and to QPSK-to-PAM3 finally. When the gain axis angle equals $27^\circ ,$ the power ratio of converted PAM4 signal is 33.3%. The input OSNR of QPSK sweeps from 15 dB to 25 dB to perform the signal EVM performances. As shown in Fig. 9(b), the converted signals have smaller EVMs comparing with QPSK signal, because of the PSA phase squeezing ability. The EVM gap between converted PAM4 signal and QPSK signal changes from 9.8% to 2.2%. The EVM gap between converted signals and QPSK becomes smaller as the input OSNR improves, because the effect of PSA phase squeezing is gradually becoming limited. PAM4 signal has the best EVM performance because other conversions requires the QPSK constellation points coincide in the constellation squeezing process. Figure 9(c) and (d) show the signal BER performances. With the input OSNR of 15 dB, at the BER of ${10^{\textrm { - }3}},$ the receiver OSNR of back-to-back (B2B) QPSK, converted OOK, PAM4, and PAM3 signals are 16 dB, 14 dB, 29 dB, and 19.7 dB, respectively. With the input OSNR of 25 dB, the receiver OSNR of B2B QPSK, converted OOK, PAM4, and PAM3 signals are 11 dB, 10.2 dB, 20.2 dB, and 15.1 dB, respectively. The receiver OSNR difference between PAM4 signal and QPSK signal is 13 dB and 9.2 dB when the input OSNR is 15 dB and 25 dB, respectively. The EVM and BER performances indicate that the constellation reforming system implements three kinds of QPSK-to-PAM conversions.
Fig. 9. Quantitative analyses of QPSK conversions. Rec. OSNR, receiver OSNR; PAM-$x^\circ$ is the converted PAM signal with PSA gain axis angle of $x^\circ .$
To expand the constellation reforming system application scenarios, a 10 GBaud square 8QAM signal is launched into the system to realize QAM-to-PAM conversions. As shown in Fig. 10(a)-(e), with the PSA gain axis angle sweeps from $0^\circ$ to $45^\circ ,$ the input 8QAM signal is squeezed into uPAM5-$0^\circ ,$ uPAM6-$22.5^\circ ,$ uPAM8-$32.5^\circ ,$ and uPAM5-$45^\circ .$ The constellations and eye diagrams are measured when the 8QAM input OSNR is 30 dB. To be noted, the uPAM5-$0^\circ$ and uPAM5-$45^\circ$ have different constellations for the different squeezing processes. After the vector moving PSA, the uPAM signals are moved into PAM signals, whose eye diagrams are depicted in Fig. 10(g)-(j). It is obvious that the power distribution of PAM5-$45^\circ$ eye diagram is more evenly than PAM5-$0^\circ .$ The signal BERs are also estimated and shown in Fig. 11. We can see that with the input OSNR of 25 dB, at the BER of ${10^{\textrm { - }3}},$ the receiver OSNR of B2B 8QAM, PAM5-$0^\circ ,$ PAM6-$22.5^\circ ,$ PAM8-$32.5^\circ ,$ and PAM5-$45^\circ$ are 20 dB, 30.3 dB, 32.4 dB, 38.9 dB, and 26 dB, respectively. With the input OSNR of 25 dB, the receiver OSNR of B2B 8QAM, PAM5-$0^\circ ,$ PAM6-$22.5^\circ ,$ PAM8-$32.5^\circ ,$ and PAM5-$45^\circ$ are 19.7 dB, 29 dB, 30.3 dB, 35.2 dB, and 25.4 dB, respectively. At the BER of ${10^{\textrm { - }3}},$ the receiver OSNR difference between PAM5-$0^\circ$ and PAM5-$45^\circ$ signals is 4.3 dB and 3.6 dB when the input OSNR is 25 dB and 30 dB, respectively, which is consistent with the difference in their eye diagrams. The receiver OSNR difference between PAM8-$32.5^\circ$ and 8QAM signals is 18.9 dB and 15.5 dB when the input OSNR is 25 dB and 30 dB, respectively. The eye diagrams and BER curves means the system achieves four kinds of 8QAM-to-PAM conversions, including 8QAM-to-PAM8 conversion. The verifications in this section indicate that the proposed system implements the QAM-to-PAM format conversions and has the ability of 2D-to-1D constellation reforming.
Fig. 10. Constellations, spectrum, and eye diagrams of 8QAM conversions. PAM-$x^\circ$ is the converted PAM signal with PSA gain axis angle of $x^\circ .$
Fig. 11. BER performances of 8QAM conversions.Rec. OSNR, receiver OSNR; PAM-$x^\circ$ is the converted PAM signal with PSA gain axis angle of $x^\circ .$
4. Conclusion
A 2D-to-1D constellation reforming system is proposed and fully analyzed by this paper. Seven kinds of 10 GBaud QAM-to-PAM conversions are theoretically realized by the constellation reforming system, including QPSK-to-PAM4 and 8QAM-to-PAM8 conversions. The system is composed of a degenerate PSA and a non-degenerate PSA. The input QAM signals are firstly constellation squeezed into uPAM signals, and then are converted into PAM signals through vector moving process. By rotating the gain axis angle of constellation squeezing PSA, the eye diagram of the output PAM signal is editable. The operating principle and theoretical derivations are introduced in detail, including the system transfer characteristics and PSA gain axis angle analytical solutions. The constellations, spectra, eye diagrams, EVM versus input OSNR curves, BER versus receiver OSNR curves of the processed signals are measured to indicate the system performances. For the 8QAM signal with the input OSNR of 25 dB and 30dB, at the BER of ${10^{\textrm { - }3}},$ the receiver OSNR of converted PAM8 signals is 38.9 dB and 35.2 dB, respectively. The proposed constellation reforming system can be viewed as an optical bridge between long-haul and short-reach optical networks, which has lots of potential applications, such as format conversion, optical aggregation/de-aggregation, flexible signal generation and shaping, etc.
Funding
National Natural Science Foundation of China (62001046); China Postdoctoral Science Foundation (2020M670230).
Disclosures
The authors declare that they have no conflicts of interest.
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