Subcarrier multiplexing based self-heterodyne coherent detection for PM-16QAM format

Optics Communications 351 (2015) 160–166

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Subcarrier multiplexing based self-heterodyne coherent detection for PM-16QAM format Junchi Jia, Shiwei Zhou, Songnian Fu n, Lei Deng, Ming Tang National Engineering Laboratory for Next Generation Internet Access System, School of Optics and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074, China

art ic l e i nf o

a b s t r a c t

Article history: Received 17 March 2015 Received in revised form 10 April 2015 Accepted 20 April 2015 Available online 23 April 2015

We propose and demonstrate subcarrier multiplexing (SCM) based self-heterodyne (SH) coherent detection for polarization-multiplexed 16 quadrature amplitude modulation (PM-16QAM) format. Three closely spaced subcarriers carrying pilot-tone (PT) and two 16QAM signals, respectively, are generated via subcarrier modulation technique. An effective digital signal processing (DSP) scheme is proposed to eliminate image frequency interference (IFI) arising in such SH coherent detection. Meanwhile, a closedform analytical BER formula is verified by numerical simulations with a deviation less than 0.3 dB at BER ¼10  3. The concept of optimum modulation index (MI) ratio between data and PT signal is derived and verified, in order to reduce the distortion of 16QAM constellation. Meanwhile, we also explore the effects of optical filter bandwidth and subcarrier frequency spacing on the quality of PT signal. Finally, we are able to obtain several optimum parameters for the proposed SH coherent detection. & 2015 Elsevier B.V. All rights reserved.

Keywords: Coherent detection Image frequency interference (IFI) Polarization-multiplexed 16 quadrature amplitude modulation (PM-16QAM) Subcarrier multiplexing (SCM)

1. Introduction Multi-level modulation formats together with coherent detection are now indispensable to increase spectral efficiency (SE) of current fiber-optic transmission system. 100 Gbps polarizationmultiplexed quadrature phase shift keying (PM-QPSK) systems are now commercially available [1,2]. High-order quadrature amplitude modulation (QAM) formats are being extensively investigated, in order to pursue higher SE [3–6]. However, advanced modulation formats, together with complex digital signal processing (DSP) implementation, not only require high optical signal-tonoise ratio (OSNR), but also become more sensitive to fiber nonlinear effects. Therefore, as a tradeoff, 16QAM format is a particularly promising candidate for spectral efficient cost-effective fiber-optic transmission system [7–9]. Extensive research has been carried out for high-speed 16QAM signal generation. 16QAM signals can be generated with two parallel or tandem in-phase/ quadrature modulators (IQMs) driven by binary signals [10,11]. One problem is that the modulators with complex structure are challenging to be fabricated. Another practical scheme to realize 16QAM transmitter is based on single IQM driven by four-level signals [12]. The performance of 16QAM signals is mainly determined by the quality of four-level electrical signals. However, the generation and processing of high-speed four-level electrical n

Corresponding author. E-mail address: [email protected] (S. Fu).

http://dx.doi.org/10.1016/j.optcom.2015.04.055 0030-4018/& 2015 Elsevier B.V. All rights reserved.

signal are relatively more difficult. Recently, 112 Gbps RF-assisted dual-carrier PM-16QAM coherent system has been experimentally demonstrated, in order to flexibly generate 16QAM signal in electrical domain and reduce costly optical components by subcarrier multiplexing (SCM) technique [13,14]. However, there exist some disadvantages in their schemes. Firstly, similar to traditional coherent detection, these schemes have a stringent demand for local oscillator (LO) with narrow linewidth and stable frequency. The complexity of realizing carrier recovery are also unavoidable problems, considering the limited range of frequency offset estimation [15,16]. In particular, the carrier phase estimation algorithms, such as blind phase search (BPS) algorithm, substantially increase the computational complexity [17,18]. One way to resolve these problems is to use self-heterodyne (SH) coherent detection. Previously, optical SH coherent system, where a continuous wave (CW) pilot-tone (PT) light was wavelength multiplexed with differential quadrature phase shift keying (DQPSK) signals before transmission and was finally chosen as the LO light at the receiver side, was proposed to simplify the optical coherent detection [19], and improve the tolerance of laser phase noise [20]. Secondly, in order to simultaneously detect all subcarrier channels and avoid image frequency interference (IFI) arising from the energy in the mirror spectrum of the LO, two LOs are indispensable for classical intradyne detection of both subcarriers [14]. Alternatively, the LO source needs to be chosen at longer wavelength for heterodyne detection [14]. The former scheme is costly due to the use of additional LO source, while the latter requires more costly electrical devices, e.g., high frequency RF sources, RF demodulators, and

J. Jia et al. / Optics Communications 351 (2015) 160–166

wideband analog-to-digital convertors (ADCs). In this paper, we propose a new SCM based SH coherent detection for polarization division multiplexing (PDM)-16QAM. Compared with our mode-division-multiplexing (MDM) based SH coherent detection for few-mode fiber transmission [21], we explore the single mode fiber (SMF) transmission performance of 112 Gbps dual-carrier PDM-16QAM signal, with the help of SCMbased SH coherent detection. After digital frequency down-conversion, the IFI can be effectively mitigated through a new IQ separation algorithm. Meanwhile, a closed-form bit error ratio (BER) formula is derived and verified by the VPI numerical simulation. The accurate analytical model allows us to optimize the modulation index (MI) ratio between the 16QAM data and PT signal. The 16QAM constellation distortion caused by MIs of both the data signal and PT is investigated. We also investigate the effects of optical filter bandwidth and subcarrier frequency spacing on the PT signal quality. The paper is organized as follows. In Section 2, we present the system configuration and the theoretical investigation of the proposed SCM based SH coherent system for PM-16QAM signal. In Section 3, we present the numerical verification and optimization. Finally, in Section 4, we outline the conclusions.

2. Operation principle 2.1. System configuration The system configuration is illustrated in Fig. 1. At the transmitter side, one 1550 nm laser diode (LD) is chosen to provide CW optical carrier. Then, the LD output is divided into two equal parts with orthogonal linear polarizations by a polarization beam splitter (PBS). Then, four independent 28 Gbps pseudorandom binary sequences (PRBSs) with a word length of 27–1 are encoded with 16QAM format on two RF subcarriers located at 11 GHz and 35 GHz, respectively, assuming 7% forward error correction (FEC) overhead. Electronic 16QAM signal is shaped by 5-order Gaussian electrical bandpass filters (EBPFs) with a 3 dB bandwidth of 13 GHz, while another RF subcarrier located at 23 GHz is used for the pilot signal. After combining three subcarriers with frequency spacing of 12 GHz, the generated electrical signals, including total 56 Gbps 16QAM and pilot signal, are amplified with a microwave electronic amplifier (EA) and drive two separated Mach–Zehnder

161

modulators (MZMs) biased at the transmission null point for the purpose of carrier suppression modulation, respectively. Finally, the 112 Gbps dual-carrier PM-16QAM signal can be obtained, after combining two polarization tributaries with a polarization beam combiner (PBC). The fiber link consisted of 80-km SMF together with erbium doped fiber amplifiers (EDFAs) only. The noise-loading setup is used to adjust OSNR value before the coherent detection. Using an optical coupler at the receiver side, one part of signal is selected for retrieving the PM-16QAM data signal, while the other part is filtered out to obtain the PT signal. A 4-order Gaussian optical bandpass filter (OBPF) with a 3 dB bandwidth of 35 GHz is used in the signal path to reject ASE noise, part of the CW carrier and the redundant lower sideband, as shown in the inset of Fig. 1. In the PT path, the optical filter is the key component to maintain the PT signal quality. Such optical filter should be narrow and ideally has a fast roll-off to reject power from the neighboring data spectra. Thus, we choose a Fabry–Perot (FP) filter with a 3 dB bandwidth of 1.9 GHz to ensure the PT quality [22]. For practical implementation, a feedback loop is required to align the center frequency of the filter with the PT frequency. However, the FP filter with Lorentzian lineshape has a quite slow roll-off, which results in more crosstalk from the neighboring data channel. Thus, we cascade another 4-order Gaussian OBPF with a 3 dB bandwidth of 10 GHz, in order to further suppress the ASE noise and part of data signals. The polarization controller (PC) is used to maintain the state of polarization of PT at 45° linear polarization. Optical polarization tracking can be achieved by using LiNbO3-based PCs [23]. In the receiver, polarization and phase-diversity coherent detection is implemented with polarization beam splitters (PBSs), optical hybrids, and balanced PDs with 35 GHz bandwidth. The detected analog currents are digitalized by four ADCs with the sampling rate of 50GSa/s, and then go into the DSP unit. In the DSP flow, the received signals are first down-converted to the baseband by a digital LO and its quadrature counterpart [24]. Then I/Q separation is realized by the proposed algorithm, as shown in Eqs. (10)–(13). 5-Order digital Bessel lowpass filters (LPFs) are implemented to suppress noise and high-frequency interference. After chromatic dispersion (CD) compensation, four butterfly 15tap T/2-spaced finite impulse-response (FIR) filters are used for polarization demultiplexing and linear equalization. The filter coefficients are optimized by the classic constant modulus algorithm (CMA) for pre-convergence. After pre-convergence, the adaptive algorithm is switched to decision-directed least mean

Fig. 1. Simulation setup of the SCM based SH coherent detection for PM-16QAM signal. Insets are the optical spectra after the OBPFs in the signal path and PT path, respectively.

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square (DD-LMS) algorithm. Finally, the BER is calculated after hard decision and symbol-to-bit mapping.

Table 1 112 G/s signal generation schemes. Tx

SH-SCM16QAM

SCM16QAM 16QAM [14] [12]

QPSK [25]

Requirement of laser linewidth MZM number/ bandwidth 4-level generator: the bandwidth/ complexity RF source number/ frequency

Low

High

High

Middle

2/35 GHz

2/28 GHz

4/21 GHz

4/35 GHz

7 GHz/simple

7 GHz/ simple

14 GHz/ complex

No

3/11 GHz, 23 GHz, 35 GHz

2/14 GHz, 24 GHz

No

No

2.2. Theoretical model For the ease of discussion, we only consider one polarization in our theoretical investigation. At the transmitter side, the optical field containing both data signal and PT signal is described as

Esm (t) = sin [AI1 (t)cos(w1t) + AQ 1 (t)sin(w1t) + B cos(wPT t) + AI2 (t)cos(w2 t) + AQ 2 (t)sin(w2 t)]⋅ Ps e jwt ≈ {J1 [AI1 (t)]cos(w1t) + J1 [AQ 1 (t)]sin(w1t) + J1 (B) cos(wPT t) + J1 [AI2 (t)]cos(w2 t) + J1 [AQ 2 (t)]sin(w2 t)} ⋅2 Ps e jwt

(1)

where J1 (⋅) is the Bessel function of the first kind with order 1, I1,2 (t) = ± 1, ± 1/3 and Q 1,2 (t) = ± 1, ± 1/3 are the in-phase and quadrature signal amplitudes, A and B are the MIs for the data signals and the PT signal, Ps is the average power of CW in one polarization, and w is its angular frequency. w1, w2 and wPT are the RF frequency for the data signals and the PT signal, respectively. In order to realize a linear electro-optical conversion, A and B are relatively small. After the OBPF in the signal path, the loaded ASE noise, can be approximately divided up into three parts, i.e., n1 (t), n2 (t), and nPT (t), according to the central frequency of the three subcarriers. Thus, we can express the optical field as

Es (t) =

+

2 ⎧ Ps ⎨ A [I1 (t) − jQ 1 (t)] + n1 (t)} e j (w + w1) t 2 ⎪ ⎩ 2 ⎤ Ps Ps 2 B + nPT (t) ⎥ e j (w + wPT ) t + A [I2 (t) { ⎥⎦ 2 2 2 ⎪

⎡ 2⎢ 2 ⎣⎢

−jQ 2 (t)] + n2 (t)} e j (w + w 2 ) t

(2)

where the factor 2 /2 is determined by the coupling factor. Note that Eq. (2) is derived with the approximation of the first-order expansion for J1 (⋅), due to the small signal modulation [13]. Accordingly, in the PT path, the optical field after OBPF can be expressed as

EPT (t) =

⎡ ⎤ 2 ⎢ Ps B + nPT (t) ⎥ e j (w + wPT ) t ⎥⎦ 2 ⎢⎣ 2

(3)

Then, the data and PT signals go through a polarization- and phase-diverse 90° hybrid, and are detected by four balanced PDs. Ignoring the common factor, the photocurrents in the in-phase and quadrature components are derived, respectively, as shown in Eqs. (4) and (5), where Δw is the frequency spacing among the RF subcarriers, n1, PT ,2I (t) and n1, PT ,2Q (t) are the real and imaginary parts of n1 (t), nPT (t), and n2 (t), respectively.

iI (t) = ⎡⎣ABPs I1 (t) + 2A Ps I1 (t) nPTI (t) + 2B Ps I1 (t) n1I (t) − 2A Ps Q 1 (t) nPTQ (t) ⎤⎦ cos(Δwt) + ⎡⎣−ABPs Q 1 (t) − 2A Ps I1 (t) nPTQ (t) + 2B Ps n1Q (t) − 2A Ps Q 1 (t) nPTI (t) ⎤⎦ sin(Δwt) + ⎡⎣ABPs I2 (t) + 2A Ps I2 (t) nPTI (t) + 2B Ps I2 (t) n2I (t)

+ 2A Ps Q 1 (t) nPTQ (t) ⎤⎦ sin(Δwt) + ⎡⎣−ABPs Q 1 (t) − 2A Ps I1 (t) nPTQ (t) + 2B Ps n1Q (t) − 2A Ps Q 1 (t) nPTI (t) ⎤⎦ cos(Δwt) + ⎡⎣ABPs I2 (t) + 2A Ps I2 (t) nPTI (t) + 2B Ps I2 (t) n2I (t) − 2A Ps Q 2 (t) nPTQ (t) ⎤⎦ sin(Δwt) + ⎡⎣−ABPs Q 2 (t) − 2A Ps I2 (t) nPTQ (t) + 2B Ps n2Q (t) − 2A Ps Q 2 (t) nPTI (t) ⎤⎦ cos (Δwt)

(5)

Note that shot noise and thermal noise are reasonably ignored, since their impact is smaller than that of the ASE noise in our proposed system. Furthermore, the product terms of noise and noise are ignored due to their smaller value than other terms. Finally, both the photocurrents are digitalized by ADC. We use iI (k) and iQ (k) to express the kth input sequences for the received inphase and quadrature components, respectively. The digital downconversion can be realized by multiplying iI (k) and iQ (k) with cos(Δwk) and sin(Δwk), respectively, which is shown as Eqs. (6)– (9). The digital down-conversion results are expressed as i1,2,3,4 (k). The terms of ABPs [Q 1 (k) − Q 2 (k)], ABPs [I1 (k) + I2 (k)], −ABPs [Q 1 (k) + Q 2 (k)], and ABPs [I2 (k) − I1 (k)], occurred in i1 (k), i2 (k), i3 (k), and i4 (k), are the interference source caused by IFI. If we implement traditional IQ separation algorithm by obtaining inphase component (i1 − i2 ) and quadrature component (i3 − i4 ), respectively, the data information cannot be retrieved due to the IFI term arising in both the in-phase and quadrature components. Alternatively, by using new linear arithmetic operations among i1,2,3,4 (k), we can realize I/Q separation without IFI term, as shown in Eqs. (10)–(13). Please note that the IFI cannot be simply remove by an optical filter prior to the coherent receiver front end, because both bandwidth and roll-off factor of such optical filter is challenging to optimize, in order to remove the LO and sidebands completely. The common factors are ignored in Eqs. (6)–(13), and the high-frequency components are also ignored, since they can be removed by the followed digital LPF. Thus, with such IFI elimination scheme, as shown in Eqs. (10)–(13), we can finally obtain the in-phase and quadrature components of the both subcarriers, in combination with the interference components.

i1 (k) = iI (k)cos(Δwk) = ⎡⎣ABPs + 2A Ps nPTI (k) ⎤⎦

− 2A Ps Q 2 (t) nPTQ (t) ⎤⎦ cos(Δwt) − ⎡⎣−ABPs Q 2 (t) − 2A Ps I2 (t) nPTQ (t) + 2B Ps n2Q (t) − 2A Ps Q 2 (t) nPTI (t) ⎤⎦ sin (Δwt)

iQ (t) = ⎡⎣−ABPs I1 (t) − 2A Ps I1 (t) nPTI (t) − 2B Ps I1 (t) n1I (t)

[I1 (k) + I2 (k)] + 2B Ps [n1I (k) + n2I (k)] − 2A Ps nPTQ (k)

(4)

[Q 1 (k) + Q 2 (k)]

(6)

J. Jia et al. / Optics Communications 351 (2015) 160–166

163

Table 2 112 G/s coherent receiver schemes. Rx

SH-SCM-16QAM

ID-SCM-16QAM [14]

H-SCM-16QAM [14]

16QAM [12]

QPSK [25]

LO number/linewidth requirement PD bandwidth ADC number/minimum sampling rate RF source number/frequency RF demodulator number Carrier recovery complexity

No 35 GHz 4/38GS/s No No No

2/High 10 GHz 8/28GS/s No No Complex

1/High 28 GHz 8/28GS/s 2/11 GHz, 21 GHz 4 Complex

1/High 21 GHz 4/28GS/s No No Complex

1/Middle 40 GHz 4/56GS/s No No Simple

i2 (k) = iI (k)sin(Δwk) = ⎡⎣ABPs − 2A Ps nPTI (k) ⎤⎦

η =0.286 analytical result η =0.286 numerical result η =0.571 analytical result η=0.571 numerical result

0.01

[Q 1 (k) − Q 2 (k)] + 2A Ps nPTQ (k)[ −I1 (k) + I2 (k)] (7)

BER

+ 2B Ps ⎡⎣n1Q (k) − n2Q (k) ⎤⎦

i3 (k) = i2 (k)cos(Δwk) = ⎡⎣−ABPs − 2A Ps nPTI (k)][Q 1 (k) + Q 2 (k) ⎤⎦ − 2A Ps nPTQ (k) [I1 (k) + I2 (k)] + 2B Ps ⎡⎣n1Q (k) + n2Q (k) ⎤⎦

1E-3

(8) 1E-4

i4 (k) = i2 (k)cos(Δwk) = ⎡⎣ABPs + 2A Ps nPTI (k) ⎤⎦

15

16

17

+ 2A Ps nPTQ (k)[ −Q 1 (k) + Q 2 (k)]

18

20

21

Fig. 2. BER as a function of OSNR for various η values.

(9)

I1I (k) = i1 (k) − i4 (k)

0

12.1

− 2A Ps nPTQ (k) Q 2 (k)

(10)

I2I (k) = i1 (k) + i4 (k) = ABPs I2 (k) + 2A Ps nPTI (k) I2 (k) + 2B Ps n2I (k) − 2A Ps nPTQ (k) Q 1 (k)

(11)

I1Q (k) = − i2 (k) − i3 (k) = ABPs Q 1 (k) + 2A Ps nPTQ (k) I1 (k) − 2B Ps n1Q (k) + 2A Ps nPTI (k) Q 1 (k)

Total input power

= ABPs I1 (k) + 2A Ps nPTI (k) I1 (k) + 2B Ps n1I (k)

11.6

-1

11.2 10.7

9.40

-2

10.3

9.85

optimum MI ratio

8.95

-3

(12)

-4

I2Q (k) = i2 (k) − i3 (k)

0.5

0.8

1.1 A/ B

= ABPs Q 2 (k) + 2A Ps nPTQ (k) I2 (k) − 2B Ps n2Q (k) + 2A Ps nPTI (k) Q 2 (k)

(13)

Considering the use of optical filter in the PT path and the digital LPFs, we derive the SNR per polarization as

SNR =

19

OSNR

[I2 (k) − I1 (k)] + 2B Ps [ −n1I (k) + n2I (k)]

1.4

1.7

2.0

Fig. 3. Q-factor contour as a function of total input power and the MI ratio of data signal and PT signal.

performance, we link the SNR to the OSNR, which is defined as

5A2 B2Ps 20A2 Ps SASE Δv + 18B2Ps SASE Δf

(14)

where SASE is the noise power spectral density per polarization, Δv is the equivalent noise bandwidth of the OBPF in the PT path, while Δf is the noise bandwidth of the digital LPF. By maximizing the SNR in Eq. (14) under a constraint of constant total input optical power, the optimal MI ratio can be derived,

(15)

Since OSNR is commonly used to evaluate transmission system

10 2 A Ps /(2SSASE Bref 9

)

(16)

where Bref is the reference bandwidth of 12.5 GHz@1550 nm. Assuming the use of Gray coding, the BER of ASE-limited PM-16QAM system with coherent detection is estimated,

BER =

1

⎛ 81Δf ⎞ 4 ⎟ γMIopt = (A/B)opt = ⎜ ⎝ 200Δv ⎠

OSNR=

⎛ ⎞ ⎛ SNR ⎞ 3 3 OSNR 9Bref ⎟ ⎟ = erfc ⎜⎜ erfc ⎜ ⎟ 8 ⎝ 10 ⎠ 8 ⎝ 10Δf 20η + 18 ⎠

(

)

(17)

where η = A2 Δv/ B2Δf , indicating that η is mainly determined by the OSNR ratio between the data signal and PT signal path.

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Fig. 4. 16QAM constellation: (a) with and (b) without our proposed IFI mitigation method.

EVMRMS(%)

0.6

9.5

0.5

7.5

8.5

9.0 7.0

0.4

A

5.5

6.0

5.0

0.3

10

14

12 11

13

16 15 15

11

8.0

17

12

6.5

13

16

14

4.5

0.2

0.1 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

B

Fig. 5. (a) Contour line of EVMRMS as a function of A and B. (b) and Inset (c) show respectively the received 16QAM constellations on the case of A ¼0.1, B ¼1, and A ¼0.3, B¼ 0.1.

3. Numerical verification and optimization 3.1. System comparison among several 112 Gbps coherent detection systems In order to clearly compare our proposed system with other typical 112 Gbps coherent detection systems, the basic

requirements in the transmitters and receivers of single-carrier PM-QPSK, PM-16QAM, and SCM based PM-16QAM coherent detection are listed in Tables 1 and 2, for the ease of comparison. SHSCM-16QAM is our proposed coherent detection system; ID-SCM16QAM and H-SCM-16QAM correspond to the intradyne and heterodyne receivers in [14], respectively. Note that the minimum sampling rate is calculated by the classic theory of baseband

J. Jia et al. / Optics Communications 351 (2015) 160–166

3.2. Analytical model validation Firstly, we present the BER performance of our proposed SH coherent detection. Analytical calculation on scenarios of η ¼0.286 and η ¼ 0.571 are compared with simulation results based on the VPI™ 9.0 platform, as shown in Fig. 2. We can see that the BER performance differences between our analytical results and VPI simulation results are less than 0.3 dB@BER ¼1e–3. This difference is mainly due to the interferences from residual high-frequency data signal, especially the impact of residual data signal on PT signal. Therefore, the accuracy of our analytical BER equation is successfully verified. Fig. 2 also shows that, under the same BER value, lower η value is helpful to achieve better detection performance, indicating that high quality of PT signal is also indispensable for SCM based SH coherent detection. Next, we verify the optimum MI ratio, since the optimum MI ratio is determined by the optimum power ratio between the data signal and PT signal, which is in favor of reducing the required OSNR levels of data 1

signal and PT signal. When the value of ((81Δf )/(200Δv)) 4 is set as 1.1, Fig. 3 shows the Q-factor contour line as a function of total input power and MI ratio γ . The maximum Q-factor can only be obtained on the condition of γ = 1.1, when total input power is constant. Therefore, the optimum MI ratio equation is successfully verified. It is interesting to find that the system performance degrades heavily, if γ < γopt .

OCNR (dB)

7 T h e b a n d w id t h o f F P f ilt e r ( G H z )

sampling and band-pass sampling [26]. The bandwidths of MZM, 4-level electrical signal generator, and PD are selected with commonly used parameters. It is shown that our proposed 16QAM generation scheme has the advantages of optical component reduction, but comes with the price of additional RF source. Similarly, our proposed coherent detection scheme has competitive features in LO, RF source, RF demodulator, and DSP complexity, in spite of the relatively high cost in PD and ADC.

165

6 12

5

21 22 23

11

4

13 15

3

14 16

2

17 19

1 7

8

20

24

18

25 27

26

28 9 10 11 12 Subcarrier frequency spacing (GHz)

13

Fig. 6. Contour line of the PNPR as a function of subcarrier frequency spacing and the bandwidth of FP filter.

shows the 16QAM constellation in case that the MI of PT signal is the dominate distortion factor. We can find that, it has an almost the same impact on the 16-clusters of the constellation. Fig. 5 (c) shows the 16QAM constellation on the scenario that the MI of data signal has a main influence. It can be clearly found that the constellation diagrams with high power will exhibit the higher distortion level. In the PT path, residual dada signals, PT, and ASE noise usually coexist. All the components will mix with the wanted data signals during the SH detection. In order to minimize the negative effect, we should filter out residual data signal and ASE noise as much as possible. The concept of optical carrier to noise ratio (OCNR) is used to quantize the PT quality, which can be expressed as

3.3. Effects of IFI, MI, PT quality, filter bandwidth and subcarrier frequency spacing

OCNR =

Fig. 4 shows the effect of our proposed I/Q separation scheme to eliminate IFI. Two constellation diagrams are compared by setting OSNR ¼22 dB and η ¼ 0.29. Fig. 4(a) shows the clear 16clusters, meaning that the overlapped I/Q signals caused by IFI is completely separated, while the constellation diagram shown in Fig. 4(b) suffers severe distortion, leading to performance degradation. It can be clearly observed that our scheme can effectively eliminate IFI, while traditional IQ separation algorithm fails to do. Since IFI is a limiting factor for SH coherent detection, our proposed I/Q separation algorithm is key to secure the system performance. In the SCM-16QAM generation, A and B need to be selected as relatively small values in order to realize a linear electro-optical conversion. When the values of the MIs are relatively large, the 16QAM constellation is distorted during the electro-optical conversion. Whereas the small MIs means that higher laser output power is required to ensure the OSNR of data signal and PT signal, which is harmful to laser. Furthermore, the induced nonlinear transmission impairment will degrade system performance. Thus, root mean-squared (RMS) error vector magnitude (EVM) is used to quantize the degree of constellation distortion. Fig. 5(a) shows the effect of MIs on the 16QAM constellation distortion. We can see that both MIs have impacts on EVMRMS . In order to ensure the value of EVMRMS less than 5%, the upper limits on the MIs of data signal and PT signal are  0.3 and 0.4, respectively. Obviously, the MI of data signal exerts a more severe influence, compared to the MI of PT. In addition, their individual impacts on the scattered clusters are different. Fig. 5(b)

where PPT , PRDS , and PASE are the power of PT, residual data signal, and ASE noise, respectively. The FP filter with narrow bandwidth is critical to obtain the high PT quality. However, it may not be kept tuned at the right frequency, which will degrade PT quality [22]. Fig. 6 shows the effects of subcarrier frequency spacing and the 3 dB bandwidth of FP filter on PT quality. We can see that the bandwidth of FP filter can degrade OCNR severely, especially when the subcarrier frequency spacing is less than 10 GHz, which is because the cascaded OBPF cannot filter out the unwanted data signals well. When the subcarrier frequency spacing is larger than 10 GHz, the curves become smoother. In this case, we can relieve the demand for the bandwidth of FP filter to 2–3 GHz. The subcarrier frequency spacing, the bandwidth of EBPF, digital LPF and the OBPF used in the signal path will greatly influence the proposed coherent detection performance. Fig. 7 shows the required OSNR@BER¼1e–3 in the case of η ¼0.29. We can conclude from Fig. 7(a) that, when the bandwidth of digital LPF and EBPF are at a range of 4.7–5.4 GHz, 11.5–14.5 GHz, respectively, the required OSNR@BER¼1e–3 is the smallest. By setting the bandwidths of digital LPF and EBPF within the range aforementioned, i.e., 4.7–5.4 GHz, 11.5–14.5 GHz, respectively, Fig. 7(b) presents the optimum frequency spacing among subcarriers in order to achieve smallest required OSNR@BER¼1e–3, when the bandwidth of OBPF is 32 GHz. Also the proposed coherent detection performance degrades severely, if the subcarrier frequency spacing is below 9 GHz, because the optical spectra of data signal are closely overlapped with the PT signal. Consequently, the optical filter in the PT path cannot function effectively.

PPT PRDS + PASE

(18)

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J. Jia et al. / Optics Communications 351 (2015) 160–166

5.8

18.8 5.4 5.0

Required OSNR @BER=1e-3

13

18.6

19.619.2

4.6

19.4

19.2 19.0

4.2 8

9

10 11 12 13 14 15 The bandwidth of EBPF (GHz)

16

Subcarrier frequency spacing (GHz)

The bandwidth of digital LPF (GHz)

Required OSNR @BER=1e-3 6.2

12 18.7

11 18.8

10 9 8 30

18.8 18.9 19.3 19.6

19.0 19.4

19.1

31

32

33

34

35

The bandwidth of OBPF in the signal path (GHz)

Fig. 7. Contour line of the required OSNR@BER¼ 1e–3, under the condition that (a) subcarrier frequency spacing and the bandwidth of OBPF in the signal path are 12 GHz and 34 GHz, respectively, (b) the bandwidths of digital LPF and EBPF are 5 GHz and 13 GHz, respectively.

4. Conclusions For the first time, we propose and demonstrate a subcarrier multiplexing based self-heterodyne coherent detection for PM16QAM format, with successful mitigation of image frequency interference through proposed DSP scheme. Meanwhile, a closedform analytical BER formula is verified by numerical simulations with a deviation less than 0.3 dB at BER ¼10–3. The concept of optimum modulation index (MI) ratio between data and PT signal is derived and verified, in order to reduce the distortion of 16QAM constellation. Then, several key parameters are optimized in order to improve system performance.

Acknowledgment This work was supported by the 863 High Technology Plan (2015AA016904), and the National Natural Science Foundation of China (61275069 and 61331010).

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