OCDM systems with PSK and QAM codes

Journal Pre-proof OCDM systems with PSK and QAM codes Takahiro Kodama, Gabriella Cincotti

PII: DOI: Reference:

S0030-4018(20)30161-9 https://doi.org/10.1016/j.optcom.2020.125538 OPTICS 125538

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Optics Communications

Received date : 29 January 2020 Revised date : 13 February 2020 Accepted date : 15 February 2020 Please cite this article as: T. Kodama and G. Cincotti, OCDM systems with PSK and QAM codes, Optics Communications (2020), doi: https://doi.org/10.1016/j.optcom.2020.125538. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

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OCDM Systems with PSK and QAM Codes Takahiro Kodama1, Gabriella Cincotti2

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1. Faculty of Engineering and Design, Kagawa University, Takamatsu 761-0396, Japan 2. Department of Engineering, University Roma Tre, Rome I-00146, Italy

Abstract: A multiport encoder/decoder can simultaneously generate multiple PSK optical codes, and it has been effectively used in asynchronous, spectrally efficient access networks. To increase the system flexibility, as well as the number of simultaneous IoT signals, we introduce novel multi-level QAM orthogonal optical codes that are generated by the multiport encoder/decoder using optical phase modulators. The QPSK modulator simultaneously operates for data modulation and orthogonal code generation. The code orthogonality is improved, compared to conventional PSK codes, and we analyze the performance of 16-code × 10 GSymbol/s, OOK-, DPSK- and DQPSK-modulated OCDM systems, using conventional PSK and the proposed QAM codes. Keywords: Optical code division multiplexing, quadrature amplitude modulation, phase shift keying.

1. Introduction

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Fixed and mobile access network unification will remove the distinction between networks and provide seamless services to users, across connected devices at home and on the move. Full-service operators can address the ongoing loss of market share due to intense competition, reducing both capital expenditure and operating expenditure [1]. Centralized radio access network (C-RAN) strategy has been proposed as an effective response to the increasing capacity demand of future wireless standards, such as long-term evolution (LTE), LTE Advance and those proposed under the 5G banner [2]. Some approaches of cloud radio-access networks are based on wavelength division multiplexing (WDM), to reduce the amount of fiber, while providing a large number of high bit-rate channels [3]. However, WDM systems with narrow channel spacing require accurate initial frequency setting and/or frequency tuning during operation, to avoid crosstalk between adjacent channels, due to frequency drifts [4]. As an alternative to WDM approach, optical code division multiplexing (OCDM) can provide another dimension for asynchronous multiple access using both time and wavelength domains, increasing the system flexibility and bandwidth granularity [5,6]. Time-spread (TS) [7] and spectral-spread (SS) [8-10] orthogonal optical codes (OC) can be efficiently used in low-latency and spectrally efficient optical access systems. Fifteen years ago, we have designed a multiport optical encoder/decoder (E/D), that has the unique capability of simultaneously generating and processing multiple phase shift keying (PSK) OCs, for a cost-effective use in the TS-based OCDM systems [11]. Each OC is equivalent to a Fourier subcarrier, and the OC orthogonal property stems from the fact that the subcarriers have almost nonoverlapping frequency spectra, so that the multiple access interference (MAI) is reduced. Optical sources with broad linewidth are preferable, to reduce the detected optical beat noise [12,13]. Fiber Bragg grating (FBG)-based optical E/Ds can be designed to suitably change the intensity and phase for each chip, thus improving orthogonality between the OCs [14]. However, the fabrication process is quite complex, and a set of different FBG-based E/Ds are needed at each ONU and in the RN to generate and process all the OCs. Recently, hybrid OCDM and orthogonal frequency division multiplexing (OFDM) systems that can reduce MAI have been proposed in literature [15,16]. OCDM systems are characterized by a fully asynchronous transmission, that is a crucial feature to independently handle various Internet of the Thing (IoT) signals associated with low-latency LTE systems. Hybrid optical and electrical multi-level PSK codes have proposed by changing the OC depending on the IoT signals to increase the system flexibility. However, in that case the number of codes is reduced due to loss of orthogonality [17]. In the past decade, we have experimentally demonstrated asynchronous 10 GSymbol/s, on-off keying- (OOK) [18,19] and differential PSK- (DPSK) [20,21] modulated OCDM systems using the multiport E/D. Four-level pulse amplitude modulation (PAM) [22] and differential quadrature PSK-(DQPSK) [23] modulated OCDM systems have been demonstrated to increase the spectral efficiency. Record 2.56 Tb/s transmission over 50-km link with full C-band have been demonstrated, using four OCs, two polarizations and eight wavelengths [24]. In these experiments, the maximum number of OCs that can be transmitted simultaneously in an asynchronous way is eight, due to MAI and beat noises: however, using pre-filtering and two cascade E/Ds, asynchronous 16 OCs × 10 Gb/s OOK OCDM transmission has been successfully demonstrated [25]. The cascade E/D configuration increases the insertion loss, such as coupling, propagation and splitting loss, and to overcome this issue, a novel set of multi-level quadrature amplitude modulation (QAM)-based OCs have been recently proposed, as the convolution of optical and electrical PSK codes [26]. The QAM OCs are generated using a multiport optical E/D and a 50 Gbaud quadrature phase shift keying (QPSK) modulator, without any digital to analog converter; in addition, this system architecture introduces flexibility into the resource assignment process, because the OCs can be electrically changed. QAM-based OCs have recently proposed in optical packet switching networks, where the OCs are used as labels to route data through the network nodes. However, the use of QAM-based OCs in OCDM networks, where data streams are encoded and multiplexed, has not been fully investigated yet, and this is the main goal of the present paper. We consider 16 QAM-based OCs that are transmitted in an asynchronous CDMA system, using OOK, DPSK and DQPSK modulation [27].

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The reminder of the paper is organized as follows. In Section II, we analyse the performance of QAM OCs and we demonstrate they outperform conventional PSK OCs, with respect to code orthogonality. The system architecture and the corresponding analysis model are described in Section III, considering thermal and shot noise, phase induced intensity noise (PIIN), as well as MAI noise. In Section IV, we analyse the performance of an asynchronous 16 OCs × 10 GSymbol/s OCDM system, using OOK, DPSK, DQPSK modulation, considering both conventional PSK and QAM OCs.

2. PSK and QAM codes

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A multiport E/D simultaneously generates N different PSK codes at its N ports; each OC is composed of N chips with same amplitude and different phases, and the chip rate is C. The impulse response at the output port k’ can be written as N 1 2 j nk '  n (1) hk ' (t )   e N   t   k '  0,1, N  1  C n 0 where j= 1 and   t  is the Dirac delta function. Figure 1(a) shows the temporal waveforms hk’(t) of the PSK OC at the k’=1 output port, for C = 200 GHz, and N=16. Each code is generated sending a single laser pulse p0(t) into the E/D input port: the OC duration is 80 ps, the free spectral range FSR=200 GHz, and the maximum baud rate is C/N=12.5 GHz. The corresponding optical spectra Hk’(f) are shown in Fig. 2(a). To increase the code orthogonality and reduce the spectral crosstalk between two OCs generated at adjacent ports, we send M=4 consecutive laser pulses with rate C/M = 50 GHz into the E/D input port to generate QAM codes. Therefore, the input laser signal is quadrature PSK (QPSK) modulated M 1 2 j mk M

ek (t )   e m 0

 mM  p0  t   C  

k  0,1, M  1

(2)

and it is reported in Fig. 1(b). The corresponding optical spectra Ek(f) are reported in Fig. 2(b). The hybrid electro-optical QAM code generated at the output port k’ is the convolution of the pulse train of Eq. (2) and the E/D impulse response of Eq. (1) Ekk ' (t )  hk ' (t )  ek (t )

N 1 M 1   mk nk '    n  mM     exp  2 j    p0  t   N    C  M n 0 m  0  k  0,1,...M  1; k '  0,1,...N  1

(3)

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that are shown in Fig. 1(c) for k=k’=1. We observe that QAM code is composed of N+M(M-1) = 28 chips, so that the maximum baud rate is reduced, with respect to conventional PSK OCs. However, the code orthogonality is increased, because the crosstalk of two adjacent codes is much reduced, as shown by the optical spectra in Fig. 2(c). The better performances of the QAM codes over the PSK codes are also evident from Fig. 1(d) and (e) showing the envelope of the autocorrelation waveform of the 16-PSK code and the multi-level QAM code after the photodiode. The crosstalk is reduced also thanks to the enhancement of the autocorrelation power, as the pulse width increases from 47 ps (Fig. 1(d)) to 70 ps (Fig. 1 (e)). However, the enlargement of the autocorrelation waveform of the QAM code is smaller than the Ts=100 ps of the symbol duration, and therefore the symbol rate can be kept the same for both PSK and QAM codes. Figures 1(f) and (g) show the envelope of the crosscorrelation waveforms for 16-PSK and multi-level QAM codes, respectively, after photodiode. We observe that the PSK codes are a set of orthogonal codes, because the crosscorrelation function vanishes in the central point, where the autocorrelation function is maximum (see Fig. 1(d) and (f)). On the other hand, the QAM codes are not orthogonal, but the crosscorrelation function assumes small values everywhere (see Fig. 1 (g)). This feature reduces the MAI noise in an asynchronous OCDM system.

Fig. 1. Convolutional multi-level QAM-based OC generation and processing; (a) multi-level PSK optical code, (b) multi-level PSK electrical code, (c) multi-level QAM code, (d, e) autocorrelation waveforms, (f, g) maximum crosscorrelation waveforms.

Figure 2(a) shows the spectra Ek(f) (k=0, 1, 2, 3) of the 4-PSK codes, and Fig. 2(b) shows the spectra Hk’(f) (k’=0,1,..,15) of 16-PSK codes; the spectra Ek(f)ꞏHk’(f) of convolutional QAM codes are shown in Fig. 2(c). The PSK codes correspond to OFDM subchannels with a sinc shaped spectrum. Compared to the 16-PSK code, the convolutional QAM code has reduced spectral

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sidelobes. The performance of the OCs set depends on the ratio between the average powers of the autocorrelation Pe and crosscorrelation signals Pj (j is the distance from the matched port j = 1, 2,… N-1) T 1 S 2 (4) Pe  Ee (t ) dt TS 0 T

2 1 S (5) E j (t ) dt TS 0 where TS is the symbol duration and Ee(t) and Ej(t) (j=1,2,… N-1) are the optical fields of the autocorrelation and crosscorrelation signals, respectively (6) Ee (t )  Ekk ' (t )  Ekk ' (t )

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Pj 

E j (t )  Ekk ' (t )  Ekk' ' (t ) ' kk '

Ekk '  Ekk' ' .

(7)

Ekk ' (t ) , and E (t ) are the optical fields of the encoder and decoder output signals given in Eq. (3). P The power contrast ratio (PCR) is defined as PCR( j )[ dB ]  10 log j and it is shown in Fig. 3, for conventional 16-PSK OCs, Pe 32-PSK OCs and the proposed hybrid QAM codes. In the case of 32-PSK OCs, we have selected the 16 OCs with the best correlation characteristics, among the available 32 OCs of the entire code set. From an inspection of Fig. 3, we observe that the code orthogonality of the QAM codes is enhanced with respect to conventional PSK, because the maximum value of the PCR parameter (that occurs at adjacent ports, i.e. for a distance j=15 from the matched port) is reduced from -8.1 dB to -16.3 dB.

3. PSK and QAM codes

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Fig. 2. Optical spectra (a) Hk’(f) optical codes, (b) Ek (f) electrical codes, (c) Ek (f) Hk’ (f) QAM codes.

Fig. 3. PCR values.

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3.1. System Architecture Figure 4 shows the architecture of an asynchronous 16-OC x 10 GSymbol/s OOK-, DPSK-, and DQPSK-modulated OCDM system. Other coherent modulation approaches have been not considered, because the pulse light source, such as mode locked laser diode (MLLD), has a short coherence length [12]. Here, the electrical codes (ECs) are generated by the QPSK modulators and the OCs are generated by the multiport E/D. In the case of OOK-OCDM, the optical short pulse stream is modulated by an intensity modulator (IM) and then sent to a QPSK modulator. As shown in Fig. 5(a), the QPSK modulator generates an electrical M=4 level PSK codes. For DPSK- and DQPSK-OCDM, an optical short pulse stream with 50 GHz repetition is launched into the QPSK modulator. The QPSK modulator generates an electrical 4-level PSK coded DPSK or DQPSK modulated signal, as shown in Fig. 5(b, c). The N=16-port E/D in the remote node (RN) generates 16-level PSK OCs, and narrowband optical band-pass filter (NB-OBPF) is used for the remaining FSR region, to maximize the spectral efficiency [20]. The OLT uses a 16-port E/D to decode the OCs. The four-level PSK ECs generated by the modulator are optically (not electrically) decoded to reduce the power consumption, using an array of four 4-port E/Ds. The cascade of N=16-port and 4-port E/Ds can be implemented on a single planar lightwave circuit, or using a different AWG configuration. Note that the multiport E/D is placed at the RN to reduce the splitting losses, in a similar way to conventional WDM architecture. Alternatively, a super-structured fiber Bragg grating optical E/D can be used in the place of a 4-port E/D [28].

Fig. 4. Architecture of QAM-OC-based OCDM access system.

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Fig. 5. Configuration of transmitter and receiver (a) OOK-OCDM, (b) DPSK-OCDM, (c) DQPSK-OCDM.

3.2. Analysis Model To numerically analyze the system performance, we have investigated a 10 GSymbol/s, OOK-, DPSK-, and DQPSK-modulated OCDM architecture, using 16 multi-level PSK- and QAM-OCs, and symbol rate detection. The shot and thermal noise variances have the following expression



N 1



j 1

 sh2  2eBR Pe 1  

 th2 

4kBTBR . RL

Pj   Pe 

(8)

(9)

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kB is the Boltzman constant, T the temperature, BR the receiver bandwidth, e the electron charge,  the photo detector (PD) responsibility and RL is the load resistance. The parameters used in the numerical simulation by MATLAB are summarized in Table 1, and, if the received power is small, thermal noise is dominant. To investigate the OCDM system performance in the worst-case scenario, with the largest values of MAI and beat noises, we assume that the peak of all crosscorrelation signals almost overlap with the peak of the autocorrelation signal, as shown in Fig. 6. Therefore, although the system can handle asynchronous signals, we assume that each encoded signal has equal power, fixed delay, random symbol phase and the same polarization. Transmission penalties due to chromatic dispersion and fiber nonlinearity can be neglected in short-reach applications. In our previous works, we experimentally demonstrated that a 50 km transmission of a 10 Gsymbol/s OCDM signal without chromatic dispersion compensation presents a penalty of less than 1 dB [25]. TABLE I PARAMETERS

Symbol

Value

kB [J/K]

1.38×10-23 300 8.5

RL [Ω]

50

e [C]

1.6×10-19

 [A/W]

0.85

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T [K]

BR [GHz]

Fig. 6. Worst case condition of asynchronous OCDM system.

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The beat noise variance has the following expression: 2   beat

 j  e (t )   j (t )

2



N 2 TL

 E j 1 0 0

2 e

(t ) E 2j (t ) cos 2  j dtd j

(10)

is the phase difference between the signals. The phase of the beat noise is a random process that varies in the range

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[-π, π] from bit to bit, with Gaussian distribution for both PSK and QAM codes [29]. Besides, MAI and beat noises have the most significant detrimental effects, when all ONUs transmit a logical “1”, except the intended ONU. In the case of OOK-OCDM system, σ12 and σ02 are the noise variances corresponding to the matched and unmatched signals, respectively 2 2  12   th2   sh2   beat   sh2   beat 2  02   th2   sh2   beat   th2 .

The BER is evaluated as

N P    j   Pe  I th   1  2 Pe j  BER   erfc   4 2 0     

where I th 



N



j2

N P Pj  j   1 Pe  j  2 Pe 1   0

 0 1  

N P     j  Pe  1    I th      2 Pe j    erfc       2 1        

(11)

(12)

(13)

is the threshold current. Figure 7(a) shows the performances of OC#0 for the case of

OOK-OCDM system, using 16-level PSK OCs, considering different number of ONUs. We observe that the beat noise is highly dependent on the number of ONUs and that the forward error correction (FEC) limit (BER = 10-3) can be achieved for only 2 simultaneous ONUs. In fact, for 4 ONUs, the BER shows an error floor. Figure 7(b) shows the BER for 32-level PSK OCs, and the performance are enhanced, with respect to the previous case, thanks to beat noise reduction related to an increased code length. On the other hand, the effectiveness of the multi-level QAM OCs in enhancing the BER performance is shown in Fig. 7(c), for different number of ONUs. It is evident that 32-level PSK code-based and QAM code-based OCDM systems can support 16 active ONUs, when the FEC is employed at the receiver; in addition QAM codes have better performances in the case of more than 4 ONUs. In the case of only 2 ONUs, the QAM OCs performance becomes worst, due to an increase of the beat noise. In the case of DPSK-OCDM system, the noise variance can be expressed same as Eq. (11). For DPSK modulation, the BER is evaluated as [29]

 P 2  1 exp   e2  2  2 1 

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BER 

(14)

The beat noise effect becomes dominant when the received power increases. Figure 8(a) shows the performances of OC#0 for the case of DPSK-OCDM system using 16-level PSK OCs and, also in this case, the FEC limit transmission can be achieved with only 2 ONUs. Figure 8(b) shows the performances of 32-level PSK OCs, and the performance improves by increasing the code length. In fact, for 4 ONUs, the BER shows an error floor. On the other hand, the effectiveness of the multi-level QAM OCs in enhancing the BER performance is shown in Fig. 8(c), for different numbers of ONUs. In the case of DQPSK-OCDM system, the noise variance is given in Eq. (11), and the BER can be evaluated as [30]

 a 2  b2  1 BER  Q(a, b)  I0 (ab)exp    2 2  

where

(15)

Q  a, b  is the Marcum Q function, I 0  ab  is the modified Bessel function of order zero. The parameters a and b are

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defined as

a

2Pe  1  1   2  1 

(16)

b

2Pe  1  1   2  1 

(17)

Figure 9(a) shows the performances of OC#0 for the case of DQPSK-OCDM system using 16-level PSK OCs, and, once more, the FEC limit transmission is achieved with only 2 ONUs. Figure 9(b) shows the performances of 32-level PSK OCs and Fig. 9(c) reports the BER for QAM codes. Again, we observe that the performance of 32-level PSK are slightly worst than QAM OCs when more than 4 ONUs are considered.

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100

100

10-2

10-2

1ONU 2ONU 4ONU 8ONU 16ONU

10-6

10-8

-20

-15

10-6

10-8

-20

-10

PD input power Pe [dBm] (a)

10-2

BER

10-4

1ONU 2ONU 4ONU 8ONU 16ONU

10-4

10-6

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BER

BER

FEC limit 10-4

100

1ONU 2ONU 4ONU 8ONU 16ONU

-15

10-8

-10

-20

-15

PD input power Pe [dBm]

PD input power Pe [dBm]

(b)

(c)

-10

Fig. 7. BERs of OOK-OCDM (a) with multi-level 16-PSK OCs, (b) with multi-level 32-PSK OCs, (c) with multi-level QAM OCs.

1ONU 2ONU 4ONU 8ONU 16ONU FEC limit

10-4

10-2

BER

BER

10-2

10-4

10-6

10-6

10-8

-20

-15

10-8

-20

-10

PD input power Pe [dBm] (a)

100

1ONU 2ONU 4ONU 8ONU 16ONU

10-2

BER

100

100

1ONU 2ONU 4ONU 8ONU 16ONU

10-4

10-6

-15

10-8

-10

-20

-15

PD input power Pe [dBm]

PD input power Pe [dBm]

(b)

(c)

-10

Fig. 8. BERs of DPSK-OCDM (a) with multi-level 16-PSK OCs, (b) with multi-level 32-PSK OCs, (c) with multi-level QAM OCs.

al P 10-2

10-2

FEC limit 10-4

BER

BER

100

1ONU 2ONU 4ONU 8ONU 16ONU

10-6

10-8

-20

-15 PD input power Pe [dBm] (a)

-10

1ONU 2ONU 4ONU 8ONU 16ONU

10-4

10-6

10-8

-20

-15

10-2

BER

100

100

1ONU 2ONU 4ONU 8ONU 16ONU

10-4

10-6

-10

10-8

-20

-15

PD input power Pe [dBm]

PD input power Pe [dBm]

(b)

(c)

-10

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Fig. 9. BERs of DQPSK-OCDM (a) with multi-level 16-PSK OCs, (b) with multi-level 32-PSK OCs, (c) with multi-level QAM OCs.

4. Conclusions

We have investigated the performances of OOK-, DPSK-, and DQPSK-modulated OCDM systems using multi-level QAM OCs generated by multiport E/D and QPSK modulators, that reduce the MAI noise, with respect to conventional PSK OCs. The numerically demonstrate that the proposed access system architecture can support 16 10 GSymbol/s asynchronous ONUs, with a larger flexibility, since QAM OCs can be changed using a QPSK modulator.

Acknowledgements

This research is supported under the Ministry of Education, Culture, Sports, Science and Technology of Japan under “Leading Initiative for Excellent Young Researchers (LEADER)” and the Support Center for Advanced Telecommunication (SCAT) Technology Research Foundation.

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Kitayama, “40G-OCDMA-PON system with an asymmetric structure using a single multi-port and sampled SSFBG encoder/decoders,” IEEE J. Lightw. Technol., vol. 32, no. 6, pp. 1132-1143, Mar. 2014. G. Manzacca, A. M. Vegni, X. Wang, N. Wada, G. Cincotti, and K. Kitayama, “Performance analysis of a multiport encoder/decoder in OCDMA scenario,” IEEE J. Selec. in Quant. Elect., vol. 13, no. 5, Sept./Oct. 2007. J. G. Proakis: Digital communications, Mc Graw Hill International Edition, (2008).

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Takahiro Kodama: Conceptualization, Methodology, Software, Validation, Investigation, Resources, Data Curation, Writing-Original Draft, Visualization, Project administration, Funding acquisition.

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Gabriella Cincotti: Formal analysis, Writing-Review&Editing, Supervision.