1. Introduction

The emerging advanced optical networks face two main challenges related to the transmission capacity and user-end cost [1-5]. To deal with the increasing traffic demand associated with advanced data application based on internet of things (IOT) and cloud computing, the network should adopt advanced optical communication techniques [6-8]. Among these techniques are high-order modulation to increase the number of bits carried by the transmitting symbol [9, 10] and using multiplexing technique to transmit multichannel on the same link [3, 11, 12]. To reduce the cost at the user end, intensity modulation/direct detection (IM/DD) schemes are preferred to be used [13-15]. The DD receiver does not use a local laser source for the detection process and hence reduces the cost and increases the receiver robustness [16, 17]. Different IM/DD schemes have been used in optical networks such as orthogonal frequency-division multiplexing (OFDM) [18, 19], carrierless amplitude phase (CAP) modulation [5, 20], and subcarrier multiplexing (SCM) [21, 22]. The SCM scheme attracts increasing interest since it does not need high-speed numerical calculations when compared with OFDM, which uses fast Fourier transform, and CAP which uses virtual in-phase (I) and quadrature-phase (Q) filters.

To increase the spectral efficiency (SE) of the SCM scheme, the following points should be taken into the consideration

(i) Modulating the subcarrier by high-order modulation formats such as quadrature-amplitude modulation (QAM) [2, 9].

(ii) Using Nyquist-half cycle (NHC) signaling where a rectangular-spectrum shape is adopted for the transmission pulses to ensure zero intersymbol interference (ISI) based on first Nyquist criterion [14, 17, 23-25]. In this case, the minimum transmission bandwidth required to transmit symbol rate with zero ISI is equal to . In other words, the raised-cosine filter shaping is redesigned here using approximated zero roll-off factor.

(iii) Transmitting only one single-sideband (SSB) of the optical modulated carrier [25, 26-28]. The SSB transmission also reduces the effect of fiber group-velocity dispersion (GVD) which limits the maximum transmission distance in high-bit rate communication fiber link [29, 30].

(iv) Using wavelength-division multiplexing (WDM) [9, 14, 22, 25, 31, 32] and polarization-division multiplexing (PDM) [11, 16, 27]. The PDM uses dual-polarization (DP) transmission to double the transmitted data rate.

Recently, NHC-SSB SCM attracts increasing interest as a high spectral efficiency-modulation scheme suitable for high-bit rate links in short- and medium-reach optical network applications [1, 17, 25, 31]. An optical link based on this modulation scheme can be implemented using IM/DD configuration which reduces the cost and increases the robustness of the link. In 2017, Zhu et al. [23] have demonstrated the transmission of 16-QAM 224 Gbps data over 160 km standard single-mode fiber (SSMF) at C-band using NHC-SSB modulation. The transmission system uses optical carrier-assisted (OCA) technique to enhance the detection efficiency of the used DD receiver. In the experiment, the optical carrier was added with an additional (signal) laser at the transmitter side and the resultant waveform was delivered along the fiber. The scheme is equivalent to heterodyne coherent detection with a local oscillator and a single-ended photodiode (PD). The experimental results of Ref. [23] set a record of fiber link length for C-band 224 Gbps single channel and single PD direct detection transmission. Therefore, the OCA-NHC SSB configuration will be used as a basis for investigation in this work. The aim of is to investigate the transmission performance of NHC-SSB system operating at different link environments. This includes a single-channel and WDM systems operating at C- and O-bands with and without optical amplification using IM/DD scheme.

2. System Configuration and Noise Analysis

2.1. System under Observation

Figure 1. Block diagram of optical-carrier assisted intensity modulation/direct detection (IM/DD) system incorporating Nyquist half-cycle (NHC) single-sideband (SSB) modulation format. PAM: Pulse amplitude modulation; RRC: Root raised-cosine; OBPF: Optical bandpass filter; PD: Photodiode; EA: Electronic amplifier, DSP: Digital signal processing

Figure 1 shows a block diagram of the single-channel system under observation. The following remarks should be noted about this system

(i) The system uses IM/DD scheme.

(ii) Ideally, the raised-cosine shaping filters should be designed with zero roll-off factor "r" to match Nyquist pulse shaping (ideal lowpass filter spectrum). Practically, r is set to a small value such as 0.02 to enable efficient filtering process in the next steps. Therefore, the transmission bandwidth is limited to

(1a)

(1b)

with r is approximated to zero. Here, is the symbol rate, is the bit rate, and M is the modulation order.

(iii) A high-order optical bandpass filter is used to select the lower-sideband (LSB) of the optical modulator output.

(iv) The system uses two laser sources. A signal laser of frequency which is modulated by the data. The second laser is called the carrier laser of frequency and acts as an assisted carrier. The fields of the modulated signal laser and carrier laser should be combined before optical detection and therefore, the detection process is based on OCA-scheme. This scheme is useful for using DD receiver to detect the optical SSB signal.

(v) The optical receiver uses a digital signal processing (DSP) unit for compensating fiber dispersion and nonlinear optics effects.

(vi) The transmission link consists mainly of a SSMF. If optical amplifiers (OAs) are used to compensate fiber losses, the link is divided into many spans. Each span consists of 50 km SSMF followed by an OA to compensate the span loss.

(vii) The field of the continuous-wave (CW) carrier laser can be combined with the field of the SSB component of the modulated signal laser at the transmitter side. This scheme is useful since both carrier and signals lasers are under control in the transmitter side. However, in WDM system, the carrier laser may be used in the receiver side to reduce the interference with near neighboring signal channels and also to reduce the effect of fiber nonlinear optics.

2.2. Receiver Noise Analysis

This subsection presents frame work to identify the noise characteristics of the detection process in the receiver. Two special cases are considered here, one corresponds to a transmission link incorporating OAs and the second one corresponds to unamplified link. The first case has been investigated briefly in Ref. [23] and will be discussed again here for comparison purposes with the second case. It is worth to mention here that unamplified links are useful for short-reach optical networks from cost and robustness points of view.

2.2.1. Noise Analysis for Amplified-Link System

This subsection presents detailed derivation of expressions describing the SNR of NHC SSB receiver incorporated in an amplified link system. The derivation stands heavily on the analysis reported in Ref. [23] and gives clear steps with remarks.

The optical signal lunched at the fiber input can be expressed as

(2)

where is the assisted optical carrier and is the SSB optical signal. The polarization of both and are assumed to be aligned along the x axis with denotes the unit vector of the x polarization. Further,

(3a)

(3b)

where

Field amplitude of the CW optical carrier.

Frequency of the CW optical carrier.

Field amplitude of the CW optical signal.

Frequency of the CW optical signal.

frequency of the RF subcarrier.

Baseband signal with |u (t)|≤1.

Assume that the optical channel has idea characteristics (i.e., the effect of attenuation, dispersion, and nonlinear optics are negligible) and the receiver performance is dominated by the contribution of amplified spontaneous emission (ASE) noise generated by the in-line optical amplifiers

(4)

Here, and denote the ASE noise sources in both polarization and is the unit vector of the y polarization. Under these assumptions, the received optical signal r(t) can be written as

(5a)

(5b)

where and are the x and y polarization components, respectively.

(6a)

(6b)

The receiver PD generates a photocurrent which is related to the square of the incident field amplitude

(7)

where is PD responsitivity with is PD quantum efficiency, q is the electron charge, h is Planck’s constan, t and is the frequency of the incident field.

Inserting eqns. (6a) and (6b) into eqn. (7) yields

(8)

where is the intermediate frequency and Re [.] denotes the real part of the complex argument.

To get a clear physical insight on eqn. (8), the photocurrent may splitted into group of components

Dc component.

Desired signal.

Signal-signal beat interference (SSBI).

Carrier-noise (from the same polarization) beating.

Signal-noise (from the same polarization) beating.

Noise-noise beating.

The expressions of these six photocurrent component are as follows

(9a)

(9b)

(9c)

(9d)

(9e)

(9f)

The electrical signal-to-noise ratio can be deduced from the photocurrent

(10)

where and are the average power of the signal and noise associated with the photocurrent, respectively.

(11a)

where Here denotes the expectation of the argument

(11b)

Here is the spectral density of the received ASE noise in each polarization and is the optical band pass filter (OBPF) bandwidth used at the receiver side to suppress the amplified spontaneous emission noise incident on the PD.

Substituting eqns. (11a) and (11b) into eqn. (10) gives

(12)

The following remarks can be noted here

(i) The power of the optical carrier and the power of the optical signal The carrier-to-signal power ratio is then given by

(13a)

The optical signal-to-noise ratio (OSNR)

(13b)

In eqn. (13b), the powers of both signal and carrier are considered with is reference optical bandwidth which is usually set to 0.1 nm in the measurement.

(ii) After the photodetection, the signal-to-SSBI ratio SIR is given by

(14)

(iii) Consider the special case when the carrier-noise beat dominates the receiver noise. This occurs when and Then the electrical SNR can be rewritten as (see eqn. (12))

(15)

2.2.2. Noise Analysis for an Unamplified-Link System

The optical signal lunched at the fiber input can be expressed by eqn. (2). The receiver PD generates a photocurrent which is related to the square of the incident field amplitude

(16)

Substituting eqns. (3a) and (3b) into eqn. (16) yields

(17)

According to eqn. (17), the photocurrent is splitted into three components

(18)

where and denote the direct-current (DC) component, desired signal, and SSBI, respectively, which are given by

(19a)

(19b)

(19c)

Few remarks concerning eqns. (19a) – (19c) are given here

(i) The DC component can be blocked by inserting a series capacitance in the current path.

(ii) The signal component represents a DSB/suppressed carrier (SC) as a modulated version of the baseband signal with an effective RF carrier having a frequency equals . Coherent (synchronous) quadrature demodulator should be used to recover the signal from the component .

(iii) The SSBI component cannot be eliminated by any filtering process since its spectrum overlaps with the signal spectrum.

The electrical signal-to-noise ratio associated with the photocurrent can be computed from eqn. (10). In the absence of optical amplification, the main receiver noise components are thermal noise, which is mainly due to the front-end electronic amplifier used to amplify the photogenerated current, carrier shot noise, and signal shot noise [32]

(20a)

where , and denote, respectively, the standard deviations (root-mean-square (RMS)) noise currents and they are given by

(20b)

(20c)

(20d)

Equation (20a) is a well-known expression for the noise associated with electronic amplifier characterized by load resistance and noise figure [33]. In this equation, is Boltzmann constant, T is the absolute temperature (in Kelvin), and is the receiver electrical bandwidth. Equations (20c) and (20d) are deduced from the fact that the power spectral density (PSD) of the shot noise equals average current), where q is the magnitude of the electric charge [34].

The electrical SNR of the unamplified-link system is then given by

(21)

where and denote, respectively, the carrier and signal power estimated at the end of the fiber link whose length is L, and they are related to the power launched at the fiber input by

(22a)

(22b)

Here L is the fiber length in km, a is the fiber power attenuation coefficient measured in km^-1, and it is related to fiber loss parameter (measured in by

(23)

Equation (21) is then rewritten as

(24)

Equation (24) is valid when the carrier laser is inserted at the fiber input. Further, the effect of fiber dispersion on degrading the quality of the received optical signal is neglected here. This assumption is justified for dispersion-compensated or dispersion-equalized links.

For the special case corresponding to inserting the carrier laser at the receiver side the carrier laser field is coupled with the received signal field, and the resultant waveform is applied to the PD), then eqn. (24) can be modified to cover this case

(25)

where is the power of the receiver-side inserted CW carrier laser. Here is the electrical SNR corresponding to the case of an unamplified link supported with carrier laser inserted at the receiver side.

3. Results

This section presents results related to NHC-SSB system operating with different transmission link environment. Eight scenarios are used to describe the link environment based on the operating wavelength, number of WDM multiplexed channels, and the presence or absence of optical amplification. These scenarios are

Scenario A1: 1310 nm single-channel system without optical amplifiers.

Scenario A2: 1310 nm single-channel system with optical amplifiers.

Scenario A3: O-band WDM system without optical amplifiers.

Scenario A4: O-band WDM system with optical amplifiers.

Scenario B1: 1550 nm single-channel system without optical amplifiers.

Scenario B2: 1550 nm single-channel system with optical amplifiers.

Scenario B3: C-band WDM system without optical amplifiers.

Scenario B4: C-band WDM system with optical amplifiers.

A 224 Gbps 16-QAM data is assumed to be carried by each single channel. Other parameters valued used in the simulation are listed in Table 1. The values of maximum transmission distance reported in this section correspond to the lengths of the fiber link which make the receiver bit error rate (BER) approaches its threshold value. A BER threshold is used here which corresponds to 7% overhead hard-decision (HD) forward-error correcting (FEC). The simulation results are obtained using Optisystem ver. 14 software package.

Table 1. System parameters values used in the simulation for the NHC-SSB system operating with 224 Gbps 16-QAM signaling. The blue- and red-color numbers are corresponding to 1550 nm 1310 nm systems, respectively

3.1. Single-Channel Transmission

Figure 2 shows the signals spectra and constellation diagrams at different points of the unamplified 1310 nm single-channel system (Scenario A1). The results are obtained using dBm, dBm (inserted at the transmitter side) and fiber length L =36 km. This link length corresponds to the maximum transmission distance, , under these conditions. Note that the a double-side band (DSB) spectrum of the modulated radio frequency (RF) subcarrier covers approximately 56 GHz bandwidth which corresponds to when . This 56 GHz bandwidth also equals the bandwidth of the transmitted optical SSB signal. Note further, the ability of used DSP unit to compensate the fiber dispersion and recover the required constellation diagram. The simulation is repeated for the unamplified 1550 nm single-channel system (Scenario B1) and the results are reported in the Appendix.

Figure 2. Spectra and constellation diagrams related to an unamplified link 224 Gbps 16-QAM system operating at 1310 nm wavelength with L=36 km, Ps=0 dBm and Pc=0 dBm (carrier at transmitter). (a) Spectrum of the QAM pulse generator output (I-phase component). (b) Spectrum of the QAM modulator input. (c) Spectrum of the QAM modulator output. (d) Spectrum of the optical modulator output. (e) Spectrum of the optical SSB signal. (f) Spectrum of signal SSB + assisted carrier. (g) Spectrum of the optical signal at the fiber output. (h) Spectrum of the amplified photocurrent. (i) Spectrum of the QAM demodulator output. (j) Spectrum of the filtered QAM demodulator output. (k) Receiver constellation diagram at the DSP input. (L) Receiver constellation diagram at the DSP output

Figures 3a and b compare the maximum transmission distance achieved by the unamplified 1310 and 1550 nm systems when the carrier is inserted at the transmitter or receiver side, respectively. Results related to amplified single-channel systems are presented in Figs. 4a and 4b. In both Figs. 3 and 4, the carrier laser power is set to 0 dBm, and the values of are estimated for different values of signal laser power

Figure 3. Variation of maximum reach Lmax with signal laser power Ps assuming unamplified 224 Gbps 16-QAM system operating with Pc=0 dBm. (a) Carrier at the transmitter. (b) Carrier at the receiver

Investigating the results in Fig. 3a and 3b reveals the following findings

(i) Moving the laser carrier from the transmitter side to the receiver side increases the maximum transmission distance by approximately 30%. In other words, (L_max)_R/(L_max)_T ≈ 1.3 where the subscripts R and T denote that the the carrier laser is inserted in the transmitter and receiver side, respectively. This conclusion is true for both 1310 and 1550 nm systems.

(ii) (L_max)_1550nm/(L_max)_1310nm ≈ 1.7 independent of the location of the carrier laser. This results indicate clearly that the systems performance is affected mainly by fiber loss and not by dispersion. Recall that the fiber GVD, D is almost negligible at 1310 nm. Further the DSP is used to compensate fiber dispersion and this is more pronounced at 1550 nm where D ≈ 16.75 ps/(nm . km). Note that the values of fiber loss used in the simulation are 0.35 and 0.2 dB/km at 1310 and 1550 nm, respectively. The ratio between the two losses is 1.75 and this is in agreement with the enhancement of L_max achieved at 1550 nm compared with 1310 nm counterpart.

The results in Figs. 4a and 4b highlight the following findings

(i) The L_max-P_s characteristics is divided into two regions controlled by a critical level of P_s (denoted here by (P_s)_critical ). When P_s < (P_s)_critical, L_max increases slightly with P_s. In contrast, L_max decreases strongly with P_s when P_s > (P_s)_critical and this behavior comes from the effect of increasing the level of signal-signal beat interference. The values of (P_s)_critical are about 6 dBm and 8 dBm for 1310 nm and 1550 nm systems, respectively.

(ii) (L_max)_R/(L_max)_T ≈ 1.1 and 1 for the 1310 and 1550 nm system, respectively, when P_s < (P_s)_critical

(iii) At P_s =0 dBm, (L_max)_1310nm/(L_max)_1550nm ≈ 4 and 4.5 when the carrier laser is inserted at the transmitter or receiver, respectively. These values to be compared with 2.6 and 3 when P_s increases to 4 dBm. This enhancement in the maximum transmission distance of the 1310 nm amplified link is expected since the system operates with zero GVD and effectively negligible fiber loss (i.e., loss-compensated link).

Figure 4. Variation of maximum reach Lmax with signal laser power Ps assuming amplified 224 Gbps 16-QAM system operating with Pc=0 dBm. (a) Carrier at the transmitter. (b) Carrier at the receiver

3.2. WDM Systems

Two NHC-SSB WDM systems are designed in Optisystem environment for O-band and C-band operation. Each of the WDM system uses 100 GHz channel spacing and carries 224 Gbps 16-QAM date rate per channel. The frequency of channel laser is computer from

Figure 5 shows the spectrum of the O-band multiplexed signal at the fiber input and after 43 km transmission over unamplified link. The results are presented for dBm, dBm (inserted at the receiver side, L=L_max=43 km, and N = 32). Note that the output spectrum is almost a copy of the input spectrum indicating the absence of distortion due to four-wave mixing (FWM) associated with fiber nonlinear optics. The only difference is the output spectrum level is reduced by 15 dB (=0.35dB/km × 43 km) due to fiber loss. The simulation results in Fig. 5 is repeated in Fig. 6 for dBm and L_max=63 km. Note that the spectrum at the fiber output is slightly distorted when compared with the spectrum at the fiber input. This distortion comes from the FWM effect.

Figure 5. Optical power spectra corresponding to unamplified 32×224 Gbps O-band WDM system operating with 16-QAM signal and Ps=0 dBm. (a) At the fiber input. (b) After 43 km transmission

The simulation is carried further to investigate the C-band multiplexed signal spectrum. The results are given in Fig. 7 and 8 assuming and 8 dBm, respectively. The fiber length is set to Lmax which equals km, respectively. Other parameters used in the simulation are dBm and N = 32. Note that the effect of FWM on the output spectrum is more pronounced when compared with Fig. 5 and 6, especially, when dBm.

Figure 6. Optical power spectra corresponding to unamplified 32×224 Gbps O-band WDM system operating with 16-QAM signal and Ps=8 dBm. (a) At the fiber input. (b) After 63 km transmission

Figure 7. Optical power spectra corresponding to unamplified 32×224 Gbps C-band WDM system operating with 16-QAM signal and Ps=0 dBm. (a) At the fiber input. (b) After 65 km transmission

Figure 8. Optical power spectra corresponding to unamplified 32×224 Gbps C-band WDM system operating with 16-QAM signal and Ps=8 dBm. (a) At the fiber input. (b) After 60 km transmission

Figures 9a and 9b show the dependence of onnumber of multiplexed channels for O-band and C-band, respectively. The results are reported for unamplified link with dBm (inserted at the receiver side). The O-band operation reveals the following results

(i) When the number of multiplexed channels N ≤ 16, the maximum transmission distance is almost independent of N. Further, L_max increases with signal laser power P_s. When P_s=0 dBm, L_max ≈ 44 km when N= 1, 4, 8, and 16. Increasing P_s to 10 dBm yields L_max ≈ 68 km.

(ii) Increasing N to 32 decreases L_max to 43 km and 50 km, when P_s=0 and 10 dBm, respectively. Note also that L_max increases with P_s and reaches 63 km when P_s=8 dBm. Increasing P_s above 8 dBm reduces the value of L_max. This behavior can be attributed to FWM effect associated with fiber nonlinear optics. Therefore, one can conclude that the optimum value of P_s=8 dBm when N=32 which gives the longest possible reach of 63 km.

Figure 9. Dependence of maximum reach of unamplified 16-QAM WDM system on number of multiplexed channels and assuming Pc=0 dBm and 224 Gbps 16-QAM channel data. (a) O-band. (b) C-band

Investigating the results of the C-band operation (Fig. 9b) highlights the following conclusions

(i) L_max is almost independent of N when N ≤ 8. When P_s = 0 dBm, L_max= 78, 77, and 75 km when N= 1, 4, and 8, respectively. Increasing P_s to 8 dBm will increase L_max to 108 km for these three values of N.

(ii) Increasing N to 16 and 32 reduces L_max and this effect is more pronounced for high values of P_s. At P_s=0 dBm, L_max = 72 and 65 km when N= 16 and 32, respectively. These values are to be compared with 90 and 60 km when P_s=8 dBm, respectively.

(iii) The optimum values of P_s which give the longest possible reach are 8 and 4 dBm for N= 16 and 32, respectively. The corresponding values of L_max= 90 and 77 km, trspectively.

The transmission performance of the amplified WDM system is also investigated for both O-band and C-band operation. Here only brief results are given corresponding to the special case of P_s= P_c= 0 dBm. The results reveal that the O-band system offers L_max= 935, 650, 560, and 450 km for N= 1, 4, 8, and 16, respectively. These results highlight the effect of FWM which is more pronounced in low dispersion fiber. The C-band system gives L_max= 210, 210, 210, and 110 km for N= 1, 4, 8, and 16, respectively. The results indicate clearly that effect of FWM plays a key role in reducing the performance 0f 16-channel system.

4. Comparison with Published Experimental Works

4.1. 1550 nm Single-Channel System

This subsection compares simulation results obtained in this work with the experimental data reported in Ref. [23]. Both simulation and experimental results are related to OCA-SCM operates with 224 Gbps NHC-SSB 16-QAM signaling. The experimental results in Ref. [23] were presented for three transmission links: B2B, one span, and two spans. Each span consists of 80 km SSMF ended with 16 dB EDFA for losses compensation. Also an EDFA was inserted at the fiber input to boost the lunch power. The gain G of this OA was adjusted to achieve the required lunch power (see Fig. 10).

Figure 10. Configuration of an optical link with boost erbium-doped optical amplifier used in the experiment of Ref. [23]

The lunch power and the optical carrier-to-signal power ratio (CSPR) were taken as independent parameters in the results presented in Ref. [23]. From Fig.10. The optical signal lunched at the fiber input can be expressed as

(26a)

(26b)

This system is simulated in this work using the following steps

(i) Set the signal laser power to a certain value, simulate the optical modulator subsystem, and record the SSB signal power .

(ii) Calculate the required carrier laser power and EDFA gain .

(iii) Set the values of other system parameters related to the transmitter, transmission link, EDFAs, and receiver as those reported in Ref. [23].

For example, to achieve = 9 dBm and dB as considered in the reference, the signal laser power is set to 5 dBm in the simulation. The simulation yields dBm, and therefor, the carrier laser power is set to 3.5 dBm to achieve dB. The total power at the coupler output equals which corresponds to dBm. The gain G of the boost EDFA is set to 5.3 dB to get a 9 dB lunch power. Under these settings, the simulation yields BERs of , and for B2B, one span, and two-span transmission respectively. These are to be compared with , and experimental BERs, respectively, as reported in Fig. 9c in Ref. [23]. Note that, both simulation and experimental BERs are lower than , which represents the BER threshold for 7% HD-FEC code. Note further that the simulation BERs, , are in the same order of the experimental ones, where . Figures 11 (a-c) show the simulated optical spectra after 0, 80, and 160 km transmission distance, respectively. The simulated and experimental constellation diagrams after 80 and 160 km are given in parts d and e of this figure.

Figure 11. Spectra of (carrier + SSB) waveforms and constellation diagrams related to amplified 224 Gbps carrier-assisted 16-QAM system operating at C-band (carrier at transmitter). (a) Spetrum after 0 km transmission. (b) Spectrum after 80 km transmission. (c) Spectrum after 160 km transmission. (d) Simulated and experimental constellation diagrams after 80 km transmission. (e) Simulated and experimental constellation diagrams after 160 km transmission

Figure 11. (Continued)

Figure 12 shows the variation of BER with lunch power after 160 km transmission with CSPR of 14 dB. The marks and in this figure correspond to the simulation results and experimental data, respectively. The experimental results are deduced from Fig. 8 in Ref. [23]. Investigating the results in this figure reveals that both simulation and experiment predict an optimum lunch power of 9 dB.

Figure 12. Variation of BER with lunch power after 160 km transmission with of 14 dB

4.2. C-Band Wavelength-Division Multiplexing System

Zou at al. [28] reported experimental results describing the transmission of 8×100 Gbps WDM signal over 320 km SSMF at C-band. Each channel operates with NHC-SSB 16-QAM signaling and DD scheme. The 320 km distance is distributed into four spans; each span uses 80 km-SSMF followed by 16 dB EDFA for loss compensation. The polarization of the odd lasers (lasers 1, 3, 5, and 7) are set orthogonal to the polarizations of the even lasers (laser 2, 4, 6, and 8) to reduce the interference between successive lasers fields due to fiber nonlinear optics. The WDM system uses 50 GHz channel spacing with additional EDFA inserted after the multiplexer to determine the required total power lunched into the fiber.

Two BER thresholds were used in Ref. [28] to assess the performance of the demonstrated system; and , which are related to 20% and 7% HD-FEC codes, respectively. Chromatic-dispersion compensation (CDC) technique was used to compensate fiber dispersion. The experiment was repeated with digital back propagation (DBP) technique to compensate both fiber dispersion and fiber nonlinearity.

To simulate the experimental system reported in [28], an assisted optical carrier is inserted in each of the WDM channel transmitters. Thus, each transmitter contains both signal and carrier lasers. This approach has two main effects. (i) The total power launched into the fiber will be increased leading to high fiber nonlinear optics effects. (ii) The spectrum of the signal at the output of the channel transmitter covers frequencies from to . For Gbps and 16-QAM signaling and , the bandwidth of the transmitter signal GHz. Therefore, channel spacing of 50 GHz with high-order 40 GHz demultiplexer bandpass filters are used to ensure negligible crosstalk in accord with the experimental results.

For comparison purposes, the above experimental work is simulated here using Optisystem software with lunch power per channel of 1 dBm and of 10.2 dB. When is set to 0 dBm, the simulation gives dBm . The carrier laser power required to achieve a of 10.2 dB is equals – 0.3 dB The lunch power per channel where G is the gain of the OA inserted after the multiplexer. Note that, dBm. Therefore, dB is used to yield dBm.

Figure 13 shows simulation results related to the system under observation when the transmission link consists of 4 spans (320 km). Parts a and b display the optical spectra at the input and output of the transmission link. Note, the output spectrum contains many intermodulation distortion components due to the effect of fiber nonlinearity. Parts c and d compare the power spectra at the transmitter output and receiver input of channel 1. The two spectra contain almost the same frequency content, which reflects the effectiveness of the receiver DSP unit in compensating chromatic dispersion and nonlinear fiber optics. This is clear further by comparing the constellation diagrams at the receiver before and after the DSP unit as shown in parts e and f of this figure, respectively.

Figure 13. Optical power spectra and constellation diagrams corresponding to unamplified (8×100 Gbps) C-band WDM system operating with 16-QAM signal and Ps=0 dBm. (a) Spectrum at the fiber input. (b) Spectrum after 320 km transmission. (c) Spectrum at the transmitter output of channel 1. (d) Spectrum at the receiver input of channel 1. (e) Receiver constellation diagram at the DSP input. (f) Receiver constellation diagram at the DSP output

Figure 14 compares the measured BERs [15] and simulated ones for of all the 8 channels after 320 km transmission. Note that the simulated results show BERs lower than the measured values, and hence, confirms the possibility of 320 km transmission even when BER threshold of is used. In fact, the simulation predicts successful transmission over 5 spans (400 km) as shown in Fig. 15 when dBm and CSPR = 10.2 dB. Figures 15 also contains results corresponding to CSPR of 8.2 and 12.2 dB and included here to address the effect of CSPR or the channels BERs. Investigating the results in Fig. 4.13 reveals that at constant lunch power per channel , using CSPR of 10.2 dB offers BERs less than the BER threshold for all the eight channels. Increasing CSPR on 12.2 dB or reducing CSPR to 8.2 dB increases the BERs of the channels and makes some of them above the BER threshold. This result can be explained as follows. . Therefore, and hence, increasing CSPR leads to increasing The BER characteristics depends on the effective SNR, which can be stated as

(27)

where the detected electrical signal strength is proportional to the product term . In this equation, is proportionality constant, represents the signal-independent noise power, and represents the signal × signal beat interference. Taking the derivative of with respect and set it to zero yields

Note that, the optimum value of CSPR depends on channel lunch power and system parameters (B₁ and B₂). If one considers a 10.2 dB is the optimum value of CSPR at dB, then . Thus, the actual generated by the optical modulator should by amplified by before lunching it into the fiber.

Figure 14. Comparison between measured BERs [28] and simulated ones for all the 8 channels after 320 km transmission assuming Pch = 1 dBm and CSPR = 10.2 dB

Figure 15. Simulated BERs of the 8 channels after 400 km transmission assuming Pch = 1 dBm

5. Conclusions

The noise characteristics and transmission performance have been investigated of optical carrier assisted NHC-SSB system designed with IM/DD scheme. Simulation results have been presented for both amplified and unamplified WDM systems operating at O- and C-bands with 224 Gbps 16-QAM channel data. The simulation results are in good agreement with published experimental data. The main conclusions drawn from this study are

(i) The C-band WDM system offers higher transmission distance compared with O-band counterpart when no optical amplification is used. When P_s=P_c= 0 dBm, L_max = 78 and 72 km when number of multiplexed channels N= 1 and 16, respectively, in the C-band system. These values are to be compared with 44 km for O-band system.

(ii) Using optical amplification to compensate the link losses will increase the transmission distance of the C-band WDM system to 210 and 110 km when N= 1 and 16, respectively, and assuming P_s=P_c= 0 dBm. These values are to be compared with 935 and 450 km for the O-band system, respectively.

(iii) Performance degradation due to fiber nonlinear optics becomes effective when N= 32 channels and this is more pronounced when P_s increases beyond 0 dBm. This leads to an optimum value for P_s which gives the longest transmission distance. For the unamplified system, (P_c)_optimum= 4 and 8 dBm for C- and O-bands, respectively. The corresponding values of L_max are 77 and 63 km, respectively.

Appendix

Results Related to 1150 nm Single-Channel Transmitter

Figure 16. Spectra and constellation diagrams related to an unamplified 224 Gbps 16-QAM system operating at 1550 nm wavelength with L=62 km, Ps=0 dBm and Pc=0 dBm (carrier at transmitter). (a) Spectrum of the QAM pulse generator output (-phase component). (b) Spectrum of the QAM modulator input. (c) Spectrum of the QAM modulator output. (d) Spectrum of the optical modulator output. (e) Spectrum of the optical SSB signal. (f) Spectrum of signal SSB + assisted carrier. (g) Spectrum of the optical signal at the fiber output. (h) Spectrum of the amplified photocurrent. (i) Spectrum of the QAM demodulator output. (j) Spectrum of the filtered QAM demodulator output. (k) Receiver constellation diagram at the DSP input. (L) Receiver constellation diagram at the DSP output