International Journal of Networks and Communications

p-ISSN: 2168-4936    e-ISSN: 2168-4944

2018;  8(3): 43-62

doi:10.5923/j.ijnc.20180803.01

 

Transmission Performance of Unamplified 1310 nm PAM-Based Data Center Optical Interconnects

Duha S. Ahmed, Raad S. Fyath

Department of Computer Engineering, Al-Nahrain University, Baghdad, Iraq

Correspondence to: Duha S. Ahmed, Department of Computer Engineering, Al-Nahrain University, Baghdad, Iraq.

Email:

Copyright © 2018 The Author(s). Published by Scientific & Academic Publishing.

This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/

Abstract

Optical links incorporating multilevel pulse amplitude modulation (PAM) with intensity modulation/direct detection (IM/DD) scheme have shown promising features when used as low-cost data center interconnects. This paper addresses the transmission performance of PAM-based optical interconnect operating at 1310 nm without using optical amplifications. Results are presented for both directly modulated laser (DML)- and externally modulated laser (EML)-based links operating with 4- and 8-PAM signaling and carry bit rate of 56, 112, and 224 Gbps. Polarization-division multiplexing (PDM) technique is applied to the EML-based link to double the bit rate without degradation the transmission distance. Analytical expressions are derived to characterize the bit error rate (BER) floor and it dependence on the relative intensity noise (RIN) of the transmission laser source. Simulation results obtained using Optisystem software show that maximum distance of 45 and 37 km can be achieved for 4- and 8-PAM system, respectively, when 112 Gbps bit rate and 0 dBm transmitter launch power are used. These are to be compared with 40 and 28 km, respectively, for 224 Gbps data rate.

Keywords: Intensity modulation/direct detection (IM/DD), Optical pulse amplitude modulation (PAM), Data center optical interconnects

Cite this paper: Duha S. Ahmed, Raad S. Fyath, Transmission Performance of Unamplified 1310 nm PAM-Based Data Center Optical Interconnects, International Journal of Networks and Communications, Vol. 8 No. 3, 2018, pp. 43-62. doi: 10.5923/j.ijnc.20180803.01.

Article Outline

1. Introduction
2. Performance of DML and EIM-Interconnects
    2.1. Directly Modulated Laser-Based Link
        2.1.1. System under Investigation
        2.1.2. Transmission Performance
    2.2. External Intensity Modulator-Based Link
        2.2.1. Single-Polarization EIM Link
        2.2.2. Dual-Polarization EIM Link
3. Noise and Bit Error Rate Characteristics
    3.1. Bit Error Rate Formulation
    3.2. Noise and BER Results
    3.3. BER-Floor Characteristics
4. Conclusions
Appendix

1. Introduction

Optical fiber links attract increasing interest for high-bit rate inter- and intra-connects for advanced data centers [1-5]. These links apply the main features and advantages of optical fiber communication for short-reach applications [6-8]. Further, the capacity of these links can be enhanced using different multiplexing techniques such as wavelength-division multiplexing (WDM) [3], [9-12], optical orthogonal frequency-division multiplexing (O-OFDM) [13-20], space-division multiplexing (SDM) [21-25], and hybrid multiplexing [26-29]. Low cost optical interconnects usually implemented using direct-detection (DD) optical receivers [30-33]. This type of receivers uses a photodiode, for optical-to-electrical conversion, followed by an electrical receiver. The DD receiver is considered cheaper than coherent optical receivers since it does not use a local laser acting as a local oscillator to be synchronized with the transmitter laser [34-36]. Further, DD receivers work efficiently with optical pulse amplitude modulation (PAM) signaling where the information is encoded on the intensity of the transmitted pulses [37-40]. Again, the intensity modulation (IM)-based optical transmitter is cheaper as compared with coherent optical transmitter. The intensity modulation can be achieved using directly modulated laser (DML) [41-45] or external intensity modulator (EIM) [46], [47]. Advanced in photonic and optoelectronic technology leads to design DML and EIM operating at bit rates above 100 Gbps [48-50].
Optical interconnects operating at 100 Gbps [51-54] and 400 Gbps [55-62] have attracted significant research efforts and standardization activities, such as the IEEE 802.3bs 400 Gbps Ethernet Task Force [62]. These links are expected to play key role in data centers and short-reach communication. An active research topic in this field is to design low-cost version of optical interconnect based mainly on IM/DD system adopting advanced modulation formats and to enhance the operating rate above 400 Gbps. One of the modulation formats which drawn significant attraction for optical interconnect is multilevel PAM which can be incorporated easily in IM/DD system and it is free of digital-to-analog converter [63-67]. Further, it can be implemented using DML which highly preferred due its low cost and simple implementation. These features have encouraged different research groups to demonstrate successfully 4- and 8-PAM optical interconnects for data centers and short reach applications at 1550 nm wavelength [5], [68-69]. These experiments have been demonstrated using multimode fibers or single mode fiber SMFs and DMLs or EIMs. The 112 Gbps bit rate has been achieved using 4-PAM [70] and 8-PAM [19] signaling. Higher bit rates can be achieved by applying wavelength-division-multiplexing techniques [11], [71].
Recently, there is interest to investigate 1310 nm-optical links for data centers. The negligible chromatic dispersion of the SMF at this wavelength enables higher bit rate transmission distance product compared with 1550 nm link and this can be achieved without using any dispersion compensation techniques which are usually adopted in 1550 nm links. In 2017, Miao et al. [72] developed scalable and fast optical switching system for 1310 nm optical interconnect carrying 4×25 Gbps, 4-PAM signals. Mosman et al. [73] demonstrated the transmission of polarization-division-multiplexing (PDM) 224 Gbps 4-PAM signals at 1310 nm over 10 km SMF using a single IM laser and DD multi-input multi-output (MIMO) DSP-based receiver. A 140 Gbps 20 km transmission of 4-PAM signal at 1310 nm has been demonstrated by Zhong et al. using externally modulated laser [74]. It is clear from the above survey that most research concerned with amplified 1550 nm PAM link where optical amplifier is used to boost the launch power and/or to compensate fiber loss.
The aim of this paper is to investigate the transmission performance of an unamplified 1310 nm optical interconnect. The interconnect is designed without using optical amplifiers which reduces the cost and increases the robustness of the link. The bit error rate (BER) characteristics of the DD receiver is analyzed for both 4-PAM and 8-PAM signals. Analytical expression is derived to describe the dependence BERfloor level on laser relative intensity noise (RIN) and other system parameters. Results are presented for 56, 112, and 224 Gbps PAM system using DML and external modulated laser (EML). The effect of applying PDM on the EML-link to double the transmission bit rate is also investigated. The transmission performance of the investigated PAM systems is obtained by simulating them using Optiwave software package ver.15.

2. Performance of DML and EIM-Interconnects

This section presents results characterize the transmission performance of data center optical interconnect based on PAM modulation. The results are reported for unamplified links operating at 1310nm wavelength with 56, 112, and 224 Gbps data rates using 4- and 8-PAM signaling are adopted at the transmitter using either DML or external modulator while the receiver uses a PIN direct detection configuration. The maximum transmission distance is estimated at BER threshold of 4.4 ×10-3 which corresponds to 7% over head hard decision (HD)-forward error correction (FEC) code. This BER threshold yields a 10-15 BER after applying the HD-FEC coder. Unless otherwise stated, the parameters values used in the calculations and simulation are listed in Table 1.
Table 1. Parameters values used in the simulation
     

2.1. Directly Modulated Laser-Based Link

2.1.1. System under Investigation
Figure. 1 shows the DML-based system under investigation. The M-PAM generator is driven by the input binary data, after converting them a M-PAM sequence using the PAM encoder and generates equal-space radio frequency (RF) PAM signal. This signal is used as the drive current for the DML. For M-PAM signaling, the laser drive current takes the following form
Figure 1. Overview block diagram of unamplified M-PAM single-channel system
(1)
Where Imin corresponds to m=0 level and ΔI denotes level spacing. The maximum rate of PAM drive current . The average value of the drive current (under the assumption of equal-probability symbols) is given by
(2)
Figure 2. Laser diode static characteristics (a) power-current characteristics (b) calculated maximum drive current required to achieve a given average emitted power
To increase the switching spaced of the DML, the OFF state corresponding to Imin is obtained by setting Imin slightly above laser threshold current so the laser is ready to switch quickly to one of the ON states. In this subsection, the semiconductor laser used in the simulation is characterized by a 20 mA-threshold current Ith with a linear power-current characteristics in the lasing region
(3)
where P is the optical power emitted from the laser diode (LD) when driven by a current I and ηS is the slope efficiency which is set to 0.4 mW/mA in the simulation. Under the assumption that , the average power Pav emitted from the laser is given by
(4a)
or
(4b)
The required Imax to achieve a specific level of Pav is then given by
(5)
(6)
The results are presents here for Imin = Ith and therefore, the emitted optical power P corresponds to the zero-order level (m=0) equals zero. Figure 2a shows that the power-current characteristics of the LD used in the simulation while Figure 2b displays the calculated maximum drive current required to achieve a given average emitted power. The drive current waveform and the corresponding emitted optical waveform are depicted in Figures 3a and 3b, respectively, for 112 Gbps 4-PAM corresponding to 0 dBm average power. Corresponding results related to 8-PAM system are given in Figures 4a and 4b.
Figure 3. Waveforms for 112 Gbps 4-PAM corresponding to 0 dBm average power (a) drive current waveform (b) emitted optical waveform
Figure 4. Waveforms for 112 Gbps 8-PAM corresponding to 0 dBm average power (a) drive current waveform (b) emitted optical waveform
The optical receivers incorporate a clock recovery circuit which is very essential in practical system to track any variation in the transmitted symbol rate. Further, a multi threshold circuit is adopted at the receiver to estimate the transmitted symbol level under observation which then be converted to a binary sequence using PAM decoder.
2.1.2. Transmission Performance
Figure 5 shows the spectrum of the waveform at different points of the link for 112 Gbps 4-PAM system operating with 0 dBm launch power (average power at the fiber input) and 50 km transmission distance. Note that the spectrum of the RF PAM signal is copied on the upper and lower sidebands of the optical carrier. Note further that spectrum of the filtered photogenerated signal is confined within 42 GHz corresponding to 0.75 (RS/2) which is the receiver electrical bandwidth. The received eye diagrams corresponding to different lengths are given in Figure 6. The results are given for transmission lengths L=0 (back-to-back (B2B)), 20, 40, and 60 km. The BER are 0, 0, 9.7×10-4 and 2.3×10-1, respectively. The eye diagram corresponding to maximum reach Lmax = 45 km is given in part e of this figure.
The simulation in Figures 5 and 6 are repeated for 8-PAM system operating with 112 Gbps bit rate and the results are given in Figures 7 and 8. Note that the spectrum of the filtered photogenerated signal in this case equals to 28 GHz corresponding to 0.75 (RS/2). The maximum reach equals to 37 km for this link. The simulation in Figures 5 and 6 are repeated for 8-PAM system operating with 112 Gbps bit rate and the results are given in Figures 7 and 8. Note that the spectrum of the filtered photogenerated signal in this case equals 28 GHz corresponding to 0.75 (RS/2). The maximum reach equals 37 km for this link.
Figure 5. Spectra of the waveforms at different points of 50 km-link assuming 112 Gbps 4-PAM signaling with 0 dBm launch power (a) RF spectrum at the transmitter (b) optical spectrum after DML (c) optical spectrum at the receiver input (d) RF spectrum of the photogenerated current (e) RF spectrum after receiver LPF
Figure 6. Receiver eye diagrams at 0 dBm launch power and for different lengths of 112 Gbps 4-PAM link (a) B2B (b) 20 km (c) 40 km (d) 60 km (e) 45 km maximum reach
Figure 7. Spectra of the waveforms at different points of 50 km-link assuming 112 Gbps 8-PAM signaling with 0 dBm launch power (a) RF spectrum at the transmitter (b) optical spectrum after DML (c) optical spectrum at the receiver input (d) RF spectrum of the photogenerated current (e) RF spectrum after receiver LPF
Figure 8. Receiver eye diagrams at 0 dBm launch power and for different lengths of 112 Gbps 8-PAM link (a) B2B (b) 20 km (c) 40 km (d) 60 km (e) 37 km maximum reach
The maximum reach Lmax is investigated for both 4- and 8-PAM links operating with 56, 112, and 224 Gbps. At L=Lmax the BER approaches the threshold level (4.4×10-3). The variation of BER with transmission distance is given in Figures 9a and 9b for 4- and 8-PAM link, respectively. The results are presented for 0 dBm transmitted power and indicate that Lmax = 49, 45, and 37 km for 4-PAM link operates with bit rate Rb of 56, 112, and 224 Gbps, respectively. These values are to be compared with Lmax = 42, 37, and 28 km respectively, for the 8-PAM links.
Figure 9. Variation of BER with transmission distance for (a) 4-PAM link (b) 8-PAM link. The results are presented for 0 dBm transmitted power
The dependence of BER on the launch power at fixed transmission length is depicted in Figures 10a and 10b for 45 km 4-PAM and 37 km 8-PAM links, respectively. The results are given for 56, 112, and 224 Gbps. Note that minimum launch power (PT)min required to achieve the BER threshold equals -2, 0, and 2 dBm for the 4-PAM link when operates with 56, 112, and 224 bit rate, respectively. The corresponding results for the 8-PAM link is -1, 0, and 2 dBm, respectively.
Figure 10. Dependence of BER on launch power at fixed transmission length (a) 45 km 4-PAM link (b) 37 km 8-PAM link
The dependence of maximum reach Lmax on the transmitter launch power PT is deduced by simulating the system for each value of PT and taking the transmission distance as the independent parameter. The results are displayed in Figures 11a and 11b for 4- and 8-PAM link, respectively. The values of Lmax are estimated for three-bit rates, 56, 112, and 224 Gbps investigating the results in Figures 11a and 11b reveals the following findings.
Figure 11. Maximum distance versus launch power (a) 4-PAM (b) 8-PAM
The maximum transmission distance in km is varied almost linearly with transmitter launch power (measured in dBm) with slope equals approximately to 2.9 km/dBm. This fact is true for both links and for the three bit rates. Note that the slope corresponds to 1/fiber loss (0.35/km used in the simulation) and indicate clearly that the system performance is loss limited.
(i) The Lmax-PT curves can be approximated by the linear relation Lmax = Lmax0 +2.9 PT (dBm), where Lmax0 corresponds to Lmax deduced at PT = 0 dBm. The values of Lmax0 equal to 49, 45 and 40 km for 4-PAM link operating with Rb= 56, 112, and 224 Gbps. These values are to be compared with Lmax0 = 42, 37 and 28 km for the 8-PAM link, respectively.
(ii) At given launch power, increasing the bit rate from 56 Gbps to 112 Gbps and from 56 Gbps to 224 Gbps will reduce the maximum reach by 4 and 8 km, respectively for the 4-PAM link. Similarly, the maximum reach reduces by 5 and 9 km for the 8-PAM link for the same increase in the data rate. For examples at PT = 2 dBm, Lmax = 55, 50, and 46 km for the 4-PAM and 48, 43, and 35 km for the 8-PAM when the Rb = 56, 112, and 224 Gbps, respectively.
(iii) For given bit rate and launch power, the 4-PAM link offers longer transmission reach compared with the 8-PAM counterpart. At PT = 2 dBm, ΔLmax = (Lmax)4-PAM -(Lmax)8-PAM equals to 7, 7, and 11 km for 56, 112, and 224 Gbps bit rate, respectively. These values of ΔLmax are almost independent of PT.

2.2. External Intensity Modulator-Based Link

In this subsection, the transmission performance of the EIM PAM link is investigated. Results are presented for both single- and dual- polarization EIM-based configurations.
2.2.1. Single-Polarization EIM Link
Figure 12 show a simplified block diagram used in this simulation. A semiconductor laser operating in continuous-wave (CW) mode is used whose output is applied to the EIM. The electrical PAM signal XPAM (t) is also applied to the modulator and acts as a modulating signal for the CW optical power. Ideally, the modulator yields an optical PAM signal PPAM (t) = XPAM (t).PCW where PCW presents the CW laser power. Under this ideal condition, the average power of the optical PAM signal PT = 0.5PCW which corresponds to 3 dB loss. Figures 13a and 13b shows the waveform of the PAM signal at the modulator output for 112 Gbps 4- and 8-level system, respectively, when PCW = 3 dBm.
Figure 12. Overview block diagram of unamplified M-PAM single-channel system using EIM link
Figure 13. Waveforms of the PAM signals at the external modulator output for 112 Gbps link operating with PT = 0.5PCW (a) 4-PAM (b) 8-PAM
Figure 14 shows the variation of maximum reach with CW laser power PCW for the 4-PAM link. The results are presented for three values of bit rates 56, 112, and 224 Gbps. The values of Lmax is almost identical to those obtained with DML link operating with launch power PT = 0.5PCW. This conclusion is expected since the average power at the fiber input is identical in both cases under these power condition.
Figure 14. Maximum distance versus the CW laser power for 4-PAM EIM link
2.2.2. Dual-Polarization EIM Link
The transmission bit rates of 112 and 224 Gbps using 4-PAM can be doubled in the EIM link if the system is re-configured using dual-polarization configuration (see Figure 15). The dual-polarization scheme can be considered as transmitting two PAM signals simultaneously over the link, each is carried by one of the two orthogonal polarization components of the optical field (X- and Y- polarization). In this configuration, the electrical field of the CW laser is adjusted into linearly-polarized state with polarization angle θP = 45° A polarization beam splitter is used then to split the CW laser power PCW into orthogonally polarized components: PX = PCW cos2θP and PY = PCW sin2θP for θP = 45°, PX = PY = 0.5PCW. Each polarization component acts as a CW optical carrier carrying half of the system bit rates. Under ideal conditions, the dual-polarization PAM link offer the same maximum reach as the single-polarization counterpart operating with half the bit rate and half the CW laser power. Eye diagrams results of X- and Y- polarization receivers of 4-PAM at maximum reach 45 and 39 km of bit rates 224 and 448 Gbps, respectively, 3 dBm CW laser power are shown in Figures 16. The maximum reach is investigated for 4-PAM link operating with bit rate 224 and 448 Gbps at different CW laser power and the results are shown in Figure 17.
Figure 15. Overview block diagram of unamplified dual-polarization EIM 4-PAM system
Figure 16. Receiver eye diagrams of dual polarization of 4-PAM (a) 224 Gbps X-polarization receiver (b) 224 Gbps Y-polarization receiver (c) 448 Gbps X-polarization receiver (d) 448 Gbps Y-polarization receiver. The results are obtained for PCW = 3 dBm and maximum reach of 45 and 39 km for the 224 and 448 Gbps links, respectively
Figure 17. Maximum distance versus CW laser power for dual polarization EIM link

3. Noise and Bit Error Rate Characteristics

This section analysis the noise and bit error rate (BER) performance of 4- and 8-PAM link.

3.1. Bit Error Rate Formulation

BER of optical PAM communication system operating with unamplified transmission link and direct detection has been addressed by Szezorba et al. [75]. Their results show that when gray labelled M-PAM signaling is used with all the symbols have equal probability and equally speed, and the decision thresholds are equidistance from adjacent symbols, the BER can be expressed as [75].
(7)
where IPh is the average photocurrent (i.e., average current generated by the photodiode) and σt denotes the standard deviation of the total noise current associated with the photo detection process (i.e., root-mean square (RMS) noise current). Further, erfc(.) represents the complementary error function of the argument. Note that the expression inside the square brackets describes the corresponding symbol error rate. Expressions corresponding to BERs of 2-, 4-, and 8-PAM systems can be deduced from eqn.7 and the results are
(8a)
(8b)
(8c)
The average photocurrent IPh is related to the average received optical power Pr by
(9a)
where RPd is the photodiode (PD) responsivity which de-scribes the optical-to-electrical conversion capability of the photodetection process and can be expressed as [75]
(9b)
where is the quantum efficiency of the PD, q is the magnitude of the electronic charge, h = 6.6026×10-34 Js Planck’s constant, and f = c/ is the frequency of the incident optical signal with it’s wavelength and c is the speed of light in free space.
The noise associated with the photodetection process comes mainly from three noise sources, namely thermal noise associated with the front-end electronic amplifier used to amplify the photocurrent, shot noise due to quantum nature of the photodetection, and relative intensity noise (RIN) which characterizes the intensity noise of the used transmitter laser. The variance of the total noise current can be written as
(10)
where and are the variances corresponding to thermal noise, shot noise, and RIN, respectively, and they are calculated as follows [75]
(11a)
(11b)
(11c)
where kB = 1.381×10-23 J/k is Boltzman constant, T is the absolute temperature (in Kelvin), and B is the receiver electrical bandwidth. The receiver electronic amplifier is characterized by RL load resistance and Fn noise figure. Few remarks related to eqns. 10 and 11 are given here
(i) The effect of the PD dark current shot noise (variance: with Id is the dark current) is negligible compared with photocurrent shot noise and therefore is not included in eqn. 10. This assumption is justified in practical receivers since Id << IPh.
(ii) There are two signal-dependent noise sources, namely photocurrent shot noise and RIN-related noise whose variances proportional to IPh and I2Ph, respectively. This implies that low-RIN laser sources should be used.
(iii) The receiver bandwidth B is related to the symbol rate where Rb is the bit rate. To ensure zero intersymbol interference (ISI) at the input of the receiver, 0.5Rs ≤ B ≤ Rs for the equalized pulse shape. Note that each of the noise variance scales linearly with symbol rate. At fixed bit rate Rb, going from 2-PAM to 4- and 8-PAM signaling will reduce the total noise to half and third, respectively.

3.2. Noise and BER Results

This subsection presents noise and BER characteristics of the DD receiver used to recover the information from an optical PAM signal received after transmission over unamplified link. The system under investigation corresponds to a single-channel transmission at 1310 nm wavelength. The parameters values used in the simulation are listed in Table 1.
Figures 18a-d show the noise characteristics of 112 Gbps 4-PAM receiver, designed with 550 Ω amplifier load resistance RL and for four values of laser RIN, -130, -140, -150, and -160 dB/Hz, respectively. In these figures, the variance of the total noise σt2 and variances of the individual noise sources are plotted in logarithmic scale versus the average received power Pr measured in dBm. The results are repeated in the Appendix for RL=50Ω. The 50 Ω load resistance corresponds to low impedance receiver front-end electronic amplifier which yields a 10-21 W/Hz thermal noise power spectral density (PSD) according to eqn. 11a. The 550 Ω load resistance corresponds to advanced receiver front-end electronic amplifier which has a transimpedance (feedback) configuration with 550 Ω feedback resistance. The feedback amplifier configuration offers the required bandwidth with higher value of resistance compared with low-impedance counterpart but with reduced thermal noise PSD = 10-22 W/Hz when 550 Ω resistance is used. Investigating these figures reveals that
(i) Both Log and Log increase linearly with Pr (dBm) but with different slops which reflect the degree of dependence of these noise components on the photocurrent IPh. Recall that Pr (dBm)=10 Log [Pr (mW)] = 30 + 10 Log [Pr (W)], then eqns. 11b and 11c can be rewritten as
(12a)
(12b)
Equations 12a and 12b indicate clearly that and increases linearly with slope equals 0.1 and 0.2, respectively.
(ii) The contribution of shot noise becomes higher than that of the thermal noise when the received optical power exceeds a certain level (denoted here by (Pr) cross-shot). This Pr level equals to 5 and -5 dBm for the parameters values used in the simulation and when RL =50 Ω and 550 Ω, respectively. Generally, according to eqns. 11a and 11b
(13)
(iii) The contribution of RIN noise becomes higher than the contribution of the thermal noise when the received optical power exceeds a certain level (Pr) cross-RIN which depends on the level of RIN of the used optical source. Using eqns. 11a and 11c yields the following expression
(14)
For the system under investigation, (Pr)cross-RIN equals -15, -10, -5, and 0 dBm for RIN = -130, -140, -150, and -160 dB/Hz, respectively when RL equals 550 Ω. For 50 Ω-receiver, (Pr)cross-RIN equals -10, -5, 0, and 5 dBm for RIN = -130, -140, -150, and -160 dB/Hz, respectively.
(iv) Both (Pr) cross-shot and (Pr) cross-RIN are independent of symbol and bit rates.
Figure 18. Noise characteristics of 112 Gbps 4-PAM receiver designed with 550Ω amplifier load resistance and for (a) RIN = -130 dB/Hz (b) RIN = -140 dB/Hz (c) RIN = -150 dB/Hz (d) RIN = -160 dB/Hz
The BER characteristics of the optical PAM receiver is calculated using eqn.7 for 4- and 8-PAM signaling and the results are displayed in Figures 19 and 20, respectively. The results are presented for three values of bit rate (56, 112, and 224 Gbps) and four values of RIN (-130, -140, -150, and -160 dB/Hz). From these figures, one can construct Tables 2 and 3 which reflect the minimum values of average received power required to maintain BER less than 10-8 and 10-10, respectively, for different system parameters. The minimum received optical power that yields the required BER level is called the receiver sensitivity. The mark (X) in these two tables denotes that this BER level cannot be reached.
Figure 19. BER characteristics of the of 4-PAM optical receiver for (a) RIN = -130 dB/Hz (b) RIN = -140 dB/Hz (c) RIN = -150 dB/Hz (d) RIN = -160 dB/Hz
Figure 20. BER characteristics of the 8-PAM optical receiver for (a) RIN = -130 dB/Hz (b) RIN = -140 dB/Hz (c) RIN = -150 dB/Hz (d) RIN = -160 dB/Hz
Table 2. Sensitivity of 1310 nm PAM receiver for BER =10-8. The mark “X” indicates that BER of 10-8 cannot be achieved under these conditions
     
Table 3. Sensitivity of 1310 nm PAM receiver for BER =10-10. The mark “X” indicates that BER of 10-10 cannot be achieved under these conditions
     
Note that at BER = 10-10 and RIN = -150 dB/Hz, the receiver sensitivity increases from -15.4 to -13.9 and -13.2 dBm when the Rb increases from 56 to 112 and 224 Gbps, respectively in the 4-PAM system. These values are to be compared with -12.4, -10.9, and -8.9 dBm receiver sensitivity, respectively, for the 8-PAM system. Note further that increasing the RIN level may lead to BER-floor characteristics where the required BER cannot be achieved by increasing the received optical power. For example, the 4-PAM modulation does not yield a 10-8 BER for 112 and 224 Gbps bit rates when the RIN = -130 dB/Hz. The effect of RIN is more pronounced for the 8-PAM modulation. At RIN = -130 dB/Hz, the 10-8 BER cannot be achieved for the three values of bit rate used in the simulation.

3.3. BER-Floor Characteristics

The analysis is extended to address the BER-floor characteristics of the PAM receiver. It is clear from eqns. 7, 10 and 11, that the BER will saturate at certain level independent of received optical power Pr when the argument of the erfc in eqn.7 approaches a constant value independent of Pr. This occurs when the RIN noise dominates the receive noise. In this case . From eqn.7, the BERfloor can be estimated as
(15)
Equation 15 states that BERfloor increases with increasing bit rate and RIN level. This is demonstrated in Figures 21a and 21b where the BERfloor is calculated as a function of RIN for 4- and 8-PAM systems, respectively. To achieve a BER-floor less than 10-10 in the 4-PAM receiver, the RIN should be less than -125, -130 and -135 dB/Hz for Rb = 56, 112 and 224 Gbps, respectively. These values are to be compared with RIN = -125, -130 and -135 dB/Hz, respectively, when 8-PAM modulation is used.
Figure 21. BER-floor as a function of RIN for (a) 4-PAM (b) 8-PAM
The calculations are carried further to deduce the power penalty, PenRIN, due to the effect of using a laser source with non-negligible RIN. The penalty is defined as
(16a)
or
(16b)
where the subscripts RIN and ideal are used to characterize a semiconductor laser having a finite RIN level and negligible RIN level, respectively. Table 4 lists the power penal-ty estimated at BER = 10-8 for both 4- and 8-PAM signaling.
Table 4. Power Penalty for BER = 10-10. The mark “X” indicates that BER of 10-10 cannot be achieved under these conditions
     

4. Conclusions

The noise characteristics and transmission performance of unamplified 1310 nm-optical link incorporating multilevel PAM signaling have been investigated when either DML or EML is used. Simulation results are presented for 56, 112, and 224 Gbps bit rates when 4- and 8-PAM are used without PDM technique. Applying PDM doubles the transmission bit rate of the EML-based link without affecting its maximum distance. The simulation results reveal that using unamplified link based on 1310 nm SMF and supported by IM/DD scheme will offer robust and low-cost interconnect for data center which does not require dispersion-compensation scheme. For 0 dBm launch power, the maximum reach is 49, 45, and 40 km when 4-PAM link is used with bit rate 56, 112, and 224 Gbps, respectively, when PDM technique is not used. These values are to be compared with 42, 37, and 28 km, respectively, when 8-PAM is used. Further, a PDM 4-PAM system can support maximum reach of 45 and 39 km at 0 dBm laser power with 224 and 448 Gbps bit rate, respectively. The BER-floor characteristics of the PAM link has been also investigated analytically to address the effect of system parameters such as bit rate and RIN of the transmitter laser source. The investigation indicates that to achieve a BERfloor less than 10-10 in the 4-PAM receiver, the RIN should be less than -125, -130 and -135 dB/Hz for Rb = 56, 112 and 224 Gbps, respectively. These values are to be compared with RIN = -125, -130 and -135 dB/Hz, respectively, when 8-PAM modulation is used.

Appendix

Noise Components of 112Gbps 4-PAM Receiver Designed with 50Ω Loads Resistance
Figure 22. Noise characteristics of 112 Gbps 4-PAM receiver designed with 50Ω amplifier load resistance and for (a) RIN = -130 dB/Hz (b) RIN = -140 dB/Hz (c) RIN = -150 dB/Hz (d) RIN = -160 dB/Hz

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