1. Introduction

The incessantly growing capacity demand in optical transport has been spurring extensive research efforts in the realm of coherent optical technology [1–10]. One key enabling component of this technology is the coherent optical receiver (CRx) that linearly maps the in-phase (I) and quadrature (Q) components of the received light in both orthogonal polarizations into the electrical domain by beating the received field with that of a local oscillator (LO) laser [1]. In addition, a CRx offers higher sensitivity compared to direct-detection [2] and enables the exploitation of M-ary quadrature amplitude modulation (M-QAM) formats consequently providing the needed larger spectral efficiency [2,3]. When incorporated with high speed analog-to-digital converters (ADCs), it also enables mitigating transmission impairments as well as compensating for hardware imperfections using digital signal processing (DSP) [1,5,6].

By incorporating coherent technology along with frequency division multiplexing (FDM) on multiple optical carriers, up to 400G coherent transceivers have been recently commercialized [7]. However, it still remains a challenge to meet the relentless growing network traffic demand [11]. Technological solutions such as space division multiplexing (SDM) that utilizes multiple fiber modes / cores have the potential to multiply the capacity per fiber [8]. Although being heavily investigated throughout the research community, SDM requires a potential replacement of the field installed fiber and developing novel enabling components. This may hinder near future field deployments of SDM. Another promising technological solution that is probably more suited for the near future is the concept of an agile/flexible software-defined optical network [9,10]. In the envisioned agile network, flexible coherent transceivers, that are capable of adapting to dynamic traffic needs and thus maximizing the network capacity, are key elements that need to be deployed at ingress/egress nodes. These flexible transceivers need to be smart, data-rate and modulation format agile and impairment aware/tolerant. In addition, the notion of agility necessitates the ability of the transceiver to transmit / receive at any optical frequency in order to adapt to the dynamic nature of the network. Since external cavity lasers (ECLs) fully tunable over the C or L band are commercially available [12], they can be incorporated as transmitter and LO lasers and hence, in principle, enable the transceiver to operate at any wavelength. At the transmitter side, tuning the laser simply varies the transmission wavelength without any observable change in the transmitted signal quality provided that the electro-optics performs similarly across the tuning range. However on the receiver side, the situation is more complex. A CRx can in principle operate in a colorless fashion by utilizing the LO laser for channel selection. Such a scheme mandates removing the DEMUX filter before the receiver which is beneficial on one hand as it reduces cost and footprint besides offering the desired transceiver flexibility, but on the other hand, it may degrade the performance depending on various parameters e.g., the number of channels co-incident at the receiver with the channel of interest, the LO power, etc. Colorless reception in the context of coherent optical communication was studied from a theoretical standpoint more than two decades ago [13]; however, the absence of commercial narrow linewidth lasers and high speed integrated circuits (ICs) prevented any practical implementation. Recently, there have been some reports on experimental colorless coherent reception by utilizing either a conventional CRx front-end followed by single-ended detection [14], which suffers from limited maximum channel count and poor dynamic range due to the inability to reject the self-beat common mode noise, or a more complicated receiver front-end followed by single-ended detection to enable rejecting the self-beat noise [15]. Later in [16], Zhang et al. presented design guidelines and performance limits of colorless reception employing balanced detection based on simulation and analytical predictions. More recently in [17], the authors demonstrated experimentally the use of an integrated PLC-based balanced coherent receiver for colorless reception of one 100G channel among 80 WDM channels.

The recent tremendous progress of the photonic integration technology allows for cost effective and volume production of coherent receivers employing balanced photodetectors which are more suited for colorless operation. Recently, integrated dual-polarization phase-diversity balanced coherent receiver photonic integrated circuits (PICs) have been demonstrated in both Si [18,19] and InP [20,21]. Si has advantages over InP as a host material since it can be made into larger wafers allowing for lower cost chips [22]. In addition, the world of analog ICs now offers linear and differential transimpedance amplifiers (TIAs) with variable gain control and bandwidths commensurate with the baud rates at which a coherent transceiver operates. Recently, researchers reported TIAs packaged and wire bonded to the PIC in one module [19,20,23]. The TIAs enhance the receiver dynamic range and provide the target voltage swing required by the analog-to-digital converters (ADCs). In addition, TIAs accompanied with the high sensitivity of coherent reception potentially enable preamplifierless operation in which the optical preamplifier prior to the receiver is removed and essentially replaced by the electrical TIAs thus saving footprint and power consumption. Recently in our work in [24], we evaluated the sensitivity limits of the Si-photonic integrated balanced CRx presented in [19] when employed in colorless and preamplifierless reception of single channel 112 Gbps PDM-QPSK and 224 Gbps PDM-16QAM. Also, we have shown preliminary results of colorless reception of 16 × 112 Gbps PDM-QPSK WDM channels.

In this paper, we extend our work in [24] and study from theoretical and experimental standpoints the performance limits of the Si-photonic CRx when employed in a WDM colorless configuration. Firstly, we show the building blocks and introduce the key characterization results of the CRx assembly. Secondly, we develop rigorously an analytical expression of the SNR at the CRx output in the case of colorless reception taking into consideration all sources of noise namely, LO-ON, SIG-SIG, SIG-ON, ON-ON and LO-LO beatings as well as the receiver shot and thermal noises, where SIG stands for signal and ON stands for optical noise incoming with the signal. As will be later explained in details, the ON incoming with the signal contains contributions of both the amplified spontaneous emission (ASE) noise from in-line optical amplifiers and the fiber nonlinearity (NL) induced noise, which can be both modeled, according to [25–27], as additive white Gaussian noise (AWGN) in the context of dispersion unmanaged transmission (UT). Compared to [16] where an analytical SNR expression was also given, the derivation performed in this manuscript, which is based on evaluating the autocorrelation functions and the power spectral densities of all terms in the differential photocurrent, is more rigorous. In addition, we propose an analytical expression for an effective common mode rejection ratio (CMRR) for the SIG-SIG beating term which takes into account the frequency dependent nature of the power imbalance and the skew mismatch between the P and N photodiodes of the CRx weighted by the power spectral density of the received signal intensity. This parameter was only arbitrarily defined in [16]. Furthermore, another distinguishing difference from the model in [16] is the inclusion of the impact of fiber nonlinearity as excess AWGN in addition to the conventional ASE noise from in-line EDFAs. Thirdly, we study experimentally the performance of the CRx in a fully colorless and preamplifierless reception of 16 × 112 Gbps PDM-QPSK WDM channels. Using a maximum LO power of 15.5 dBm, we evaluate the BER of each channel at various transmission distances at received signal powers of −3 and −21dBm per channel. Next, we restrict our measurements to one of the center channels of the WDM spectrum and perform an extensive set of measurements where we sweep the LO power, the received signal power, the distance and the number of channels presented to the CRx. This set of measurements aims at evaluating the performance limits of the CRx when used for colorless reception. All trends observed in the experimental results match those expected from simulations in [16]. In fact, results reveal that in the regime of high received signal power, the residual SIG-SIG beat noise from the out-of-band (OOB) channels degrades the performance especially for lower LO to signal power ratios and this degradation becomes relatively less pronounced as the transmission distance increases. In the regime of low received signal power, the shot noise and receiver thermal noise degrade the performance especially for very low LO powers and short transmission distances. Two key CRx specifications that dictate the achievable dynamic operating range are highlighted namely the responsivity and the CMRR, which impact the performance in the regimes of low and high received signal powers, respectively. Finally, we employ our experimental SNR results to fit the proposed analytical model to our experimental data using the least-squares criterion. An excellent match between experimental and analytical SNRs is found. We finally use the model to extrapolate the SNR curves beyond our experimental capabilities and predict the SNR when the number of channels is larger than 16. We conclude that the CRx allows for colorless selection of the test channel out of a fully populated WDM spectrum with 80 channels while achieving error-free operation after 4800 km transmission provided that the LO and received signal powers are properly set.

This paper is organized as follows. In section 2, the architecture of the SiP CRx assembly is presented and the main device-level characterization results are introduced. Section 3, supported by derivations in appendices A and B and the list of mathematical symbols used in Table 1, presents an analytical model for the SNR at the output of the CRx where various noise sources that impact the SNR in a colorless reception scheme are outlined. In section 4, we depict the system-level WDM experimental results obtained using the CRx on 16 × 112 Gbps PDM-QPSK channels where the impact of LO power, received signal power, number of channels and transmission distance on the performance of colorless reception are studied experimentally and compared to theory presented in section 3. Finally, concluding remarks are given in section 5.

Table 1. List of Symbols and Notation

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2. Si-photonic integrated balanced coherent receiver design and characterization

The coherent receiver is based on silicon photonics (SiP) technology which enables a very compact design. Figure 1(a) gives a view of the assembly. Strip waveguides of 220 nm (height) × 500 nm (width) are used to convey the light in the optical chip. A single-mode and a PM fiber whose end facets are polished at an angle close to 45° are used to couple the light from the data-carrying signal and LO respectively into the SiP chip. Polarization diversity is obtained via a 2D surface grating that couples orthogonal linear polarization states from the data-carrying signal in two separate waveguides. For the LO, a 1D grating coupler is used, followed by a 1 × 2 multimode interference (MMI) splitter. The light from each polarization of the incoming signal is combined to the light from the split LO using 2 × 4 MMI couplers. The light from the two 2 × 4 MMI couplers is coupled out of the chip using eight 1D grating coupler and sent to two 1 × 4 photodiode arrays which are flip chip mounted onto the 6 mm × 6 mm SiP chip. The photodiodes are used in balanced pairs and connected to TIAs. The SiP chip and TIAs are fixed onto a ceramic substrate. RF lines connect the AC-coupled differential outputs of the TIAs to eight pins on the CRx package in a GSGSG configuration. For the sake of the present experiments, an RF interface board is used to provide access to a set of four single-ended outputs (XI⁺, XQ⁺, YI⁺ and YQ⁺) on K connectors. The assembled CRx presents a small-signal bandwidth of 22 GHz and a quadrature error of less than 3°. The effective responsivity at 192.9 THz averaged over all 8 photodiodes (PDs) is 0.025 and 0.029 A/W for the SIG and LO ports, respectively. These effective responsivities include (besides the PD responsivities) the 3 dB intrinsic loss of the polarization beam splitter (PBS) and the 6 dB intrinsic loss of the 2 × 4 MMI coupler in addition to their excess loss as well as coupling losses in and out of the SiP chip. Figure 1(b) shows the overall small signal frequency response including the photodiodes, the TIA and the RF lines on the ceramic. The overshoot in the response is due to the TIA. Finally, Figs. 2(a) and 2(b) show the CMRR versus frequency curves for the LO and SIG ports, respectively measured at the four output ports at 192.9 THz according to the procedure described in [28]. We notice that the CRx provides a DC CMRR better than −14 and −18 dBe for the LO and SIG ports, respectively.

 

Fig. 1 (a) Picture of the PIC of the CRx showing the main buliding blocks, (b) Overall frequency response of the Si-photonic CRx assembly.

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Fig. 2 CMRR versus frequency curves measured at 192.9 THz at the four output RF ports of the CRx when light is applied at the (a) signal port, (b) LO port.

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3. Theoretical performance evaluation of a colorless coherent receiver

After laying out the CRx chip architecture, the performance of the CRx when employed for colorless coherent reception is evaluated analytically in this section. We present the various noise sources that dictate the performance of colorless CRx operation, highlighting the key CRx specifications that impact the performance. An analytical expression for the SNR at the CRx output is developed. The SNR analytical model derived will be employed later in the manuscript to verify the experimental results presented in forthcoming sections.

Although an analytical SNR expression for the colorless scenario when employing coherent balanced detection has been presented in [16], a more rigorous and complete approach is adopted in this manuscript. Without loss of generality, we consider one of the four CRx output ports {XI,XQ,YI,YQ} and derive an expression of the autocorrelation function (ACF) (and then the power spectral density PSD) of the differential photocurrent after imperfect balanced detection. The desired signal term as well as various noise terms in the final differential photocurrent are identified and their respective ACFs (and PSDs) are derived methodically in terms of input fields to the CRx. Compared to [16], the expressions we obtain hereafter are more complete and the systematic approach adopted throughout the derivation leads to an expression for an “effective CMRR” which is a system parameter that quantifies the ability of balanced detection to reject the SIG-SIG beating, taking into account the frequency dependent nature of the power imbalance and the skew mismatch between the P and N photodiodes of the CRx weighted by the PSD of the received signal intensity. This quantity termed “effective CMRR” was proposed and only arbitrarily defined in [16]. Furthermore, another distinguishing difference from the work in [16] is that the optical noise incoming with the received signal assumed in our model contains the impact of not only the ASE noise from in-line EDFAs but also the induced noise due to fiber nonlinearity where both noise sources can be modeled as AWGN in the context of dispersion unmanaged transmission [25–27].

The procedure used to derive the ACFs and PSDs for various terms in the differential photocurrent follows the one outlined in [29]. We start by writing the photocurrents at the outputs of the P and N photodiodes (PDs), denoted by $i^P\left(t\right)$ and $i^N\left(t\right)$, in terms of the real electric fields of the signal (all WDM channels and their accompanying optical noise) and LO as

Similar to [29], we express the real-valued fields in Eqs. (1) and (2) in terms of baseband complex envelops (denoted by boldface symbols throughout the manuscript) as

In case of ideal balanced detection, i.e. $R_{SIG,i}^P=R_{SIG,i}^N$, $R_{LO,s}^P=R_{LO,s}^N$, $h^P\left(t\right)=h^N\left(t\right)$ and $\delta =0$, the SIG-SIG, ON-ON, SIG-ON and LO-LO noise terms in Eq. (7) cancel out since these terms are common to both the P and N PDs and will be entirely rejected. In this case, the LO-ON beating as well as the thermal and shot noises become the only noise sources contributing to the final differential photocurrent. However in reality, imperfect balanced detection due to frequency dependent power imbalance and skew mismatch between the P and N photocurrents will lead to residual noise power due to imperfect common mode rejection. For the rest of the derivation, we assume imperfect balanced detection and derive the time-averaged ACF of $\Delta i\left(t\right)$ in Eq. (7), which is denoted by ${\overline{\Gamma }}_{\Delta i}\left(\tau \right)$, as follows

Using Eq. (9), we can evaluate the SNR achieved after offline DSP if we assume that the receiver side DSP will mitigate transmission impairments by employing various algorithms, some of which involving filtering of the final sampled photocurrent. If we assume only linear equalization within the DSP, i.e. no NL mitigation algorithms, and lump all filtering performed in DSP in the transfer function $H_{rx-DSP}\left(f\right)$, one can calculate the final SNR after DSP as the total power of the useful LO-SIG term after DSP filtering divided by the total AC power from various noise sources after filtering, which yields

Also, the scaling factor $\beta$ is defined in appendix A as the ratio between the AC power from the filtered photocurrent generated by the field intensity of one channel and its DC electrical power. In appendix B, a more thorough study of $\beta$ is performed to assess its dependence on the residual chromatic dispersion (CD) and polarization orientation of the received signal. It should be noted that Eq. (11) was proved by considering only one of the four outputs provided by the CRx; however, the derived SNR expression has the same form for all ports except for using the parameters of each port, e.g. responsivities and frequency responses. Hence, an overall average SNR can be calculated by averaging the SNRs calculated at the four ports.

The quantity ${\overline{CMRR}}_{SIG}$ denotes the so-called “effective CMRR” of the SIG-SIG beating which is a system parameter (not a CRx parameter) that quantifies the ability of imperfect balanced detection to reject the common-mode SIG-SIG beating while taking into account the CRx parameters, namely, the effective responsivities, frequency responses and time skew for the P and N paths up to current subtraction inside the TIAs, as well as the system parameters, namely, the residual CD, polarization orientation and pulse shape which are imbedded in the PSD of the intensity $S_{{\left|{\tilde{E}}_{SIG}\right|}^2}^{AC}\left(f\right)$ (see Eq. (40) in appendix A). In fact, the effective CMRR definition given above contains the quantity ${\left|H^P\left(f\right)R_{SIG}^P-H^N\left(f\right)e^{j2\pi f\delta }{R}_{SIG}^N\right|}^2$ which quantifies the CRx ability to reject the common mode SIG-SIG beating incoming from the SIG port. Since this rejection ability is frequency dependent, the effective CMRR expression also weighs this quantity using the PSD of the common mode quantity being rejected, i.e. the field intensity, as represented by $S_{{\left|{\tilde{E}}_{SIG}\right|}^2}^{AC}\left(f\right)$ in the ${\overline{CMRR}}_{SIG}$expression. Dividing by the denominator in the effective CMRR expression means that ${\overline{CMRR}}_{SIG}$ is a measure of how strong the power of the residual common mode SIG-SIG beating is compared to that of the differential LO-SIG beating. This explains why the denominator is proportional to the product of responsivities of the SIG and LO ports whereas the numerator is proportional to the square of the responsivity of the SIG port. Finally, we should note that the above expression for the effective CMRR was obtained in a systematic and rigorous manner in the derivation included in appendix A. This differs from [16] where the authors proposed the interesting concept of an effective CMRR, being a single averaged value applied to the common mode beating and defined quite arbitrarily as the CMRR value at half the Nyquist frequency.

4. WDM experiment, results and discussion

In this section, we evaluate experimentally the system-level performance of the SiP CRx module whose chip architecture was described in section 2. First, we introduce the experimental setup used to assess the CRx performance using 16 × 112 Gbps PDM-QPSK WDM channels. Subsequently, we present the experimental results, starting with the BER for all 16 channels at different distances and received signal powers. Afterwards, we present a series of extensive measurements obtained for one of the center WDM channels where the LO power, received signal power, distance, and number of channels presented to the CRx are swept. A thorough discussion of the results is given, focusing on the major noise sources affecting the performance of the colorless operation of the CRx for different operating parameters in view of the analytical SNR expression derived in section 3. Finally, we use the experimental SNR data to fit the analytical SNR expression derived in section 3. The fitted SNR model is then used to predict the SNR at other operating parameters beyond our experimental capabilities, e.g. larger number of WDM channels.

4.1. Experimental setup

Figure 3 shows the experimental setup used in various WDM measurements presented in the following subsections. CW light from 16 distributed feedback (DFB) lasers (50 GHz spaced and centered at 192.9 THz) are multiplexed using a 50 GHz arrayed waveguide grating WDM multiplexer and then bulk modulated by means of a QAM transmitter. The QAM transmitter comprises a single polarization LiNbO₃ double-nested Mach-Zehnder modulator and two high-speed RF amplifiers to drive the two quadratures. Binary I and Q electrical signals are fed to the QAM transmitter from two MICRAM DACs driven by two Xilinx FPGAs at 28 Gbaud to realize 16 × 112 Gbps PDM-QPSK WDM channels on a 50 GHz grid. Then, a polarization beam splitter (PBS), variable optical delay line (VODL) and polarization beam combiner (PBC) are employed for PDM emulation with a decorrelation delay between the two orthogonal polarizations equivalent to 700 symbols at 28 Gbaud. After optical amplification, odd and even WDM channels are decorrelated by ~7.5 ns using a 50 GHz interleaver / de-interleaver. The resulting optical signal was attenuated using a variable optical attenuator (VOA) to set the launch power at −2 dBm per channel which was experimentally found to be the optimum launch power that achieves the right balance between fiber nonlinearity and ASE noise from in-line EDFAs. At this launch power, which was kept constant throughout the experiment, both ASE and NL-induced noises are non-negligible and hence, they were both included in the SNR model presented in section 3. Next, the resulting signal was launched into a recirculating loop containing four spans of 80 km of SMF-28e⁺ fiber, each span being followed by an erbium-doped fiber amplifier (EDFA) having a noise figure of 5 dB. In addition, an optical WaveShaper from Finisar is inserted after the second in-line EDFA for gain flattening.

 

Fig. 3 Experimental setup for WDM experiments, (IL: Interleaver, DFB laser: Distributed Feedback laser, AWG: Arrayed Waveguide Grating, PBS: Polarization Beam Splitter, PBC: Polarization Beam Combiner, VODL: Variable Optical Delay Line, ECL: External Cavity Laser, OSA: Optical Spectrum Analyzer, VOA: Variable Optical Attenuator).

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At the output of the loop, no noise loading is performed hence the OSNR is only dictated by the ASE noise from in-line EDFAs around the loop as well as the fiber NL-induced noise. We used a 99:1 coupler to monitor the WDM spectrum on an optical spectrum analyzer (OSA) and to measure the OSNR. After 1600, 3200 and 4800 km of transmission, i.e. 5, 10 and 15 loops respectively, the measured OSNRs, assuming a 0.1 nm reference bandwidth, were 21.4, 18.9 and 17.6 dB, respectively. After the 99:1 coupler, we distinguish between two reception configurations: 1) a fully colorless configuration in which the attenuated signal carrying all 16 channels is fed directly to the signal port of the CRx module at a total power level P_SIG,tot ( = N_chP_SIG) controlled by the VOA, i.e. elements in the grey shaded box are skipped, 2) another configuration in which the WDM signal is first amplified to a constant total power of 22 dBm, subsequently filtered using a wavelength & bandwidth tunable filter, and then attenuated using a VOA to set the total received power level (P_SIG,tot) before finally entering the CRx, i.e. elements in the grey shaded box are employed. Inserting the EDFA prior to the CRx allows us to sweep P_SIG,tot, and subsequently the received power per channel (P_SIG), to levels larger than the received power from the loop. As will be observed in the next subsection, the sweep range of P_SIG extends up to 5 dBm per channel in order to evaluate the impact of colorless reception on the dynamic range of the CRx. After the EDFA, the wavelength & bandwidth tunable filter had its center frequency constantly set to that of channel 9 (with channel 1 having the smallest frequency) and its bandwidth swept to vary the number of channels presented to the CRx denoted by N_ch. Using this filter, we can vary N_ch between 1 and 16, where the extreme cases correspond to fully filtered and fully colorless reception schemes, respectively.

In reception configuration (1), the frequency of the LO laser is swept to the center frequency of the channel desired to be selected out of the 16 available channels. However in configuration (2), the LO frequency is constantly set to channel 9 (channel of interest in this configuration) and the bandwidth of the tunable filter is set to control the number of out-of-band (OOB) WDM neighbors (N_ch - 1) co-incident on the CRx with channel 9. In both configurations, the VOA sets the received power level per channel (P_SIG) as desired prior to the CRx. At all received power levels, the voltage swing provided by the TIAs at the output of the CRx is maintained at a constant 320 mVpp (single-ended). Finally, the four electrical signals are sampled at 80 GSa/s using one Agilent DSOX96204Q real-time scope and stored for offline processing using a myriad of standard DSP algorithms to mitigate various impairments.

Offline processing starts by IQ power imbalance compensation and quadrature error correction using Gram-Schmidt orthogonalization, resampling to 2 samples per symbol, chromatic dispersion (CD) compensation in the frequency domain [1,5,6] and frequency offset removal using the periodogram method [32]. Polarization is then demultiplexed using a 31-tap butterfly equalizer whose taps are updated using the constant modulus algorithm (CMA) with a step size of 1 × 10⁻³ [1]. Phase noise was mitigated by a decision-directed phase locked loop (DD-PLL) [33]. After hard decision on a symbol-by-symbol basis, the achieved electrical SNR was evaluated and BER was finally calculated.

4.2 Experimental results and discussion

In this subsection, we present all experimental results obtained using the setup depicted in Fig. 3. In subsection 4.2.1, we show the results of reception configuration (1) in which fully colorless and preamplifierless strategy is employed. Next, subsection 4.2.2 presents all results collected on channel 9 employing reception configuration (2) where the EDFA and the tunable wavelength & bandwidth filter in the grey shaded box in Fig. 3 are inserted prior to the CRx. Using this configuration, various operating parameters such as the received signal power per channel (P_SIG), LO power (P_LO), number of channels (N_ch) incident on the CRx, and distance (L) are swept. Results collected from channel 9 include the SNR measured after offline DSP while sweeping the aforementioned parameters to evaluate the impact of each parameter on the performance of colorless CRx operation and to identify the dynamic range of the CRx for various number of channels. Based on the results, we also identify the key specifications of the CRx that are crucial for colorless operation. In subsection 4.2.3, we use the experimental SNR data at various operating parameters to fit the analytical SNR expression derived in section 3. The fitted SNR model is then used to predict the SNR at other operating parameters beyond our experimental capabilities, e.g. larger N_ch.

4.2.1 Configuration (1): BER for all channels at various distances using fully colorless and preamplifierless reception at either −3 dBm/ch or −21 dBm/ch

BERs of all 16 WDM channels were calculated and are plotted in Fig. 4 for 3200, 4480 and 4800 km transmission at two different P_SIG (−3 and −21 dBm per channel). All results in Fig. 4 are collected in the fully colorless and preamplifierless reception termed above by reception configuration (1). The LO power (P_LO) was set to 15.5 dBm and its frequency was tuned to select each one of the 16 channels before data was acquired. Insets at the right of Fig. 4 also show the WDM spectra in back-to-back and after 3200 km transmission obtained using a 0.05 nm resolution bandwidth on the OSA. Throughout the manuscript, we assume 3.8 × 10⁻³ forward error correction (FEC) threshold, which is typical for the hard-decision FEC algorithm with 7% overhead defined in [34]. Then, if we carefully examine the BERs of all 16 channels, we can claim a 4800 km reach for all channels at P_SIG of −3 dBm which slightly decreases to 4160 km at −21 dBm per channel. As will be explained in upcoming subsections, the good performance (reach) achieved by the CRx for fully colorless and preamplfierless reception with very low received signal power of −21 dBm per channel is enabled by moderate CMRR and responsivity possessed by the CRx.

 

Fig. 4 BER for all WDM channels using fully colorless and preamplifierless reception at different transmission distances and at per channel received signal power of −3 and −21 dBm. Insets show the received WDM spectra in back-to-back and after 3200 km transmission where we observe a fairly flat spectrum due to the gain flattening waveshaper in the loop.

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4.2.2 Configuration (2): SNR of channel 9 when using a varying number of channels

Having evaluated the CRx colorless / preampliferless operation for each channel across the spectrum, we now focus on channel 9 specifically. All measurements on channel 9 presented in the upcoming subsections, which involve sweeping various experimental parameters such as P_LO, P_SIG, N_ch and L, will use the SNR calculated after offline DSP instead of BER as the performance metric. The reason for using SNRs instead of BERs is that SNRs allow us to assess the performance quantitatively in back-to-back and short transmission distance scenarios when BERs are usually below 10⁻⁵. Evaluating BERs in this low-error regime would require acquiring and storing a number of symbols exceeding the memory of the real-time scope used. Also, later in this section, utilizing the experimental SNRs allows us to perform direct comparison with analytically predicted SNRs based on the derived SNR expression in section 3.

Figure 5 shows the relationship between experimentally evaluated BER and SNR for channel 9. In Fig. 5(a), we plot the calculated BER on a double log scale versus the transmission distance whereas Fig. 5(b) shows the corresponding SNR evaluated at these distances. Using both curves, we plot in Fig. 5(c) the BER versus SNR relationship found experimentally. We find that a 9.2 dB SNR corresponds to the 3.8 × 10⁻³ FEC threshold which is 0.67 dB higher than the theoretical SNR of 8.53 dB at this BER level for 28 Gbaud QPSK assuming an ideal additive white Gaussian noise (AWGN) channel [35]. By means of Fig. 5(c), all SNR results that will be presented in the forthcoming subsections can be mapped into BER values in a straightforward manner.

 

Fig. 5 Measurement results of channel 9: (a) BER versus transmission distance, (b) SNR evaluated after offline DSP versus distance, (c) BER versus SNR using both experimental results and theory where the experimental SNR corresponding to FEC threshold is marked.

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4.2.2.1 Impact of received signal power and number of channels presented to the CRx on the SNR of channel 9 at various distances and LO powers

From this point forward, the entire measurements are performed only for channel 9 in the WDM spectrum. In Figs. 6(a)–6(f), we show the SNR versus P_SIG at different LO powers of 15.5, 12, 9, 6, 3 and 0 dBm, respectively. In each subplot, we plot the SNR curves with different colors corresponding to various number of channels (N_ch) presented to the CRx where N_ch is set to either 1, 5, 11 or 16 channels, ranging from fully filtered to colorless reception respectively. Also in each subplot, SNR curves measured at various transmission distances of 0, 1600, 3200 and 4800 km are plotted together where the top group of four curves always corresponds to the back-to-back case whereas the bottom set of curves represents the 4800 km transmission case. By examining Figs. 6(a)–6(f), we notice that the sweep range of P_SIG starts at −24 dBm for P_LO = 15.5 and 12 dBm (see Figs. 6(a) and 6(b)), whereas for P_LO = 9, 6, 3 and 0 dBm the sweep range of P_SIG had to be reduced to start at −21, −18, −15 and −12 dBm, respectively (see Figs. 6(c)–6(f))). The reason for increasing the lower end of the P_SIG sweep range for P_LO ≤ 9 dBm is to be able to achieve the fixed target voltage swing of 320 mVpp after the TIAs at the CRx output. For that reason, at each P_LO ≤ 9 dBm, the minimal value of the P_SIG sweep range was fixed to the least power level at which the TIAs could provide the 320 mVpp target swing when their respective gain was set to maximum (5 kΩ differential transimpedance Z_t). Since for a fixed target voltage swing, the required Z_t for the TIAs is proportional to $\sqrt{P_{LO}{P}_{SIG}}$, we notice in Figs. 6(c)–6(f) that as P_LO is decreased by 3 dB going from one subfigure to the next, the starting point of the P_SIG sweep range (at maximum Z_t) increases by 3 dB supporting the above proportionality.

 

Fig. 6 SNR of channel 9 versus received signal power per channel P_SIG after 0, 1600, 3200 and 4800 km transmission with varying number of channels presented to the CRx at an LO power of: (a) 15.5 dBm, (b) 12 dBm, (c) 9 dBm, (d) 6 dBm, (e) 3 dBm, (f) 0 dBm. In each subfigure, different colors represent different number of channels N_ch according to the legend. Also, SNR evaluated after 0, 1600, 3200 and 4800 km transmission are shown in each subfigure where the top set of four curves in each subfigure is evaluated in back-to-back and the bottom set is after 4800 km transmission.

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Looking at the SNR variation with P_SIG throughout Figs. 6(a)–6(f), we notice that regardless of P_LO, L and N_ch, the SNR improves as P_SIG is increased to an extent after which the SNR starts to decrease if P_SIG is further increased. This means that an optimum P_SIG exists for each P_LO, L, and N_ch. Furthermore, if a certain target required SNR at a certain P_LO, L and N_ch is to be achieved, one can specify a dynamic range for P_SIG within which the target SNR is at least guaranteed. It is noticeable that the dynamic range of P_SIG at a given L and P_LO decreases as N_ch is increased from 1 to 16 showing the impact of colorless reception. Finally, the dynamic range of P_SIG at a given L and N_ch is also found to decrease when P_LO is decreased.

The two reasons for the SNR degradation at the low and high ends of P_SIG are distinct. At high received signal power (P_SIG ~0 dBm), the SNR degradation observed with a further increase of P_SIG is due to the residual SIG-SIG beat noise which is expressed by the last term in the denominator of Eq. (11). This SIG-SIG beat noise is proportional to N_chP_SIG² which explains why the SNR degrades as P_SIG is increased and why this degradation is more pronounced as more channels are presented to the CRx. In fact, we can re-write Eq. (11) by neglecting the thermal and shot noises at high P_SIG and dividing by P_LOP_SIG, which yields

where LSR is the LO to signal power ratio at the CRx input. We can see from Eq. (12) that for a fixed OSNR, i.e. fixed distance, the SNR depends on the effective CMRR defined in section 3, N_ch and LSR. If more channels are introduced to the CRx, the SNR degrades due to larger SIG-SIG beating from the OOB neighbors. Also, the impact of the SIG-SIG beat noise can be greatly reduced if high enough LSR is employed, which is also apparent in Fig. 6 by observing the impact of P_LO on the SNR difference between the cases of N_ch = 1 and N_ch = 16, i.e. the SNR penalty due to colorless reception compared to filtered reception denoted by ΔSNR_1,16, at a given L and at P_SIG = 0 dBm.

Since we are now interested in the high end of P_SIG and studying the impact of N_ch on SNR, we re-plot in Fig. 7 a portion of the results shown in Fig. 6 by focusing only on the SNR at P_SIG = 0 dBm. Figures 7(a)–7(f) show the SNR after 0, 1600, 3200 and 4800 km transmission versus N_ch at LO powers from 15.5 dBm down to 0 dBm, all at P_SIG = 0 dBm. This exactly corresponds to LSRs ranging from 15.5 dB to 0 dB. By examining Fig. 7 carefully, we notice that for LSR ≥ 9 dB, i.e. P_LO ≥ 9 dBm, ΔSNR_1,16 in Figs. 7(a)–7(c) is found to be < 1.2 dB at any of the various distances travelled, which is a reasonably small degradation given the transceiver flexibility and hardware savings gained in an entirely colorless reception scheme. In fact, this 1.2 dB SNR penalty due to colorless reception is only pronounced in back-to-back at P_LO = 9 dBm whereas ΔSNR_1,16 is less after transmission. This can be explained in light of the approximate SNR expression in Eq. (12) by noting that the OSNR decreases as L increases and hence the SIG-SIG beat term becomes less significant relative to the first term. On the other hand for LSR < 9 dB, ΔSNR_1,16 in Figs. 7(d)–7(f) increases significantly where it becomes most apparent in Fig. 7(f) when LSR = 0 dB. In view of Eq. (12), it should be finally noted that the SNR degradation due to colorless reception can be greatly reduced by developing coherent receivers with improved CMRRs which results in a better rejection for the SIG-SIG beating from the OOB channels.

 

Fig. 7 SNR of channel 9 versus N_ch at P_SIG = 0 dBm after 0, 1600, 3200 and 4800 km transmission at P_LO of (a) 15.5 dBm, (b) 12 dBm, (c) 9 dBm, (d) 6 dBm, (e) 3 dBm, (f) 0 dBm.

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Looking back at Fig. 6 for low received signal powers (P_SIG ≤ −12 dBm), we notice that the SNR degrades quickly as P_SIG decreases and that the SNR is independent of N_ch. Referring back to the general SNR expression in Eq. (11), we re-write the expression by neglecting the SIG-SIG beat term for low P_SIG and dividing by P_SIGP_LO, which yields

 

Fig. 8 SNR of channel 9 versus N_ch at P_SIG = −12 dBm after 0, 1600, 3200 and 4800 km transmission at P_LO of (a) 15.5 dBm, (b) 12 dBm, (c) 9 dBm, (d) 6 dBm, (e) 3 dBm, (f) 0 dBm.

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Finally, it should be also noted that the CRx responsivity is a key specification in this low P_SIG regime because according to Eq. (13) if all parameters stay the same while R_SIG and R_LO are increased, the SNR will consequently increase (note that $c_2\propto {\left(R_{SIG}{R}_{LO}\right)}^{-1}$). Physically speaking, larger responsivities translate into larger photocurrents from the PDs relative to the fundamental CRx noise. Although the CRx used in our experiments possess a moderate responsivity due to relatively high coupling losses into the SiP chip, it still allows for good performance at low P_SIG. For example when P_LO = 12 dBm, the SNR after 1600-4800 km transmission degrades by < 1 dB when P_SIG decreases from 0 to −18 dBm while providing the same output voltage swing using the TIA gain.

4.2.2.2 Impact of LO power on the SNR of channel 9 at various distances and number of channels presented to the CRx for both regimes of high and low received signal power

In this subsection, we explicitly show the impact of the LO power on the SNR of channel 9. In Fig. 9, we re-plot a portion of the results shown in Fig. 6 where we show the SNR versus P_LO at various distances and number of channels presented to the CRx for both regimes of high and low received signal powers (P_SIG = 0 and −15 dBm, respectively). For the P_SIG = 0 dBm case in Fig. 9(a), we observe how significant it is to choose a high LSR which greatly reduces the SNR penalty due to colorless reception. For example, changing the LSR from 0 to 12 dB reduces ΔSNR_1,16 from 1.5 to 4.7 dB (for distances travelled from 4800 to 0 km) to 0.1-0.65 dB. This agrees with Eq. (12) as discussed in the previous subsection. Moving to Fig. 9(b) when P_SIG = −15 dBm, we notice that increasing P_LO improves the SNR and that the SNR is independent of N_ch which agrees with Eq. (13). As mentioned in section 3, the LO-LO beat noise was not observed throughout all experimental data because the RIN of our lasers is below −145 dB/Hz. However, it is noteworthy that as P_LO is increased beyond 15.5 dBm (maximum output power from our ECLs) at P_SIG = −15 dBm (see Fig. 9(b)), the LO-LO beat noise should eventually lead to SNR degradation.

 

Fig. 9 SNR of channel 9 versus P_LO after 0, 1600, 3200 and 4800 km transmission at various N_ch and at P_SIG of: (a) 0 dBm, (b) −15 dBm.

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4.2.2.3 Two dimensional (2-D) plots of SNR of channel 9 versus LO power and received signal power at different distances in case of 1 (filtered) and 16 channels (colorless)

In this subsection, we re-present the experimental data of Fig. 6 corresponding to the extreme cases of N_ch = 1, i.e. filtered operation and N_ch = 16, i.e. fully colorless operation. Here, we present the SNR data as two dimensional (2-D) plots versus both P_SIG and P_LO as the two independent variables being swept. Figure 10 depicts these 2-D plots where different SNR values are encoded into different colors according to the color bars beside each subfigure (red representing higher SNR whereas blue representing smaller SNR). In all Figs. 10(a)–10(h), the small x’s mark the positions of experimental data points across the 2-D space (P_SIG, P_LO). All values between those points are evaluated using linear interpolation using the two nearest experimental data points resulting in continuous and smooth color-coded surfaces. The four rows of subfigures in Fig. 10 represent data after 0, 1600, 3200, and 4800 km transmission, respectively, whereas the left column of subfigures represent the filtered case (N_ch = 1) and the right column represent the colorless case (N_ch = 16). We should also notice that each pair of subfigures in any row share the same SNR color bar to ease the comparison within each row between the filtered and colorless scenarios. Also, we observe in all subfigures a white space at the bottom left corner where no surface is plotted. This range of (P_SIG, P_LO) has no experimental data since the target voltage swing of 320 mVpp could not be achieved within this range when both P_SIG and P_LO are small.

 

Fig. 10 Color coded 2-D plots of SNR versus both P_SIG and P_LO for (a) back-to-back and N_ch = 1, (b) back-to-back and N_ch = 16, (c) 1600 km transmission and N_ch = 1, (d) 1600 km transmission and N_ch = 16, (e) 3200 km transmission and N_ch = 1, (f) 3200 km transmission and N_ch = 16, (g) 4800 km transmission and N_ch = 1, and (h) 4800 km transmission and N_ch = 16.

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Also, we plot in each subfigure (if applicable) a black contour line corresponding to the parameters (P_SIG, P_LO) that achieve an SNR of 9.2 dB (FEC threshold). If we now compare Figs. 10(g) and 10(h) in the last row, we notice that the operating range where error-free operation is achieved, i.e. when SNR > 9.2 dB which is the area above the contour, is tighter in case of N_ch = 16 compared to N_ch = 1 due to the residual SIG-SIG self beat noise impact in the case of colorless reception which degrades the SNR as P_SIG increases and P_LO decreases. Within the operating range, we notice that for a fixed P_LO, there is a dynamic range for P_SIG within which error-free operation is possible and that this dynamic range gets wider as P_LO increases. Generally, the SNR degradation observed in the left edge of the surfaces in Figs. 10(a)–10(h) is due to the fundamental receiver shot and thermal noises. On the other hand, we notice a SNR degradation in the bottom right corner (where the LSR is smallest) of all subfigures in the right column representing the colorless scenario, due to the residual SIG-SIG self-beat noise due to neighboring WDM channels in this case. In fact, one should also expect SNR degradation near the top right corner of all subfigures due to saturation effects when both P_SIG and P_LO are large. In this case, the TIAs may get overloaded leading to nonlinear distortion of the signal which in turn degrades the SNR. From a system design perspective, the TIA overload problem is governed by two important parameters namely the maximum single-ended DC current (I_DC) and the peak-to-peak differential AC current (I_ACppd), which are calculated similar to [16] as follows

4.2.3 Verification of experimental results using the analytical SNR model

In this subsection, the goal is to verify the match between the experimental data presented in the preceding subsections and the behavior predicted by the analytical SNR model given by Eq. (11). In order to do so, the analytical SNR model in Eq. (11) is fitted to the experimental data. We first re-write Eq. (11) after re-expressing the denominator which represents the various noise sources as follows

The next step is to estimate ${\alpha }_1,{\alpha }_1,\mathrm{...},{\alpha }_5$ in Eq. (16) using the experimental data plotted in Fig. 6. For the purpose of fitting the model, we use only the experimental data obtained after transmission corresponding to $N_{loops}$ equal to 5, 10 and 15 because at these distances, the scaling factor $\beta$ saturates to a constant value of 0.55 (see appendix B) and hence ${\alpha }_5$ can be assumed constant. Since we have many SNR data points at various operating parameters namely, $P_{LO}$,$P_{SIG}$,$N_{ch}$ and $N_{loops}$, estimating the coefficients ${\alpha }_1,{\alpha }_1,\mathrm{...},{\alpha }_5$ requires solving an over-determined system. In order to do so, we use the linear least-squares method where the following two vectors and matrix are formed

By plugging the estimated coefficients from Eq. (17) into the SNR model of Eq. (16), we now have a known analytical SNR model that can be employed to either verify the experimental data or evaluate the SNR at other operating conditions, e.g. another N_ch. Figure 11 shows a comparison between the experimental SNR data and the evaluated SNR data from the fitted analytical model where the SNR is plotted against P_SIG for various transmission distances. Figures 11(a) and 11(b) present the data when P_LO is set to 12 dBm and N_ch is 1 and 16, respectively whereas Figs. 11(c) and 11(d) present the data when P_LO is set to 3 dBm and N_ch is 1 and 16, respectively. In obtaining Fig. 11, we performed two least-squares fits of the SNR model: one for the back-to-back case and one for the transmission case, since ${\alpha }_5$ is expected to be different in both scenarios. The reason for the expected difference of ${\alpha }_5$ between the two scenarios is that ${\alpha }_5$ includes the effect of the scaling factor $\beta$ which is dependent on the amount of CD (see appendix B for more details on the scaling factor $\beta$) and hence fitting the SNR model is done for the back-to-back data and transmitted data separately. Indeed, ${\alpha }_5$ found from fitting the model to the transmitted data was 1.74 times larger than the fitted ${\alpha }_5$ using the back-to-back data. This ratio matches well the expected value based on the theory in appendix B (see Fig. 13) if we use $\beta$ of 0.55 for the transmitted data and $\beta$ of 0.316 for the back-to-back data assuming the worst case polarization orientation of the received signal (45° relative to the PBS of the CRx). Furthermore, we should anticipate that ${\alpha }_5$ is the same for all transmitted data since $\beta$ saturates quickly to a value of 0.55 when the residual CD is more than 3 ns/nm (see Fig. 13 in appendix B). Looking back at Fig. 11, we notice a good agreement between the SNR curves derived from the model compared to the experimental curves which verifies both the validity of the proposed model in Eq. (16) and the accuracy of the experimental data.

 

Fig. 11 SNR versus P_SIG comparing both experimental data points with the points evaluated from the fitted SNR analytical model after 0, 1600, 3200 and 4800 km at the following operating conditions: (a) P_LO = 12 dBm and N_ch = 1, (b) P_LO = 12 dBm and N_ch = 16, (c) P_LO = 3 dBm and N_ch = 1, and (d) P_LO = 3 dBm and N_ch = 16.

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Besides the agreement between the model and the experimental SNR data, we can also use the estimated value of ${\alpha }_5$ (in case of transmitted data) to calculate ${\overline{CMRR}}_{SIG}$ assuming $\beta =0.55$ which can be easily done by comparing the last term in the denominators of Eqs. (11) and (16). We found that ${\overline{CMRR}}_{SIG}$ obtained from the fitted coefficient is −19 dB. In order to verify this value, we used the analytical definition of ${\overline{CMRR}}_{SIG}$ presented below Eq. (11) in section 3 in addition to the CMRR versus frequency curves obtained via characterization of the CRx which were depicted in Fig. 2(a) of section 2. The value found through the analytical expression of ${\overline{CMRR}}_{SIG}$ was −17.5 dB which is in good agreement with the one obtained from fitting.

Next, we make use of the SNR model found in Eq. (16) to predict the SNR performance if the same CRx is used in operating conditions different from those of our experiment. For example, we use the model to predict the performance when the number of WDM channels co-incident on the CRx is larger than 16. In Fig. 12, we plot the SNR versus N_ch after 0, 1600, 3200 and 4800 km transmission for both the model and experiment. It can be observed that the sweep range of N_ch is limited to 16 in case of the experimental data whereas we employ the analytical model to predict the SNR if the CRx is used for colorless reception when N_ch is up to 80. In Figs. 12(a) and 12(b), a high P_LO of 12 dBm is chosen and P_SIG is set to 0 and −12 dBm, respectively whereas in Figs. 12(c) and 12(d) a low P_LO of 3 dBm is chosen and P_SIG is set to 0 and −12 dBm, respectively. If we compare Figs. 12(a)–12(d), we notice that the impact of increasing N_ch on the SNR degradation is the most in Fig. 12(c) where the residual SIG-SIG beat noise has the largest impact for small P_LO and high P_SIG, i.e. small LSR. For example, the SNR after 1600 km transmission degrades by nearly 6 dB as N_ch changes from 1 to 80. On the other hand, we observe no impact from varying N_ch on the SNR performance in Fig. 12(b) when P_LO = 12 dBm and P_SIG = −12 dBm. In fact, the model allows us to predict error free operation (SNR > 9.2 dB) after 4800 km transmission when N_ch = 80. In order to verify that our SNR predictions when N_ch = 80 are correct from the TIA saturation perspective, we also use Eqs. (14) and (15) to verify if I_DC and I_ACppd are going to be below the TIA ratings. Indeed, if we plug the largest P_SIG and P_LO used in Fig. 12 into Eqs. (14) and (15), i.e. 0 dBm and 12 dBm respectively, and use N_ch = 80, we obtain I_DC = 2.43 and I_ACppd = 2.69 mA which are below the TIA maximum ratings. We finally conclude that all SNR points drawn from the model in Fig. 12 are within the linear regime of operation of the TIAs.

 

Fig. 12 SNR versus N_ch comparing the experimental data points with the points evaluated from the fitted SNR analytical model after 0, 1600, 3200 and 4800 km at the following operating conditions: (a) P_LO = 12 dBm and P_SIG = 0 dBm, (b) P_LO = 12 dBm and P_SIG = −12 dBm, (c) P_LO = 3 dBm and P_SIG = 0 dBm, and (d) P_LO = 3 dBm and P_SIG = −12 dBm.

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5. Conclusion

In this paper, we present a comprehensive theoretical and experimental study of the performance of a SiP integrated balanced CRx when employed for colorless reception in a WDM setup. The layout of the CRx chip is depicted and characterization results of its parameters are shown. Then, an analytical SNR expression of the output photocurrent is derived rigorously while pinpointing noise sources in a colorless scheme. Next, experimental results are presented where 16 × 112 Gbps PDM-QPSK WDM channels are used. We study the impact of varying system parameters on the performance of colorless reception. Results show that the LO beating with incoming optical noise including ASE and NL-induced noises is a dominant noise source regardless of the received signal power. In addition, we identify the SIG-SIG beating due to OOB WDM channels as an additional important noise source in the regime of high received signal power. On the other hand, thermal and shot noises have a significant impact on SNR in the regime of low received signal power. In addition, we conclude that the CMRR and sensitivity are two important CRx specifications that impact the performance at high and low received signal power regimes, respectively. Finally, an excellent match between experimental and analytical SNRs is proven. After fitting the SNR model, we conclude that the SiP CRx is capable of colorless operation with a WDM spectrum comprising 80 channels as long as the LO-to-signal power ratio is properly set.