1. Introduction

As data and video traffic continue to grow with no end in sight, service providers feel great pressure to deploy reconfigurable optical network architectures to enable flexible and efficient service provisioning in order to address unpredictable traffic demand. At the center of this versatility is reconfigurable optical add/drop multiplexers (ROADMs) [1], which is capable of routing each data channel independently at any node. In today’s network, colored optical demultiplexers are used, where optical filters at fixed wavelengths provide the optical frequency discrimination required for direct detection receivers. A growing trend is to employ “colorless” ROADM architectures, where the ROADM broadcasts a given number of optical channels to the drop path and a coherent receiver selects the optical channel of interest from the rest. This enables any wavelength to be flexibly routed to any receiver without manual intervention, simplifying provisioning of new services and opening the door for backup protection against transceiver failure as well as bandwidth-on-demand services. All these crucial applications require an optical receiver that can, without the need of an optical filter, detect any wavelength channel out of a number of incident DWDM channels.

The fact that an optical demultiplexer is not necessary when coherent detection is employed has been known for more than two decades [2]. With coherent receivers, channel selection can be achieved simply by tuning the local oscillator (LO) close to the desired channel and the filtering is achieved in the baseband to suppress any mixed signal-signal beat notes. Balanced receivers have also long been recognized to enable homodyne detection and to allow tight channel spacing, with the distinct advantage of further suppressing the signal self-beat common mode noise [3]. However, the lack of high-speed mixed signal circuits, the difficulty of making an ideal balanced photo-detector, and a lack of commercially viable narrow linewidth LO lasers two decades ago, limited the practical understanding of the intricate receiver design tradeoffs, and, to certain extent, resulted in a shift of research focus to optically amplified systems with direct detection. Recently, largely due to the success of commercializing digital signal processing (DSP) technologies, coherent detection, specifically with 40-Gb/s and 100-Gb/s polarization-multiplexed quadrature phase shift keying (PM-QPSK) optical modulation formats, have proven to be real and ready for commercial deployment [4, 5]. For colorless reception, recent literature reports the use of single-ended receiver designs, which either suffer from limited channel count and very poor dynamic range [6], or require the involvement of a more complicated receiver front-end [7]. We note that with the maturity of integrated photonic technologies [8] and volume production, the cost of balanced detection receivers is anticipated to closely approach that of single-ended versions.

In this paper, we report DWDM line system and receiver design guidelines when a 100Gb/s coherent balanced receiver is used to discriminate an optical channel from a number of aggressors, with the target of enabling full band colorless reception. Key link design parameters, such as link-end amplified spontaneous emission (ASE) noise level, link residual chromatic dispersion (CD), and the orientation of the polarization tributaries of each out of band (OOB) channel, are considered as the signature of the received optical signal. We first analyze in detail various noise and interference sources in a colorless coherent receiver optical front end (OFE). The interplay between several key component specs, such as the relative intensity noise (RIN) of the LO laser, the common mode rejection ratio (CMRR) of the balanced detector, and the electrical thermal noise from the TIA, are explored. Specifically, the CMRR-suppressed OOB channels’ self-beat notes, which fold themselves into the baseband signal spectrum, are identified as the main interference in colorless applications. CMRR is also discussed in detail from both the P/N skew and P/N power imbalance (“P” and “N” means positive and negative differential paths) contributions and effective CMRR, defined as a single frequency-independent value, is introduced to simplify the analysis. We further introduce simple analytical equations to predict system behavior at both sides of the input signal dynamic range. At low input signal power, an optimum LO power exists which balances thermal noise with the residual LO-RIN beat noise. At high input signal power, we show that the dominant noise effect is the residual self-beat noise from OOB channels. This interference term not only scales with the number of OOB channels and the CMRR of the OFE, but also depends on the link chromatic dispersion as well as the orientation of the polarization tributaries relative to the receiver. This OOB residual self-beat noise requires higher LO power as the per channel signal power increases. The results obtained using the simple analytical equations are shown to be in good agreement with numerical simulations. Finally, by considering the TIA overload, we predict analytically the operating bounds of colorlessly detecting the desired channel out of a full band of 80 channels. We show that dispersion managed links outperform dispersion unmanaged links by 5dB in terms of input dynamic range.

2. Noise sources in a colorless coherent receiver

Figure 1 shows a typical polarization-diverse coherent receiver with balanced detection. It consists of a free running LO, two polarization beam splitters (PBSs), two 90 degree hybrid mixers to demodulate the in-phase and quadrature channels, and four sets of balanced photodiodes (PDs) followed by four differential transimpedance amplifiers (TIAs). Balanced detection is employed for its superior common mode suppression feature, as opposed to single-ended detection schemes [9]. The imperfection mainly comes from amplitude and path length mismatches between the P and N differential paths of the four tributary outputs of a 90 degree hybrid mixer and will be discussed in detail in the next section.

 

Fig. 1 Block diagram of an integrated optical coherent receiver for colorless reception. LO: local oscillator; PBS: polarization beam splitter; OFE: optical front end, which contains two 90 degree hybrid mixers and four sets of balanced photodiodes. TIA: transimpedance amplifier. The input Rx signal carries N number of out of band (OOB) channels, with residual CD in the range of 0ps/nm to 50ns/nm, and varying orientation of the two polarization tributaries. The input dynamic range should be supported from −20dBm to 0dBm per channel.

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We first discuss the noise terms unique to the colorless application. Here, OOB is defined as wavelength bands other than the data channel under detection. As shown in Fig. 1, when multiple channels are presented to the coherent intradyne receiver, the interference term at baseband is not due to the LO beating with the OOB channels, nor the OOB channels beating with each other, because those mixing products are out of the baseband detection bandwidth. The interference term is due to each of the OOB channel mixing with itself. We call this interference term “OOB self-beat noise”. Signal-ASE beat noise and ASE-ASE beat noise from the OOB channels will also show up in the receiver, but the strength is much smaller when we consider similar occupied bandwidth for both ASE and the OOB channels. As discussed in [6], if we use the per channel average power squared to represent this “OOB self-beat noise” variance, a scaling factor, which takes into account the detailed signal-signal beat spectrum, must be present. This scaling factor is a function of the residual CD and the orientation of the polarization tributaries of the OOB channel at the input to the receiver. This could be understood from the fact that both CD and polarization orientation will increase the PAPR of each OOB data signal [6], and thus enhance the beat-noise variance. On the other hand, these interference terms from the OOB channels are common to both photodiodes in a balanced detector and are thus greatly suppressed inside the differential TIA. The suppression ratio is quantified by the CMRR of the OFE [9, 10].

We then briefly discuss the intrinsic noise terms associated with the coherent balanced receiver [3, 10]. These noise terms will dictate the low end of the input signal dynamic range.

Shot noise is a manifestation of the fact that an electric current consists of a stream of electrons that are generated at random times. Four sets of balanced receivers independently add uncorrelated shot noise of their own onto the overall incident signal. In colorless receivers, it will scale will the number of OOB channels, as well as the LO power. For a nominal LO power to signal power ratio, the amount of excess shot noise is relatively small compared to other noise terms. The dark current is usually small and can thus be neglected.

Thermal noise is due to random thermal motion of electrons in a resistor, manifesting as a fluctuating current even in the absence of an applied voltage. Usually, noise generated by the transimpedance amplifiers (TIAs) is the dominating thermal noise term and the amount added depends on the front-end design. A simple approach to account for the thermal noise is to use the equivalent TIA input-referred noise current density [10].

Another important noise source comes from the relative intensity noise (RIN) of the LO. From each photodiode’s perspective, the beating between the LO and its intensity noise acts as an interference term onto the useful signal-LO beat term. Balanced detection will suppress this term by a finite rejection ratio. The residual will leak through and act as a non-negligible interference noise term, especially when the LO power is high.

3. Effective CMRR in a coherent balanced receiver

When the received signal and the LO are equally split and synchronized from the last 2x2 coupler inside the 90 degree hybrid to each set of balanced PD, perfect cancellation of the common mode can be achieved. In reality, power imbalance and skew mismatch leads to a finite CMRR. Power imbalance can result from deviations in a 50/50 splitting ratio from the last coupler as well as unequal responsivities of the PDs. Skew mismatches are due to the P and N path length differences from the output of the last 2x2 coupler to the two inputs of the differential TIA. If we define the CMRR as the power ratio of the residual common mode with respect to the combined common mode [11], and translate that into the frequency domain, one can write the CMRR of a balanced mixer as follows [10],

Due to the frequency dependent nature of the CMRR, there is a need to introduce the concept of “effective CMRR” as a single averaged factor which can be applied to residual beat noise terms. To do so, we show in Fig. 2(a) the one-sided optical spectrum of a 32-Gbaud PM-QPSK signal. The spectrum notches at the baud frequency of ~32GHz. The Nyquist frequency is defined as half the symbol rate, which is ~16GHz for our case. At 10GHz offset, the signal is attenuated by ~3dB with respect to the carrier wavelength. Based on Eq. (1), we plot the CMRR as a function of frequency for various combinations of P/N skew and P/N power imbalance. Based on the 16-20GHz nominal receiver analog bandwidth as well as the frequency dependent shape (depends on P/N power imbalance and P/N skew) of the CMRR curve, we choose CMRR at 8-10GHz (around half the Nyquist frequency) as the “effective CMRR” value. Although the effective CMRR does not give an exact account of the total common mode noise, it provides the effect of the residual noise and allows one to make quantitative predictions on the receiver performance. A mapping of a combination of skew and power imbalance to effective CMRR value is thus shown in Fig. 2(b). Here the P/N power imbalance is shown as $10*\log 10(\alpha )$in dB. For instance, 0.5dB corresponds to a 53% to 47% power splitting imbalance, which could be achieved in a typical 2x2 coupler.

 

Fig. 2 (a) CMRR as a function of frequency for various P/N skew levels and P/N power imbalance values. The normalized one-sided 32-Gbaud PM-QPSK optical spectrum is also overlaid. (b) Effective CMRR value based on different combinations of P/N skew values and P/N power imbalance values. The effective CMRR is extracted from (a) at around 8 to 10 GHz frequency content.

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4. Theory for performance of a coherent colorless receiver

After laying out the various noise sources in a colorless receiver and the definition of the “effective CMRR”, we analytically derive the performance bounds by examining the dominant noise sources under different operating scenarios. The currents at port P and port N of any of the four balanced photo-detectors can be represented as follows,

After balanced current subtraction, the signal to noise ratio (SNR) at the output of the OFE (i.e., at the input to the differential TIA) is shown below,

The SNR degradation (from the input to the output of the OFE) can be quantified by examining the strength of the additive noise terms except for the first term, signal to interference ratio (SIR) is introduced below to capture this SNR degradation. Note that here the “interference” in SIR is generally referred to as both the interference from OOB channels as well as the noise sources from the receiver.

Equation (5) can be simplified to provide insight if we consider two extremes of the input dynamic range. For low input power, i.e., −20dBm per channel, SIR can be represented by

Based on the analysis in an earlier publication of ours [10], and mainly due to the quadratic dependence of LO power from the LO-RIN beat noise term, an optimum LO power exists which maximizes the SIR and thus in turn minimizes the performance degradation.

On the high-end of the input power, i.e., 0dBm/channel, SIR can be simplified as,

An even simpler equation can be provided if we convert Eq. (7) from linear scale to logrithmic scale,

Equation (8) reveals that as long as one has a large LO to signal power (per channel) ratio (LSR) or a good balanced detector (high CMRR value), there is potential to support a large number of OOB channel, without sacrificing too much the SIR value, and thus maintaining a reasonable system performance. Based on [6], the scaling factor,$\beta$, depending on the amount of CD and the orientation of the polarization with respect to the fixed polarization axis of the PBS, ranges from 0.05 to 0.55. This range corresponds to a variation of 10-11dB in power, which matches the PAPR variation ranges caused by the combination of CD and polarization orientation. In our analytical simulations, we derive the dBQ penalty out of the SNR penalty shown above assuming Gaussian distribution of overall noise sources.

5. OFE Numerical simulations and analytical predictions

In order to validate the above analytical model, numerical simulations are carried out in Matlab. To generate the transmitter, 126.5 Gb/s (31.625 GBaud) non-return-to-zero polarization multiplexed quadrature phase shift keying (NRZ-PM-QPSK) modulated signal is prepared with up to 2¹⁹-1 pseudo random bit sequence (PRBS) length on each of the four tributaries with different seeds. OOB channels ranging from 0 to 80 wavelengths (total number of channels from 1 to 81 channels) are generated with the same bit rate and modulation format at 50GHz spacing. To mimic the statistically uncorrelated multi-channel transmitter in a practical system, diverse PRBS seeds and different timing delays are used to randomize each channel. Orientation of the polarization tributaries for each channel are also varied based on the Jones angle and ellipticity with respect to the receiver PBS. DWDM signals are transmitted through various net CD values ranging from 0ps/nm to 50ns/nm, representing dispersion managed and unmanaged (DCM-free) links, respectively.

On the receiver side, a laser with 100 kHz linewidth and a RIN value of −145 dB/Hz is used for the local oscillator (LO), with an output power swept from 0 dBm to 20 dBm. The two 90 degree hybrids are modeled to have perfect I/Q and X/Y power balance, whereas the P/N skew and P/N power imbalance represents the source of imperfection, which contribute to an effective CMRR ranging from −13dB to −25dB. Excess loss from the hybrid is assumed to be 2 dB and the PD responsivity is set at 0.6 A/W. Thermal noise is modeled to have a differential TIA input noise current density of 18.2 pA/sqrt(Hz). The overall receiver analog bandwidth is modeled as having a 3dB bandwidth of 16GHz with a 5th order Butterworth shape. The two samples per symbol analog-to-digital converter (ADC) has an effective number of bits (ENOB) of 6, which is close to ideal for PM-QPSK signals. A 2x2 butterfly adaptive equalizer is realized in the frequency domain using least mean square (LMS) algorithm. Viterbi-viterbi based carrier phase estimation is performed to compensate for the phase noise. Error counting is performed to calculate the bit-error-rate (BER) and then converted to Q² factor to quantify the system performance. Figure 3 summarizes the key parameters used in our numerical simulations.

 

Fig. 3 Key parameters with brief description used in the numerical simulation.

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To support an input dynamic range from −20dBm to 0dBm per channel, and assuming no additional power adjustment of the already equalized levels at the receiver input, we carry out simulations on both ends of the power range and assess independently the impact of both OFE and link parameters on the system performance. We demonstrate the analytical models presented in the previous section are in good agreement with numerical simulations.

5.1 At low input signal power

When the input power per channel is weak, i.e. −20dBm/channel, the receiver performance is mainly limited by the various noise sources. We show in Fig. 4(a) both numerical and analytical simulations of Q² penalty (with respect to the performance when the LO power is optimum) as a function of the LO power for single channel operation. The CD is set to 0ps/nm and polarization orientation is random as the PAPR has negligible effect when the signal power is low. As understood from the previous section as well as in our previous publication [10], an optimum LO power exists which balances the thermal noise with the residual LO-RIN beat noise. For an effective CMRR of −25dB (P/N skew of 2ps), the optimum LO power is around 11dBm. If the effective CMRR is reduced to −19dB (P/N skew of 4ps), the optimum LO power is lowered to 8dBm, roughly half of the CMRR reduction, as predicted by our analytical model. Comparing to the loss-limited case [10], the tolerable range of the LO power is much larger in the noise-limited case, as the −30dBm/0.4nm ASE noise floor (corresponding to an OSNR of 16dB/0.1nm and an input power of −20dBm/channel) is the dominant term compared to the other noise sources. We note that with reasonable LO power providing more than 25dB LSR, we can anticipate that the optimum LO power is independent of the number of OOB channels.

 

Fig. 4 (a) Numerical and analytical simulations of Q² Penalty as a function of LO power for two different P/N skew values and single channel reception. The numerical simulation and analytical equations are seen to be in good agreement. (b) Numerical and analytical simulations of Q² penalty versus number of OOB channels.

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Figure 4(b) shows that for a nominal LO power of 13dBm and an effective CMRR of −19dB (PN skew of 4ps), the system performance is largely independent of the number of OOB channels when the input power per channel is low (e.g. −20dBm). This can be explained by the fact that the residual self-beat noise from the OOB channels is negligible compared to the LO power, and thus contributes little additional interference noise to the ASE noise floor. The numerical simulation shows a slightly higher penalty (0.2-0.3dB) than the analytical predictions. This dependence can be attributed to the beating between the sidebands of the adjacent channel pairs which build up slightly when the OOB channel count increases.

5.2 At high input signal power

When the input power per channel is strong, i.e. 0dBm/channel, the receiver performance is expected to degrade with increasing number of OOB channels. However, as predicted by Eq. (8), increasing the LO power or improving the CMRR value can both significantly minimize the penalty. We show in Fig. 5(a) the Q² penalty versus the number of OOB channels for different LO power, for a fixed signal power per channel of 0dBm and an effective CMRR of −19dB for a P/N skew of 4ps. The overall CD is 50ns/nm to represent a dispersion uncompensated (DCM-free) link, corresponding to a beta factor of 0.55. For a given number of OOB channels, higher LO power helps suppress the “residual self-beat noise” and thus improve the system performance. When the OOB channel count is 40, increasing the LO power from 7dBm to 13dBm reduces the Q² penalty by approximately 1.5dB at an OSNR of 16dB/0.1nm.

 

Fig. 5 (a) Numerical and analytical simulations of Q² penalty as a function of number of OOB channels for various LO powers. (b) Numerical and analytical simulations of Q² penalty as a function of OOB channel number for various P/N skew values. The numerical simulation and analytical equations are seen to be in good agreement.

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Figure 5(b) shows the impact of P/N skews on the performance of colorless reception. For 40 OOB channels, reducing the skew from 8ps to 2ps (equating to a CMRR improvement of 12dB) improves system performance by close to 3.5dBQ. As evident from Eq. (8), both CMRR and LO power contribute on the same scale to the SIR. Figure 5(a) and 5(b) show very good agreement between our numerical simulations and analytical models.

5.3 Enhancing the input dynamic range

By combining both the low and high end of the input power range, we are able to assess the impact of colorless reception on the receiver input dynamic range. Analytical simulations are carried out using Eq. (5) for considering the complete SIR contributions. Link CD is set to 0ps/nm and the orientation of polarization tributaries of the OOB channels is random, corresponding to an average beta factor of 0.25, which is used in our analytical simulations. Figure 6(a) shows that by normalizing the colorless system performance to that of the single channel Q² factor, increasing the number of OOB channels only impacts the high-end input power limit. For a 13dBm LO power and an effective CMRR of −19dB (P/N skew of 4ps), the input dynamic range is reduced from −20dBm to ~5dBm to −20dBm to 0dBm when the OOB channels are increased from 10 to 40.

 

Fig. 6 (a) Numerical and analytical simulations of Q² Penalty as a function of input signal dynamic range for different number of OOB channels. (b) Numerical and analytical simulations of Q² Penalty as a function of input signal dynamic range with 41 OOB channels for different LO power and P/N skews. It is shown that increasing the LO power only enhances the high end of the dynamic range, while increasing the CMRR enhances both sides of the dynamic range. The numerical simulation and analytical equations are seen to be in good agreement.

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To further illustrate the impact of LO power and CMRR on the performance of colorless reception, Fig. 6(b) shows the simulation results when the OOB channels are set to 40. The inner three curves corresponds to an effective CMRR of −19dB (P/N skew of 4ps), while the LO power is changed from 13dBm to 19dBm. We see that increasing the LO power enlarges the high-end input power limit (thanks to a higher LSR value), but sacrifices the low-end input power limit due to a higher residual LO-RIN beat noise. On the other hand, the purple curve shows the benefit of enhancing the CMRR on both ends of the input dynamic range. For a fixed 13dBm LO power, reducing the P/N skew from 4 to 2ps helps increase the dynamic range by close to 10dB (4dB improvement on the low-end and 6dB improvement on the high-end). This can be explained by a higher CMRR helping reduce the residual LO-RIN beat noise as well as the residual self-beat noise from the OOB channels. The analytical simulations are seen to be in good agreement with numerical simulations.

5.4 Impact of polarization orientation with and without CD

Knowing that the polarization orientation on each channel has implication to the scaling of the self-beat noise, we carry out numerical simulations to assess the dependence on the polarization orientation for different CD values in the link. 0 degree oriented channels are considered to be the best case, as there will be no polarization mixing between the X and Y tributaries in the receiver. 45 degree oriented channels are considered to be the worst case, as the mixing between X and Y is the strongest for every channel hitting the receiver, producing the highest PAPR value and photo-current variance. The above distinctions are only obvious when the link CD is small. As CD increases in the link, the dominant PAPR contribution comes from pulse spreading and thus the polarization orientation induced PAPR effect is masked. To illustrate, Fig. 7(a) shows both the numerical and analytical simulations for different combinations of CD and polarization orientation. The number of OOB channels is set to 10 and the LO power is fixed at 0dBm to magnify the system impact from PAPR. We see that when CD is 0ps/nm, the performance varies significantly as a function of polarization orientation. At 0dBm per channel power, the variation due to polarization orientation can be seen to exceed 1dBQ. This variation is significantly reduced when the residual CD at the receiver is larger than ~1ns/nm for our 32GBaud system. In the 1ns/nm to 50ns/nm range, the performance is comparable, showing no impact from the polarization orientation. However, the performance is degraded compared to the zero CD case due to the larger PAPR induced current variance, which is manifested in the self-beat noise terms. For a beta factor of 0.1, 0.2, 0.3 and for best, random, and worst polarization orientation cases, the analytical model is seen to match well with the numerical simulation.

 

Fig. 7 (a) Numerical and analytical simulations of Q² Penalty as a function of input signal dynamic range with 11 OOB channels for various conditions of residual CD and polarization orientation. It is shown that with dispersion compensated links (CD = 0ps/nm), the high-end input dynamic range can be affected by the polarization orientation of OOB channels (b) Analytical predictions of Q² Penalty as a function of input signal dynamic range with 81 OOB channels for dispersion managed (CD = 0ps/nm) and unmanaged (CD = 50ns/nm) links. It is shown that dispersion managed links with random polarization can achieve an input dynamic range from −20dBm to 0dBm.

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To analytically predict the performance variation at higher OOB channel count, Fig. 7(b) shows the Q² penalty versus the input signal power for an 80 OOB channel system. LO power is set to 13dBm and the effective CMRR is −19dB (P/N skew is 4ps). We see similar variation in terms of polarization orientation when there is no CD in the link. ~0.87dBQ variation is predicted when the signal power is 0dBm/channel. With CD in the link, the performance is not impacted by the orientation angle, as the PAPR and thus the self-beat noise variance saturates to a fixed level.

6. TIA overload and performance bounds

The above analysis shows the limitation imposed by the OFE for colorless reception and suggests using higher LO power to suppress the additive interference terms. On the other hand, the influx of LO power coupled with the multi-channel signal power could overload the TIA and introduce nonlinear distortion to the signal. To understand this overload effect, we examine Eq. (2) and (3) closer and derive the following equations for the two critical TIA overload specs, namely the single-ended DC current and the differential AC current [12].

To quantify the impact of both DC and differential AC current on the number of OOB channels and the amount of CD, we assume the following to assess the worst case performance: 0dBm input signal power, 16dBm LO power, and 13dBm total loss. Figure 8(a) shows the numerical calculations of DC current as the OOB channel count increases. We see that the DC current nonlinearly increases with the number of OOB channels, as LO and total signal power trade dominant roles for different OOB channel counts. We also note that CD has no impact on the DC current. Figure 8(b) shows the numerical calculation of the differential AC current with respect to the link CD for two different OOB channel counts. As anticipated from the PAPR analysis, the AC current quickly saturates to a steady state value when the CD is beyond 1ns/nm, which corresponds to a duration of approximately 10 symbols for our 32GBaud PM-QPSK signal. This saturation level has no dependency on the number of OOB channels, as discussed earlier. We also note that when CD is zero, the AC current is slightly higher for the 80 OOB channel case compared to the single channel case. This can be attributed to the random polarization mixing for the multichannel case, which increases the PAPR.

 

Fig. 8 (a) Numerical results of DC current at the input of the TIA versus chromatic dispersion for different number of channels ranging from 1 to 81. It is shown that DC current scales nonlinearity with the number of channels, and is not dependent on the amount of CD. (b) Numerical results of AC peak-to-peak differential (ppd) current at the input of the TIA versus chromatic dispersion for single channel and 81 channels reception. It is shown that ACppd current rises rapidly in the 0 to 1ns/nm range and quickly saturates when the CD is beyond 1ns/nm. On the other hand, the AC current is largely independent on the number of OOB channels.

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Based on the above analysis from both numerical and analytical simulations, we use our analytical model to derive the performance bounds when the coherent receiver is intended to detect the desired channel out of a fully loaded DWDM system. We pick 80 OOB channels in the following analysis. Effective CMRR is set at −18dB by considering both a 4ps skew and 0.5dB power imbalance. Figure 9 shows the operating regions in terms of both the input signal power per channel and the allowable LO power. We see that at low input signal power, residual LO-RIN beat noise dominates when the LO power is high (the black “LO-RIN beat noise” limit is the 0.5dBQ penalty curve), while the thermal noise dominates when the LO power is low (the purple “thermal noise” limit is the 0.5dBQ penalty curve). At high input power, residual self-beat noise from OOB channels (0.5dBQ purple line) dictates the minimum LO power limit. On the other hand, the TIA overload exhibits two bounds for both the DC and differential AC current (4mA and 3mAppd in this example). Figure 9(a) and 9(b) correspond to two extreme residual CD cases. We see for dispersion unmanaged link (CD = 50ns/nm), both the residual self-beat noise from OOB channels and the TIA AC overload lead to a tighter operating region for the signal and LO power. This is attributed to the PAPR increase from the OOB channels with high CD and the PAPR increase from the desired channel with high CD, respectively. For dispersion managed links (CD = 0ps/nm), the TIA overload limit is bounded by the DC current for 80 OOB channels, and, interestingly, the input dynamic range is increased by almost 5dB (from −6dBm to −1dBm) compared to the dispersion unmanaged links. We can also anticipate that by further enhancing the CMRR of the OFE, both the black line and purple line will move outward, enlarging the operational range.

 

Fig. 9 Analytical prediction of the operating bounds of full C-band (81 channels) colorless reception, considering both OFE noise limits and TIA nonlinear distortion limits, for: (a) Dispersion unmanaged (CD = 50ns/nm) links. (b) Dispersion managed (CD = 0ps/nm) links. It is shown that dispersion unmanaged links have significantly narrower operating bounds due to the higher peak-to-average power ratios caused by the accumulated CD, as well as the TIA differential AC current overload limit.

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7. Discussion

The beta factor scaling of the self-beat noise from the OOB channels deserves further discussion. We show that both residual CD and orientation of polarization tributaries relative to the receiver PBS have an impact on this scaling factor through the PAPR, which causes the signal-signal beat spectrum to vary in time such that the beat noise variance is modified. We note that PMD in the link tends to depolarize the signal and will thus randomize the polarization orientation of the channel at the PBS in the receiver. One can anticipate that the modulation format and bit rate will also have implications on this beta factor. Mixed symbol rate and format systems, such as 10Gb/s OOK, 40Gb/s DPSK, 40Gb/s PM-QPSK and 40Gb/s PM-BPSK will exhibit different self-beat spectrum compared to 100Gb/s PM-QPSK neighboring channels. Channel spacing also impacts the interference noise. One can imagine that tighter channel plan will result in non-negligible beating of adjacent signals with each other and folding into the baseband detection bandwidth. This adjacent-signal beat noise scales with the number of OOB channels and could be a contributing factor to the overall interference noise. On the other hand, variably attenuating the OOB channels with respect to the data channel under detection could help alleviate the interference noise and help achieve the full band colorless reception with wide dynamic range. Regarding limitations introduced by the TIA, we analyzed both the DC and differential AC current limit. However, one should also consider the single-ended AC current contribution to the overall nonlinear distortion inside the TIA. Preliminary analysis reveals that this single-ended AC current carries both the common-mode AC and differential-mode AC and is, therefore, dependent on both the number of OOB channels and the residual CD and polarization orientation in the link.

8. Conclusion

In this paper, we report design guidelines for colorless coherent receivers. Residual self-beat noise from OOB channels is identified as the main interference contribution in colorless applications. Effective CMRR is introduced to scale the strength of the residual noise. A scaling factor is needed to include the PAPR-induced noise variance effect caused by link CD and polarization orientation of the OOB channels. Equations on signal to noise ratio degradation are derived to form analytical models, which are shown to be in good agreement with numerical simulations. By considering the TIA overload limit, we predict analytically the operating bounds of colorless detection. We show that the dispersion unmanaged links have a 5dB reduced dynamic range compared to dispersion managed links.