We present results for VCSEL based links operating PAM-4 signaling using a commercial 0.13µm CMOS technology. We perform a complete link analysis of the Bit Error Rate, Q factor, random and deterministic jitter by measuring waterfall curves versus margins in time and amplitude. We demonstrate that VCSEL based PAM–4 can match or even improve performance over binary signaling under conditions of a bandwidth limited, 100meter multi-mode optical link at 5Gbps. We present the first sensitivity measurements for optical PAM-4 and compare it with binary signaling. Measured benefits are reconciled with information theory predictions.
© 2006 Optical Society of America
Multilevel signaling as a means for increasing data rates in electrical backplanes has been widely explored to overcome frequency-dependent, media losses . This has lead to advances in CMOS chip technology and the availability of commercial chips that are now able to implement Pulse Amplitude Modulation (PAM) with up to 4 levels. By contrast, only preliminary investigations have been performed for multilevel signaling over optical links owing to the complexity of link measurements and the need to integrate photonic drivers into newer electrical chip technologies . Examples illustrating the difficulty in the latter are the duobinary signaling approaches where utra-long haul optical links at 10Gbps have recently been demonstrated to be advantageous over binary signaling  and additionally, other reports for improved throughputs over electrical backplanes at 25Gbps . However, the duobinary approach used in these experiments was based on discrete components to accomplish the multilevel signaling. Clearly, there remains a significant challenge in integrating duobinary drivers directly onto a CMOS platform and we are unaware of the commercial availability of such chips.
Signaling by optical PAM–4 is reported to offer distinct advantages in mitigating frequency dependent dispersion in fibers  somewhat akin to the electrical case. For instance, in optical links dispersion produces Inter Symbol Interference (ISI) penalties and in multimode fiber the modal dispersion represents a 10 dB power penalty in a 50 m link in low cost 160 MHz-km fiber at 10 Gbps. Distinct question naturally arise such as the quality of optical linearity needed from a VCSEL to achieve the entire PAM-4 signaling advantage . To date little to no real performance characteristics for PAM-4 with VCSELs has been reported other than eye pictures . In fact, most attention on multilevel signaling has centered on amplitude margins where Signal to Noise ratio (and related Q) is measured and compared with theory. Here, only electrical PAM-4 signaling has addressed this issue where as optical data is currently unavailable. Also, and from a more general view, multilevel signaling in the optical domain remains relatively unexplored since little to no consideration has been devoted to timing analysis (jitter), let alone a comparison of this metric to theory. Standard bodies place special emphasis on jitter in optical links owing to clock recovery requirements, phase noise in the laser and impairments from modal mismatches, discontinuities and reflections in the transport media.
In the present work we begin a comprehensive investigation of VCSEL links operating under PAM-4 signaling using commercially available 0.13µm CMOS technology. We are able to quantify Q factors, signal to noise, random and deterministic jitter, and sensitivity for the first time. This enables the first complete comparison between PAM-4 and binary optical signaling. Our goal is to determine the optimal signaling method for a given optical link that takes into account the optical medium, the timing margins, link bandwidth, and the optical device reliability. We report 5Gbps operation of a VSCEL, packaged in a conventional TO can, in which PAM-4 signaling is demonstrated to overcome rise time limitations in the transmitter as well as a potential modal noise in the multi-mode fiber link that otherwise degrades binary signaling. Bandwidth limitations are also an important issue for binary signaling of VCSELs beyond 20Gbps. In fact, PAM-4 signaling over VCSELs could become a plausible option here after factoring in the additional reliability degradation encountered at higher data-rates for binary signaling .
2. Experimental setup
The driver is a commercial CMOS chip that contains PAM-4 capability. Briefly, this chip has multilevel signaling functionality, internal eye detector, Bit Error Rate (BER) analyzer and scope tool built with 0.13 µm CMOS technology on a standard Si platform. Additional functionality for the chip include pre-emphasis and trailer taps that automatically optimize the eye quality for a given link medium. The Tx and Rx drivers on the chip were based on differential CML signaling that was readily accessible through SMA connectors on circuit board layout for the chip. A single-ended, Tx output of the chip drove the VCSEL through a bias-T and was received by a New Focus amplified detector (1580) with a responsivity of 0.4 A/W. A balun was used to convert the photo-detector signal back to differential mode and then electrically tied to the CML inputs to the CMOS chip. The balun represents a 3 dB electrical loss to the receiver circuit. The link consisted of a 100m spool of multimode fiber and also four connectors with patch cords. Multiple connectors, as required for all practical link conditions, are known to produce modal noise which often introduces bandwidth penalties . The VCSEL deployed in our setup was a Emcore 2.5Gbps product containing a 13µm oxide aperture device packaged in a standard (low speed) TO can  that was fitted with a LC fiber connector. We soldered this product to a SMA connector. Use of the Emcore 10 Gbps VCSEL with a 6 micron aperture was deployed at higher speeds. A picture of the experimenatal set up is shown in Fig. 1(a). Because there are different bandwidth limitations associated with specific components that comprise the setup in Fig. 1(a) (e.g., the CMOS chip, VCSEL transmitter and fiber) we explore link quality at different data rates in order to extract out performance penalties. Hence, some data rates we report are not restricted to the core communication feeds.
An example L-I-V characteristic for a 10Gbps VCSEL is shown in Fig. 1(b) and illustrates how the PAM-4 signals map onto the VCSEL. The characteristic response of the Emcore 2.5Gbps VCSEL, although different, qualitatively aligns to the PAM-4 levels much as Fig. 1(b) depicts. The threshold current in Fig.1 (b) is about 1.1 mA and deviation from a perfectly linear L-I response sets in above 7mA. This nonlinear VCSEL response could arise from thermal rollover or even mode coupling into the fiber. Effort was taken to minimize the penetration into this nonlinear region of the VCSEL’s response. The voltage characteristics in Fig. 1(b) are typical for this model (aperture size) of VCSEL which further can be easily biased for use with the CML output driver from the CMOS chip. The upper level PAM-4 transition as shown in Fig. 1(b), the 11 transition, most likely incurs mild degradation from the non-linearity of the VCSEL. We expect the other PAM transitions to be in the strictly linear regimen of the VCSEL.
We measured the (20:80) rise time for the 2.5Gbps VCSEL transmitter and found it to be 115 ps. Frequency dependent small signal measurement confirms the slow response of 2.5Gbps VCSEL characteristic as gleaned from Fig. 2. For comparison, the small signal responses from both the 2.5 and 10 Gbps VCSELs are presented. The optical response for the 2.5Gbps VCSEL clearly degrades for increasing frequency above 1.5 GHz. A peak is observed at 8GHz as a shoulder superimposed on an otherwise uniform bandwidth roll off response. This peak corresponds to the resonant frequency of the VSCEL and can be observed to shift with applied bias current. This rise time allows 2.5 Gbps binary link operation but lacks the required bandwidth to reach 5 Gbps without degradation. The 10Gbps VCSEL is not limited by this same bandwidth degradation.
In our first experiment we operated at a speed 2.5 Gbps that produced 2 symbols per bit that optically resulted in an aggregate data rate of 5 Gbps through the VCSEL link with PAM-4. A picture for a multilevel eye of the VCSEL link is shown in Fig. 3(a), which further reveals that transitions spanning more than two levels have been intentionally avoided by the chip’s PAM-4 algorithms. The bias current of the VCSEL was adjusted under frozen trailer taps to optimize the BER and eye quality. Acquisition of the on-chip waterfall curve versus margins in amplitude or phase (time) enabled relatively quick optimization of the link quality. The optimal VCSEL bias was determined to be 10 mA and corresponded to an optical power of −7dBm being launched in the link at room temperature. These correspond to conditions for all the data reported here. Figure 3(a) shows the waterfall curve versus amplitude margin for an optimized link. The fitted curve extrapolates to BER of 3 10-17. These were confirmed by running the link error free over three days of operation and even links at 6.25Gbps deploying the 10Gbps VCSEL were equally error free to similar quality. The data patterns were obtained by transmitting pseudorandom sequences of 2 31-1 word lengths. Our demonstration of the sub 10-15 BER regimes is a practically important metric that clearly establishes the absence of noise floors for implementing this new signaling method. Such metrics are required by many system applications. To our knowledge our results represent the first demonstration of optical PAM–4 with a VCSEL that have reached this important regime.
Binary signaling at 4.9Gbps is also shown as Fig. 3(b) in which the modulation amplitude and bias current to the VCSEL precisely matched the PAM-4 conditions. Figure 3 illustrates a significant motivation for PAM-4 signaling. Clearly, the slope parameter has decreased in going from PAM-4 to binary. We estimate a Q factor of 7.1 for binary where and the corresponding Q factor of for PAM-4 is 10.4. This translates to a SNR of 26 dB for PAM-4 and 23 dB for binary. The binary penalty is caused by the rise time limitation in the transmitter, fiber, as well as modal noise in the connectors.
An analysis of timing jitter also provides support for the benefit of multilevel signaling versus binary as did amplitude margins in the 4.9Gbps link. Waterfall curves versus timing margin for PAM-4 and binary are shown in Fig. 4(a) and 4(b). This data was fitted with a dual parameter model to extract jitter characteristics in which the curve’s slope parameter corresponds to random jitter (RJ) while the curve opening corresponds to deterministic jitter (DJ). DJ and RJ values are attached to the plots. Interesting optical random jitter is only slightly greater for PAM-4 (5.1ps) versus binary (4.8ps). However, there is an increase in deterministic jitter for operating binary (95 ps) over PAM-4 (61 ps). Also, the PAM-4 eye opening in Fig. 4(a) is 76ps which is about a 1/3 UI. UI is the unit interval in time and becomes unity for a time corresponding to a full bit period. Hence, the PAM-4 eye at 4.9Gbps remains open within specifications for typical Clock Data Recovery circuitry (CDRs). However, the eye opening for binary signal at 4.9Gbps is 40 ps and falls below the ¼ UI opening metric needed by CDRs (an approximate rule of thumb). Under these specific bandwidth impairments PAM–4 does enable link operation whereas binary failed to reach performance. However, under this rise time issue, at different bias and modulation, PAM-4 was improved over binary signaling. While improved binary operation can be achieved at higher VCSEL modulation and bias conditions PAM-4 is comparatively better under matching conditions.
We have also performed measurements of attenuated power versus BER to extract sensitivity metrics for optical PAM-4 versus binary at 6.25Gbps. In this particular example we utilized a 10Gbps VCSEL with a short optical multimode patch cable (<3m) and was not bandwidth limited by the package  or modal noise limited by the fiber  in Fig. 5 for both cases. Binary was measured with an Anritsu BER at 6.25 Gbps where as optical PAM-4 was derived from the CMOS chip. The BER, when plotted against received power, can be fit to a linear dependence in both cases with no apparent noise floors to 10-12. Each optical component in our experiment was connectorized for use with multimode fiber and hence several connectors were deployed as is typically required for links used in real applications. Hence the launch conditions and mode coupling conform to typical industry standard specifications. Sometimes modal noise can be reduced by insertion of short single mode patch cord. However there is a large power penalty to strip out the higher order modes using this approach The BER versus attenuated power is shown a sensitivity of -16.5dBm is deduced at 10-12 BER in Fig. 5. This is close to the theoretical sensitivity limit of −19.3dBm that we estimate for our detector sensitivity. For optical PAM-4 we measure a sensitivity of −10.3 dBm. The measured PAM-4 power penalty over binary of 6dB can also be compared with information theory predictions. The expected power penalty in sensitivity for operating PAM–4 compared with binary is about 4.1 dB which is a direct result of three multilevel signaling eyes versus one for binary. The actual optical sensitivity penalty for M level PAM versus a binary comparison is given by
The numerator accounts for reducing the eye amplitude by three in PAM-4 where as the denominator factors in the longer integration time the receiver detects the signal in multilevel signaling . One reason the optical sensitivity penalty in our experiment may exceed theory associates with non-linearities in VCSEL output that acts to compress the PAM levels. Further, our chip BER algorithm deploys the worst of the three eyes in accomplishing the error detection analysis. The level of compression is directly observed in eye picture of Fig. 3 for the PAM-4 case as is signified by the reduction in level spacing for the lower of the three eyes. This eye picture is inverted in sense as the lower level coincides with the 11 PAM-4 level shown in Fig. 1(b). Compression penalties for optical PAM-M have been estimated in reference .
In the case of the 2.5Gbps transmitter at 5 Gbps experiments our PAM-4 measurements resulted in a net 3-4 dB advantage over binary signaling. Here, the PAM-4 approach not only overcame the SNR penalty of 9.5dB expected from theory (see eqn. 2) but also a significant bandwidth roll off of the VCSEL that overly degraded binary signaling. Because true PAM-4 signaling is performed using half the bandwidth deployed under binary signaling then a significant advantage should be realized in our experiment. Judging from the small signal results in Fig. 2 the advantage that PAM-4 has over binary is distinctly obvious for the 2.5Gbps transmitter case. In fact, based on an analysis of Fig. 3, one may expect the net gain for PAM-4 with the 2.5 Gbps transmitter to be far greater than that extracted from our margin measurement of Fig. 3 (i.e., 3-4dB). Again, our PAM-4 chip measures BER with the worst of the compressed eye and hence the PAM-4 advantage over binary may fall short of the full theoretical expectation. Furthermore our chip’s PAM-4 algorithm eliminates transitions spanning more than two levels and hence has a reduced multilevel functionality.
Commensurate with the 3-4 dB PAM-4 gain based on the amplitude margin analysis of Fig. 3 we also observe a significant jitter advantage in Fig. 4. One might anticipate in advance that the jitter benefit is entirely a deterministic jitter improvement for multilevel signaling since pattern dependant jitter always accompanies bandwidth limited transport (impairing the 5Gbps binary in our case). It would further be tempting to equate the degradation in jitter metric with an amplitude penalty akin to jitter penalty treatments found in literature . One notable observation of Fig. 4 is that PAM-4 random jitter did not significantly change relative to the binary signaling case. In addition, we are not aware of any treatments quantifying the overhead for PAM-4 versus binary signaling in terms of a jitter penalty in dB. Nevertheless, the PAM-4 amplitude gain is only 3 dB out of 26 dB and hence represents a relatively small change in signal to noise ratio. But this is precisely the issue when quantifying the PAM-4 advantage from a fundamental analysis. From a theoretical perspective, Q and random jitter should be impacted on similar footing since improvements in signal to noise translates into a commensurate reduction in random jitter. From this perspective the improvements in Q and random jitter are modestly similar within our experimental uncertainty . However, improvements in deterministic jitter should arise from the bandwidth roll off characteristics within the link. This supports the reason DJ is found to be far better for the PAM-4 signaling case whereas RJ is relatively unchanged. Therefore our preliminary analysis of the data appears well founded and reconciled with information theory predictions.
The theoretical 9.5 dB SNR penalty for implementing PAM-4 signaling to reach a two fold increase in data rate is part of a larger question. Generally, VCSEL links under binary operation incur excess powers upon launch in order to achieve the low random jitter specifications needed by standards. The overhead in power penalty for implementing PAM–4 could be traded in by this spare link power. To determine the optimal signaling method for a given optical link it is further necessary to account the optical medium, the timing margins, link bandwidth, and the optical device reliability. We find PAM–4 mitigated a bandwidth limitation within one of our links by offsetting a (-9.5 dB theory penalty) to produced a 3-4 dB gain and a DJ advantage. Further, we expect that this technique may be scalable to higher bit-rates as well. Fig.6 shows an eye diagram of our experimental link operating at 8Gbps (4Giga-symbols per second) and uses the 10Gbps VCSEL. The Nyquist frequency of our electrical PAM–4 chip was about 1.8GHz which prevents driving the optical link with PAM–4 cleanly at 10Gbps (5Giga-symbols per second).
We next outline explicit examples whereby PAM–4 signaling might become a plausible option for doubling the baud rate for VCSEL based links . The specific example we explore is doubling the baud rate of a 10Gbps VCSEL. However, this construction applies equally to regimens for which doubling the data rates for even record quality VCSELs may be of interest. First, the SNR overhead penalty for deploying PAM4 versus binary signaling at same baud rate is 
To deliver the same data throughput, the baud rate of binary signaling needs to be doubled resulting in a bandwidth spectrum of the signal twice as wide as PAM–4. This condition could lead to a transmitter bandwidth limit and hence a SNR degradation that we estimate can be written as
where SNRslope is the bandwidth roll off of a transmitter’s response. From Eq. (2) it is clear that PAM–4 becomes advantageous over binary when the following conditions develop.
Next we consider the second order frequency characteristics for a 10Gbps VCSEL . When driving the data rate of this VCSEL beyond the small signal characteristic’s 3dB point, the roll-off exceeds 40dB/dec regardless of the value of it’s damping ratio (see Fig. 7 depicting our simulation of the small signal response for a 10GHz VCSEL). Hence, the SNR degradation slope then becomes larger than 40dB/dec for such a VCSEL. Under this condition such a VCSEL could advantageously deploy PAM4 to double the data rate instead of signaling with binary. The PAM–4 advantage over binary for a 10Gbps VCSEL is confirmed based on our eye simulation also presented in Fig.7. The resonance frequency of this VCSEL is 10GHz. Clearly, our simulation depicts open multilevel signaling eyes versus closed binary-NRZ-eyes under 20Gbps signaling. This conclusion is verified for all the parameter space explored. The premise that multilevel signaling can be a possible option to extend VCSEL data rates beyond its small signal bandwidth limitation has now been confirmed by the eye simulations shown in Fig. 7 Even the eyes for NRZ-binary at 10Gbps show degradation in the form of rise time limitations as the VCSEL damping factor increases.
The PAM–4 option may offer distinct benefits for VCSEL links beyond 20Gbps or greater operation where optical bandwidth impairments become a major concern . In a second advantageous issue, we have recently shown the failure rate of a VCSEL has an explicit power law dependence on data rate . The failure rate increases with the data rate to the fourth power. Thus PAM–4 signaling can result in a substantially improved transmitter reliability. Since 2 symbols are sent each bit during PAM–4 this signaling approach could potentially have a sixteen fold advantage in VCSEL reliability compare to binary signaling using the identical VCSEL.
This material is based upon work supported by DARPA under Contract No. NBCH3039002.
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