Verifying PAM4 Performance in High-Speed Designs



A close look at PAM4 helps explain why it’s making a difference and how to capitalize on this innovative technology

After falling behind over the past few years, Ethernet is once again tracking with Moore’s Law and is now pushing global networking speeds to new levels. With the advent of 100 Gb/s, it’s safe to say that Ethernet is back. And forthcoming 400G Ethernet products promise to deliver new performance that ups the network bandwidth by a considerable margin once again.

The game changing innovation, particularly where 400G is concerned, is 4 level pulse amplitude modulation (PAM4) signaling. As serial data rates increased beyond 25G per channel, signal impairments caused by the increase in bandwidth compelled Ethernet standards bodies to make a major shift in approach. Simple, baseband, non-return to zero (NRZ) signal modulation techniques could not keep up and have been left behind in favor of more bandwidth efficient PAM4.

The reasons for the move to PAM4 are readily apparent: this modulation technique allows doubling of data rate while keeping the bandwidth by transmitting two bits in each symbol, as shown in Figure 1. It’s important to distinguish PAM4’s data rate from its symbol rate. The symbol rate is in baud (Bd) units. For example, a 56 Gb/s PAM4 (data rate) signal is transmitted at the symbol rate of 28 GBd.

NRZ generally describes baseband high/low signaling, but the formal description is 2-level pulse amplitude modulation, or PAM2. Since PAM4 signals do not return to zero after each symbol, they are also an NRZ signaling scheme. Therefore, while we use the shorthand expressions, more precisely it’s not NRZ vs PAM4; it is more accurate to refer to the two schemes as PAM2-NRZ and PAM4-NRZ.

Figure 1: PAM2-NRZ and PAM4: baseband signaling and eye diagrams.

The eye diagrams in Figure 1 offer some useful insights. With its multiple symbol levels, PAM4 is more sensitive to amplitude noise than PAM2-NRZ. While PAM4 signals also suffer greater ISI than PAM2-NRZ at a given symbol rate, they suffer much less at the same data rate. Being able to avoid symbol rate increase—and corresponding loss and ISI—is a major reason for switching from PAM2-NRZ.

PAM4 signal analysis borrows a great deal from the jitter and noise analysis developed for PAM2-NRZ. As such, PAM4 technology at 25+ GBd benefits from the innovations that have helped PAM2-NRZ thus far. These include differential signaling, clock recovery, and equalization at both the transmitter and receiver.

Optical systems can operate above 25 GBd with PAM2-NRZ, so the switch is less urgent but still important, because PAM4-based systems will offer power and cost advantages. Coherent modulation techniques such as dual-polarization quadrature phase shift key (DP- QPSK), can also use similar symbol rates between 25 and 50 GBd. It can easily accommodate transport across thousands of kilometers, but at a greater cost. So shorter reaches, like those across data centers, of 500 m to 10 km, can be accommodated by optical PAM4 transceivers more effectively and with reduced power requirements.

Understanding PAM4 Signals
Drawing a PAM4 eye diagram, as shown in Figure 2, in contrast to a PAM2-NRZ eye, is a simple and effective way to grasp the complexity of four separate symbol levels, six rising and falling edges, twelve distinct transition possibilities, and four different non-transitions. Even the 50 percent bit transition density of PAM2-NRZ changes to 75 percent PAM4 symbol transition density.

Figure 2: This shows how PAM4 signal properties compare to PAM2-NRZ.

Each of the PAM4 levels are specified as mean voltages, VA, VB, VC, and VD, for electrical signals and mean power for optical, PA, PB, PC, and PD. The four symbols are referred to as level 0, level 1, level 2, and level 3—so that the sequence shown in Figure 1 is typically described as {0, 1, 2, 3, 1, 3, 0}.

Since PAM4 signals have four levels, they have three interdependent eye diagrams that are interdependent because transitions from one symbol to another can affect more than one eye. Since noise affects each eye independently, PAM4 signals are at least three times more sensitive to amplitude noise than PAM2-NRZ. Each of the three eye diagrams can be analyzed like PAM2-NRZ eyes for width and height.

This sensitivity requires forward error correction (FEC) for PAM4 signals, allowing the maximum uncorrected bit error rate (BER) to be increased to 10-6 for electrical signaling and even higher for optical. From a test perspective, this relaxed BER constraint is a huge advantage because it allows measurement of pre-FEC performance down to BER ~ 10-6 in seconds. In the past, it either took a large fraction of an hour to reach down to BER ~ 10-12−10-15 or the use of risky extrapolation techniques.

FEC encodes binary logic into a set of data bits that include the overhead of FEC’s parity-like bits.  The resulting bit stream is then Gray coded and formatted into PAM4 symbols. The received data stream is Gray decoded back into a bit stream. This bit stream is then processed by FEC, which can correct a limited number of bit errors.

The way that Gray coding combines the most significant bit (MSB) and least significant bit (LSB) in each PAM4 symbol means that symbol errors caused by amplitude noise are more likely to cause one bit error than two while jitter is more likely to cause two bit errors per symbol error. Most standards specify either minimum acceptable BER before FEC or a raw symbol error rate (SER).

PAM4 Equalization
To open eye diagrams that have been closed by ISI, PAM4 systems employ equalization. ISI is caused by the frequency-dependent loss nature of the channel frequency response. Transmitter feed-forward equalization (FFE), which includes pre- and de-emphasis, and passive continuous time linear equalization (CTLE) at the receiver are techniques that boost the high frequency components of the waveform relative to its low frequency components to invert the effect of the channel. Increased high frequency content also aggravates crosstalk. Decision feedback equalization (DFE) at the receiver is a nonlinear technique that helps invert the channel response but without amplifying uncorrelated undesirables such as crosstalk.

While all three equalization techniques, transmitter FFE, CTLE, and DFE, are often combined to mitigate ISI in PAM2-NRZ systems, most PAM4 systems use only one or two of them: transmitter FFE or CTLE or FFE + DFE or CTLE + DFE.

PAM4 Test Signals
The PAM4 version of a pseudo-random binary sequence (PRBSn) pattern is called a PRBS quarternary pattern, PRBSnQ. PRBSn patterns include 2n-1 bits, every permutation of n consecutive bits. QPRBSn patterns are assembled by Gray coding a PRBSn pattern and its inverse. The inverse is included for balance, resulting in PRBSQn patterns with 2n symbols.

Most transmitter tests should be performed with either a QPRBS9 or a QPRBS13 test pattern. Receiver tests should be set up and calibrated with QPRBS13 but performed with QPRBS31.

Evaluating Electrical PAM4 Transmitters
A typical set up for analysis of PAM4 electrical transmitters is shown Figure 3. This testing requires an instrument-quality reference receiver that doubles as a signal analyzer. As shown, options can include a high-bandwidth real time oscilloscope, an equivalent-time sampling scope, or a bit error rate (BER) test system with PAM4 support. Regardless of the system use, the reference receiver should apply a fourth-order Bessel-Thomson filter with bandwidth of about 1.25×fB (depending on the application), where fB is the symbol rate.

Many of these measurements are automated by PAM4 analysis packages, but since PAM4 technology is still evolving, you’ll need to make sure the automated measurements you need for a particular application are supported.

Figure 3: Typical set-up for PAM4 transmitter testing.

SNDR Becomes Critical
Both IEEE and OIF-CEI have introduced the concept of replacing many of the historical methods of compensable intersymbol interference (ISI) jitter analysis with a technique of comparing the actual averaged pulse response determined from the transmitter to an extracted linear model. This technique uses a linear fit pulse peak, where the extracted pulse response is leveraged to perform the signal to noise and distortion ratio (SNDR).

With SNDR, the imperfections of the signal, noise, and distortion are summed, and their amplitude (RMS) is compared to the size of the signal. SNDR is less sensitive to ISI caused by factors such as insertion loss and reflections, and ISI can be compensated by equalizers in Tx and Rx. But SNDR includes all other sources of transmitter noise and distortion. A result above 27 dB is a pass in today’s electrical backplane standards (25 Gbps NRZ KR4) and 26 dB for electrical cables (25 Gbps NRZ CR4). For PAM4 this result needs to be even higher. For example, 200GBASE-KR4 requires SNDR ≥ 32.5 dB.

The advantage of SNDR is it offers designers flexibility in how they may reach conformance with several degrees of freedom and permits a strategy of compromise in one specification, while overdriving another to compensate. For silicon evaluators, it’s advantageous to see a single figure of merit, which is a composite of many silicon sub-specifications, when it comes to determining the best device.

There are several key instrument considerations to account for when performing SNDR measurements. The instrument (signal acquisition) bandwidth for IEEE 802.3bs/cd requires a 33-GHz system, with a response following a fourth order Bessel-Thomson response. The flat group delay or linear phase of this filter is key to minimizing instrument-induced ISI.

Evaluating PAM4 Optical Transmitters
Specific techniques for evaluating optical PAM4 transceivers have not been formalized. However, analysis based on the performance parameters detailed in Table 1 can be used to adequately evaluate PAM4 transmitter performance in most applications.
Traditionally optical signals should be analyzed with a measurement optical bandwidth slightly higher than the symbol rate. Some specifications refer to this requirement as 0.75×fB because in terms of the electrical bandwidth (after the photo detector) the bandwidth is 0.75×fB . (The two bandwidths are not the same since the optical-electrical converters is a square-law detectors). The latest optical signals for PAM4 are measured at 0.5×fB

Table 1: These are typical performance parameters for 13-29 GBd optical PAM4 transceivers.

Unlike differential electrical transmitters, optical transmitters have physically distinct “on” and “off” states. Many of the standard characterization parameters for optical transmitters should be measured separately for both the inner eye structure and the outer structure. Below are some key considerations.

  • OMAinner, the optical modulation amplitude of the inner eye structures are determined by the difference of high and low power for each eye: OMA01= P1 − P0, OMA12 = P2 − P1, and OMA23 = P3 − P2. The inner OMA that has greatest effect on BER is called OMAinner = min (OMA01, OMA12, OMA23).
  • OMAouter= P3 − P0.
  • Extinction ratio (ER) can be separated into inner and outer values, too, though it usually is only quoted for the outer eye, ER = 10 log(P3/P0).
  • Relative intensity noise (RIN) is the ratio of the rms noise of the unmodulated laser in the off state at a specific frequency per unit bandwidth to the total power of the unmodulated laser at any of the symbol levels. RIN of the outer eye structure is likely to be the only one specified.
  • RIN×OMA is the ratio of ambient light noise to the average modulated power per unit bandwidth.

Optical transmitters have different linearity problems than differential electrical transmitters. In some modulation implementations, transitions from low to high power states occur faster than high to low. The result is a tendency for the three PAM4 optical eyes to be misaligned. The higher the baud rate, the greater the deviation. High rate optical receivers may require independent time-delay sampling points for each eye: (tlow, Plow), (tmid, Pmid), and (tupp, Pupp).

Time deviation is the average deviation of the points of minimum ISI from the eye center in percent of a unit interval (UI):

where fB is the symbol rate.

The amount of time delay that a system can tolerate depends on the logic detection scheme, but if the decision circuits time-delay sampling point is the same for all three eye diagrams, time deviation should be less than 5-10 percent. Time delay tends to be a greater problem in optical than electrical systems.

Evaluating PAM4 Receivers
The measure of a receiver’s performance is how it does in the worst conditions it’s likely to encounter. Stressed receiver tolerance tests measure a receiver’s tolerance to signal impairments. Like 25+ Gb/s PAM2-NRZ, both electrical and optical PAM4 receivers are subject to tolerance tests. The idea is to probe a receiver’s weaknesses in a wide variety of difficult environments.

Electrical PAM4 receivers are subject to jitter and noise tolerance tests plus separate interference and crosstalk tolerance tests. To determine an optical receiver’s performance margin, increasing levels of stress are applied, and the BER performance of the receiver is evaluated. One example is to test the receiver’s BER margin with decreasing inner and outer OMA and ER, increasing RIN and chromatic dispersion, and with signals that have increasing time deviation.

Moving Forward with PAM4
In advancing from 25 to 50 Gb/s, high speed serial data transmission technology has crossed an inflection point. The technical advances that have enabled multi-gigabit data rates with PAM2-NRZ signal modulation on standard PCB backplanes can no longer economically produce the signal integrity required for reliable data transfer. The solution is to double the data rate without changing the symbol rate by evolving from PAM2-NRZ to PAM4.

This move, however, introduces new test and measurement challenges with reduced signal-to-noise ration and increased signaling complexity. These challenges can now be met with a combination of test instrumentation including real-time and sampling oscilloscopes and BERT error detectors along with PAM4 analysis tools and applications.

Heike Tritschler is a Technical Segment Lead at Tektronix, where she is responsible for coherent and electrical solutions. Tritschler has held various positions with Tektronix during her eight years with the company, including marketing manager and sales for BERT products. Her extensive background in technology marketing and engineering includes positions with Infineon, Picolight, JDSU, and Picosecond Pulse Labs. She holds a bachelor’s degree in engineering from Fachhochschule, Furtwangen. 

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