ADI In-depth丨Cable Distribution System In-Band Distortion? Ultra-Wideband Digital Pre-Distortion Teaches You to “Fight Fire with Fire”

Power amplifier (PA) digital pre-distortion (DPD) is a term that many people working in cellular system network R&D will be familiar with. Migrating this technology to cable can bring significant power efficiency and performance improvements, but it also brings significant challenges.

When a power amplifier operates in a nonlinear region, its output will be distorted. This distortion can affect in-band performance and can also cause unwanted signals to spill over into adjacent channels. Spillover is particularly important in wireless cellular applications, so the adjacent channel leakage ratio (ACLR) is strictly specified and controlled. One of the prominent control techniques is to digitally shape or predistort the signal before it reaches the power amplifier, thereby eliminating nonlinearities in the power amplifier.

The cable environment is completely different. First, it can be considered a closed environment. What happens in the cable does not extend outside the cable! The operator owns and controls the entire spectrum. Out-of-band (OOB) distortion is not a concern, but in-band distortion is critical. Service providers must ensure the highest quality in-band transmission channel so that they can utilize the maximum data throughput. One way to do this is to operate the cable power amplifier strictly in the linear region. The price of this operating mode is very poor power efficiency.

Figure 1. Power efficiency of a cable power amplifier driver.

Figure 1 provides an overview of a typical cable application. Although the system consumes nearly 80 W, only 2.8 W of signal power is delivered. The power amplifier is a Class A architecture with very low efficiency. The maximum instantaneous peak efficiency can be calculated to be 50% (assuming an inductive load when the signal envelope is maximum). If the power amplifier is operating completely in the linear region, considering the very high peak-to-average ratio of the cable signal (typically 14 dB) means that the amplifier needs to operate at an average of 14 dB below the onset of signal compression to ensure that signal compression does not occur even at the peak of the signal. Backing off is directly related to the amplifier operating efficiency. When the amplifier is backed off 14 dB to accommodate the various cable signals, the operating efficiency is reduced by 10 –14/10 . Therefore, the operating efficiency is reduced from the theoretical maximum of 50% to 10 –14/10 × 50% = 2%. Figure 2 provides an overview of this situation.

Figure 2. Peak-to-average ratio drives fallback mode and significantly reduces efficiency.

In summary, power efficiency is the main issue. Lost power affects cost, but just as importantly, it consumes scarce resources in the cable distribution system. Cable operators add more features and services, which require more processing, and the power required for processing may be limited by the existing power budget. If the wasted power consumption can be captured from inefficient power amplifiers, it can be reallocated to these new features.

The proposed solution to the inefficiency of the PA is digital pre-distortion. This is an approach that is being adopted throughout the wireless cellular industry. Digital pre-distortion allows the user to operate the PA in a more efficient but more nonlinear region and then pre-correct the distortion in the digital domain before sending the data to the PA. The essence of digital pre-distortion is to shape the data before it reaches the PA to counteract the distortion introduced by the PA, thereby extending the linear range of the PA, as shown in Figure 3. This extended linear range can be used to support higher quality processing, provide lower modulation error rate (MER), or allow the ^PA to run at lower bias settings, thereby saving power. Although digital pre-distortion has been widely used in wireless cellular infrastructure, implementing digital pre-distortion in a cable environment has unique and challenging requirements.

Figure 3. Digital predistortion overview.

As shown in Figure 4, the actual operating efficiency for the cable application is about 3.5%! Implementing DPD reduces the system power requirement from 80 W to 61 W, saving 19 W, a 24% power saving. The power requirement for each PA was previously 17.5 W, but now it drops to 12.8 W.

Figure 4. Overview of energy saving achieved through digital pre-distortion scheme.

The value of digital pre-distortion is self-evident, but it presents many unique challenges when implemented in cable applications. Therefore, these technical challenges must be met within existing resources. For example, the solution itself must be energy efficient, as there is little value in optimizing power amplifier efficiency if the power saved goes into powering the solution. Likewise, digital processing resources need to be appropriate so that they can efficiently reside in current FPGA architectures. Very large/complex algorithms with non-standard hardware requirements and extensive architectural changes are unlikely to be adaptable.

Perhaps the most significant difference between the cable application environment and the wireless cellular environment is the operating bandwidth. In cable, approximately 1.2 GHz of bandwidth must be linearized. The wide bandwidth challenge is compounded by the fact that the spectrum starts at only 54 MHz from DC and the signal bandwidth is greater than the channel center frequency. It is important to remember that the PA can save power by driving it into a nonlinear operating region, which improves efficiency but at the expense of nonlinear products. Digital predistortion must remove the nonlinearities introduced by the PA, especially those that fold back into the band. This poses unique challenges in cable applications.

Figure 5. Illustration of harmonic distortion terms in traditional narrowband

Figure 5 summarizes the broadband harmonic distortion terms that we might expect for a conventional narrowband (narrowband is defined later in this section) upconverted baseband signal that has passed through a nonlinear amplification stage. Nonlinear power amplifier outputs are often described by power series expressions, such as the Volterra series, which have the following form:

It can be thought of as a generalization of the Taylor power series with memory effects. It is important to note that each nonlinear term (k = 1,2, … , K) generates multiple harmonic distortion (HD) products. For example, the fifth order has three harmonic terms: the first, third, and fifth. It is also important to note that the bandwidth of a harmonic is a multiple of its order. For example, the width of the third order harmonic term is three times the excitation bandwidth.

In cable, the location of the harmonics on the spectrum (starting at DC at only 54 MHz) presents a special challenge for DPD that is not as relevant as large signal bandwidth. Harmonic distortion occurs in all nonlinear systems. The focus of DPD for cable is on harmonic distortion that falls in-band. As can be seen in Figure 5, in a traditional narrowband application, the focus would be on the third and fifth order harmonics. Although other harmonics are formed, they are outside the band of interest and can be removed by traditional filtering. We can define wideband and narrowband applications in terms of fractional bandwidth, where the fractional bandwidth is defined as follows:

(fn = highest frequency, f1 = lowest frequency, fc = center frequency). When the fractional bandwidth exceeds 1, the application is considered wideband. Most cellular applications have a fractional bandwidth of no more than 0.5. Therefore, their harmonic distortion behavior follows the characteristics shown in Figure 6.

Figure 6. Narrowband simplification; only products around the first harmonic need to be considered.

For such a narrowband system, only the in-band distortion around the first harmonic needs to be removed by DPD, since all other products are removed by using a bandpass filter. Also note that since there are no even-order products in the band, DPD only needs to deal with odd-order terms.

In cable applications, we approximate fn ~1200 MHz, fl ~50 MHz, and fc ~575 MHz, which gives a fractional bandwidth of 2. To determine the lowest harmonic distortion order that needs to be corrected, the following formula can be used:

(Kmin is the lowest nonlinear order to be considered), or in numerical terms this is 50 MHz × 2 = 100Mhz, which is less than 1200 MHz, so the second-order harmonic distortion is well within the operating band and must be corrected. Therefore, if the decision is made to operate the cable power amplifier outside of the safe and extremely linear operating range, the resulting harmonic distortion will be as shown in Figure 7.

Figure 7. Effects of broadband harmonic distortion in broadband cable applications

Compared to wireless cellular applications where only odd-order harmonics need to be considered, in cable applications both even-order and odd-order terms are in-band, creating multiple overlapping distortion regions. This has a significant impact on the complexity and sophistication of any DPD solution, as the algorithm must pass simple narrowband assumptions. The DPD solution must accommodate terms for every order of harmonic distortion.

In narrowband systems, even-order terms can be ignored and odd-order terms produce 1 term per band of interest. Digital predistortion in cable applications must account for both odd- and even-order harmonic distortion and must also take into account that each order may have multiple overlapping in-band elements.

Considering that the processing of traditional narrowband DPD solutions is done at complex baseband, we are mainly concerned with harmonic distortion that is symmetrically located around the carrier. In broadband cable systems, although the symmetry of those terms located around the first harmonic is maintained, this symmetry no longer applies to higher-order harmonic products.

Figure 8. Annotation of frequency offset requirements in complex baseband processing for wideband digital predistortion

Traditional narrowband DPD is done at complex baseband, as shown in Figure 8. In these instances, only the first harmonic product is within the frequency band, so its baseband product is directly converted to RF. When considering wideband cable DPD, higher-order harmonic distortion must be frequency offset so that the baseband products after upconversion are correctly located in the actual RF spectrum.

A closed-loop DPD system uses a transmit and an observation path. In an idealized model, neither path is bandwidth limited and both are wide enough to pass all DPD terms. That is, they are wide enough to pass both in-band and out-of-band terms.

Figure 9. Idealized DPD solution with no bandwidth limitation

Figure 9 shows an overview of one implementation of DPD. Ideally, the path from the digital upconverter (DUC) (via DPD) to the DAC and through the PA would have no bandwidth limitations. Likewise, the ADC in the observation path would digitize the full bandwidth (note that for illustration purposes, we show a 2x bandwidth signal path. In some wireless cellular applications, this can be extended to 3x to 5x bandwidth). The ideal scenario would be to completely cancel the distortion introduced by the PA by creating both in-band and out-of-band terms through DPD. It is important to note that in order to accurately cancel the distortion, the terms need to be created outside the bandwidth of the signal of interest.

In practical scenarios, the signal path has bandwidth limitations and the digital pre-distortion performance cannot meet the requirements of the ideal solution.

Figure 10. Decreased performance of DPD as bandwidth limitations in the signal path limit the OOB terms.

The JESD link between the FPGA and the DAC, the DAC image rejection filter, and the power amplifier input matching. The most significant impact of these limitations is on the out-of-band performance. From the simulation shown in Figure 10, it can be seen that the digital pre-distortion cannot correct the out-of-band distortion. In the cable, it is particularly important to consider that the out-of-band distortion will cause in-band performance degradation. Bandwidth limitations in the signal path can and do affect the in-band performance.

Emissions outside the band of interest (54 MHz to 1218 MHz) are in a section of the spectrum not used by others and are also attenuated due to the inherent cable losses at high frequencies. The observation path only needs to monitor what happens within the operating band.

Out-of-band radiation does not need to be considered, but radiation generated outside the band and extending into the band does need to be considered. Therefore, although out-of-band radiation does not need to be considered, the terms that form these radiations need to be considered. This scenario is very different from wireless cellular applications because the observation bandwidth requirements are typically 3 to 5 times the operating band. In cables, the focus is on in-band performance, so only the impact of out-of-band terms on in-band performance needs to be considered.

For DOCSIS 3, the frequency range is 54 MHz to 1218 MHz. DPD generates quadratic, cubic, …, cancellation terms. Although the correction only needs to be done over the cable bandwidth, in the DPD actuator, these terms are spread over a wider bandwidth (e.g., the third order bandwidth is spread to 3 times 1218 MHz). To maintain the stability of the conventional DPD adaptation algorithm, these out-of-band terms should be kept around the loop. Any filtering of the DPD terms tends to make the adaptation algorithm unstable. There are frequency band limitations in cable systems, so conventional algorithms may fail.

Like all other transmission media, cables introduce attenuation. This attenuation is generally considered to be related to the quality of the cable, the distance the cable is laid, and the transmission frequency. If relatively uniform received signal strength is to be achieved at the receiving end of the cable, i.e. across the operating spectrum, then pre-emphasis (tilt) must be added at the transmitting end. Tilt can be thought of as the inverse transfer function of the cable. It applies pre-emphasis or shaping that is proportional to the transmission frequency.

The shaping is achieved by a low power passive analog equalizer called a tilt compensator, which is placed before the power amplifier. There is little or no attenuation at high frequencies and more attenuation at low frequencies. The signal at the output of the tilt compensator can have up to 22 dB of equalized gain variation across the entire operating spectrum.

Figure 11. Tilt compensator solution

The tilt compensator shapes the signal and maintains the shaped profile as it is processed through the power amplifier. Traditional DPD schemes would see the shaping as an impairment and try to correct for it, since the DPD is a (non-linear) equalizer. It seems reasonable that if the inverse of the tilt is added to the observation path, its effects can be mitigated. But this is not the case. Power amplifiers are non-linear, so the commutativity does not apply, that is:

To operate optimally, the DPD processing block requires a clear understanding of the signal present at the input of the PA. In cable DPD applications, tilt compensation must be maintained while the PA is modeled using the DPD algorithm. This presents some very unique and difficult challenges. A stable, low-cost solution that does not equalize the tilt is required. While the nature of the solution cannot be disclosed in this article, ADI has found an innovative solution that will be detailed in a future publication.

As shown in Figure 4, a typical cable application will split the output of one DAC into four paths and provide them to four independent power amplifiers. To maximize power savings, digital pre-distortion needs to be implemented on all of these power amplifiers. A feasible solution may be to implement four independent digital pre-distortion modules and DAC modules. This solution works, but it will reduce efficiency and increase the cost of system implementation. The additional hardware has both capital and power costs.

Not all PAs are created equal, and while process matching (during manufacturing) can provide units with similar personalities, differences still exist and grow larger with aging, temperature, and supply fluctuations. However, using one PA as a master and developing an optimized DPD for it, then applying it to other PAs, does provide system performance benefits, as shown in the simulation results in Figure 12.

The curve on the left shows the PA performance without DPD. The nonlinear operating mode results in distortion, which is reflected in the MER1 performance (ranging from 37 dBc to 42 dBc). Closed-loop DPD is applied to the output of the observed master PA; the green curve on the right side of the graph shows the enhanced performance. DPD has corrected for the PA distortion, resulting in an overall performance shift that provides a MER of 65 dBc to 67 dBc. The remaining curve in the middle of the graph shows the performance of the slave PAs, i.e., the PAs that are corrected for the master PA. It can be seen that implementing closed-loop DPD with only one PA observed can benefit the performance of all PAs. However, there are still operating points where the slave PAs fail. The performance of the slave PAs ranges from 38 dBc to 67 dBc. The wide range itself is not a problem, but part of this range is below the acceptable operating threshold (typically 45 dBc for cables).

Figure 12. Single-pass digital predistortion using multiple power amplifiers (simulation results)

The unique system architecture in cables presents additional challenges for DPD. Optimizing performance requires a closed-loop DPD solution. But traditionally, doing so in cables would require additional hardware in each PA path. The best solution would provide the enhanced functionality of closed-loop DPD to each PA, but without the additional hardware cost.

As mentioned earlier in this article, cable DPD presents very unique and difficult challenges to the designer. If these challenges are addressed within the constraints of power and hardware, the benefits are not diminished; if the power saved in the PA is used for an additional DAC or FPGA, there is little value in saving power in the PA. Likewise, power savings must be balanced against hardware cost. ADI addresses this challenge by combining high performance analog signal processing with advanced algorithmic solutions.

A high-level overview of the ADI approach is shown in Figure 13. The solution can be thought of as having three key elements: the use of advanced converter and timing products, an architecture that enables comprehensive signal chain monitoring/control, and the application of advanced digital predistortion algorithms that leverage existing knowledge to achieve optimal performance.

Figure 13. Cable DPD solution using advanced converters and the SMART algorithm.

The algorithm is the heart of the solution. It uses its extensive knowledge of signal processing and the transfer function of the signal path to shape the output while adjusting the dynamic control of certain aspects of the signal path. A dynamic system solution not only means that system designers can save significant power, but these power savings can be directly converted into performance improvements. Using the algorithm, once the user defines the MER1 performance level that the system must operate at, system adjustments are implemented to achieve that performance on all outputs. It is important to note that the algorithm also ensures that performance thresholds are met while maintaining optimal power efficiency for each power amplifier. The power amplifiers are all powered below the power required to achieve the target performance.

The implementation of this solution was outlined earlier. The characteristics of the algorithm itself are ADI proprietary IP and are beyond the scope of this article. The SMART algorithm has the ability to learn the system path and then change the nature of the data transmitted through the path as well as the characteristics of the path itself to provide the best results. We define the best result as: maintaining MER quality while reducing power requirements.

The path characteristics as well as the nature of the transmitted signal are constantly changing. The algorithm has a self-learning capability to handle dynamic adaptability. More importantly, the adaptation occurs during system operation without interrupting or distorting the transmitted stream.

The cable environment remains an important infrastructure for delivering data services. As technology continues to evolve, the demands for spectrum and power efficiency are increasing. The development of new generation technologies is increasing the demand and driving the realization of higher order modulation schemes and better power efficiency. These enhancements must come without compromising system performance (MER), and although digital pre-distortion provides a possible way to achieve it, its implementation in cable applications poses very unique and difficult challenges. ADI has developed a comprehensive system solution to meet these challenges. The solution includes silicon-based chips (DAC, ADC and clock), power amplifier control and advanced algorithms. The combination of all three technologies provides users with an adaptable solution in which they can easily achieve power and performance requirements with minimal compromise. The software-defined solution also supports an easy transition from legacy cable technology to the next generation cable technology, which is expected to include full duplex (FD) and envelope tracking (ET).