Power Amplifier (PA) Designers Tackle High Peak-to-Average Power Ratio (PAPR) with Digital Predistortion (DPD)

by David Vye, Director of Technical Marketing, AWR Group, NI

Performance targets for 5G New Radio (NR) require the use of cyclic-prefix orthogonal frequency-division multiplexing (CP-OFDM) waveforms, as well as inter- and intra-band carrier aggregation (CA), first introduced in LTE-Advanced Rel. 10, to enhance spectral efficiency, especially for the crowded sub-6 GHz bands. The high spectral efficiency and wide bandwidths in communication systems employing these techniques can result in signals with high PAPR, which creates challenges for PA designers struggling to simultaneously meet bandwidth, linearity, and efficiency requirements.

These high peak-power levels drive the PA into gain compression, where device nonlinearities generate higher distortion levels. This requires greater output backoff (OBO) from the P1dB compression point of the device. This linearity is needed in order to minimize signal distortion and reduce bit-error rate (BER) and adjacent channel interference (ACI).

In addition to linearity, high power-added efficiency (PAE) is also needed to reduce power consumption in order to extend mobile device battery life and reduce base station operating expenses. As the PA operates at power levels below saturation, the efficiency degrades. This creates an issue in the presence of high PAPR signals where the back-off input power is well below saturation. As a result, designers are challenged to maintain high PAE while at the same time achieving low signal distortion under high PAPR.

The PAPR of a signal is defined as the ratio of its instantaneous peak power to its time-averaged power, which can be determined from the signal’s complimentary cumulative distribution function (CCDF). PAE degradation for PAs operating at higher backoff power levels is illustrated in Figure 1.

Addressing the Design Challenge
Different PA design strategies can be employed to improve linearity and efficiency performance, including the use of different architectures. Linearization techniques such as feedback, feed forward, or digital predistortion (DPD) can also be used to cancel out distortion resulting from device nonlinearities. In addition, crest factor reduction (CFR) techniques such as peak canceling, peak windowing, and clipping/filtering can be applied on the reference waveform to reduce the PAPR, allowing the PA to operate at higher average power levels for improved efficiency. Together, these techniques reduce the signal distortion that leads to spectral regrowth.

The NI AWR Design Environment platform, specifically Visual System Simulator™ (VSS) software can be used to understand the impact on PA performance due to CA and different modulation schemes (Figure 2).

VSS software, along with Microwave Office circuit design software, provides designers with simulation tools from which to develop front-end components, including PAs employing different linearization technologies. VSS software offers virtual test benches supporting multiple wireless communication standards for the investigation of the relationship between PA performance and input signals. Together, VSS and Microwave Office software tools allow designers to pursue optimum linearity and efficiency for a comprehensive PA characterization and design flow, integrated with custom DPD solutions.

System Simulations/Analysis Define PA Requirements
PAPR is a statistical quantity of a random signal. In OFDM systems, the large number of subcarriers periodically (and somewhat randomly) add to or subtract from one another, thus creating waveforms with a nearly Gaussian distribution of power variation. As a result, OFDM signals tend to have a PAPR ranging from 10 to 13 dB (Table 1), with CA driving up the PAPR by another 2.5-3 dB. Different OBO levels related to PAPR requirements are required depending on the number of aggregated component carriers (CCs) and the CA configuration.

The CCDF curve, as illustrated in Figure 3, describes the statistical behavior of a signal, showing how often a particular power level is exceeded. VSS software calculates CCDF versus PAPR to help designers determine OBO specifications and includes a CCDF measurement example project, CCDF_Measurement, [1] that provides a straightforward illustration of CCDF simulation/plotting for three different modulation sources: quadrature phase shift keying (QPSK), offset QPSK (OQPSK), and multilevel quadrature amplitude modulation (QAM), with average signal power of -40 dBW. In this example, the CCDF shows that the signal power will exceed the average power by 3 dB with a probability of 0.1 for the 16-QAM source (Figure 3, brown trace).

Another example within VSS software, 32_Carrier_QPSK_CCDF, [2] demonstrates the impact of CA on PAPR and CCDF, as well as the resulting implications on component (PA) specifications. Based on the clipping/saturation level of the amplifier or the desired peak threshold value, the distortion in the power spectrum and the constellation can be observed. The average signal power level of each signal is controlled by the parameterized channel-power variable, which can be tuned, along with the root-raised-cosine (RRC) pulse shaping, as the simulation is running.

The measurement graphs shown within Figure 4 display the spectrum of one signal along with the resulting spectrum of combining 32 signals together. This VSS project monitors the impact on the CCDF measurement as a function of channel power and RRC pulse shaping, as well as the total average power (dBm) of the 32 signals.

It is also worth noting that cellular service operators have implemented CA on download (DL) and upload (UL) to further increase consumer data throughput. Up to 400 MHz of instantaneous bandwidth can be achieved through CA (using four 100 MHz channels) within the sub-6 GHz NR allocated spectrum.

The signal source in the VSS example project, 5G_PA_Analysis_FBMC_GFDM_OFDM, [3] supports adjustable parameters such as carrier frequency, subcarrier spacing, number of subcarriers, and subcarrier mapping to address the full range of 5G NR specifications. Each modulation source block is followed by a linear pre-amplifier, nonlinear PA, and corresponding demodulator. Figure 5 shows the results of two PAs driven by different subcarrier mappings and the impact on output spectrum and CCDF versus the PAPR characteristics, providing the analysis necessary to develop linearized PAs.

Principles of DPD
A predistorter is a device placed in front of a PA to inverse the effect of its nonlinear transfer characteristics. The predistorter contains feedback information that calculates coefficients used for inverting the characteristic of the PA, as shown in Figure 6 (top). The predistorter can be placed on the IF signal, the RF signal, or the baseband. Although predistortion can be implemented in an analog or digital manner, advancements in digital signal processing (DSP) technologies have made the digital implementation, namely DPD, a popular choice.

It is important for the designer to understand the nature of the signal distortion introduced by the amplifier in order to implement a sufficient DPD solution. PAs comprise several blocks, including the active device (transistor), the input and output impedance networks, and the bias networks. Each block contributes to different PA characteristics. Static nonlinearity is a major source of distortion and is attributed to the nonlinear DC characteristics of the active device, whereas memory effects are attributed to the frequency response of the matching networks and device parasitics. They are also attributed to trapping effects and temperature changes due to the power dissipation. While the nonlinear behavior is more dominant than the memory effects, DPD may be needed to compensate for both [4].

Therefore, designers must select an accurate (behavioral) model structure that can best represent the nonlinearity and memory effects to implement the appropriate pre-distortion. PA baseband behavioral models can be classified in three categories:

• Memoryless models
• Models with linear memory
• Models with nonlinear memory [5]

Memoryless models assume that the instantaneous output signal depends only on the instantaneous input signal of the amplifier. These models are based on the quasi-static AM/AM and AM/PM properties of the PA. Various memoryless models have been proposed in the literature, including the power series or polynomial model [5] and the lookup table (LUT) mode. VSS software supports several DPD algorithms, (inclusive of a commercially available NanoSemi model), however for purposes of this article, the focus will be on a LUT DPD example. A more advanced example was presented by T. Gotthans et. al [6] that integrates multiple custom DPD algorithms (memory polynomials, generalized memory polynomials, and more) inside NI AWR software using C and C++ language to facilitate and optimize PA/DPD design, test, joint optimization, and field-programmable gate array (FPGA) implementation.

Lookup Table (LUT)
The LUT derives the AM/AM and AM/PM conversions of a PA from raw measurement data using averaging or polynomial fitting and stores these conversions (amplitude and phase) in two lookup tables. For a given input amplitude, the LUT model indexes the corresponding AM/AM and AM/PM conversion values. The lookup table is used basically as a static DPD but can be enhanced as a dynamic DPD.

The LUT derives the AM/AM and AM/PM conversions of a PA from raw measurement data using averaging or polynomial fitting and stores these conversions (amplitude and phase) in two lookup tables. For a given input amplitude, the LUT model indexes the corresponding AM/AM and AM/PM conversion values. The lookup table is used basically as a static DPD but can be enhanced as a dynamic DPD.

The advantage of the LUT is low complexity, but the drawback is that it does not inherently capture memory effects that may be essential to properly address PA behavior for the envisaged large NR bandwidths. While these models often require few parameters to model the nonlinear behavior and may be restricted to simple amplifier architectures, they do offer firsthand-cut qualitative analysis.

Note: Solutions that address nonlinear models with linear memory by assuming that the PA memory effects can be modeled with a combination of linear filters and a memoryless nonlinearity are available [4] [5]. Accounting for the nonlinear memory effects may be required for wideband communication signals. A more rigorous model includes the Volterra series expansion, which comes at the cost of computational complexity. Several simplified approaches based on different reduced model techniques have been reported [5].

LUT Example
The VSS predistort network example project, Predistort_Network, [7] is a practical example that shows how to use the software to construct a DPD system for reducing spectral regrowth at the output of an amplifier. This project uses an LUT-based DPD constructed from the AM/AM and AM/PM characteristics of the amplifier, which can be derived from measurement, the device manufacturer’s datasheet, or in this case, simulated with Microwave Office software in situ at the transistor level through co-simulation with VSS.

The AM/AM and AM/PM graph plots the large-signal transfer characteristics of the project amplifier, calculated by VSS measurements using the PA characterization test bench driving the AMP_1900 PA defined in the Microwave Office circuit schematic (Figure 7). The same VSS measurements are used to derive the inverse AM/AM and AM/PM characteristics and calculate the LUT coefficients needed to predistort the in-phase (I) and quadrature (Q) components of the PA before amplification. The coefficients calculated by the output equations are stored in the LUT data file and used by the LUT blocks in the predistorter. This file contains three columns; the first column consists of the signal power level at the input of the predistorter and the second and third columns consist of the real and imaginary components of the coefficients used to predistort the IQ signal.

The project’s DPD system subcircuit uses a VSS source to drive the PA shown in Figure 7, as well as two versions of DPD subcircuits (floating-point and fixed-point) in conjunction with this PA, which is shown in Figure 8a. The DPD subcircuit in the system diagram LUT Predistorter (upper insert in Figure 8a) calculates the instantaneous power level of the input signal, which is then used to select the correct I and Q coefficients, using interpolation if necessary.

The input signal is scaled by this coefficient, resulting in a digitally predistorted output. The lower DPD subcircuit in the system diagram implements a fixed-point DPD by first converting the input signal and LUT coefficients to fixed-point DPD and then performing a similar function as the upper DPD subcircuit. The output is converted to floating-point DPD and sent to the amplifier. The LUT coefficients for the fixed-point implementation are also calculated separately in the LUT quantization system schematic, with the simulation results shown in the LUT fixed-point table (Figure 8b).

Figure 9, left graph, shows the spectrum prior to amplification, the resulting spectrum of direct amplification, and the spectrum generated with floating-point and fixed-point DPD. The plots to the right in the figure show the AM/AM (top) and AM/PM (bottom) characteristics of the amplifier compared to those of the PA with DPD.

The VSS example project also contains a script that automates LUT coefficient generation by automating the AM/AM and AM/PM measurements, calculating the LUT coefficients, storing them in the data file, and then restarting the simulation with the updated coefficients. Designers can thereby insert a new Microwave Office PA design in place of the default one and implement a new LUT predistorter for their own particular device.

Conclusion
5G NR is driving the trend of enhancing data rates and capacity through the use of spectrally efficient modulation waveforms and CA, resulting in high PAPR and wider bandwidths. To maintain higher efficiency, PA designers must adopt advanced linearization techniques that enable the amplifier active device to operate closer to saturation. Microwave Office circuit simulation software specializes in PA analysis and works directly with VSS system simulation software to quantify the linearity measurements such as CCDF, EVM, and ACPR that are essential in meeting these emerging technical challenges.

Complimentary Trial
The examples mentioned in this article are available for download at the URL address listed in the references and work with an active license of VSS software. Software evaluations are available at https://www.awr.com/download-free-trial

References

1. http://kb.awr.com/display/examples/CCDF_Measurement
2. http://kb.awr.com/display/examples/32_Carrier_QPSK_CCDF
3. http://kb.awr.com/display/examples/5G_PA_Analysis_FBMC_GFDM_OFDM
4. D. Schreurs, M. O’Droma, A. A. Goacher, and M. Gadringer, RF Power Amplifier Behavioral Modeling. Cambridge, 2008.
5. https://www.chalmers.se/en/centres/ghz/publications/Documents/Lic_thesis_18-%20Digital_predistrotion_for_the_linearization_of_power_amplifiers.pdf
6. T. Gotthans1, G. Baudoin2, O. Venard2, M. Abi Hussein2 and S. Wang2, EuMW17 – RF/Microwave PA Forum – Nurenberg, 11th of October 2017
7. http://kb.awr.com/display/examples/Predistort_Network

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