Digital Predistortion (DPD) technology

Digital Predistortion (DPD) technology

Introduction

Rf transmitter designers are confronted with contradictory design trade-offs. In a spectrally congested environment, the demand for higher data throughput complicates modulation formats, which in turn imposes strict requirements on the linearity of power amplifiers (PA). In addition, the demand for enhancing energy efficiency and higher power output has driven designers to make devices operate in nonlinear regions. The commonly used technique to address this trade-off is the digital predistortion (DPD) algorithm - it enables designers to operate in the efficient but nonlinear regions of amplifiers while maintaining the linearity of the transmitted signal required by most digital modulation formats. This article will explore the driving factors of these trends, measurement techniques for characterizing nonlinear devices, common DPD models, requirements for DPD instruments, and the measured results of PA in mobile devices.

The Complexity and Linearization Requirements of Wireless Modulation

Early wireless standards adopted simple modulation formats such as Gaussian Minimum Frequency Shift Keying (GMSK) and Phase Shift Keying (8-PSK). This type of system has a low data rate, and designers benefit from its relatively narrow signal bandwidth and small peak-to-average power ratio (PAPR). In contrast, modern wireless standards achieve higher data rates by occupying more bandwidth and adopting high-order digital modulation techniques, such as IEEE 802.11ac and LTE Advanced. These standards employ advanced technologies such as 256-QAM, Orthogonal Frequency Division multiplexing (OFDM), and carrier aggregation. Their digital communication signals not only have a wider bandwidth but also a significantly increased PAPR. The increase in data rate brought about by wider transmission bandwidth and higher-order modulation schemes comes at the cost of higher linearity requirements and lower PA power efficiency. Table 1 lists the typical parameters of these wireless signals.

Table 1. Common Parameters of Wireless Standard Signals

Rf power amplifiers are one of the main sources of nonlinearity in RF transmitters. Figure 1 shows the in-band effect of PA nonlinearity on 64-QAM modulated signals - the constellation diagram at the PA output end is significantly compressed, resulting in an increase in bit error rate and deterioration of error vector magnitude (EVM) performance. In addition to in-band distortion, nonlinearity also reduces out-of-band performance, as shown in Figure 1. This figure shows the spectrum regeneration phenomenon at the PA output end of mobile devices under 5MHz LTE excitation.

Figure 1. The influence of nonlinearity on performance (a) In-band compression of 64-QAM constellation diagram (b) The influence of nonlinearity on out-of-band performance

Amplifier Power Efficiency

An important performance indicator of a power amplifier is the power-added efficiency (PAE), which is defined as the percentage of the power obtained by the signal to the power supplied by the power supply. It is generally believed that an efficiency close to 50% is considered outstanding performance. Figure 2a shows the relationship between the output power and PAE of a typical PA; Figure 2b shows the typical characteristics of nonlinear output power varying with input power.

Figure 2. Typical impact of PAPR on PA power additional efficiency: (a) Relationship between PAE and output power (b) Relationship between output power and input power

Although the amplifier is most efficient when approaching the peak power, the linearity of the device performs poorly at this time. For signals with high PAPR, if their peak output is restricted to an acceptable linearity point, the average power of the signal will be forced to be in the inefficient region. This concept is shown in Figure 2, which includes the power-time (PVT) curve of common LTE signals. It should be noted that, depending on the design, the acceptable linearity point may be a few dB lower than the peak efficiency point. In this case, the maximum output power of the PA is not fully utilized, resulting in additional efficiency losses.

Nonlinear AM-AM and AM-PM Characterization of Devices

Figure 3 shows the typical gain compression characteristics of the amplifier (as a function of the input power). Gain distortion is the main cause of nonlinearity, but the amplifier also introduces phase distortion related to the input power, further reducing the modulation accuracy. The standard method for quantifying these effects in the industry is to obtain AM-AM and AM-PM data through AM-PM measurements.

Figure 3. (a) AM-AM and (b) AM-PM data

Each graph shows the measured data and the fitting results of the 7th-order polynomial curve. The AM-PM measurement is accomplished by scanning the input power of the device and measuring its response. Subsequently, the distorted output signal is aligned with the excitation waveform to calculate the complex gain sample by sample. There are two ways to provide test excitation: power scan continuous wave (CW) signals or wideband modulated waveforms with a sufficiently high PAPR to cover the target power range. Because the modulated waveform can capture the memory effect of the device, it can simulate the performance of PA under actual working conditions more accurately than the power scan CW, and thus is usually more favored. Figure 3 shows the AM-AM and AM-PM characteristics of the PA when a 20MHz, 100RB LTE signal is applied. The gain of an ideal amplifier should not vary with the input power. Similarly, the ideal AM-PM response of a PA should show a constant phase shift at all power levels. The polynomial curve fitting trajectories of the two sets of data in Figure 3 reflect the static nonlinear characteristics.

Digital predistortion technology

Figure 4 shows a simple system architecture of digital predistortion, in which the predistorter is cascaded with the DAC, RF upconversion circuit and nonlinear PA. The predistortor applies reverse distortion to the baseband signal, making the cascaded system exhibit linear characteristics. From the perspective of modulation, Figure 4 demonstrates the working principle of DPD: in the 64-QAM constellation diagram, symbols close to the peak amplitude require additional gain to counteract the compression characteristics of PA; Although not easily detectable, these symbols will also be rotated to correct the phase distortion introduced by the PA.

Figure 4.64-QAM constellation diagram shows the conceptual operation of DPD and the state model of the DPD system, where x is the time-domain excitation, h(x) is the predistorter, f(x) is the PA model based on AM-AM and AM-PM, and y(x) is the PA output

A large number of literatures have conducted research on PA modeling and predistortion techniques. Most DPD technologies can usually be classified into memory-free or memory-equipped types. Memoryless predistortion is a nonlinear function. Its output sample only depends on the current input sample, which has the advantages of simple modeling and calculation. However, as the signal bandwidth increases, its performance often deteriorates. The DPD model for correcting the memory effect of devices is usually not only a nonlinear function of the current input sample, but also related to a finite number of historical samples. Practice shows that for broadband signals, the performance of the model with memory is superior to that of the model without memory, but its performance improvement comes at the cost of increased computational complexity.

No-Memory AMPM Lookup Table (LUT)

The AM-AM and AM-PM responses of the device under test (DUT) can be obtained by modulating AMPM measurements. The measured gain and phase information can be combined into a single complex polynomial model f(x). The most direct linearization method is to find the predistorter h(x) and make it form a linear response when cascaded with the PA. As shown in Figure 4, x(t) is the time-domain excitation, h(x) is the predistortor, f(x) is the PA model, and y(x) is the response. The cascade response of the amplifier and the predistorter to the excitation waveform x(t) can be expressed as y(x)=f(h(x)). If the excitation waveform x is expressed in polar coordinate form, x: ejϴ, and PA has a nominal linear gain G, then the ideal output is yideal(x)=G∙ x: ejϴ. Therefore, a predistortor h(x) capable of achieving linear output should satisfy:

If the AM-AM and AM-PM responses are modeled by k-order polynomials, then the combined complex response f(x) can be expressed as shown in (2).

For higher-order K, determining the analytical expression of f^ -1 (g∙x) is quite difficult. Therefore, the inverse operation of the AM-AM and AM-PM models f(x) needs to be numerically solved within the range of the calculated input power, and then the results are stored in the lookup table (LUT). Subsequently, the k-order complex polynomial can be fitted to the predistortor LUT, thereby obtaining the expression of h(x) :

The graphical representation of this operation is shown in Figure 5, in which, in addition to the ideal device characteristics, the exaggerated AM-AM response of the amplifier is also plotted. Here, it is assumed that the AM-AM response is modeled using a K-order polynomial. For the input signal with an amplitude of Pin, it can be known through polynomial calculation that compared with the ideal values Pout and ideal (given by y=G∙x), the output is compressed by dP dB. Figure 5 shows that merely increasing the input power by dP dB to Pin 'does not yield a linear output. As the PA has entered the compression zone, this phenomenon was expected. However, by numerically calculating the inverse function of the AM-AM response, the predistorted input Pin,DPD that can produce a linear output can be found.

Figure 5. System model for the DPD lookup table based on AMPM, where x is the time-domain excitation and h(x) is the predistorter

Figure 6 shows that the memory-free predistorter can effectively linearize the average AM-AM and AM-PM responses of nonlinear PA. However, the sample cloud around the best-fitting curve indicates that there is still a significant residual memory effect in the corrected response. These memory effects can reduce system performance, but they can be corrected through more complex DPD models.

Figure 6. Response of LTE devices corrected by 7th-order memoryless polynomial DPD

Memory models

The most comprehensive model of nonlinear systems with memory is the Volterra series, as shown in (4). However, as the nonlinear order K and memory depth M of the model increase, the complexity of the model will rise sharply, which makes the Volterra series difficult to use in most practical applications due to the excessive computational load.

In practical applications, nonlinear systems with memory, such as RF power amplifiers, can be fully modeled using only a part of the terms in the complete Volterra series. Common Volterra derivative models include the Memory Polynomial, Wiener and Hammerstein models. The implementation complexity of these models has been significantly reduced, yet they can offer performance comparable to that of a complete Volterra series. The memory polynomial model is one of the more commonly used predistortion techniques. It is composed by selecting a subset of the Volterra series, as shown in Formula (5) :

Rewriting Equation (5) using the vector representation of N sample blocks yields formula 6:

从概念上讲，为预失真器创建模型的最直接方法是首先对PA进行建模，然后计算其逆模型。对于带记忆的非线性系统（如记忆多项式模型），一种求逆的方法是使用p阶逆模型。该模型会生成另一个带记忆的非线性系统，但多项式阶数更高。高阶特性可能导致系统不稳定，因此预失真器的首选建模方法是采用所谓的间接学习架构，如图7所示。

Figure 7. For determining the indirect learning architecture based on the coefficients of the Volterra predistorter

Essentially, this architecture enables engineers to model inverse distortion through PA, and when applied to the transmitted signal x, it can generate a cascaded linear output y. If the output y is scaled according to the linear gain G of the amplifier, then u=y can be regarded as the transmitted signal x with the combined residual distortion of the amplifier and the predistorter. Subsequently, by finding the mapping w between the distorted PA output u and the predistorted transmission signal z, the inverse distortion model can be created. When converging, u=x and z= Z. thus such that:

Which U can press (6 c) structure, the xk, q [n] is replaced by UK, q [n], the xk, q = U [n], [n] - q | U [n] - q | ^ k - 1. The least squares solution of Equation (7) is in its common form:

In this experimental setup, vector z is initialized as the transmission signal x. The next section will apply the results obtained in (8) to the actual LTE power amplifier.

The measured performance of LTE power amplifiers based on mobile devices

The performance improvement brought by the adoption of DPD linearization technology largely depends on the characteristics of the specific device design. Figure 8a shows the in-band distortion characterized by error vector amplitude (EVM) at different power levels. The 10MHz LTE waveform used in this figure has a peak-to-average power ratio (PAPR) of approximately 8dB. Below +21dBm, memory-free DPD can improve EVM by 5dB. After adopting the five-tap memory model, the EVM can be further improved by 5dB, with an overall increase of 10dB. When the average output power is between +21dBm and +23dBm, the device shows significant compression, and the gains of the two DPD algorithms tend to be consistent - at this point, the sum of the average output power and PAPR exceeds the maximum output power of the device. However, when the power exceeds the maximum output power of the device, DPD can only correct phase distortion.

Figure 8. In the LTE 10MHz scenario: (a) Relationship between EVM and average power (b) Relationship between ACPR and average power

Figure 8b shows the out-of-band distortion characterized by the adjacent channel power ratio (ACPR). Similar to scenarios where EVM is below +21dBm, memoryless DPD can improve ACPR by more than 10dB. In contrast, the adoption of the 5-tap memory model only brings a marginal improvement of 0.5dB, indicating that the memory effect of the device has a greater impact on in-band distortion than out-of-band distortion. Figure 9 shows the power-added efficiency (PAE) of the devices within the same average output power range - as expected, PAE increases proportionally with the output power. The slight increase in PAE at a specific power is attributed to the gain expansion achieved after applying DPD. For this specific PA, if the system requires the EVM to be less than -43dB, the maximum output power is +21dBm when DPD is not used. After adopting the 5-tap memory DPD correction, the output power range can be expanded by 1.5dB, increasing the PAE from 18% to 23%.

Figure 9. Relationship between PAE and Output Power in the LTE 10MHz scenario

Instrument requirements for digital predistortion

Figure 10 shows a typical test configuration of a wireless power amplifier. In this test system, the application of DPD places higher demands on the instrument in four aspects: synchronization, bandwidth, dynamic range and linearity.

Figure 10. Test configuration of power amplifier instruments for typical mobile devices

The specific bandwidth requirements are closely related to the implementation method and performance goals of DPD. In some cases, the bandwidth required for configuring a system to test PA under DPD conditions is 7 to 10 times that of the signal itself. Figure 11a shows the power spectrum of the signal before predistortion, while Figure 11b shows the same signal after applying DPD. For this specific signal, after using the 7th-order memory-free polynomial model, the bandwidth increased by more than seven times when measured at a signal power higher than -100 DBM /Hz. In addition to a wider bandwidth, DPD will also increase the peak-to-average power ratio (PAPR) of the signal driving the PA. Therefore, the test instrument needs to provide a larger dynamic range to adapt to the predistorted signal. In Figure 11, the PAPR of the predistorted signal is 3.7dB higher than that of the original signal.

Figure 11. LTE signal spectrum: (a) Before the predistortion stage; (b) Conclusion after the predistortion stage

Conclusion

The evolution of wireless technology has compelled mobile device designers to view active linearization as a solution to the dual demands of high data rates and higher efficiency. In mobile applications, digital predistortion (DPD) is becoming a common technique for correcting the nonlinearity of power amplifiers (PA). Although the concept of correcting defects is simple, the complexity of PA behavior prompts engineers to deeply understand the principles and driving factors of DPD technology. Since each device design is different, there is no single model or algorithm that can be applied to all pas. Looking ahead, the application of DPD technology in wireless devices is rapidly spreading, which requires engineers to adopt test technologies that can meet these strict requirements.