# Agnostic Envelope Linearization of Dynamically Supplied Power Amplifiers for Mobile Terminals
## 1 Introduction  
Power efficient and linear amplification of radio frequency (RF) power amplifiers (PAs) is an old but still hot topic of research, since with the eruption of new technologies (in 4G, 5G, and beyond), new challenges arise in terms of required transmit power, transmission, and reception with multiple antennas, dynamic bandwidth allocation (i.e., numerology), dynamic or concurrent frequency bands of operation, and high peak-to-average power ratio (PAPR) waveforms as a consequence of targeting spectrally efficient high-capacity transmission (i.e., high-order M-QAM modulation schemes and orthogonal frequency-division multiplexing--OFDM). Several adaptive digital predistortion (DPD) schemes have been proposed to linearize RF PAs in macro base stations [1, 2], where the DC power consumption of the RF PA is significantly higher than the DC power consumption of the digital signal processing (DSP) hardware. However, the linearization of the user equipment (UE) requires low-complexity and, preferably, open-loop linearization solutions, since the DC power consumption of the digital signal processing (DSP) significantly impacts the overall transmitter power consumption [3, 4, 5]. In addition, many efforts have been devoted to find highly efficient amplification topologies capable of maintaining high power efficiency figures over significant back-off levels [6]. Power amplifier architectures based on dynamic load modulation, such as Doherty PAs [7], load modulated balanced amplifiers (LMBA) [8], or outphasing or LINC PAs [9], have been widelyproposed in the literature. Moreover, dynamic supply modulation techniques, such as envelope tracking (ET) PAs [10; 11; 12], have been adopted in commercial solutions for mobile terminals in order to mitigate the DC power dissipated as heat when handling signals with high PAPR. The overall power efficiency in ET PAs results from the product of the RF PA drain power efficiency times the efficiency of the envelope tracking modulator (ETM). The ETM is responsible for delivering the instantaneous power required by the RF PA; therefore, its design is key to determine the trade-off between linearity and power efficiency in ET PAs. Typically, a linear-assisted hybrid configuration [13; 14; 15; 16] is adopted in the design of ETMs. When dealing with wideband envelope signals (according to the rule of thumb, the signal's envelope is around three to five times the bandwidth of the complex baseband signal), the ETM performance in terms of linearity and power efficiency is degraded. A solution to cope with the aforementioned trade-off is to generate a slower (i.e., bandwidth or skew-rate limited) version of the original supply envelope through a specific shaping function [17; 18]. In addition, as reported in [19], unwanted nonlinear distortion in the envelope path may arise due to the intrinsic topology of the hybrid ETM when amplifying wideband signals. In particular, the coupling between the ETM and the RF PA is not ideal (more evident at higher frequencies), and thus, due to this load effect, the RF leakage cannot be eliminated or absorbed by the ETM and it is combined with the supply voltage, degrading the overall linearity at the RF PA output. An envelope leakage cancellation (ELC) method was proposed by the authors of this paper in [19] to linearize the unwanted RF leakage and nonlinear distortion effects when operating the ET PA with a 60 MHz bandwidth 5G NR test signal. The ELC method relied on the envelope generalized memory polynomial (EGMP) behavioral model to generate a cancellation signal capable of compensating for the unwanted RF leakage in the dynamic supply path. Unfortunately, this solution assumes that the output of the ETM is available through a dedicated observation path (including an analog-to-digital converter--ADC--with sampling rate at least 6\(\times\) the I-Q signal bandwidth) to estimate the leakage error.