Traversing the Volterra series for digital predistortion applications
Date
2024-12
Authors
Fonseca, Aaron James
Major Professor
Advisor
Bolstad, Andrew
Dickerson,, Julie
Dobson, Ian
Hansen, Scott
D'Alessandro, Domenico
Li, Shuang
Committee Member
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Abstract
Digital predistortion is a technique for mitigating the nonlinear distortion that occurs when radio frequency (RF) power amplifiers (PAs) operate close to saturation. Digital predistorters (DPDs) are nonlinear systems that predistort input signals such that the distortion introduced by the PA is negated. Designers of DPDs must select: (a) the mathematical model of the predistorter, (b) the excitation signals used to train the predistorter, and (c) the estimation algorithm used to compute the predistorter's parameters. While there are many nonlinear systems that can serve as the mathematical model for a predistorter, one that has seen widespread use is the Volterra series. In addition to its capacity for uniform approximation, the Volterra series has many structural properties that make it ideal for addressing the deeper aspects of predistortion beyond mere estimate modeling.
The first contribution of this dissertation presents a novel method of designing simulatable nonlinear models whose true inverses are known. This allows designers of excitation signals and estimation algorithms to quantitatively assess predistorter estimates using a normalized l2 distance to ground truth. Armed with this metric, a collection of PAs designed using the known-inverse method were simulated and the performance of two estimation algorithms, the Moore-Penrose inverse (pseudoinverse) and recursive least squares (RLS) algorithm were compared. Results found that the pseudoinverse algorithm was extremely susceptible to noise compared to RLS (which was more robust and produced more consistent results). Knowledge of ground truth also revealed that the traditional performance metric of spurious-free dynamic range (SFDR) did not always accurately indicate algorithm performance but could, in fact, be highly misleading; specifically, some estimates that indicated acceptable performance under SFDR had, in actuality, diverged from the known solution.
The second contribution of this dissertation is an algorithm for calculating Volterra series' input product vectors (used for computing the response of Volterra series-based systems) using a minimal amount of multiply instructions. Such an algorithm is beneficial for applications utilizing input product vectors in addition to a Volterra series' response. Simulation results show that the method presented outperforms or performs comparably to a similar time-domain method proposed by Enzinger et al. for quickly computing input product vectors and substantially outperforms a frequency-domain method proposed by Morhac for increasing memories and orders of an underlying Volterra kernel.
Advancements in machine learning (ML) have inspired exploration into alternative ML-based predistorter models. One such model is support vector regression (SVR). Recent literature has demonstrated the advantages of SVR over Volterra series models with respect to the amount of memory required to achieve acceptable results. However, nearly all work that demonstrated these advantages employed predistorters operating at baseband. Baseband predistortion has two notable drawbacks: (a) the effective memory required to predistort a complex baseband signal is double that required for an analogous modulated signal, and (b) the predistorter estimates produced under baseband predistortion are localized to the carrier frequency at which they were trained. Advances in FPGAs, ASICs, and parallelization can facilitate predistorter operation within the post-baseband stages of the RF signal chain, yet no work offers a comparative assessment between baseband and post-baseband configurations of SVR and Volterra series predistorters.
The third contribution of this dissertation provides a novel comparison of SVR and Volterra series predistorters operating at baseband and post-baseband stages using a simulated PA. Simulation results found that post-baseband SVR and Volterra series predistorters could produce estimates not localized to particular carrier frequencies, a benchmark not achieved by baseband estimates. The results also replicated the advantage of SVR over Volterra series models for post-baseband predistorters operating at lower memory values. Finally, the results demonstrated that post-baseband predistorters achieved performance metrics that were either superior or comparable to baseband predistorters of equivalent model and memory.
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dissertation