# A Sparse Bayesian Technique to Learn the Frequency-Domain Active Regressors in OFDM Wireless Systems

## TL;DR

This paper introduces a frequency-domain approach using sparse Bayesian learning to model and predict nonlinear distortion in OFDM wireless systems efficiently.

## Contribution

The novel contribution is the development of FD-SBL, a frequency-domain sparse Bayesian learning algorithm for modeling power amplifier distortion in OFDM systems.

## Key findings

- The FD-SBL algorithm achieves a validation NMSE of −47 dB for a 30 MHz bandwidth signal.
- FD-SBL outperforms TD-SBL in terms of execution time and numerical stability for higher bandwidth signals.
- The proposed method provides accurate distortion prediction with reduced computational complexity.

## Abstract

Digital predistortion and nonlinear behavioral modeling of power amplifiers (PA) have been the subject of intensive research in the time domain (TD), in contrast with the limited number of works conducted in the frequency domain (FD). However, the adoption of orthogonal frequency division multiplexing (OFDM) as a prevalent modulation scheme in current wireless communication standards provides a promising avenue for employing an FD approach. In this work, a procedure to model nonlinear distortion in wireless OFDM systems in the frequency domain is demonstrated for general model structures based on a sparse Bayesian learning (SBL) algorithm to identify a reduced set of regressors capable of an efficient and accurate prediction. The FD-SBL algorithm is proposed to first identify the active FD regressors and estimate the coefficients of the PA model using a given symbol, and then, the coefficients are employed to predict the distortion of successive OFDM symbols. The performance of this proposed FD-SBL with a validation NMSE of −47 dB for a signal of 30 MHz bandwidth is comparable to −46.6 dB of the previously proposed implementation of the TD-SBL. In terms of execution time, the TD-SBL fails due to excessive processing time and numerical problems for a 100 MHz bandwidth signal, whereas the FD-SBL yields an adequate validation NMSE of −38.6 dB.