Closed-form analysis for indirect learning digital pre-distorter for wideband wireless systems

Abstract

Indirect learning architecture (ILA) for digital pre-distortion (DPD) is commonly used to linearize power amplifiers (PA). To the author’s best knowledge, most of the DPD results in the literature obtain the matrix form of the least-square solution in order to get the DPD coefficients numerically. There exists no explicit closed-form for these coefficients that can be used as plug-and-play in simulations, or used for further closed-form analysis of important measures such as signal-to-noise ratio (SNR) and mean square error (MSE), bit-error rate (BER), …etc. In this paper, we analyze the ILA-DPD system for general memory-polynomial PA models. We provide a closed-form solution for the DPD coefficients. We first present the analytical methodology for deriving the mathematical expressions for each DPD coefficient and then introduce an open-access code that generates the DPD coefficients in symbolic form that is used to mathematically model the DPD. We consider case studies for PA and show that the analytical DPD solution matches the Monte Carlo simulations. Moreover, we also provide a closed-form solution for the iterative adaptive ILA-DPD. Our analysis shows that in the case of a large training block length the non-iterative DPD achieves approximately the same performance as an iterative DPD with a shorter training block length. System impairments are also considered, e.g. the thermal noise and the quantization noise in analog–digital conversion (ADC). We derive the normalized mean square error (NMSE) for the transmit chain in the presence of these impairments. The NMSE expression is verified through numerical simulations.