A Direct Learning Adaptive Scheme for Power-Amplifier Linearization Based on Wirtinger Calculus

Performance of radio frequency power amplifiers is often significantly degraded by nonlinearity and memory effects. We study the applicability of complex-domain adaptive filtering to the problem of predistortion kernel learning for power-amplifier linearization. The least-squares error function that arises while deriving the optimal predistortion function is often real with complex-valued arguments, therefore, nonanalytic in the Cauchy-Riemann sense. To avoid the strict Cauchy-Riemann differentiability condition for non-holomorphic functions (e.g. mean-square error), we resort to the theory of Wirtinger calculus, which allows construction of differential operators in a way that is analogous to functions of real variables. By deploying the new differential operators, digital pre-distortion coefficient optimization is carried out in a space isomorphic to the real vector space, at a computational complexity that is significantly lower than that of the real space. We also derive proper Hessian forms for minimization of the objective function and propose a variety of descent-update algorithms, namely Newton, Gauss-Newton, and their quasi-equivalent variants for this problem. Performance assessments and experimental validation of the proposed methodologies are also addressed.