Iterative linearization methods suited for digital pre-distortion of power amplifiers

Abstract

Abstract-This paper deals with iterative linearization of a nonlinear dynamical system. The methods proposed are suited for digital pre-distortion of power amplifiers working close to saturation, as it is common for efficiency reasons. Two methods (a well known successive approximation method based on a fixed-point formulation and a Newton method) are compared with respect to convergence speed, robustness against model uncertainties, and complexity. The presented methods are used to linearize a Volterra model of a measured power amplifier.

Linearization of Time-Varying Nonlinear Systems Using A Modified Linear Iterative Method

“…2. Richardson equalizer based on the Volterra system Hn with three iterations of (14) and the initialization in (15). Due to the finite number of iterations, the reconstructionx[n] = x[n] (3) is only an approximation of the desired reconstruction result x[n].…”

“…If H n is causal, (14) is indeed realizable as a samplebased iteration, i.e., the reconstruction x[n] (r+1) of the sample x[n] depends only on previous reconstructions x[k] (r) , where k ≤ n. While the approximation x[n] (r) will equal the desired input sample x[n] if r → ∞ and if the iteration converges, a practical system can, of course, only implement a finite number of iterations. This is not a limitation per se as the number of iterations can be chosen so that the accuracy of the approximation suffices for the specific application.…”

“…The maxima of ψ x,n are at 0.5644, which is significantly less than one, and thus the condition in (25) . Post-and pre-linearization is performed with the Richardson equalizer in (14) using H n in (18) and (20), respectively, and the initialization in (15). In Fig.…”

“…The SNR initially improves because the iteration converges for the majority of samples, but finally it starts to deteriorate because of the divergence at the signal peaks as illustrated in Fig. 14. In this context, it is important to recognize that due to the structure of the Richardson equalizer in (14) and the memory in H n the divergence can propagate to neighboring samples with repeated iterations. Concluding, the condition for convergence is rather conservative and the linearization method presented in this paper may be utilized in cases of more severe distortion.…”

High-Speed Fabry–Pérot Optical Modulator in Silicon With 3-μm Diode

“…NRZ data transmission with open eyes and low noise holding levels requires the equalization of the driver on-state modulation level. A Volterra model [7] was used to determine pre-emphasis coefficients for the electrical driving signal as shown in Fig. 6(a).…”