Optimal nonlinear digital signal processing : a dynamical systems approach

Abstract

This thesis addresses optimal nonlinear digital signal processing problems aimed to improve power efficiency of modern wireless transmission systems. The first part of this thesis is motivated by peak-to-average power ratio reduction of communication signals. The problem is formulated as minimization of a frequency-weighted convex quadratic cost subject to time-domain output amplitude constraints. A new method for converting optimality conditions into finite-latency stable systems generating optimal outputs with arbitrary precision is proposed. The second part contains analysis of the nonlinear distortion introduced into the base-band (discrete-time) input-output dynamics of the communication systems by the (continuous-time) power amplifier nonlinearity. It is shown that when the nonlinearity is represented by a Volterra series model the resulting baseband equivalent model is a series interconnection of a discrete-time Volterra series model, of the same degree and equivalent memory depth, and a linear system. The result suggests a new, analytically motivated, structure of digital pre-distortion (DPD) of power amplifier nonlinearities. The third part of the thesis focuses on analysis and design of digitally implemented pulse-width modulators (DPWM) used as quantizers for power amplifiers in switched-mode operation. A time-domain input-output model of DPWM which offers new insight into nonlinear behavior of this system is developed. A modified Lloyd-Max quantization based algorithm for linearization of the baseband of a DPWM output is proposed.