A Dynamical Systems Approach to Minimizing PAPR

In this talk, we consider a problem of designing discrete-time systems which are optimal in frequency-weighted least squares sense subject to a maximal output amplitude constraint. It can be shown for such problems, in general, that the optimality conditions do not provide an explicit way of generating the optimal output as a real-time implementable transformation of the input, due to the instability of the resulting dynamical equations and sequential nature in which criterion function is revealed over time. We show that, under some mild assumptions, the optimal system has exponentially fading memory and propose a causal and stable finite-dimensional nonlinear system which, under an L1 dominance assumption about the equation coefficients, returns high-quality approximations to the optimal solution. We then show that the task of minimizing peak-to-average-power ratio (PAPR) of an upsampled discrete-time signal can be formulated as the above optimization problem. We further discuss the impact of the above result on the PAPR reduction problem.