Linear prediction of bandlimited processes with flat spectral densities

Abstract

Lyman et al. (2000) developed some important properties of a continuous-time linear predictor applied to a bandlimited random process, and discussed how such a prediction could be applied to the problem of mobile radio fading. In this paper, we solve explicitly for the optimal predictor, in the mean-square sense, when the process spectral density is not within the band limits and the predictor impulse response is energy constrained. As basis functions, we use time-shifted versions of the prolate spheroidal wave functions, leading to a simple algebraic optimization problem that is solved using a Lagrange multiplier. We show how to use the solution to compute the minimum mean squared prediction error under the energy constraint. Then, we discuss the case of a bandlimited process embedded in white noise, showing how to determine if a certain mean squared prediction error can be attained.