Discrete-Time Signal Design for Maximizing Separation in Amplitude

Given a discrete-time, linear, shift-invariant channel with finite impulse response, the problem of designing finite-length input signals with bounded amplitude (l∞ norm) such that the corresponding output signals are maximally separated in amplitude (l∞ sense) is considered. In general, this is a non-convex optimization problem, and appears to be computationally difficult. An optimization algorithm that seems to perform well is described. Optimized signal sets and associated minimum distances (minimum l∞ separation between two distinct channel outputs) are presented for some example impulse responses. A conjectured upper bound on the minimum distance is given that is easily computed given the impulse response of the channel, the number of inputs, and the input length. This upper bound is shown to be valid for a limited class of impulse response functions.