A Receding Horizon Algorithm to Generate Binary Signals with a Prescribed Autocovariance

Optimal test signals are frequently specified in terms of their second order properties, e.g. autocovariance or spectrum. However, to utilize these signals in practice, one needs to be able to produce realizations whose second order properties closely approximate the prescribed properties. Of particular interest are binary waveforms since they have the highest form-factor in the sense that they achieve maximal energy for a given amplitude. In this paper we utilize ideas from model predictive control to generate a binary waveform whose sampled autocovariance is as close as possible to some prescribed autocovariance. Several simulated examples are presented verifying the veracity of the algorithm. Also, a proof of convergence is given for the special case of bandlimited white noise. This proof is based on expressing the system in the form of a switched linear system.