The minimal divergence solution to the Gaussian masking problem

The problem of designing a stationary Gaussian noise process of fixed variance so as to optimally mask the possible presence of a given additive stationary Guassian signal process is considered. A sub-optimal solution is obtained by minimizing the divergence distance between the noise and signal-plus-noise processes. Recursive time and frequency domain expressions for the divergence are derived in terms of successive auto-regressive approximations of the processes. For short observation times, the minimal divergence masking problem may then be solved by the unconstrained minimization of a convex - and recursively computable - function in the time domain. For long observation times, the problem reduces to that of minimizing the asymptotic divergence rate. This problem may be solved in the frequency domain by straight-forward algebraic techniques. A number of examples are given which illustrate the methodology.