Optimum Quadratic Detection of a Random Vector in Gaussian Noise

This paper considers the problem of detecting a sample vector from a signal random process which is imbedded in additive Gaussian noise. The probability distributions of the signal-plus-noise process are unknown. The correlation matrices are assumed known for the Gaussian noise process and for the signal-plus-noise process. It is assumed that a quadratic operation will be used to form the test statistic. The optimum operation from this class is derived, using the deflection criterion as the criterion of optimality. Conditions for factorization of the optimum weight matrix are given, and the optimum signal correlation matrix is derived.