A fast numerical method for determining the optimum SNR of an array subject to a Q factor constraint

The problem of finding the optimum current excitations for a point-detector array which extracts a signal from background noise using the criterion of maximizing the SNR subject to a constraint on the supergain ratio (or
Q
factor) has recently been solved. The formulation reduced the problem to one of solving for the roots of a polynomial whose coefficients are, in general, complex. We demonstrate that by making a certain transformation, it becomes possible to employ a state variable technique which changes the problem into one of finding the eigenvalues of a real matrix which is considerably faster to do.