Signal-noise ratio maximization using the pontryagin maximum principle

The applicability of the Pontryagin maximum principle to signal-noise ratio maximization is explored. Attention is focused on the reformulation of the problem so that the maximum principle may be used. The basic aspect of the reformulation is to cast the problem into the form of differential equations instead of integral equations. Two problems are solved. The first, a variation of the matched filter problem, could have been solved by other methods. However, the maximum principle provided a very neat and systematic approach. The second problem, signal design with both an energy and an amplitude constraint imposed on the signal, is solved numerically. It appears to be intractable by other methods. One of the advantages of the maximum principle formulation is that, by working with differential equations rather than with integral equations, numerical techniques may be more easily used.