A Riemannian Distance Approach to MIMO Radar Signal Design

We consider the signal design problem for a Multi-Input Multi-Output (MIMO) radar. The goal is to design a signal vector having a desired covariance (CoV) matrix while ensuring that the side-lobes of the ambiguity functions are small. Since CoV matrices are structurally constrained, they form a manifold in the signal space. Hence, we argue that the difference between these matrices should not be measured in terms of the conventional Euclidean distance (ED), rather, the distance should be measured along the surface of the manifold, i.e., in terms of a Riemannian distance (RD). In either case, the signal optimization problem is quartic in the design variables. An efficient algorithm based on successive convex quadratic optimization is developed and is effective in producing good approximate solutions. Comparing the designs using ED and RD, we find that the convergence of the algorithm can be significantly faster by optimizing over the manifold (RD) than by optimizing in ED. More importantly, for tight constraints, the use of RD yields solutions which satisfy the constraints far better than the use of ED.