A Riemannian Distance in Signal Design for MIMO Radar

Abstract

We examine the signal design for Multiple Input Multiple Output (MIMO) radar by matching a desired beam pattern, while suppressing the auto-correlation and crosscorrelation sidelobes. We further reason that since the estimated covariance matrix of the transmitted signal forms a manifold in the signal space, the di erence between the estimated covariance matrix and the desired one should be measured in terms of Riemannian distance (RD) instead of the commonly used Euclidean Distance (ED). We transform the design problem into a convex (CVX) optimization problem which can be solved e ciently by convex optimization methods. Applying RD concept of measure to our design objective function, results show that the performance of our design is superior to that of using ED for the objective.