Joint Design of Transmit Sequence and Receive Filter Based on Riemannian Manifold of Gaussian Mixture Distribution for MIMO Radar

To improve target detection performance in non-Gaussian backgrounds, the joint design of transmit sequence and receive filter for multiple-input–multiple-output (MIMO) radar is studied. By approximating the probability density function of observed non-Gaussian data with the Gaussian mixture model (GMM), a Riemannian manifold of Gaussian mixture distribution is developed to depict the complicated background first. Then, maximizing the geometric distance on manifolds, which is converted by maximizing the discrimination between the target and clutter, is proposed as the criterion for the joint design of transmit sequence and receive filter. Thereby, under the constant-modulus constraint, the joint design problem can be transformed into an optimization problem. However, the proposed optimization problem is nonconvex and constrained. To solve this problem, a Riemannian optimization framework is provided. By taking the advantage of the underlying geometric and algebraic structure of the constraint space, the original constrained optimization problem in Euclidean space can be transformed into the unconstraint optimization problem over Riemannian product manifolds. Moreover, to obtain the global optimal solution, the Riemannian gradient of the geometric distance cost is derived for the conjugate gradient algorithm. Experiments demonstrate that the proposed method shows advantages in detection performance compared with competitive methods.