Bounds for a Mixture of Low-Rank Compound-Gaussian and White Gaussian Noises

We consider the problem of estimating the parameters of a low-rank compound-Gaussian process in white Gaussian noise. This situation typically arises in radar applications where clutter is relevantly modeled as compound-Gaussian with a rank-deficient covariance matrix of the speckle. Using a minimal and unconstrained parametrization of the problem, we derive lower bounds for estimation of the parameters describing the covariance matrix. First, assuming the textures are deterministic, the Cramér-Rao bound is derived, which enables one to assess the impact of the time-varying textures on the estimation performance. Then, considering the textures as random, hybrid bounds are derived. In addition, we derive a lower bound for estimating the projector on the clutter subspace. Numerical simulations enable one to evaluate the impact of random, time-varying textures compared to the conventional case of constant texture, i.e., of Gaussian subspace signals in Gaussian noise.