Bayesian Estimation of Bessel K Form Random Vectors in AWGN

We present new Bayesian estimators for spherically-contoured Bessel K form (BKF) random vectors in additive white Gaussian noise (AWGN). The derivations are an extension of existing results for the scalar BKF and multivariate Laplace (MLAP) densities. MAP and MMSE estimators are derived. We show that the MMSE estimator can be written in exact form in terms of the generalized incomplete Gamma function. Computationally efficient approximations are given. We compare the proposed exact and approximate MMSE estimators with recent results using the BKF density, both in terms of the shrinkage rules and the associated mean-square error.