An information geometric approach to ML estimation with incomplete data: Application to semiblind MIMO channel identification

Abstract

In this paper, we cast the stochastic maximum-likelihood estimation of parameters with incomplete data in an information geometric framework. In this vein, we develop the information geometric identification (IGID) algorithm. The algorithm consists of iterative alternating projections on two sets of probability distributions (PDs); i.e., likelihood PDs and data empirical distributions. A Gaussian assumption on the source distribution permits a closed-form low-complexity solution for these projections. The method is applicable to a wide range of problems; however, in this paper, the emphasis is on semiblind identification of unknown parameters in a multiple-input multiple-output (MIMO) communications system. It is shown by simulations that the performance of the algorithm [in terms of both estimation error and bit-error rate (BER)] is similar to that of the expectation-maximization (EM)-based algorithm proposed previously by Aldana, but with a substantial improvement in computational speed, especially for large constellations.