An Information Geometric Approach to ML Estimation With Incomplete Data: Application to Semi-Blind MIMO Channel

IEEE Transactions on Signal Processing, Vol. 55, No.8, August 2007.
Amin Zia, J.P. Reilly, Jonathan Mantony, and Shahram Shirani

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 identi¯cation (IGID) algorithm. The algorithm consists of iterative alternating projections on two sets of probability distributions (PD); i.e., likelihood PD's 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 semi{blind identi¯cation of unknown parameters in a multi-input multi-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 EM-based algorithm proposed previously [1], but with a substantial improvement in computational speed, especially for large constellations.