Recursive channel estimation for wireless communication via the EM algorithm

On-line expectation-maximization (EM) algorithm along with stochastic approximations is employed in this paper to estimate unknown time-invariant/variant-parameters recursively in an adaptive manner based on maximum likelihood (ML) criterion. The impulse response of a linear transmission channel is modeled in different ways; unknown deterministic vector/process and Gaussian vector/process with unknown stochastic characteristics. In association with these channel impulse response (CIR) models, different types of recursive least squares (RLS) and Kalman filtering and smoothing algorithms are derived directly from the on-line EM algorithm. The EM algorithm as a powerful tool unifies the derivations of some adaptive estimation methods which include RLS and Kalman whose original criterion is minimum mean square error (MMSE), but under linear and Gaussian conditions can achieve ML or maximum a posterior (MAP) criterion.