A Maximum Likelihood Solution to Doa Estimation for Discrete Sources

In this contribution, we propose a maximum likelihood solution to the direction-of-arrival estimation for discrete sources (a problem which arises in digital communication context). The likelihood expression being in general very involved , direct solutions or approximations of the likelihood equations are likely to be rather messy. To alleviate this problem, we resort to the standard complete/incomplete data model, where the observations play the role of the incomplete data while the source signals are the missing data. We then maximize the incomplete likelihood (the likelihhod of the observations) by iteratively maximizing the complete likelihood function using (i) the deterministic ECM algorithm and (ii) a stochastic version of it, the SEM, which is eeciently implemented by resorting to a Gibbs sampler. Extensive numerical simulations show that this method out-performs the standard higher-order statistics based techniques. Numerical investigation of the Cramer-Rao lower bound is also undertaken.