Improved subspace DoA estimation methods with large arrays: The deterministic signals case

This paper is devoted to the subspace DoA (direction-of-arrival) estimation using a large antennas array when the number of available snapshots is of the same order of magnitude than the number of sensors. In this context, the traditional subspace methods fail because the empirical covariance matrix of the observations is a poor estimate of the true covariance matrix. Mestre et al. proposed recently to study the behaviour of the traditional estimators when the number of antennas M and the number of snapshots N converge to +infin at the same rate. Using large random matrix theory results, they showed that the traditional subspace estimate is not consistent in the above asymptotic regime and they proposed a new consistent subspace estimate which outperforms the standard subspace method for realistic values of M and N. However, the work of Mestre et al. assumes that the source signals are independent and identically distributed in the time domain. The goal of the present paper is to propose new consistent estimators of the DoAs in the case where the source signals are modelled as unknown deterministic signals. This, in practice, allows to use the proposed approach whatever the statistical properties of the source signals are.