Direction of arrival estimation of correlated signals using a dynamic linear array

In this paper, we evaluate a new second-order statistics based direction of arrival (DOA) estimation method for possibly coherent sources by considering a uniform linear array (ULA) as the underlying array, and a periodic scanning where a single scanning period consists of several time slots and in different time slots, different sets of antennas in the ULA are activated leading to a dynamic array having possibly less active sensors per time slot than correlated sources. The spatial correlation matrices of the output of the antenna arrays for all time slots are collected and they can be presented as a linear function of the correlation matrix of the incoming signal at the investigated angles. Depending on the number of investigated angles, the number of time slots per scanning period, and the number of active antennas per time slot, it is possible to present our system of linear equations as an over-determined system. As long as the rank condition of the system matrix is satisfied, it is possible to first reconstruct the spatial correlation matrix of the outputs of the underlying array using LS. Given this spatial correlation matrix, we offer three alternatives. First, we can estimate the correlation matrix of the incoming signal at the investigated angles using LS. However, this option is vulnerable to a so-called grid mismatch effect. In order to mitigate this effect, we also propose structured total least-squares (S-TLS) as a second option in order to reconstruct the correlation matrix of the incoming signal at the perturbed investigated angles given the reconstructed spatial correlation matrix of the outputs of the underlying array. As a third option, we can also apply spatial smoothing and multiple signal classification (MUSIC) on the reconstructed spatial correlation matrix of the underlying array to directly obtain the DOA estimates.