Computationally Efficient DOA and Carrier Estimation for Coherent Signal Using Single Snapshot and Its Time-delay Replications

In this article, we propose two computationally efficient approaches to jointly estimate direction of arrival (DOA) and carrier for coherent signals using a given single snapshot with uniform linear array. First, the proposed methods construct the Khatri–Rao product-like data vector by introducing $P$ -level delays from the array output. Second, a row elementary transformation is applied to the structured data vector, the rotational invariance structure of the carrier vector is exploited and thereby the carrier is derived. To be able to proceed, the special structure of the data vector is also exploited to estimate the coherent waveform. As a result, the DOA estimation problem can be recast into two Frobenius-norm-based optimization problems: one is referred to as linear search-based covariance-like matrix fitting method, which is suitable for estimating spaced angles that are well separated. The other one is called subspace separation-based covariance-like matrix fitting method, which is suitable for estimating closely spaced angles. The proposed methods develop one-dimensional (1-D) search and $K$ 1-D search procedures, respectively, and hence they are computationally efficient compared to the classical methods. The simulation results illustrate that the performance of the proposed methods is better than the spatial smoothing-based multiple signal classification method under different scenarios.