Simultaneously estimating DOA and phase error of a partly calibrated ULA by data reconstruction

The paper considers the problem of how to simultaneously estimate the direction-of-arrival (DOA) of a source signal and the phase error of a uniform linear array (ULA). We introduce a new method to estimate those parameters for a partly calibrated ULA. As its name suggests, partly calibrated ULA means a array with some of its sensor elements have been calibrated. In particular, our method can be well executed when there is only one calibrated sensor. Firstly, the proposed method reconstructs some sets of data from the array snapshots. According to the subspace theory, a set of linear combination associated with DOA and array phase errors can be extracted with the help of eigenvalue decomposition (EVD). The unknown DOA and sensor phase erros can thus be described by a set of linear equation and its solution can be obtained by least squares (LS) approach. Different from other partily calibrated array based methods, this method can even work well under the condition that the calibrated element is not consecutively located round the reference one. The proposed method is both simple and effective, and simulation comparisons with other algorithms validate its effectiveness.