Near-Field Localization for Non-circular Sources in the Presence of Sensor Phase Uncertainties

We address the problem of locating multiple near-field non-circular sources in the presence of sensor phase errors. Such phase error may arise in MIMO applications where perfect phase synchronization is not achieved. Using source non-circularity and based on the virtual ESPRIT idea, we define three cumulant matrices to form two matrix pencils, whose generalized eigenvalues are dependent only on the amplitude but not on the phase of the near-field propagation geometry. We introduce a linear operator to estimate the generalized eigenvalues of the defined matrix pencils, and then apply our recently proposed SPatial Amplitude Ratio based Estimator (SPARE) approach to estimate angle and range parameters of the sources. We define the presented algorithm as Rotational SPARE (R-SPARE) since it obtains the spatial amplitudes from the rotational structures embedded in the defined matrices. R-SPARE shares all advantages offered by the SPARE. We finally examine the performance of R-SPARE via numerical simulations.