Enhanced Blind Calibration of Uniform Linear Arrays with One-Bit Quantization by Kullback-Leibler Divergence Covariance Fitting

Abstract: One-bit quantization has recently become an attractive option for data acquisition in cutting edge applications, due to the increasing demand for low power and higher sampling rates. Subsequently, the rejuvenated one-bit array processing field is now receiving more attention, as "classical" array processing techniques are adapted / modified accordingly. However, array calibration, often an instrumental preliminary stage in array processing, has so far received little attention in its one-bit form. In this paper, we present a novel solution approach for the blind calibration problem, namely, without using known calibration signals. In order to extract information within the second-order statistics of the quantized measurements, we propose to estimate the unknown sensors' gains and phases offsets according to a Kullback-Leibler Divergence (KLD) covariance fitting criterion. We then provide a quasi-Newton solution algorithm, with a consistent initial estimate, and demonstrate the improved accuracy of our KLD-based estimates in simulations.