Robust Time–Frequency Correlations: Definition and Application in Non-Gaussian Signal Processing

The article delves into the classical use of the ambiguity function (AF) in radar systems for direction-of-arrival (DOA) estimation, blind source separation, and joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimation. It highlights the limitations of traditional methods in non-Gaussian, impulsive noise environments, which are common in real-world scenarios. To address these challenges, the article introduces two novel robust time–frequency correlation functions: the ambiguity-entropy function (AEF) and the fractional lower order ambiguity-entropy function (FLOAEF). These functions are designed to suppress the influence of impulsive noise on both the amplitude and phase of signals, thereby enhancing the accuracy of TDOA/FDOA joint estimation. The article presents a detailed definition of these functions and their application in impulsive noise environments, supported by extensive simulation experiments. The results demonstrate the superior performance of the proposed algorithms compared to existing methods, particularly in strong impulsive noise conditions. The simulations cover various scenarios, including different kernel bandwidths, characteristic exponents, generalized signal-to-noise ratios, and multipath environments, providing a thorough evaluation of the proposed algorithms' robustness and accuracy.