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In this paper, a novel concept, the Sigmoid transform based cyclic correlation, is proposed and a relative estimator named the Sigmoid transform based cyclic cross-ambiguity function is also derived to handle the joint estimation problem in the presence of impulsive noise and co-channel interference. Based on these definitions, a novel joint estimation method of the time delay and the Doppler frequency shift is proposed. Simulations have verified its superior performances over existing methods based on cyclic ambiguity function or generalized fractional lower-order cyclic cross-ambiguity function, especially under impulsive noise. Meanwhile, it is more applicable for practical applications since it is parameter-free.

A Robust Joint Estimation Method of Time Delay and Doppler Frequency Shift