Time-domain and frequency-domain exponential ambiguity functions and their application in joint estimation of delay and Doppler shift

The classical ambiguity function (AF) in radar signal processing often has a low and fixed resolution in the presence of adjacent multi-targets. The frequency-domain exponential ambiguity function (FEAF) was previously presented with a variable exponent p introduced in the frequency-domain expression of the AF whose range resolution and output signal-to-noise ratio can be mutually replaced by controlling the exponent p. However, the FEAF mainly improves the range resolution of reference signals, but it cannot improve its velocity resolution. In this study, on the basis of symmetry theory in the time and frequency domains, a time-domain exponential ambiguity function (TEAF) was defined by indexing the time-domain expression of AF. The time-frequency properties of the defined TEAF are similar and symmetric to those of the FEAF. On the basis of the combination of the FEAF and TEAF with multi-exponents and a modified CLEAN algorithm for stepwise elimination and estimation of targets, the authors proposed a new joint estimation algorithm for delays and Doppler shifts of multi-targets. Simulation experiments indicated that the proposed estimation algorithm achieves higher accuracies in delay and Doppler shift estimation in comparison with the traditional AF-based estimation algorithm and the FEAF-based estimation algorithm.