Broadband signal analysis and design for radar and sonar systems require the use of a wideband ambiguity function (WAF) to estimate their performance. The properties of WAF for FM signals are studied and the results of numerical computation are compared with the theoretical expressions. The main findings presented here include the following. (a) A broadband LFM signal is not a Doppler tolerant one. At high velocity, the magnitude of WAF is similar to the signal envelope, and its range resolution decreases obviously. (b) an LPM signal exhibits a fairly good range resolution, even at very high velocity. The performances of Doppler tolerant signals for three models are described and compared. The different envelopes for the LPM case have little influence on the behavior of WAF. (c) The unbiased delay estimation for both LFM and LPM signals, with bandwidth B= f max− f min and duration T, can be obtained by a special shift in time, which is such that t ∈ ( f minT/B, f maxT/B). An approximate method for derivation of WAF, based on the Doppler cross-power spectrum and the stationary phase principle, is proposed. Such an analysis is applied to a bat’s sonar signal.
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Zhen-biao Lin (1988) studied this question.