Wideband ambiguity function and optimized coded radar signals

A system efficiently combining radar and communication requires signals with a large time-bandwidth product to achieve high resolution for radar and high data rate. The narrowband approximation of this wideband signal leads to errors. The narrowband conditions in literature are a gross indication of when the narrowband treatment of a signal is invalid. In this paper a mathematical expression is derived quantifying the error committed when applying the narrowband approximation. This expression decomposes the difference between wideband and narrowband correlation in two components: one only depending on the physical problem parameters (a, tau) and the signal bandwidth, duration, and carrier frequency; the other depending only on the particular signal assumed. This paper proposes a method to evaluate quantitatively when the narrowband approximation is inadequate, and a minimization algorithm to select a signal coding that minimizes the error caused by treating a wideband signal correlation with the narrowband approximation.