Nullifying ACF grating lobes in stepped-frequency train of LFM pulses

An effective way to increase the bandwidth of a coherent pulse-train is to add a frequency step Δf between consecutive pulses. A large Δf implies a large total bandwidth, hence improved range resolution. However, when the product of the frequency step times the pulse-duration t_p, is larger than one (t_p Δf > 1), the autocorrelation function (ACF) of the stepped-frequency pulse-train suffers from ambiguous peaks, known as "grating lobes." It is well known that replacing the fixed-frequency pulses with linear FM (LFM) pulses of bandwidth B can reduce those grating lobes. We present a simple analytic expression for the ambiguity function (AF) and ACF of such a signal and derive from it very simple relationships between Δf, B, and t_p that will place s exactly where the grating lobes are located, and thus remove them completely.