Removing autocorrelation sidelobes by overlaying orthogonal coding on any train of identical pulses

A coherent train of identical linear FM (LFM) pulses is used extensively in radar because of its good range and Doppler resolution. Its relatively high autocorrelation function (ACF) sidelobes are sometimes reduced through spectrum shaping (e.g., nonlinear FM, or intrapulse weighting on receive). We show how to completely remove most of the ACF sidelobes about the mainlobe peak, without any increase to the mainlobe width, by diversifying the pulses through overlaying them with orthonormal coding. A helpful byproduct of this design is reduced ACF recurrent lobes. The overlaid signal also results in reduced Doppler tolerance, which can be considered as a drawback for some applications. The method is applied to several trains of identical pulses (LFM and others) using several orthonormal codes. The effect on the three important properties of the radar signal: ACF, ambiguity function (AY), and frequency spectrum is presented. The effect on Doppler tolerance is studied, and implementation issues are discussed. The new design is also compared with complementary and sub-complementary pulse trains and is shown to be superior in many aspects.     

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 /spl Delta/f between consecutive pulses. A large /spl Delta/f implies a large total bandwidth, hence improved range resolution. However, when the product of the frequency step times the pulse-duration t/sub p/, is larger than one (t/sub p/ /spl Delta/f > 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 /spl Delta/f, B, and t/sub p/ that will place s exactly where the grating lobes are located, and thus remove them completely.     

Modified Costas signal

A modification to the Costas signal is suggested. It involves an increase of the frequency separation /spl Delta/f beyond the inverse of the subpulse duration t/sub b/ combined with adding linear FM (LFM) with bandwidth B, in each subpulse. Specific relationships between /spl Delta/f and B will prevent autocorrelation grating lobes, that would normally appear when t/sub b//spl Delta/f>1.