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

• Published in: IEEE transactions on aerospace and electronic systems Vol. 39; no. 2; pp. 694 - 703
• Main Authors: Levanon, N., Mozeson, E.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-04-2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aircraft components; Autocorrelation; Autocorrelation functions; Bandwidth; Electronic systems; Exact solutions; Frequency; Gratings; Lobes; Mathematical analysis; Narrowband; Oceans; Phased arrays; Radar; Signal analysis; Signal resolution; Trains
• ISSN: 0018-9251; 1557-9603
• DOI: 10.1109/TAES.2003.1207275

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 nulls exactly where the grating lobes are located, and thus remove them completely.