Published in IET Radar, Sonar and Navigation Received on 25th May 2007 Revised on 3rd March 2008 doi: 10.1049/iet-rsn:20070078 ISSN 1751-8784 Design of frequency-coded waveforms for target detection T.D. Bhatt 1 E.G. Rajan 2 P.V.D. Somasekhar Rao 3 1 Department of ECE, MGIT, Gandipet, Hyderabad, India 2 Pentagram Research Centre (P) Ltd., 201, Venkat Homes, MIGH-59, Mehdipatnam, Hyderabad, India 3 Academic Staff College, JNT University, Hyderabad, India E-mail: president@pentagramresearch.com Abstract: The authors propose a novel approach to the design of frequency-coded waveforms using modified pushing sequences. The resulting waveforms show that there is considerable enhancement in delay-Doppler resolution in the ambiguity function. 1 Introduction Delay-Doppler resolution of a radar system refers to the ability of the system to separate two closely spaced targets. Traditionally, pulse compression methods are being used to solve the problem of separating two closely spaced targets. However, this separation is accomplished at the expense of introducing sidelobes in the matched-filter response, which may mask weak targets and possibly prevent their detection altogether. Costas sequences are generally used in the design of frequency-coded waveforms, which ensure high delay- Doppler resolution [1]. In this context, many researchers have been working with different ways of using Costas sequences effectively in the radar signal design [2–7]. An important property of Costas sequences is that a sequence of length N when used in the radar signal design would yield an ambiguity function (AF) with sidelobes of maximum height 1/N times of its mainlobe height. Hence, use of longer Costas sequences would result in better approximation of the ideal thumbtack- like AF, which is actually desired for high delay-Doppler imaging and measurement. Moreover, in order to achieve a desired sidelobe structure, the Costas waveform should be synthesised using constant frequency chips combined in an appropriate manner. Then, it would be easy to analyse the delay-Doppler ambiguity characteristics of each of these chips since they are localised in time and frequency. In fact, this is done with the help of difference matrix and sidelobe matrix pertaining to the Costas sequence used in the waveform design. Other kinds of frequency-coded waveforms have also been investigated such as stepped-frequency pulse train [8], modified Costas signals [9] and linear frequency modulation (LFM) chirp waveforms, to name a few. It is a known fact that chirp or chirp-like waveform is used in the design of Doppler tolerant waveforms. But, a Doppler tolerant waveform has a ridge-like AF and this does not give high resolution causing a concern for a reliable target detection and discrimination of targets [10–12]. However, alternative techniques are also presented in [13, 14], which are stated to improve the AF. In radar scenario, no waveform is optimum for target resolution in general. Rather, there is an optimum waveform for each target environment. If it is known that all targets are contained within some narrowly confined space, then the thumbtack function would not be the best ambiguity surface. When a target space is narrowly confined, the volume of the ambiguity surface may not be spread uniformly in delay and Doppler. On the other hand, an optimum ambiguity surface should be of a sharp central spike surrounded by a clear area with no volume, with the bulk of the volume pushed away from the central peak such that the interference is more or less avoided [10, p. 141]. The very purpose of an AF with a clear area about the central spike is to eliminate the self-clutter in situations where the entire occupied target space can be fitted within the clear area. It is immaterial how the volume is distributed outside the clear area. In this direction, a recent development that is recommended for use in the design of frequency-coded waveforms is the notion of pushing sequences introduced by Chang and 388 IET Radar Sonar Navig., 2008, Vol. 2, No. 5, pp. 388–394 & The Institution of Engineering and Technology 2008 doi: 10.1049/iet-rsn:20070078 www.ietdl.org