Design and performances evaluation of new Costas‐based radar waveforms with pulse coding diversity

Abstract

Costas codes are a variant of pulse compression waveforms, largely studied for their attractive time-frequency properties. Their 'thumbtack-like' ambiguity function (AF) makes them highly suitable for delay and Doppler estimation, in radar and sonar applications. However, this behaviour depends heavily on the length of the code: the improvement in delay-Doppler resolutions and AF sidelobes level needs an increase in the size of the code. In this study, designs that allow good performance without increasing the size of the code are proposed. They are based on a modification of Costas codes by widening frequency separation between hops and replacing rectangular pulses by other waveforms. This will lead to a removal of autocorrelation function grating lobes that normally appear when frequency separation is increased. The originality of the work lies in the proposal of diversified pulse waveforms, such as phase codes, Slepian sequences, and other Costas codes, to encode main Costas pulses. A performance comparison of the proposed approaches is supplied. Such waveforms could also be of interest for applications where waveform diversity is desired

A review of radar signals in terms of Doppler tolerance, time-sidelobe level, and immunity against jamming

“…At any slice of these slices, only one frequency is transmitted, and each frequency is used only once. The complex envelope of Costas code is given by [21]: where: and Hopping order strongly affects the ambiguity function of the signal. Therefore, Welch construction algorithm is usually used to find out the hopping order that makes the corresponding ambiguity function such as thumbtack [20].…”

Multi‐user radar waveforms based on doubly coded Costas signals

“…The DCCS introduces flexibility by adding degrees of freedom to manipulate the time bandwidth product, that is t p Δ f , L and t s Δ f s . However, a valid combination is constrained by two main conditions [20]: Smaller auto‐correlation function (ACF) mainlobe width of secondary code compared with first main code grating lobe position: L 2 × t s Δ f s ≥ t p Δ f . Non‐overlapping main and secondary code grating lobes: , for all (in other words Δ f is not a multiple of Δ f s and vice versa). To address these signals in a multi‐user context, we define auto‐ and cross‐hit array as follows. Definition 1 [1] : The cross‐hit array of two Costas codes C 1 and C 2 is defined as the number of hits between the code C 1 and a translated version of the code C 2 shifted horizontally (by a t p step) and/or shifted vertically (by a Δ f = 1/ t p step).…”

“…Phase coded Costas sub‐pulses and linear frequency modulation (LFM) modulated ones are proposed in [16–19]. Other Costas sub‐pulse natures such as spectrally balanced Slepian sequences are explored in order to improve signal diversity [20]. In this work, the modified version used is the doubly coded Costas signal (DCCS) illustrated in Fig.…”

Design and Processing of a Novel Chaos-Based Stepped Frequency Synthesized Wideband Radar Signal

“…For either stepped frequency or frequency-coded applications, linear modulation produces a range–Doppler coupling effect. A previous study [ 15 , 16 ] used Costas sequences to solve this problem. The maximum ambiguity sidelobe is the reciprocal of the coded sequence length.…”