Radar Pulse Compression With Spline-Interpolated NLFM Waveforms and Matched/Mismatched Filtering

Abstract

Pulse compression is a key technique in radar systems, enabling the simultaneous achievement of high sensitivity and fine range resolution while maintaining low peak transmit power. To meet these requirements, nonlinear frequency-modulated waveforms are commonly employed. Several techniques have been proposed for designing nonlinear frequency modulation (NLFM) pulses relying on the stationary phase principle or modeling the instantaneous frequency within the pulse. In this article, we propose a model of the instantaneous frequency based on spline interpolants with fixed, nonuniformly distributed knots. We investigate several types of splines, showing that many of them allow the instantaneous frequency to be expressed as a linear function of some unknown parameters. A matched filter (MF) approach is first considered with the objective of minimizing the $p$ -norm of the output sidelobe levels for a given range resolution. The linear formulation not only simplifies the computation of the waveform but also that of the objective function gradient, thereby enabling a more efficient optimization. We also analyze the impact of Doppler shift on the MF output and propose the use of a mismatched filter to attenuate some of the artifacts caused by its presence. Also in this case, the mismatched filter is modeled by means of spline interpolants, and an optimization procedure of its parameters is proposed. The effectiveness of the proposed methods is demonstrated by presenting several waveform examples, designed with different choices of their parameters, e.g., duration and sweep frequency, and comparing performance metrics with those of other methods in the literature.