Frequency hopping waveforms and Compressed Sensing: Application to airborne detection and reconnaissance.

Summary Changes in the context of airborne radar processing imply more and more improvements that justify the search for an alternative to adaptive filtering, which is the process classically used to estimate the parameters of detected targets. Compressed Sensing opens the prospect of a new treatment, equally effective in multiple target configurations, with better tracking and recognition performance than the classical approach. We aim to apply this processing to so-called frequency hopping waveforms. The integral choice of the definition parameters of the transmitted signal completely determines the measurement matrix of the Compressed Sensing procedure, which solution provides all the desired information on the observed scene. For each frequency hopping signal, and of constant amplitude, the corresponding measurement matrix is obtained by extracting some rows from a particular extended Fourier matrix, the 2D Fourier matrix. The construction of the generation of the measurement matrix is important because the success of the reconstruction depends on the algebraic properties of this matrix.