Application of Vilenkin-Crestenson Functions in Ground-Based Radar Using Probing Pulses

This paper presents a MATLAB model of a radar system focused on comparing different methods of orthogonal transformation for processing reflected sounding signals. Three approaches are considered: the Fast Fourier transform, the Walsh-Hadamard transform, and the Vilenkin-Crestenson transform. The constructed model includes generating a probing pulse, propagating it with noise and reflections from targets, performing matched filtering, and subsequently processing it using the selected transforms. We analyzed the effectiveness of these methods in terms of signal energy compression in coefficient space, noise immunity, and ease of implementation. The results showed that the Fourier transform is most effective for harmonic components and Doppler shift analysis; the WalshHadamard transform is suitable for binary-coded pulses; and the Vilenkin-Crestenson transform has advantages when working with multi-valued ($q$-ary) codes and provides a more compact signal representation. These results demonstrate that choosing the right transformation method during processing is key to optimizing radar systems in noisy environments.