Waveform design and processing for underwater integrated detection and communication based on affine Fourier dictionary

This paper addresses the challenge of optimizing detection and communication performance in integrated systems for underwater detection and communication by proposing a waveform design and signal processing method based on an overcomplete wavelet Fourier dictionary. First, by leveraging the multiresolution properties of wavelets and the time–frequency localization of the Fourier transform, a nonorthogonal overcomplete waveform is designed tailored to underwater doubly dispersive channels, thereby enhancing performance under Doppler shifts and multipath effects. Next, a sparse reconstruction algorithm is introduced based on a multiresolution dictionary that extracts signal features layer by layer, reducing computational complexity while improving target detection accuracy and underwater communication. Finally, by analyzing the upper and lower bounds of the pairwise error probability, the improvement in bit error rate achieved by the waveform design is quantified. Simulation results show that the proposed method outperforms conventional approaches in terms of the wideband ambiguity function, detection probability, and pairwise error probability, providing theoretical support for integrated systems for underwater detection and communication.