Joint Optimization of Underwater Acoustic ISUDC Waveform Design and Sparse Channel Estimation Algorithms

Integrated systems for underwater detection and communication (ISUDC) plays a pivotal role in improving sonar integration and efficiency and has become a key research focus. This paper tackles the underwater doubly dispersive wireless channel (DDWC) by introducing a novel transmitter side waveform design and a receiver side channel estimation algorithm based on affine frequency division multiplexing (AFDM) within the ISUDC framework. At the transmitter we employ AFDM as the core signal and target minimization of weighted sidelobes in the wideband ambiguity function (WAF). We use numerical analysis to quantify coding effects on the WAF and apply optimized random phase perturbations in P4 encoding via particle swarm optimization (PSO) to enhance detection and improve time Doppler resolution. At the receiver we develop a sparse channel estimation method based on an affine Fourier dictionary, which uses pilot signals to estimate phase perturbations and exploits delay Doppler sparsity to improve accuracy in dynamic underwater environments while reducing multipath interference. We also derive new bounds on the pairwise error probability (PEP) for underwater acoustic DDWC, including numerical lower bounds and Chernoff upper bounds. Simulations demonstrate that jointly optimizing waveform design and channel estimation reduces PEP and normalized mean square error (NMSE), provides superior detection for consecutive identical coded symbols and yields an ideal "thumbtack" shaped WAF. The proposed framework delivers a reliable and efficient solution for ISUDC in complex underwater environments.