Underwater acoustic (UWA) communication wirelessly supports oceanographic surveys and infrastructure inspections. This paper proposes a UWA communication scheme that combines multiple-input–multiple-output (MIMO) signaling, orthogonal signal division multiplexing (OSDM), and basis pursuit denoising (BPDN) to utilize UWA channel sparsity and achieve more reliable communication. The feasibility of MIMO-OSDM using BPDN is verified using a sound propagation simulation with ray tracing. Additionally, we conduct a sea trial employing two mobile transmitters and four fixed receivers to assess the demodulation performance of our proposed system in comparison to conventional OSDM schemes at equivalent data transmission rates. The experimental findings indicate that the proposed MIMO-OSDM framework, when coupled with BPDN, outperforms existing approaches in terms of bit error rate (BER), including those utilizing least squares (LS) in MIMO-OSDM configurations and BPDN in single-input–multiple-output-OSDM (SIMO-OSDM) setups. We conclude that MIMO-OSDM using BPDN outperforms both SIMO-OSDM using BPDN and MIMO-OSDM using LS under the same data rate. The proposed method is expected to become a viable solution that supports oceanographic surveys and infrastructure inspections.