This paper considers a broadband model for underwater acoustic (UWA) multiple-in multiple-out (MIMO) systems. Delay-Doppler-spread function based sparse channel estimation approach is proposed. The dominant components on the delay-Doppler plane are identified using the sparse Bayesian learning (SBL) estimate technique, then the multipath Doppler components can be estimated individually and compensated upon each channel tap finger. Furthermore, the receiver utilizes an iterative reduced state maximum likelihood sequence estimation (IRS-MLSE) structure, reducing the computational complexity and improving the system performance through analyzing a set of experimental data in SPACE08. In training mode, the proposed SBL approach shows a 2 ∼ 3-dB reduction in signal prediction error. In decision-directed mode, the SBL based IRS-MLSE decoding metric with independent Doppler shift compensation shows a lower bit error rate (BER) than conventional sparse or nosparse channel impulse response (CIR) estimate, reaching 4.94 × 10−4 at 5th iteration.