This paper introduces a novel precoder design aimed at reducing pilot overhead for effective channel estimation in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) applications utilizing high-order modulation. We propose an innovative demodulation reference signal scheme that achieves up to an 8x reduction in overhead by implementing a delay-domain sparsity constraint on the precoder. Furthermore, we present a deep neural network (DNN)-based end-to-end architecture that integrates a propagation channel estimation module, a precoder design module, and an effective channel estimation module. Additionally, we propose a Bayesian model-assisted training framework that incorporates domain knowledge, resulting in an interpretable datapath design. Simulation results demonstrate that our proposed solution significantly outperforms various baseline schemes while exhibiting substantially lower computational complexity.