Measuring transmembrane water exchange can provide potential biomarkers for tumors and brain disorders. Diffusion Magnetic Resonance Imaging (dMRI) is a well-established tool that can non-invasively measure water exchange across cell membranes. Diffusion Exchange Spectroscopy (DEXSY) is one of the dMRI-based frameworks used to estimate exchange. DEXSY provides a detailed picture of multi-site exchange processes but requires a large quantity of data. Several models based on the DEXSY framework have been proposed to reduce the acquisition time. Filter Exchange Imaging (FEXI) and curvature models are two of them that only require certain samples of the DEXSY dataset. Diffusion-Exchange Weighted (DEW) Imaging model is another data reduction method accounting for restricted diffusion within cells and can use a specific subset of the DEXSY dataset to measure exchange. Furthermore, a more general expression of the DEXSY signal, referred to as the general model, can theoretically analyze the full space or reduced DEXSY datasets and estimate exchange. However, the results of the subsampling schemes and the data reduction models have not been compared to the full space estimation.  Therefore, this thesis aims to experimentally explore the feasibility of estimating exchange using these four models (the general, FEXI, curvature and DEW models) with the data acquired using a low-field benchtop MR scanner, and compare the estimates from the general model with different subsampling schemes and the data reduction models to the full space estimation. For this purpose, a double diffusion encoding (DDE) sequence was modified from an existing sequence on the benchtop MR scanner and a DEXSY experiment was conducted on this MR scanner and a yeast phantom to acquire a full space dataset. The exchange parameters estimated from the full space dataset using the general model were used as "ground truths" to evaluate the estimates from the reduced datasets analyzed using the general, FEXI and curvature models. Moreover, two alternative subsampling schemes named the shifted DEW and new trajectory schemes were proposed and employed to measure exchange. The results indicate that all the methods except the curvature sampling scheme employed with both the general and curvature models provided comparable estimates to the "ground truths". The shifted DEW and new trajectory sampling schemes performed better over others in terms of consistency with the "ground truths" and low variations between voxels, suggesting the theoretical and experimental optimization of these two subsampling schemes can be further studied and developed.