The relaxation-induced dipolar modulation enhancement (RIDME) technique allows the determination of distances and distance distributions in pairs containing two paramagnetic metal centers, a paramagnetic metal center and an organic radical, and, under some conditions, also in pairs of organic radicals. The strengths of the RIDME technique are its simple setup requirements, and the absence of bandwidth limitations for spin inversion which occurs through relaxation. A strong limitation of the RIDME technique is the background decay, which is often steeper than that in the double electron electron resonance experiment, and the absence of an appropriate description of the intermolecular background signal. Here we address the latter problem and present an analytical calculation of the RIDME background decay in the simple case of two types of randomly distributed spin centers each with total spin S = 1/2. The obtained equations allow the explaination of the key trends in RIDME experiments on frozen chelated metal ion solutions, and singly spin-labeled proteins. At low spin label concentrations, the RIDME background shape is determined by nuclear-driven spectral diffusion processes. This fact opens up a new path for structural characterization of soft matter and biomacromolecules through the determination of the local distribution of protons in the vicinity of the spin-labeled site.