Layered perovskite A2BO4 compounds were studied by a combination of X-ray powder diffraction (XRD) analysis, Raman spectroscopy, and density functional theory (DFT) calculations. Ti4+-doped Ca2MnO4 ceramics with high near-infrared (NIR) reflectivity were selected as a test case. After elucidating their crystal structures (I41/acd) by XRD analysis, Raman spectroscopy was applied. Raman peaks were observed at approximately 178, 290, 330, 463, 500, and 562 cm-1, which were confirmed by DFT calculations, and were in modes identical to those reported for Sr2IrO4 in the same space group. An additional peak was observed at approximately 780 cm-1 for the Ti4+-doped samples, indicating that a silent A2g mode was activated by doping with Ti4+, similar to the A1g (breathing) mode found in B-site-substituted simple perovskite and B-site-ordered double perovskite structures. The XRD patterns of the doped samples did not exhibit any additional X-ray reflections, except for the pattern typical of nondoped Ca2MnO4. Thus, these results were attributed to the presence of the Ti-Ti correlation with a certain distance. The calculated band gap energies of Ca2MnO4 and Ca2Mn0.75Ti0.25O4 were approximately 1.8 eV, which was in reasonable agreement with the experimental value. The DFT calculations also revealed that one of the factors contributing to the enhancement of NIR reflectivity upon introduction of Ti4+ ions is the reduced density of states (DOS) near the Fermi level.