Abstract In order to investigate the regular variations of the ionosphere, the least-squares harmonic estimation is applied to the time series of ionospheric electron densities derived from about five years of Global Positioning System radio occultation observations by FORMOSAT-3/COSMIC satellites. The analysis is done for different latitudes and altitudes in the region of Iran. The least-squares harmonic estimation is found to be a powerful tool for the frequency analysis of the completely unevenly spaced time series of radio occultation measurements. Although the obtained results are slightly different from the exact expected cycles (i.e. annual and diurnal components with their Fourier decompositions, and the 27-day period) due to the low horizontal resolution of radio occultation measurements, high vertical resolution of the observations enables us to detect not only the total electron content variations but also periodic patterns of electron densities at different altitudes of the ionosphere. The dominant diurnal and annual signals together with their Fourier series decompositions are obtained, which are consistent with the previous analyses on the total electron content. In the equatorial anomaly band, the annual component is weaker than its Fourier decomposition periods. In particular, the semiannual period dominates the annual component, indicating the relationship between the semiannual variation of the electron densities and the ionospheric equatorial anomaly. From detection of the phases of the components, it is revealed that the annual signal generally has its maximum value in summers at high altitudes, and in the winters at low altitudes. This is probably due to the higher [O/N2] ratios in winter than in the summer in the lower ionosphere. Furthermore, the semiannual component mostly peaks around solstices or about a month before/after them.