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As the SKA is expected to be operational in the next decade, investigations of the radio sky in the range of 100 MHz to 10 GHz have become important for simulations of the SKA observations. In determining physical properties of galaxies from radio data, the radio SED is often assumed to be described by a simple power law, usually with a spectral index of 0.7 for all sources. Even though radio SEDs have been shown to exhibit deviations from this assumption, both in differing spectral indices and complex spectral shapes, it is often presumed that their individual differences cancel out in large samples. We constructed the average radio SED of radio-excess active galactic nuclei (RxAGN), defined as those that exhibit a 3 $\sigma$ radio luminosity excess with respect to the value expected only from contribution from star formation, out to z~4. We combined VLA observations of the COSMOS field at 1.4 GHz and 3 GHz with GMRT observations at 325 MHz and 610 MHz. To account for nondetections in the GMRT maps, we employed the survival analysis technique. We selected a sample of RxAGN out to z~4. We find that a sample of RxAGN can be described by a spectral index of $\alpha_1=0.28\pm0.03$ below the break frequency $\nu_b=(4.1\pm0.2)$ GHz and $\alpha_2=1.16\pm0.04$ above, while a simple power-law model yields a single spectral index of $\alpha=0.64\pm0.07$. By binning in 1.4 GHz radio luminosity and redshift, we find that the power-law spectral index, as well as broken power-law spectral indices, may increase for larger source sizes, while the power-law spectral index and lower-frequency (, Comment: 12 pages, 11 figures