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The first repeating fast radio burst (FRB), FRB 121102, was found to beassociated with a spatially coincident, persistent nonthermal radio source, butthe origin of the persistent emission remains unknown. In this paper, wepropose that the persistent emission is produced via synchrotron-heatingprocess by multiple bursts of FRB 121102 in a self-absorbed synchrotron nebula.As a population of bursts of the repeating FRB absorbed by the synchrotronnebula, the energy distribution of electrons in the nebula will changesignificantly. As a result, the spectrum of the nebula will show a humpsteadily. For the persistent emission of FRB 121102, the total energy of burstsinjecting into the nebula is required to be about$3.3\times10^{49}\,\unit{erg}$, the burst injection age is over $6.7\times10^4\,\unit{yr}$, the nebula size is $\sim0.02\,\unit{pc}$, and the electronnumber is about $3.2\times10^{55}$. We predict that as more bursts inject, thebrightness of the nebula would be brighter than the current observation, andmeanwhile, the peak frequency would become higher. Due to the synchrotronabsorption of the nebula, some low-frequency bursts would be absorbed, whichmay explain why most bursts were detected above $\sim1~\unit{GHz}$.

Persistent Radio Emission from Synchrotron Heating by a Repeating Fast Radio Burst Source in a Nebula