  The first repeating fast radio burst (FRB), FRB 121102, was found to be
associated with a spatially coincident, persistent nonthermal radio source, but
the origin of the persistent emission remains unknown. In this paper, we
propose that the persistent emission is produced via synchrotron-heating
process by multiple bursts of FRB 121102 in a self-absorbed synchrotron nebula.
As a population of bursts of the repeating FRB absorbed by the synchrotron
nebula, the energy distribution of electrons in the nebula will change
significantly. As a result, the spectrum of the nebula will show a hump
steadily. For the persistent emission of FRB 121102, the total energy of bursts
injecting into the nebula is required to be about
$3.3\times10^{49}\,\unit{erg}$, the burst injection age is over $6.7\times
10^4\,\unit{yr}$, the nebula size is $\sim0.02\,\unit{pc}$, and the electron
number is about $3.2\times10^{55}$. We predict that as more bursts inject, the
brightness of the nebula would be brighter than the current observation, and
meanwhile, the peak frequency would become higher. Due to the synchrotron
absorption of the nebula, some low-frequency bursts would be absorbed, which
may explain why most bursts were detected above $\sim1~\unit{GHz}$.
