  In order to understand certain observed features of arc-like giant radio
relics such as the rareness, uniform surface brightness, and curved integrated
spectra, we explore a diffusive shock acceleration (DSA) model for radio relics
in which a spherical shock impinges on a magnetized cloud containing fossil
relativistic electrons. Toward this end, we perform DSA simulations of
spherical shocks with the parameters relevant for the Sausage radio relic in
cluster CIZA J2242.8+5301, and calculate the ensuing radio synchrotron emission
from re-accelerated electrons. Three types of fossil electron populations are
considered: a delta-function like population with the shock injection momentum,
a power-law distribution, and a power-law with an exponential cutoff. The
surface brightness profile of radio-emitting postshock region and the
volume-integrated radio spectrum are calculated and compared with observations.
We find that the observed width of the Sausage relic can be explained
reasonably well by shocks with speed $u_s \sim 3\times 10^3 \kms$ and sonic
Mach number $M_s \sim 3$. These shocks produce curved radio spectra that
steepen gradually over $(0.1-10) \nu_{\rm br}$ with break frequency $ \nu_{\rm
br}\sim 1$ GHz, if the duration of electron acceleration is $\sim 60 - 80$ Myr.
However, the abrupt increase of spectral index above $\sim 1.5$ GHz observed in
the Sausage relic seems to indicate that additional physical processes, other
than radiative losses, operate for electrons with $\gamma_e \gtrsim 10^4$.
