We investigated particle acceleration and shock structure associated with an unmagnetized
relativistic jet propagating into an unmagnetized plasma. Strong magnetic fields generated
in the trailing shock contribute to the electrons transverse deflection and acceleration.
We have calculated, self-consistently, the radiation from electrons accelerated in these
turbulent magnetic fields. We found that the synthetic spectra depend on the bulk Lorentz
factor of the jet, its temperature and strength of the generated magnetic fields. We have
also investigated accelerated electrons in strong magnetic fields generated by kinetic
shear (Kelvin-Helmholtz) instabilities. The calculated properties of the emerging
radiation will guide our understanding of the complex time evolution and/or spectral
structure in gamma-ray bursts, relativistic jets in general, and supernova remnants.