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 electron’s 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 also investigate synthetic spectra from accelerated electrons in strong magnetic fields generated by kinetic shear (Kelvin-Helmholtz) instabilities. The calculated properties of the emerging radiation aid our understanding of the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets in general, and supernova remnants.