We have investigated particle acceleration and shock structure associated with an unmagnetized rel-ativistic jet propagating into an unmagnetized plasma for electron-positron and electron-ion plasmas. Strong magnetic fields generated in the trailing jet shock lead to transverse deflection and acceleration of the electrons. We have self-consistently calculated the radiation from the electrons accelerated in the turbulent magnetic fields for different jet Lorentz factors. We find that the synthetic spectra depend on the bulk Lorentz factor of the jet, the jet temperature, and the strength of the magnetic fields generated in the shock. We have investigated the generation of magnetic fields associated with velocity shear between an unmagnetized relativistic (core) jet and an unmagnetized sheath plasma. We discuss particle acceleration in collimation shocks for AGN jets formed by relativistic MHD simulations. Our calculated spectra should lead to a better understanding of the complex time evolution and/or spectral structure from gamma-ray bursts, relativistic jets, and supernova remnants