A perturbation theory for the coupled nonlinear Schrödinger (NLS) equations is developed to investigate the effect of the background radiation on the soliton amplitude, frequency and polarization angle. By resorting to the theory of the inverse scattering transform, it is shown that the background radiation can be taken into account by evaluating the off diagonal terms of the scattering matrix associated with the coupled NLS equations. The theory is applied to the characterization of the soliton amplitude decrease observed in the propagation in the presence of loss and periodical amplification.
