We deal with the problem of determining the profile of a perfectly conducting rough surface from single-frequency and multistatic data. The two fundamental polarizations are investigated, in a two-dimension scattering configuration. Emitting and receiving antennas are positioned on a probing line some wavelengths above the profile. It is shown how the boundary integral equation method can be adapted to the case where the antenna footprint is much wider that the rough part of the profile. The Newton-Kantorovich iterative inversion process is then performed on these synthetic data. Its accuracy and robustness to additive noise are studied in the context of random rough surfaces with correlation length smaller than the wavelength and slope root mean square up to 0.9.