The excitation of spin waves by a microwave current injected into a coplanar waveguide with finite-width ground lines on a continuous Permalloy film is investigated both experimentally and numerically. Phase sensitive micro-focused Brillouin light scattering has been employed to reveal the spatial profile of the propagating spin waves in the magnetostatic surface wave geometry. The experimental results have been satisfactorily reproduced by means of micromagnetic simulations. The exciting microwave field used in this simulation has the spatial profile defined by the coplanar waveguide and user-defined periodic boundary conditions were employed in order to simulate the extended system. The resulting space and time dependent evolution of the magnetization has been analyzed by means of one and two dimensional fast Fourier transform algorithm in order to obtain the spatial profile and the frequency spectrum of the excited spin waves as well as their dispersion relations. Evidence is given to asymmetric emission from the two sides of the coplanar waveguide due to the symmetry breaking related to the sense of precession of the dynamical magnetization, as well as to the near-field effects of the extended spin wave emitter.