Two-dimensional hybrid particle-in-cell (PIC) simulations are carried out on a constant L-shell (or drift shell) surface of the dipole magnetic field to investigate the generation process of near-equatorial fast magnetosonic waves (a.k.a equatorial noise; MSWs hereafter) in the inner magnetosphere. The simulation domain on a constant L-shell surface adopted here allows wave propagation and growth in the azimuthal direction (as well as along the field line) and is motivated by the observations that MSWs propagate preferentially in the azimuthal direction in the source region. Furthermore, the equatorial ring-like proton distribution used to drive MSWs in the present study is (realistically) weakly anisotropic. Consequently, the ring-like velocity distribution projected along the field line by Liouville’s theorem extends to rather high latitude, and linear instability analysis using the local plasma conditions predicts substantial MSW growth up to +- 27deg latitude. In the simulations, however, the MSW intensity maximizes near the equator and decreases quasi-exponentially with latitude. Further analysis reveals that the stronger equatorward refraction at higher latitude due to the larger gradient of the dipole magnetic field strength prevents off-equatorial MSWs from growing continuously, whereas MSWs of equatorial origin experience little refraction and can fully grow. Furthermore, the simulated MSWs exhibit a rather complex wave field structure varying with latitude, and the scattering of energetic ring-like protons in response to MSW excitation occurs faster than the bounce period of those protons so that they do not necessarily follow Liouville’s theorem during MSW excitation.