The acoustic analogy is adopted to characterise the signature of a seven-bladed submarine propeller, relying on a high-fidelity large-eddy simulation, performed on a computational grid consisting of 840 million points. Results demonstrate that the nonlinear terms of the Ffowcs-Williams and Hawkings equation quickly become dominant moving away from the propeller along the direction of its wake development. While the linear terms experience a decay moving downstream, the nonlinear terms grow in the near wake, as a result of the development of wake instability. In particular, this growth affects frequencies lower than the blade frequency. Therefore, the acoustic signature of the propeller is mainly tonal in the near field only, due to the thickness and loading components of noise from the surface of the propeller and the periodic perturbation caused by its tip vortices. They develop instability at a faster rate, compared with the hub vortex, triggering the process of energy cascade towards higher frequencies and contributing in this way to broadband noise.