Intense acoustic loads from jet noise cause noise pollution and induce failures, such as the malfunctioning of electronic devices and fatigue failure of internal/external structures. Consequently, the prediction of jet noise characteristics is crucial in the development of high-speed vehicles. This study presents acoustic experiments and predictions for an under-expanded, unheated jet using a small-scale prototype. Outdoor measurements are carried out using a vertical ejection setup. Acoustic characteristics are measured using both linear and circular microphone arrays. Additionally, numerical prediction of the same jet noise is performed using a detached eddy simulation and the permeable Ffowcs-Williams and Hawkings acoustic analogy. The vertical experimental setup exhibits the typical acoustic characteristics of a supersonic jet in terms of directivity and broadband shock-associated noise. Moreover, the numerical prediction exhibits satisfactory accuracy for the jet downstream, where the large-scale turbulence structures of the directivity predominate. However, discrepancy increases in the domain of lower directivity. The presented experiment and prediction will be extended to future studies regarding the noise of various deflector duct configurations impinging on supersonic jets.