In supersonic aerospace applications, aerospike nozzles have been subject of growing interest. These devices lead to enhanced thrust performance compared to conventional nozzles due to continuous altitude adaption and improved thrust vector control. However, supersonic non-ideally expanded jets generate high noise levels. For further industrial development, the identification of the noise generation mechanisms in such configurations is necessary. This study sheds light on the noise components of a cold jet exhausting an aerospike nozzle. Implicit Large Eddy Simulations (ILES) are deployed to simulate the jet at a Nozzle Pressure Ratio (NPR) = 3. For far-field acoustic computation, the Ffowcs-Williams Hawkings (FWH) equation is applied. A mesh sensitivity study is performed and the jet instantaneous and time-averaged flow characteristics are analyzed. The annular shock structure displays short non-attached shock-cells and longer attached shock-cells. Downstream of the aerospike, a circular shock-cell structure is formed with long shock-cells. Two-point cross-correlations of data acquired at monitoring points located along the shear layers allow to identify upstream propagating waves associated to screech. Power spectral density at monitoring points in the annular shock-cell structure allow to identify its radial oscillation modes. Furthermore, a vortex sheet model is adapted to predict the annular shock-cells length and the BBSAN central frequency. High sound pressure levels (SPL) are detected at the determined BBSAN central frequencies. Finally, high SPL are obtained at the radial oscillation frequencies for the annular shock-cell structure.