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 are known to generate high levels of noise. The aeroacoustic behaviour of circular and rectangular nozzles has been largely discussed whereas data on the aeroacoustic behaviour of aerospike nozzles is scarce. For further industrial development, the identification of the noise generation mechanisms in such configurations is necessary. This study sheds light on the main noise components of a cold jet exhausting an aerospike nozzle. Implicit Large Eddy Simulations (ILES) are deployed to simulate the flow of the cold aerospike 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 first performed. Then, the configuration is analyzed in terms of near-field instantaneous and time-averaged flow characteristics. It is of crucial interest to characterize the features of the shock-cell structures. The annular shock structure near the aerospike bluff body displays two non-attached shock-cells of length L/Dj ∼ 0.43. The annular jet is then reattaching and this reattachment leads to longer shock-cells of length L/Dj ∼ 0.77. Downstream of the bluff body, a second expansion process takes place and leads to the emergence of a circular shock-cell structure with a first shock-cell length of L/Dj ∼ 1.20. The interaction between the vortical flow structures in the shear layers and the shocks generates Broadband Shock-Associated Noise (BBSAN). In order to enhance understanding of the noise generation mechanism for this configuration, several analyses are performed. Two-point cross-correlations of data acquired in monitoring points located along axial lines in the circular shear layers are used for quantifying the upstream propagating waves associated to a strong tonal component at a Strouhal number St = 0.51. This strong tonal component is known as screech. It is generated by a feedback mechanism between the coherent fluid flow structures propagating downstream in the jet shear layer and the upstream propagating acoustic waves generated at the same frequency by vortex-shock interactions, waves that are interacting with the nozzle lip and excite shear layer instabilities at the frequency of screech. Power spectral density of the radial velocity at monitoring points in the annular jet structure displays three main peaks at St = 0.68, St = 1.21 and St = 2.59. These frequencies correspond to the oscillation modes of the annular shock-cell structure in radial direction. Furthermore, a vortex sheet model is adapted to predict the length of the annular shock-cells. A good agreement is reached between the analytically derived shock-cell length and the simulation results. The shock-cell length is used to predict the central frequency of BBSAN as a function of observation angles. The far-field spectra show mixing noise as well as Broadband Shock-Associated Noise, related to the interaction between the convected vortices in the shear layers and the shock-cell structure. High sound pressure levels (SPL) are detected in agreement with the BBSAN central frequencies which were computed using the annular and circular shock-cell length. Finally, high SPL are obtained at the radial oscillation frequencies for the annular shock-cell structure.