Radio sensing can be integrated with communication in what the authors call future perceptive mobile networks. Due to the complicated signal structure, it is challenging to estimate sensing parameters such as delay, angle of arrival, and Doppler when joint communication and radar/radio sensing is applied in perceptive mobile networks. Radio sensing with signals compatible with a fifth-generation (5G) new radio standard using one-dimension (1D) to 3D compressive sensing (CS) techniques under 5G channel conditions is studied. In the case of 1D-3D CS techniques, they formulate the parameter estimation as a sparse signal recovery problem. These algorithms demonstrate respective advantages, but also show shortcomings in dealing with clustered channels. To effectively exploit the cluster structure in multipath channels, they also propose a 2D cluster Kronecker CS algorithm for significantly improved sensing parameter estimation via introducing a prior probability distribution. Simulation results are provided and they focus the respective advantages and disadvantages of these techniques that validate the effectiveness of the proposed algorithms.