Harmonic retrieval is essential in radio channel sounding, estimation, and modeling. In our previous work, we proposed a CNN-based approach combined with additional steps on the likelihood function. This paper extends the approach to perform joint 4D harmonic retrieval by utilizing the samples from a multi-antenna receiver in frequency, time, and the spatial domains of a radio channel transfer function. The proposed architecture also reliably estimates the number of spectral components on measurements. Hence, our approach can estimate four-dimensional parameters from a signal without prior knowledge of the unknown number of paths. Therefore, the architecture jointly solves the model order selection problem and the parameter estimation task in 4D