Multidimensional channel sounding measures the geometrical structure of mobile radio propagation. The parameters of a multipath data model in terms of directions, time-of-flight, and Doppler shift are estimated from observations in frequency, time, and space. A maximum likelihood estimation framework allows joint high resolution in all dimensions. The prerequisite for this is an appropriate parametric data model that represents the multipath propagation correctly. At the same time, a device data model is necessary that typically results from calibration measurements. The used model should be as simple as possible, since its structure has a considerable effect on the estimation effort. For instance, the inherent effort in parameter search is reduced if the influence of the parameters is kept independent. Therefore, the data model is characterized by several approximations. The most important is the “narrowband assumption,” which assumes a low relative bandwidth and also avoids considering any frequency response in magnitude and phase. We extend the well-known multidimensional Richter maximization approach (RIMAX) parameter estimation framework by including proper frequency responses. The advantage reveals itself with high bandwidth in the mmWave and sub-THz range. It allows for a more realistic modeling of antenna arrays, and it breaks with the usual narrowband model and allows a better modeling of mutual coupling and time delay effects. If the interacting object extends over several delay bins (hence, an extended target in radar terminology), we propose a model that assigns a short delay spread and a frequency response to the propagation path that associates it with the respective object. We verify the validity of the device model by numerical experiments on simulated and measured antenna data and compare it with RIMAX. In addition, we use synthetic data based on ray-tracing results and measurements both ranging from 27.0 to 33GHz with known ground-truth information and show that the proposed estimator delivers better performance for higher relative bandwidths than the conventional RIMAX implementation.