Due to operational constraints for underwater data acquisition, simulating realistic sonar data, like images, swath bathymetry profiles or interferometric signals, is crucial for tuning detection and classification algorithms according to sensors settings, sea-bottom nature and topography. Moreover, the robustness of any performance estimation or prediction can be greatly enhanced, as soon as such a simulation tool provides a modular and flexible underwater world representation (multiple sensors, environments and acquisition conditions). For signal and array processing, it is essential not only to generate the signal energy backscattered by a resolution cell, but also to produce a phase information that conveys its theoretical statistical properties. To this end, this paper proposes a Brownian motion-based approach to generate complex Gaussian signals from the contribution of a set of extended single scatterers inside a resolution cell. The resulting process preserves the conservation of energy when integrating on surfaces, as well as the decorrelation between different areas of the sea bottom, and the right interference between two sensors for interferometric applications.