Channel modeling for wireless communications using ambit processes

Developing accurate and computationally efficient channel models for mobile wireless channels poses a formidable challenge, primarily due to the highly dynamic nature of such environments and the involvement of a large number of modeling parameters. In this paper, we propose a novel geometrical model to simulate mobile wireless channels based on a framework developed from the theory of ambit processes. Under reasonable assumptions, the underlying mathematical structure of the proposed channel model enables the characterization of mobile wireless channels in terms of fading statistics, spatio-temporal channel correlation, and Doppler spectrum, besides ensuring tractable analysis. Using the ambit process model, we develop an algorithm that enables fast simulation of macro-cellular channels and accounts for key features of such channels including the appearance and disappearance of multi-path components, spatial consistency, and further captures the correlation between time-evolving delay and Doppler associated with multi-path components. Finally, we simulate macro-cellular channels using the proposed algorithm to obtain crucial insights about the channel characteristics. Numerical results indicate that the proposed channel modeling approach serves as a fairly accurate and computationally efficient design framework for wireless communication systems.