Modeling and Analysis of Stochastic Radio Channels

Several of today’s most popular and widely used stochastic radio channel models rely in their construction on one-dimensional point processes. The first use of point processes as a tool for stochastic modeling of time-invariant radio channels can be traced back nearly half a century to the seminal work by Turin, with follow-up developments by Suzuki and Hashemi. Subsequently entered the popular contribution by Saleh and Valenzuela as well as the more recent extension by Spencer. Similarly, and originally proposed by Papantoniou, the use of one-dimensional point processes has also repeatedly been suggested as a modeling tool for time-variant stochastic radio channels. Despite a pronounced use for modeling purposes, neither point processes nor their underlying theoretical framework have been favored in the literature as tools for the subsequent analysis. For example, the classical channel model by Saleh and Valenzuela has been widely used for simulation purposes such as performance assessments of communication systems. However, due to the models’ heuristic construction the resulting channel properties and characteristics are not well-understood or not well-known (e.g. the shape of the power-delay profile). In this work we view a representative selection of popular radio channel models from a new and highly facilitating perspective. We naturally exploit the fact that the original constructions of these channel models rely on point processes. By use of the theory of spatial point processes we obtain novel insight on the different channel models, their underlying structures and properties. The theoretical key to our achievements is the application of Campbell’s Theorem. In one of our main contributions we revisit the classical multipath channel model by Saleh and Valenzuela. We show that the model is comprised by the union of two dependent point processes, namely a Poisson point process and a Cox point process. We exploit this conceptual view to re-derive the intensity of path components and the channel’s power-delay profile in a much simpler and more insightful way compared to previous derivations (the intensity rises linearly with propagation delay and the powerdelay profile is not exponentially decaying). In essence, our conclusions arise as a direct result of the point process perspective and in particular due to the wide applicability and straightforward use of Campbell’s Theorem.