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Propagation graph (PG) is a stochastic channel simulation method for scattering propagation. In this article, an embedded-PG (EPG) approach, an extension of conventional PG, is proposed to simulate reflection and scattering multi-path behaviors in wireless channels. In this method, multiple propagation paths are categorized into scattering-path, reflecting-path, and scattering-reflecting mixed paths among reflectors and scatterers. The matrix recursive formula of conventional PG modeling is used to calculate scattering-path, a recursive mathematical transformation is applied to adapt reflecting-path into the recursive formula, and an embedded graph method is used to decompose mixed-path into scattering effects and reflection effects. The proposed simulation approach is validated by comparison with conventional PG and measurement in 39 GHz millimeter-wave (mm-wave) time-variant corridor scenario. Power delay profiles (PDPs) and spatial consistency of multiple paths observed in concatenated-PDPs (CPDPs) obtained by EPG are more consistent with measurement than conventional PG, differences of mean delay and delay spread between simulations and measurement in typical snapshots are within 3 ns and 1.5 ns, respectively.

Embedded Propagation Graph Model for Reflection and Scattering and Its Millimeter-Wave Measurement-Based Evaluation