A Directivity-Dependent Rician K-Factor Model for Indoor Industrial Channels

Abstract

We derive a physics-based, closed-form model linking antenna directivity to the root-mean-square (RMS) delay spread and mean excess delay in large reverberant indoor environments. Starting from the Rician K-factor-the ratio of line-of-sight (LOS) to scattered power we show that K scales with the total transmit-plus-receive (Tx+Rx) antenna gain through a single reverberance factor that quantifies scatter anisotropy. For an arbitrary scatter power delay profile (PDP), we derive a general identity connecting sigma, tau, and K; the exponential scatter model is the physically motivated special case. Ray-tracing simulations over 100 random link placements in a 57300 m3 industrial hall at 75 GHz validate the model. Compact design rules map target delay-spread values to the minimum required antenna gain, enabling wideband mmWave industrial links.