A Positive Semidefinite Autocorrelation Function for Modeling 3D Gaussian processes

This is the authors' abstract. We don't add key points for this paper.

The generation of spatially consistent random variables (SCRVs) in ℝ2and ℝ3described by a predefined autocorrelation function (ACF) is an important feature for channel modeling in fifth-generation (5G) systems. However, most of the existing ACF models only provide strictly non-negative (SNN) correlation and the ones that provide negative correlation are mostly non-positive semi-definite (PSDe). Motivated by this and also by measurements found in the literature, this paper proposes an ACF model that extends the exponential decaying ACF by allowing negative correlations. The model is proved to be PSDe in ℝ2and ℝ3and its capability to fit channel measurements in millimeter-wave (mmWave) bands is also analyzed. Furthermore, it provides an analytical derivation of a sum-of-sinusoids (SoS) method capable of generating a Gaussian process (GP) in ℝ3characterized by the proposed ACF. The proposed SoS method is compared to a state-of-the-art (SoA) solution and presents gains up to 13 dB and 1.5 dB in terms of spatial-mean-square error (SMSE) and mean square error (MSE), respectively, while demanding lower computational complexity.