A Spatially Consistent Gaussian Process for Dual Mobility in the 3D Space

Spatially consistent random variables (SCRVs) have been used in many channel models to ensure a smooth time evolution and correlation of the channel coefficients among closely located terminals. However, most of the existing methods which generate SCRVs are restricted to mobility in the two-dimensional (2D) space and those that cover the three-dimensional (3D) space are still limited in terms of accuracy and/or complexity of processing and memory. This letter proposes a sum-of-sinusoids (SoS) method to generate a Gaussian process (GP) described by two different spatial autocorrelation functions (ACFs) considering single and dual mobility in the 3D space. The method was derived analytically for each of the considered ACFs and extends existing methods from the 2D to 3D space. Comparisons with existing baseline solution is carried out showing that the proposed method presents gains in terms of average squared error (ASE) up to 20 dB. Furthemore, the proposed method using only 100 coefficients presented an ASE around 10 dB smaller when compared with the baseline solution using 1000 coefficients.