Examples of Ergodic Capacity Analysis of RIS-Aided Systems with Spatially Correlated Channels

This is supplementary material for the publication: I. M. Tanash and T. Riihonen, "Ergodic Capacity Analysis of RIS-Aided Systems with Spatially Correlated Channels," in IEEE International Conference on Communications., May 2022. The provided material demonstrates examples of ergodic capacity analysis of RIS-aided systems over correlated channels. In particular, the material includes a dataset that contains the sets of the optimized coefficients which correspond to the novel logarithmic approximation ( Eq. 18 in the paper) of the ergodic capacity with four terms (N=4). In particular, these coefficients are used to plot the approximation of the ergodic capacity for the non-central chi-square and the Gamma distributions with 100 reflecting elements (M=100) and 400 reflecting elements (M=400) with the network setup determined in Section IV. It is referred to the case with M=100 as EXP1 and to the case with M=400 as EXP2 in the dataset. A Matlab script (Example.m) is also included in the supplementary material as an example to illustrate the ergodic capacity shown by figure Example.jpg (Fig. 3 in the paper) after extracting the corresponding coefficients from the provided dataset.