3D vs. 2D channel models: Spatial correlation and channel capacity comparison and analysis

Abstract

Results of recent measurement campaigns demonstrate a significant increase in the degrees of freedom introduced by the elevation domain, and consequently, a large capacity gap as predicted by 3D and 2D MIMO channel models. To gain further insight into the effects of the elevation domain on MIMO system performance, we derive new spatial correlation (SC) expressions for 3D and 2D channel models, given rectangular arrays of cross-polarized antennas. The main result relates 3D SC to the 2D counterpart, allowing us to quantify the effects of the elevation domain on SC. Furthermore, our result allows us to derive the following three simple relationships between 2D and 3D correlations. We show that for a small elevation angle spread, the difference between 2D and 3D SCs grows quadratically in both vertical separation and angle spread. For the case of small vertical spacings, we derive a bound on the above correlation gap. Furthermore, we show that the elevation effects on correlation can be accurately decoupled, allowing us to express the 3D SC matrix as a Hadamard product of a 2D SC matrix and an elevation component. Collectively, our results demonstrate the need for accurate channel modeling when evaluating the performance of 3D MIMO systems.