Multi-channel power allocation based on market competitive equilibrium in cognitive radio networks

The correlation among signals arriving at different elements of the antenna array has a significant impact on the performance of multiple-input multiple-output (MIMO) system. To investigate the inter-element correlation when slant polarized antennas are used, a general approach for calculating the correlation coefficient is proposed based on a model that incorporates the antenna configuration, namely the antenna spacing and the slant angle, as well as the channel parameters, such as the power azimuth spectrum (PAS) and the crosspolarization discrimination (XPD). By applying this method to the 3rd generation partnership project (3GPP) spatial channel model (SCM), the expression of the inter-element correlation when the PAS follows the Laplacian distribution is obtained. The approximate expressions are also given for two special cases, i.e., the case where the angular spread (AS) of the PAS is small, and the case where the AS is so large that the PAS can be approximated by the uniform distribution. Using these expressions, the impact of the antenna configuration and the channel parameters on the correlation is analyzed. Following that, the trend of inter-element correlation with the slant angle is investigated. Finally, the equivalent relation between the slant angle and the antenna spacing is studied. The results can provide guidelines for the antenna configuration under different propagation conditions.