MIMO capacity of multipath-clustered channels using Fourier transform techniques

Fading correlation is one of the fundamental limits on the performance of multi-antenna (MIMO) systems. Accurate modeling of the angular probability density function (pdf) of the incoming multipath is essential for accurate prediction of the correlation and, hence, the MIMO capacity. Previous studies were limited to the case of single-cluster distribution or uniform pdf. Measurements indicate that multipath often arrives in several angular clusters and with non-uniform angular cluster pdf. We begin with the popular single cluster model and extend it to the case of multi-cluster channel. The single cluster model with various cluster pdfs is studied in both the angular domain and the angular spectrum domain (u-domain). Using Fourier transform techniques, it is shown that the spatial correlation is the inverse Fourier transform of a scaled and shifted version of the cluster pdf in the u-domain. We further prove that the spatial correlations for all the pdfs is roughly the same given the same angular spread. It is shown that the correlation in the two clusters channel has an oscillatory behavior as antenna spacing increases regardless of multipath AOA distributions; the envelope of the correlation is determined by the single cluster angular spread while the oscillations within the envelope are determined by the inter-cluster angular spread. The cluster angular pdf has negligible impact on the MIMO capacity and, hence, simpler uniform model can be used without degradation in accuracy.