Performance analysis of combining techniques with correlated diversity

Diversity combining schemes are successfully applied in communication systems. In many recent publications the performance of different diversity combining schemes in different fading scenarios and with different modulation schemes was analyzed and analytical expressions for the performance derived. It turned out that the performance depends on the statistics of the fading, especially on the correlation of the diversity branches. In this work, we study the impact of correlation on the performance of the maximum ratio, equal gain, and selection combining schemes without computing directly the error rate. The performance depends only on the eigenvalues, i.e. powers, of the correlation matrix and not on the eigenvectors. Therefore, majorization theory can be used as a measure of the correlation. We show that the performance of maximum ratio combining and equal gain combining are Schur-convex functions with respect to the correlation eigenvalues, i.e. correlation increases the error rate. Surprisingly, the behavior of selection combining depends on the SNR: for small SNR, correlation decreases the error rate, whereas for high SNR, correlation increases the error rate. Finally, we illustrate the theoretical results by numerical simulations.