New Analytical Method to Investigate the Effect of Normalized Doppler rate on the Capacity of MIMO channels Using Karhunen-Loeve Expansion

Abstract

In this paper the effect of normalized Doppler rate fN on the capacity of MIMO channels with any arbitrary fading spectrum in fast fading environment is investigated. A channel with land mobile fading spectrum with the autocorrelation function introduced by Jake is considered for simulations. Normalized Doppler rate fN is actually the product of the actual Doppler rate fD and the duration of the transmitted symbol T. The discrete version of Karhunen-Loeve expansion is utilized to produce a complex Gaussian process in which each of its instant values is correlated to past values based on an arbitrary autocorrelation function. This expansion is also used to expand the channel matrix with each entry being a complex Gaussian process. This is a computationally efficient technique for statistical simulations to evaluate the ergodic capacity and can be used to avoid lengthy numerical computations.