An Improved Method for Estimating the Time ACF of a Sum of Complex Plane Waves

Time averaging is a well-known technique for evaluating the temporal autocorrelation function (ACF) from a sample function of a stochastic process. For stochastic processes that can be modelled as a sum of plane waves, it is shown that the ACF obtained by time averaging can be expressed as a sum of auto-terms (ATs) and cross-terms (CTs). The ATs result from the autocorrelation of the individual plane waves, while the CTs are due to the cross-correlation between different plane wave components. The CTs cause an estimation error of the ACF. This estimation error increases as the observation time decreases. For the practically important case that the observation time interval is limited, we propose a new improved method for estimating the time ACF of a sum of plane waves. The main idea behind the proposed method is to introduce a kernel function aiming to reduce the CT effect, while preserving the ATs. In this way, we can improve the estimation of the ACF. We show that the proposed method outperforms the standard time averaging technique. The performance of both methods is evaluated using a synthetic channel model consisting of a sum of complex plane waves.