Complex and Envelope Covariance for Rician Fading Communication Channels

In practice, the measurement of the covariance function (which characterizes a time- and frequency-selective fading communication channel) involves envelope detecting the received signals before correlating. Envelope covariance is insufficient for an accurate evaluation of system performance and rather a complex covariance is needed. In this paper the relationship between complex covariance and envelope covariance for a Rician fading communication channel is derived. It includes the well-known case of Rayleigh fading. For the assumption of the symmetric power spectrum of the narrow-band random process there exists a monotonic relationship which allows the evaluation of the complex covariance once the envelope covariance is measured. The derived equation for the unsymmetric power spectrum is discussed. The results obtained show that the envelope covariance represents a lower bound of the magnitude of the complex covariance.