Mutual Information of Multipath Channels with Imperfect Channel Information

Analysis of mutual information is important to wireless transmission over fading channels, and is usually done by assuming perfect channel state information (CSI) available at the receiver. In many practical applications, however, the CSI must be estimated by sending a limited number of pilot symbols and thus, can suffer from considerable inaccuracy. The influence of CSI inaccuracy on achievable mutual information, though analyzed in the past, is not well understood. The difficulty arises from the presence of a product term of signal and channel estimation error in the received signal model, and the lack of appropriate tools to determine its probability density function. This situation forces the adoption of a bounding technique in current literature by treating the product term either as a signal component or as a noise component. In this paper, we take a different methodology by accurately fitting the received signal with the multivariate Pearson's type-7 (MPT-7) distribution. The new results are simple in expression, very accurate as evidenced by simulation, and capable of directly revealing the dependence of the achievable mutual information on a particular channel estimator.