Capacity of iteratively estimated channels using LMMSE estimators

This paper explores how iterative channel estimation, symbol detection and decoding at the receiver affects the achievable capacity compared with a non-iterative, purely pilots-based scheme. First, a bound is put on the linear minimum mean-square error (LMMSE) estimator of doubly selective radio channels. Subsequently, a bound on the capacity using an LMMSE estimator is found. These bounds take into account the uncertainty in symbol detection on channel estimation, and incorporate the effect of channel estimation error on channel capacity. The paper describes how bounds can be calculated for typical multipath and fast fading radio channels. The interaction between the symbol detector and the decoder is depicted by exploiting an extrinsic information transfer (EXIT) chart, where a bound on the detector curve is found. With optimal LMMSE pilot-based channel estimation, the bounds demonstrate that iterative channel estimation has little advantage except at fading rates greater than 1% of the symbol rate. To make the results more concrete, finite order modulations are also investigated and compared with the case of Gaussian distributed symbols, showing that the latter can be used to approximate the performance of the former in a more convenient way.