On the Capacity of Iteratively Estimated Channels Using LMMSE Estimators

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This paper investigates the capacity of radio channels when iterative channel estimation, data detection, and decoding are employed. Knowing the capacity gain from iterative detection versus purely pilot-based channel estimation helps a designer compare the performance of an iterative receiver against a noniterative receiver and select the best balance between performance and cost. A bound is put on the linear minimum mean square error (LMMSE) channel estimation error, based on which a bound on the capacity is obtained. The attainable capacity is related to the channel estimation error of the receiver. The bounds take into account the uncertainty in symbol detection on channel estimation and incorporate the effect of channel estimation error on channel capacity. The interaction between the symbol detector and the decoder is analytically characterized and depicted in an extrinsic information transfer (EXIT) chart, where a bound on the detector curve is found. With optimal LMMSE pilot-based channel estimation, the results of this paper demonstrate that iterative channel estimation provides insignificant capacity advantage at fading rates below 1% of the symbol rate, although a computational-cost gain is still available. Iterative channel estimation provides a capacity benefit if suboptimal pilot signaling is used to provide initial channel estimates.