In the previous chapters, large MIMO detection algorithms were presented under the assumption of perfect knowledge of channel gains at the receiver. However, in practice, these gains are estimated at the receiver, either blindly/semi-blindly or through pilot transmissions (training). In FDD systems, channel gains estimated at the receiver are fed back to the transmitter (e.g., for precoding purposes). In TDD systems, where channel reciprocity holds, the transmitter can estimate the channel and use it for precoding. Due to noise and the finite number of pilot symbols used for channel estimation, the channel estimates are not perfect, i.e., there are estimation errors. This has an influence on the achieved capacity of the MIMO channel and the error performance of detection and precoding algorithms. This chapter addresses the effect of imperfect CSI on MIMO capacity, how much training is needed for MIMO channel estimation and channel estimation algorithms and their performance on the uplink in large-scale multiuser TDD MIMO systems.

MIMO capacity with imperfect CSI

The capacity of MIMO channels can be degraded if the CSI is not perfect. Gaussian input distribution, which is the capacity achieving distribution in the perfect CSI case, is suboptimal when CSI is imperfect [1],[2]. Lower and upper bounds on the mutual information for iid frequency-flat Rayleigh fading point-to-point MIMO channels have been derived for the imperfect CSI case in [3] assuming Gaussian input, where the MMSE channel estimate is assumed at the receiver and the same channel estimate is assumed to be available at the transmitter.