Bounds on the ergodic capacity of training-based multiple-antenna systems

Multiple-antenna concepts for wireless communication systems promise high spectral efficiencies by proper exploitation of the randomness in multipath propagation. In this paper, we investigate the impact of channel uncertainty caused by channel estimation errors on the capacity of Rayleigh and Ricean block-fading channels. We consider a training-based multiple-antenna system that reserves a portion of time to sound the channel. The training symbols are used to estimate the channel state information (CSI) at the receiver by means of an arbitrary linear estimation filter. No CSI is assumed at the transmitter. We present an equivalent system model for training-based multiple-antenna systems, which specifies the channel by the estimated (and hence, known) channel coefficients and an uncorrelated, data-dependent noise. Based on this equivalent model, which includes the special cases of perfect CSI and no CSI, we derive upper and lower bounds on the maximum instantaneous mutual information and the ergodic capacity, and extend previous results to arbitrary (and possibly mismatched) linear channel estimators and to correlated Ricean fading