Information Capacity of Implicit Receiver Training in Unknown MIMO Channels

The capacity of a channel subject to frequency selective fading is a fundamentally well known result when perfect channel side information (CSI) or explicit training is available at the receiver for performing MMSE MIMO estimation. However, in practical wireless applications, the channel estimation problem operates initially without full knowledge of the channel parameters. This problem expatiates further when the channel is time varying, where a continually transmitting source may need to expend a significant portion of its resources on training. The capacity for training based MMSE MIMO estimation is well known where the redundancy incurred depends on the rate at which the channel varies. On the other hand, implicit training based (Blind) estimation does not require the transmission of known Pilot symbols with the cost that the signaling alphabet cannot generally be Gaussian when utilizing methods involving steepest descent or higher order statistics. In this paper, a subspace method (the MUSIC algorithm) of estimation is investigated and compared with two other techniques, namely the Goddard algorithm and the MMSE algorithm). It is shown that the MUSIC algorithm can approach the explicit MMSE training capacity of 5bits/Hz within 1dB for a very slow varying fading channel. It is also shown that for a channel subject to a more significant time variation, up to 2dB improvement can be realized with implicit training for less than 4bits/Hz capacity.