Dynamic Transmit Covariance Design in MIMO Fading Systems With Unknown Channel Distributions and Inaccurate Channel State Information

Abstract

This paper considers dynamic transmit covariance design in point-to-point MIMO fading systems with unknown channel state distributions and inaccurate channel state information subject to both long term and short term power constraints. First, the case of instantaneous but possibly inaccurate channel state information at the transmitter (CSIT) is treated. By extending the drift-plus-penalty technique, a dynamic transmit covariance policy is developed and is shown to approach optimality with an $O(δ)$ gap, where $δ$ is the inaccuracy measure of CSIT, regardless of the channel state distribution and without requiring knowledge of this distribution. Next, the case of delayed and inaccurate channel state information is considered. The optimal transmit covariance solution that maximizes the ergodic capacity is fundamentally different in this case, and a different online algorithm based on convex projections is developed. The proposed algorithm for this delayed-CSIT case also has an $O(δ)$ optimality gap, where $δ$ is again the inaccuracy measure of CSIT.

This paper extends our INFOCOM 2016 paper (see comments in v2 for extension) and its short version will appear in IEEE Transactions on Wireless Communications. Note that a constant coefficient in Theorem 4 of INFOCOM 2016 paper was incorrectly given and is corrected in footnote 6 in this paper.(However, this minor error does not affect any other results or conclusions in INFOCOM 2016 paper.)