Minimax robust power allocation over parallel communication channels

Adapting the transmission strategy under partial or uncertain channel state information (CSI) at the transmitter is of importance in practical systems with imperfect channel knowledge. In this work, we consider the problem of power allocation in a system of parallel communication sub-channels with uncertain CSI. We adopt the robust (minimax) optimization methodology and attempt to arrive at a novel precoding strategy that guarantees a certain worst-case performance, but without being too conservative in terms of average performance. To this end, we precisely model the underlying sources of uncertainty, and characterize the typical norm-constrained uncertainty set by an additional unbiasedness constraint. This helps to reduce the severity of the worst-case scenario, and in turn leads to a less conservative, robust minimax power allocation strategy with superior average performance.