Optimal transmit-diversity precoders for random fading channels

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Abstract
Optimal transmitter-receiver designs obeying the water-filling principle are well-known and widely applied when the propagation channel is deterministically known and frequently updated at the transmitter. Because the latter may be costly or impossible to acquire in rapidly varying wireless environments, we develop in this paper statistical water-filling-like criteria for stationary random fading channels. The resulting optimal designs require only knowledge of the channel's correlation matrix that does not require frequent updates and can be easily acquired. Applied to a multiple transmit-antenna paradigm, the optimal precoder and loading algorithm outperform not only the conventional equal-power allocation across all antennas but also their deterministic water-filling counterparts in fast fading scenarios.