Optimal training design for MIMO-OFDM systems under spatially correlated doubly selective fading channels

In this paper, we design an optimal training scheme for multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems under spatially correlated time- and frequency-(doubly) selective fading channels. We first develop the optimal pilot symbols and placement of pilot clusters with respect to the minimum mean square error (MMSE) of the linear channel estimate. We then derive the optimal power allocation for pilot symbols in a two-water-level way: by maximizing the averaged capacity lower bound, how much power to be allocated for training is determined subject to the global water level (or the constraint of total transmit power); subsequently, pouring power to the pilot symbols with an approximately optimal water-filling scheme subject to the local water level (or the constraint of assigned power for training). In addition, for a particular OFDM size, the optimal number of pilot clusters is derived by maximizing the capacity lower bound and by minimizing the channel estimate's MMSE.