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Optimal training design and channel estimation for spatially correlated multi-user Multi-Input Multi-Output with Orthogonal Frequency-Division Multiplexing (MIMO-OFDM) systems is still an open research problem of great interest. This paper applies tractable semi-definite programming to obtain the optimal training signal for the general case of spatial channel correlations for multi-user MIMO-OFDM. The optimal solution in closed-form expression is also derived for a special case of transmit correlations. Analytical and simulation results demonstrate the excellent performance of the proposed designs and their performance advantage over the equi-powered training designs.
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