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In communication systems that use orthogonal frequency-division multiplexing and multiple transmit and receive antennas, beamforming (BF) is conventionally carried out on a subcarrier basis. The computational requirements are high as dedicated discrete Fourier transform (DFT) processors are needed for each antenna. Considerable complexity reductions can be achieved by symbol-wise BF, which performs the transmit and receive BF operations in the time domain, and therefore requires only one DFT processor per terminal. In this paper, we investigate symbol-wise BF for the mitigation of co-channel interference on spatially correlated channels, which are modelled with the Kronecker model. We show analytically that symbol-wise BF is the optimal BF scheme when the channel is frequency-flat or fully correlated, and present a novel iterative algorithm for the computation of the optimal antenna weights. Monte-Carlo simulations confirm that the relative performance loss of symbol-wise BF becomes negligible when approaching full correlation.