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Using cyclic prefix (CP), the transmission schemes, orthogonal frequency-division multiplexing (OFDM), single carrier block transmission, and time reversal, can be unified as linear block precoding. Considering frequency-selective channels, this paper studies linear block precoding for CP-based multi-point transmission with individual antenna power constraints under capacity maximization criterion. We prove that, the optimal precoder could be, but not necessarily, in the form of OFDM transmission (i.e., an inverse discrete fourier transformation (IDFT) matrix multiplying a complex diagonal matrix). Further, we show that the capacity maximization problem with individual power constraints can be simplified as an unconstrained problem, which allows us to solve the problem using the simple gradient decent method. Simulation results show that the proposed precoding method achieves near-optimal performance.