The optimum transmitters for maximum information throughput when two independent users share a dispersive channel are investigated. The channel is assumed to be linear and time invariant and is described by a

matrix of transfer functions. The noise at each receiver is additive and Gaussian and may have a nonwhite spectrum. Assuming naive superposition (the interfering signal is treated as noise) it is shown that for many practical channels, frequency division multiplexing is optimum, and the structure of the optimum transmitters is obtained.