Digital Transmission Over Cross-Coupled Linear Channels

For a multiuser data communications system operating over a mutually cross-coupled linear channel with additive noise sources, we determine the following: (1) a linear cross-coupled receiver processor (filter) that yields the least-mean-squared error between the desired outputs and the actual outputs, and (2) a cross-coupled transmitting filter that optimally distributes the total available power among the different users, as well as the total available frequency spectrum. The structure of the optimizing filters is similar to the known 2 × 2 case encountered in problems associated with digital transmission over dually polarized radio channels.