Bounds for minimum Euclidean distance for coded multiuser CDMA systems

We study two properties of the minimum Euclidean distance (d² _min) for a coded multiuser system. They are the upper bound of d²_min and the effect of non-orthogonal spreading. We prove that if all users use trellis codes with same memory length and same number of input bits but different mapping signal sets, then the upper bound of the normalized minimum distance for trellis coded multiuser CDMA system with non-orthogonal spreading is identical to that of the single-user case. It indicates that the trellis coded multiuser system may recover the minimum distance loss of the uncoded multiuser system due to the non-orthogonal spreading (if there is a such loss). Then we investigate the effect of non-orthogonal spreading on a coded system. We derive and study several upper and lower bounds for the ratio of d²_min between the system with non-orthogonal spreading and orthogonal spreading. The numerical results are presented to illustrate the theories