A short review on multiuser communication systems is given. System design for iterative multiuser decoding is improved by means of large system results from statistical physics and random matrix theory. With the application of multiuser detection for wireless communications in mind, it is shown how a system of linear equations with random coefficients can be solved efficiently exploiting the asymptotic convergence of its eigenvalue spectrum. In addition, the conditional convergence of the diagonal elements of a power of a random matrix drawn from a Marchenko--Pastur ensemble is established.

PACS numbers: 89.70.+c, 84.40.Va, 02.60.Dc, 05.90.+m