Reduced-rank multiuser detectors based on vector and matrix conjugate gradient Wiener filters

Using the notion of expanding subspace and the framework of reduced-rank signal processing, we present our latest discovery on applying the vector and matrix conjugate gradient (CG) methods to design reduced-rank linear MMSE multiuser detectors (MUD) for code division multiple access (CDMA) systems. We show that for a synchronous CDMA system with K users, each using a distinct length N spreading code, the vector CG method converges to the full-rank linear MUD in at most K steps (K ≤ N). The matrix CG method converges to the full-rank linear MUD in one step. Furthermore, when the Gold codes are used as spreading codes in combination with a groupwise power control scheme, early convergence in the vector CG Wiener filter can be reached in just L steps (L ≪ K ≤ N), typically L = 2-4 independent of the user number K and the spreading length N.