Capacity and Error Performance of Reduced-Rank Transmitter Multiuser Preprocessing Based on Minimum Power Distortionless Response

In this contribution we first derive a transmitter multiuser preprocessing (TMP) scheme for a general multiuser multiple-input-multiple-output (MIMO) system based on the minimum power distortionless response (MPDR) criterion, which minimizes the power in the context of a given downlink mobile terminal (MT) under the distortionless condition. This optimization problem results in a solution, which has the same form as the minimum mean-square error (MMSE) multiuser detection (MUD). Hence, we then extend the well-known rank-reduction techniques in MMSE-MUD to the MPDR-TMP in order to mitigate the possible implementation problems of the MPDRTMP. In our study three classes of rank-reduction algorithms are considered, which are derived, respectively, based on the eigen-analysis methods of principal components (PC) and crossspectral metrics (CSMs) as well as on the Taylor polynomial approximation (TPA) approach, which does not depend on the eigen-analysis. In this contribution both the capacity and error performance of a downlink space-division multiple-access (SDMA) system is investigated, when either the full-rank or reduced-rank MPDR-TMP is invoked. From our study and simulation results, it can be shown that the MPDR-TMP scheme is highly efficient for achieving the capacity and for suppressing the multiuser interference (MUI). The reduced-rank techniques can be employed by the MPDR-TMP, so as to reduce its implementation complexity while achieving the near full-rank performance of the full-rank MPDR-TMP.