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For space-division multiplexing (SDM) via block diagonalization on multiuser multiple-input multiple-output (MIMO) wireless downlink, it is shown that receive antenna selection (RAS) is necessary for maximizing the achievable sum rate. This is true even when all receive antennas are equipped with radio frequency (RF) chains and RAS reduces the upper bound on the broadcast sum capacity, and when the orthogonalized channels use optimal processing. Similarly, spatial-mode selection (SMS) is necessary for sum rate maximization when receive-weight matrices are used for spatial-mode allocation. RAS/SMS may release transmission resources that can fully be utilized via additional user scheduling to yield further sum rate gains. Optimal user selection for sum rate maximization is subsumed within an exhaustive RAS/SMS process for multiantenna terminals, and both selection processes become identical for single-antenna terminals. RAS/SMS thus helps reduce the performance gap from the optimal sum capacity even for small user pool sizes. A block antenna/mode selection approach is introduced to help overcome the drawbacks of existing algorithms. Since RAS/SMS involves antenna/mode ranking, a systematic method for resource allocation with sum rate loss minimization is inherently provided. This way, a streamlined process that combines user selection, RAS/SMS, and resource allocation is developed for sum rate maximization of block-diagonalized SDM.