In a closed-loop wireless communication system, a codebook-based feedback mechanism is provided to enable non-unitary precoding for multi-stream transmission, where in each stream is optimized with suitable transmission power allocation and AMC. The codebook-based feedback mechanism uses a precoding codebook having a power allocation matrix which is constrained to specify that beamforming always applies full power to a predetermined beam. With this constraint, a one-bit power allocation feedback index may be used to switch between beamforming and spatial multiplexing.