The compressed beamforming weights feedback is used in the MIMO-OFDM IEEE 802.11n/ac WLAN to reduce the amount of feedback information. The precoded sub-system at the receiver side of this system needs to perform singular value decomposition (SVD) on the estimated channel matrices at all sub-carriers, and to quantize the angles representing the right singular vectors to be fed back to the transmitter. Under the exemplary scenario of four antennas at the access point and two antennas at the station, our designed architecture for the precoding sub-system can compute the quantized angles fast enough to meet the requirement of the 80 MHz bandwidth transmission for the IEEE 802.11n/ac standard. Furthermore, by taking advantage of the SVD outputs, we demonstrate algorithmic complexity reduction for computing the preprocessing QRD for the tree search detectors. Surprisingly, although additional function to provide preprocessing QRD for future signal detection, our architecture for computing both SVD and QRD requires approximately the same amount of gates as one earlier architecture to compute the SVD only.