Comparative Study of SVD and QRS in Closed-Loop Beamforming Systems

Abstract

We compare two closed-loop beamforming algorithms, one based on singular value decomposition (SVD) and the other based on equal diagonal QR decomposition (QRS). SVD has the advantage of parallelizing the MIMO channel, but each of the sub-channels has different gain. QRS has the advantage of having equal diagonal value for the decomposed channel, but the subchannels are not fully parallelized, hence requiring successive interference cancellation or other techniques to perform decoding. We consider a closed-loop system where the feedback information is a unitary beamforming matrix. Due to the discrete and limited modulation set, SVD may have inferior performance to QRS when no modulation set selection is performed. However, if the selection of modulation set is performed optimally, we show that SVD can outperform QRS.