Block-Diagonal Geometric Mean Decomposition (BD-GMD) for Multiuser MIMO Broadcast Channels

Matrix decompositions play an important role in analyzing the capacity and designing the transceiver for multiple input multiple output (MIMO) channels. In the single user case, by relying on the decision feedback equalizer (DFE) at the receiver or Tomlinson-Harashima precoding (THP) at the transmitter, the geometric mean decomposition (GMD) can be used to create identical signal-to-noise ratios (SNR) for each decoupled subchannel. In this paper, we propose a new matrix decomposition, called the block-diagonal GMD (BD-GMD), for the multiuser MIMO broadcast channel. Applying THP at transmitter and linear equalization in each of the receivers, each user can achieve identical SNRs for its subchannels, thus equal-rate coding can be applied for each user. Furthermore, by using transmit power control and the BD-GMD, we design a scheme that achieves equal-rate coding for the subchannels of all users. Computer simulations have shown that the proposed schemes have better BER performances than zero-forcing THP (ZF-THP) and equal-rate ZF-THP schemes.