Block Diagonalization for Frequency-Selective Multiuser-MIMO Downlinks

The capacity of frequency-flat multiuser MIMO downlinks is achieved with nonlinear dirty paper coding (DPC). Linear processing techniques, such as block diagonalization (BD), offer relatively low computational cost with respect to DPC and can also achieve capacity in certain cases. However, BD is not easily translated to frequency-selective channels since the channel matrix has a space-time structure (unlike the space-only information in frequency-flat channels), which induces an additional inter-symbol interference (ISI) component in the received signal. In this paper, we demonstrate that BD is feasible in frequency-selective channels when the transmitted block length is sufficiently large and the number of transmit antennas is greater than or equal to the number of users. We also present three novel techniques based on BD for frequency-selective MU-MIMO systems: time-reversal-based BD (TRBD), equalized BD (EBD), and joint processing BD (JPBD). These techniques use perfect channel state information at the transmitter (and also at the receiver, in the case of JPBD) to mitigate or eliminate both ISI and inter-user interference. We demonstrate that TRBD and EBD yield zero multiplexing gain (high SNR regime) but perform well under low SNR, while JPBD has a multiplexing gain approximately equal to the number of users for a sufficiently large transmit block length. Extensive numerical simulations show that the achievable rate performance of the proposed techniques improves that of time-reversal beamforming, a common technique for frequency-selective MU-MIMO downlinks.