Space-Time Block Diagonalization for Frequency-Selective MIMO Broadcast Channels

The most important linear precoding method for frequency-flat MIMO broadcast channels is block diagonalization (BD) which, under certain conditions, attains the same nonlinear dirty paper coding channel capacity. However, BD is not easily translated to frequency-selective channels, since space-time information must be included in the transceiver design. In this paper, we demonstrate that BD is possible in frequency-selective MIMO broadcast channels to eliminate inter-user interference and derive the conditions on the number of transmit antennas and the transmission block length (as functions of the number of users and channel delay spread) for the existence of BD precoders. We also propose three different approaches to mitigate/eliminate inter-symbol interference in block transmissions: time-reversal-based BD (TRBD), equalized BD (EBD), and joint processing BD (JPBD). We show that any transmit-processing-only method (including TRBD and EBD) yields zero diversity and multiplexing gains (high SNR regime). We also demonstrate that JPBD, which uses linear processing at the transmitter and the receiver, approximates full multiplexing gain for a sufficiently large transmit block length, and show its diversity-multiplexing tradeoff. Extensive numerical simulations show that the achievable rate and probability of error performance of all the proposed techniques remarkably improve that of conventional time-reversal beamforming. Moreover, JPBD provides the highest achievable rate region for frequency-selective MIMO broadcast channels.