Diversity-Multiplexing Tradeoff of GMD/UCD with Antenna Selection

Assuming both the channel state information at the transmitter (CSIT) and receiver (CSIR), we can design a transceiver to readily approach the performance limit of MIMO systems, e.g., the geometric mean decomposition (GMD) and uniform channel decomposition (UCD) schemes. The high performance of the MIMO systems comes with increased hardware complexity. To reduce the system complexity, we consider selecting L_t transmit and L_r receive antennas in a MIMO system with M_t transmit and M_r receive antennas (L_t les M_t and L_r les M_r). We analyze the D-M tradeoff of GMD/UCD combined with optimal antenna selection. Approximating the error probability with the Q-function, we show that UCD can achieve the optimal diversity-multiplexing (D-M) tradeoff using uncoded quadrature amplitude modulation (QAM). In contrast, the GMD scheme is D-M tradeoff suboptimal in general but is optimal if min{L_t, L_r} les M_r + M_t-l/M_rM_t.