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 unform channel decomposition (UCD) schemes. The high performance of the MIMO systems comes with increased hardware complexity. To reduce the system complexity, we consider selecting Lt transmit and Lr receive antennas in a MIMO system with Mt transmit and Mr receive antennas (Lt ≤ Mt and Lr ≤ Mr). 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{Lt, Lr} ≤ Mr.Mt/Mr+Mt-1.