Analysis on Transmit Antenna Selection for Spatial Multiplexing Systems: A Geometrical Approach

In recent years, the remarkable ability of multiple-input multiple-output (MIMO) wireless communication systems to provide spatial diversity or multiplexing gains has been clearly demonstrated. For MIMO diversity schemes, it is well known that antenna selection methods that optimize the post-processing signal-to-noise ratio can preserve the diversity order of the full MIMO system. On the other hand, the diversity order achieved by antenna selection in spatial multiplexing (SM) systems, especially those exploiting practical coding and decoding schemes, has not thus far been rigorously analyzed. In this paper, a geometrical framework is proposed to theoretically analyze the diversity order achieved by transmit antenna selection for independently encoded spatial multiplexing systems with linear and decisionfeedback receivers. For a system with T N transmit and R N receive antennas, it is rigorously shown that a diversity order of ( 1)( 1) T R N N − − can be achieved for a SM system in which 2 L = antennas are selected from the transmit side. For 2 L > , it is shown that the achievable diversity order is bounded below by ( 1)( 1) T R N L N L − + − + . Furthermore, the same geometrical approach is used to evaluate the diversity-multiplexing tradeoff curves for spatial multiplexing systems with transmit antenna selection.