  Recently, the remarkable potential of a multiple-input multiple-output (MIMO)
wireless communication system was unveiled for its ability to provide spatial
diversity or multiplexing gains. For MIMO diversity schemes, it is already
known that. by the optimal antenna selection maximizing the post-processing
signal-to-noise ratio, the diversity order of the full system can be
maintained. On the other hand, the diversity order achieved by antenna
selection in spatial multiplexing systems, especially those exploiting
practical coding and decoding schemes, has not been rigorously analyzed thus
far. In this paper, from a geometric standpoint, we propose a new framework for
theoretically analyzing the diversity order achieved by transmit antenna
selection for separately encoded spatial multiplexing systems with linear and
decision-feedback receivers. We rigorously show that a diversity order of
(Nt-1)(Nr-1) can be achieved for an Nr by Nt SM system when L=2 antennas are
selected from the transmit side; while for L>2 scenarios, we give bounds for
the achievable diversity order and show that the optimal diversity order is at
least (Nt-L+1)(Nr-L+1) . Furthermore, the same geometrical approach can be used
to evaluate the diversity-multiplexing tradeoff curves for the considered
spatial multiplexing systems with transmit antenna selection.
