On the Maximal Diversity Order of Spatial Multiplexing With Transmit Antenna Selection

Zhang recently derived upper and lower bounds on the achievable diversity of an NR timesNT i.i.d. Rayleigh fading multiple antenna system using transmit antenna selection, spatial multiplexing and a linear receiver structure. For the case of L = 2 transmitting (out of NT available) antennas the bounds are tight and therefore specify the maximal diversity order. For the general case with L les min(NR ldrNT) transmitting antennas it was conjectured that the maximal diversity is (NT-L+1)(NR-L+1) which coincides with the lower bound. Herein, we prove this conjecture for the zero forcing and zero forcing decision feedback (with optimal detection ordering) receiver structures.