On the maximal diversity order of spatial multiplexing with transmit antenna selection

Zhang et al. recently derived upper and lower bounds on the achievable diversity of an N-R X N-T, 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 N-T available) antennas the bounds are tight and therefore specify the maximal diversity order. For the general case with L <= Mill(NR, AFT) transmitting antennas it was,conjectured that the maximal diversity is (N-T - 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.