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 $N_R \times N_T$ 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 $L \leq \min(N_R,N_T)$ transmitting antennas it was conjectured that the maximal diversity is $(N_T-L+1)(N_R-L+1)$ 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.