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

TL;DR

This paper proves a conjecture regarding the maximal diversity order in spatial multiplexing with transmit antenna selection for certain receiver structures, confirming the theoretical maximum achievable diversity.

Contribution

It provides a proof of the conjectured maximal diversity order for zero forcing and decision feedback receivers in MIMO systems with antenna selection.

Findings

Maximal diversity order is (N_T-L+1)(N_R-L+1) for the specified system.

The conjecture is proven for zero forcing and decision feedback receiver structures.

Bounds on diversity are tight for L=2, and the proof extends this to general L.

Abstract

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 <= 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.