Main objective of this paper is to compare the performance and complexity of optimal and sub-optimal transmit antenna selection methods for quadrature spatial modulation (QSM). Antenna selection schemes are classified into optimal and sub-optimal based on their average bit error rate (ABER) performance. Selection of antenna requires criteria such as amplitude of channel, correlation between antennas, Euclidean distance (ED), or combinations of these criteria. The ABER performance of ED-based antenna selection scheme is optimal with higher complexity compared with the other sub-optimal scheme considered. This is validated through the complexity analysis and simulation results. © 2021, Springer Nature Singapore Pte Ltd.