In this paper, we consider multi-carrier systems with multiple transmit antennas under a power balancing constraint. Applying transmit antenna selection and discrete rate adaptive modulation using M-ary quadrature amplitude modulation (QAM) according to the channel variation per subcarrier, we develop an optimal antenna selection scheme in terms of maximum spectral efficiency where all the possible grouping to send the same information bearing signals in a group of subcarriers are searched and the groups of subcarriers to provide the frequency diversity gain are formed. In addition, we propose a suboptimal method to reduce the computational complexity of the optimal method. The suboptimal scheme consider only the subcarriers under outage and those are combined sequentially until it meets a required SNR. Numerical results show that the proposed suboptimal method with diversity combining outperforms the optimal antenna selection without diversity combining introduced in , especially for low SNR region and offers the spectral efficiency close to that of the optimal method with diversity combining, while maintaining lower complexity.