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The performance of multi-input multi-output (MIMO) systems with variable-power (VP) adaptive modulation (AM) and antenna selection (AS) over Rayleigh fading channels for both perfect and imperfect channel state information (CSI) is presented. In this study, the optimum fading gain switching thresholds for attaining maximum spectrum efficiency (SE) subject to a target bit error rate (BER) and an average power constraint are derived. It is shown that the Lagrange multiplier in the constrained SE optimisation is unique if the existence conditions for MIMO systems with transmit AS and receive maximal-ratio combining under perfect or imperfect CSI are satisfied. By using the switching thresholds, we obtain closed-form expressions of the SE and average BER for VP and constant-power (CP) systems. Simulation results for SE and BER are in good agreement with the theoretical analysis. The results show that the VP-AM system using AS with the derived VP control scheme provides better SE than the CP counterpart and the VP-AM system with space-time coding and can fulfil the target BER for different signal-to-noise ratios (SNRs).