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The performance analysis of a space-time coded multiple-input-multiple-output (MIMO) system that employs different variable-power adaptive-modulation (VP-AM) strategies with outdated channel-state information (CSI) over Rayleigh fading channels is presented. The optimal design of VP-AM with power control (PC) in time (VP-AM-TIME) is first developed. The optimum switching thresholds of VP-AM-TIME for attaining maximum spectrum efficiency (SE) subject to a target bit error rate (BER) and an average power constraint are derived. A closed-form expression of the optimal temporal PC in terms of the Lambert function is obtained. A suboptimal VP-AM-TIME is also developed to further simplify the algorithm. The existence and uniqueness of the Lagrange multiplier that was used in the constrained optimization for the optimal and suboptimal VP-AM-TIME are investigated. By using the switching thresholds, we obtain closed-form expressions of SE and average BER. Then, a VP-AM scheme with joint spatial-temporal power control (VP-AM-JOINT) is developed. The joint spatial-temporal PC problem can be solved by transforming it into an inner-outer optimization problem. Theoretical analysis and simulation results show that the proposed optimal VP-AM-TIME can obtain the same performance as the existing optimal VP-AM-TIME but with much lower computational complexity, and the new suboptimal VP-AM-TIME outperforms the existing suboptimal scheme and obtains a performance closer to the optimal scheme. The results also show that the new VP-AM-JOINT scheme is always superior to the optimal VP-AM-TIME and provides considerable gains in SE over a wide range of feedback delays, although the two schemes have almost the same performance when the feedback delay becomes large.