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In closed-loop multiple input and multiple output (MIMO) systems, using a transmit power allocation scheme can increase capacity. However, the use of a space division multiplexing (SDM) scheme, which does not separate the MIMO channel into orthogonal channels, causes nonlinearity between the transmit power and the corresponding signal to interference plus noise ratio (SINR) of each data stream at the output of the detector (e.g. utilizing a MMSE detector with parallel interference canceller at the receiver). This makes it difficult to obtain the optimal power allocation value for each data stream. This paper proposes a novel power allocation scheme with an iterative algorithm for MIMO systems to solve the above problem. Furthermore, we incorporate transmit antenna selection into our proposed power allocation scheme in order to attain further capacity enhancement. Several computer simulation results are provided to show the effectiveness of our proposed techniques.