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In this paper, we investigate the subcarrier allocation problem in multi-user multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems (also known as MIMO-OFDMA) with spatial multiplexing. Due to the numerous advantages of OFDM schemes, this type of system is becoming increasingly popular for deployment in next generation wireless systems. We first consider the problem of maximizing the capacity of the downlink channel, which results in a joint optimal subcarrier allocation and power loading problem. However, the computational complexity involved in this joint optimization problem is of order 0(KN), where K is the total number of users and N is the total number of subcarriers in the system. We next propose a new suboptimal scheme of low complexity and extend our framework by incorporating spatial multiplexing. Finally, we evaluate the performance in terms of bit error rate (BER) and capacity of the system via simulation and give some analytical bounds.