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Space-division multiple access (SDMA) and orthogonal frequency-division multiplexing (OFDM) can be combined to design a robust communications system with increased spectral efficiency and system capacity. This combination is one of the most promising candidates for future wireless local area network implementations. However, one drawback of OFDM systems is the high peak-to-average power ratio, which imposes strong requirements on the linearity of power amplifiers (PAs). Such linearity requirements translate into high back-off that results in low power efficiency. In order to improve power efficiency, a PA nonlinearity cancellation (PANC) technique is introduced in this paper. This technique reduces the nonlinear distortion effects on the received signal. The performance of the new technique is evaluated with simulations, which show significant power efficiency improvements. To obtain meaningful results for comparison purposes, we derive a theoretical upper bound on the bit error rate performance of an SDMA-OFDM system subject to PA nonlinearities. In addition, a novel channel estimation technique that combines frequency- and time-domain channel estimation with PANC is also presented. Simulation results show the robustness of the cancellation method also when channel estimation is included.