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In this paper we analyze the combined performance of noise-cancellation and diversity-combining in an ACO-OFDM system. Noise cancellation and diversity combining are two techniques which have each been shown to improve the performance of ACO-OFDM, each giving a maximum improvement of 3dB. As noise cancellation reduces the noise at the detection point, while diversity combining adds two different signal components, it might be expected that combining the two techniques could give further performance gains. In this paper we show analytically that no additional performance gain can be achieved by combining the techniques. Simulation results are presented which are consistent with the analysis. It is also observed that the noise cancellation is more computationally efficient than diversity combining.