One of the main drawbacks of orthogonal frequency division multiplexing (OFDM) systems is the high peak-to-average power ratio (PAPR) of the transmitted signals, which can cause the introduction of intercarrier interference (ICI) due to the presence of nonlinear power amplifiers (PAs). In this paper, a theoretical analysis of the ICI in nonlinear OFDM systems with polynomial PAs is made. Contrary to other works, this analysis provides an exact description of the nonlinear ICI. Moreover, three receivers for channel estimation and ICI cancellation in OFDM systems with polynomial PAs are proposed, based on the concept of power diversity that consists in retransmitting the information symbols several times with a different transmission power each time. The transmission powers that minimize the sum of the residual mean square errors (MSEs) provided by the proposed receivers are derived in the case of a third-degree polynomial PA. An important advantage of the proposed receivers is that the optimal transmission powers do not depend on the channel and the PA coefficients.