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To enable full-duplex (FD) operation in underwater acoustic systems, the strong self-interference (SI) from the near-end transmitter should be efficiently cancelled. Digital cancellation is considered as the main approach for the SI cancellation. It is believed that the key challenge in achieving a high level of cancellation is to overcome the nonlinear distortion in the transmit and receive chains. The majority of the nonlinearity is introduced by the power amplifier (PA), which can be dealt with by using the PA output as the reference signal for digital cancellation. Further nonlinearity comes mainly from the hydrophone pre-amplifier. For applications working in half-duplex mode, the pre-amplifier can normally be assumed to be linear due to the low received signal level. For FD operations, the strong SI might result in a nonlinear response of the pre-amplifier, and this nonlinearity should be equalized to achieve a high cancellation performance. In this paper, we propose a technique for equalizing the nonlinearity in the pre-amplifier. This is done using a basis expansion model of the nonlinear equalizer response. More specifically, the Legendre polynomials are used as the basis functions. The expansion coefficients are updated to reduce the mean squared error or a cost function derived based on the power spectrum of the received signal. The performance of the equalizer is evaluated using the experimental data with artificial nonlinear distortion and with real nonlinearity introduced by the hydrophone pre-amplifier. Both sets of results demonstrate that nonlinear distortions can be effectively equalized using the proposed adaptive equalization technique.