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Shallow water acoustic communication is challenging due to the delay and Doppler spread resulting from acoustic scattering from surface gravity waves. A channel estimate based decision feedback equalizer (CEB-DFE) has been shown to be very effective at mitigating these channel effects. One component of the DFE that is often overlooked is the effective noise correlation matrix. In much of the literature, the effective noise correlation matrix is approximated by a scaled identity matrix, where the scaling is assumed to be near the reciprocal of the signal to noise ratio (SNR). For the underwater channel, explicitly estimating the full effective noise correlation matrix leads to a reduction of the residual data estimation error. In this paper we show that correlated changes in channel impulse response coefficients cause the effective noise correlation matrix to have off-diagonal terms. Since the correlated changes tend to occur slowly over time, the effective noise correlation matrix is Toeplitz. An algorithm which exploits this fact to reduce computational complexity is presented and is demonstrated using experimental data.