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In this paper, stable fast Kalman (SFK) and variable step size (VSS) LMS algorithms for use in training mode and decision-directed mode equalizations, respectively, are proposed in order to improve the performance of terrestrial 8-VSB DTV receiver. The SFK algorithm is intended for fast initial convergence and optimality of estimating the equalization coefficients in the training mode. The VSS LMS algorithm is employed for its simple implementation, robustness, good tracking behaviors, and its ability to update the step-size adaptively in the multi-path fading. Our simulation results show its fast initial convergence and stability of steady-state behavior over the conventional adaptive equalizer and other algorithms. The results also show that the proposed equalizer provides about 1.5 dB signal-to-noise ratio (SNR) improvement at SER of 3.0×10-6 as compared to LMS DFE.