Iterative equalization techniques are effective in mitigating inter-symbol interference (ISI). In this paper, we first study and compare three low-complexity adaptive-channel-estimation-based turbo equalization (ACE-based TEQ) algorithms over high-frequency (HF) waveform channels based on the STANAG 4285 standard. These reduced-complexity equalization algorithms include the minimum mean-square error (MMSE), the MMSE decision feedback equalization (MMSE-DFE) and the soft feedback interference cancellation (SFIC). To address the issue of the HF channel time-variation, an explicit adaptive channel estimator is used to determine the unknown channel coefficients. In addition, we have also proposed a hybrid ACE TEQ algorithm. Numerical results show that the ACE-SFIC-based TEQ scheme is the best in terms of trade-off between bit-error rate (BER) and implementation complexity for the STANAG 4285 military waveforms.