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We have previously demonstrated that turbo equalization, or iterative equalization and decoding, can improve the receiver performance for medium-rate HF waveforms (up to 2400 bit/s using 8-PSK). In this paper, we apply turbo equalization to the high-rate waveforms (up to 9600 bit/s using 64-QAM) of STANAG 4539, and investigate the performance using simulations. The soft-in/soft-out (SISO) equalizer used is based on soft intersymbol interference cancellation followed by a linear filter. For the high-rate waveforms we find that this equalization algorithm needs some tweaking in order for the iterative procedure to converge. But when it does converge, turbo equalization outperforms a conventional single-pass receiver using decision-feedback equalization (DFE) by 6-7 dB in required signal-to-noise ratio to obtain a bit error rate of 10-4. Issues regarding computational complexity are also discussed.