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Adaptive turbo frequency-domain channel estimation is incorporated with low complexity turbo space-frequency equalization (TSFE) for single-carrier (SC) multi-user detection. The simplified turbo recursive least square (RLS) channel estimation algorithm provides nearly the same performance as its full complexity version, with a tremendous complexity reduction. With PSK modulations, the simplified turbo RLS channel estimation reduces to turbo LMS channel estimation. With a low training overhead, the simplified turbo RLS channel estimation provides a performance comparable to the case with perfect channel state information (CSI).