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Our proposed orthogonal decision feedback detector (ODFD) contains an orthogonal feedforward filter and a decision feedback structure. Compared with the decorrelating decision feedback detector (DDFD), our QR-factorization-based ODFD is computationally more efficient in dynamically updating the feedforward and feedback filter pairs. This feature is beneficial when the number of users in a system changes frequently. Using the Gaussian approximation, which was used to compute the approximate bit-error probabilities (BEPs) of multiusers for the successive interference canceller (SIC), we calculate the approximate BEPs of multiusers for the DDFD and our ODFD. The Gaussian approximation leads to good approximate BEPs for DDFD and to fine approximate BEPs for ODFD, but to poor approximate BEPs for SIC. The accuracy of these approximate BEPs is also justified by the results from Monte Carlo simulations.