Approximate bit error probability calculation of decision-feedback linear multiuser detectors

Using the Gaussian approximation, we calculate the approximate bit error probabilities (BEPs) or three multiusers. The accuracy of approximate BEPs for successive interference canceller (SIC), decorrelating decision feedback detector (DDFD), and orthogonal decision feedback detector (ODFD) depends on two factors. The first factor is whether the desired component at the input to the threshold is correlated with undesired component. The second factor is whether the approximate variance of the Gaussian undesired component contains non-zero covariance terms. The Gaussian approximation leads to good approximate BEPs for DDFD, to fair 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.