Asymptotically optimal nonlinear MMSE multiuser detection based on multivariate Gaussian approximation

In this paper, a class of nonlinear minimum mean-squared error multiuser detectors is derived based on a multivariate Gaussian approximation of the multiple-access interference for large systems. This approach leads to expressions identical to those describing the probabilistic data association (PDA) detector, thus providing an alternative analytical justification for this structure. A simplification to the PDA detector based on approximating the covariance matrix of the multivariate Gaussian distribution is suggested, resulting in a soft interference-cancellation scheme. Corresponding multiuser soft-input, soft-output detectors delivering extrinsic log-likelihood ratios are derived for application in iterative multiuser decoders. Finally, a large-system performance analysis is conducted for the simplified PDA, showing that the bit-error rate (BER) performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector. Methods from statistical neurodynamics are shown to provide a closely related alternative large-system prediction. Numerical results demonstrate that for large systems, the BER is accurately predicted by the analysis and found to be close to optimal performance