Nonlinear MMSE Multiuser Detection Based on Multivariate Gaussian Approximation

In this paper, a class of nonlinear MMSE multiuser detectors are derived based on a multivariate Gaussian approximation of the multiple access interference. 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 performance of this detector can be accurately predicted and related to the replica method analysis for the optimal detector. Methods from statistical neuro-dynamics are shown to provide a closely related alternative large system prediction. Numerical results demonstrate that for large systems, the bit error rate is accurately predicted by the analysis and found to be close to optimal performance.