A correlation based analysis for approximate MAP detectors and iterative receivers

In this paper, we consider two approximate maximum a posteriori probability (MAP) detectors for code division multiple access (CDMA) systems. We show that if the sum of multiple access interferences (MAI) is Gaussian (with certain mean and variance from the extrinsic information), the (well-known) minimum mean square error (MMSE) detector with soft interference cancellation (SIC), called the MMSE-SIC detector, becomes the MAP detector. Thus, for a large number of users, the MMSE-SIC detector becomes asymptotically the MAP detector. In addition, we consider a correlation based analysis for the iterative detection with the approximate MAP detectors to see the performance limit. Then, the correlation analysis is further generalized to analyze the performance of the iterative receiver consisting of an approximate MAP detectors and channel decoders for coded signals.