Iterative multiuser joint decoding: optimal power allocation and low-complexity implementation

We consider a canonical model for coded code-division multiple access (CDMA) with random spreading, where the receiver makes use of iterative belief-propagation (BP) joint decoding. We provide simple density-evolution analysis in the large-system limit (large number of users) of the performance of the BP decoder and of some suboptimal approximations based on interference cancellation (IC). Based on this analysis, we optimize the received user signal-to-noise ratio (SNR) distribution in order to maximize the system spectral efficiency for given user channel codes, channel load (users per chip), and target user bit-error rate (BER). The optimization of the received SNR distribution is obtained by solving a simple linear program and can be easily incorporated into practical power control algorithms. Remarkably, under the optimized SNR assignment, the suboptimal minimum mean-square error (MMSE) IC-based decoder performs almost as well as the more complex BP decoder. Moreover, for a large class of commonly used convolutional codes, we observe that the optimized SNR distribution consists of a finite number of discrete SNR levels. Based on this observation, we provide a low-complexity approximation of the MMSE-IC decoder that suffers from very small performance degradation while attaining considerable savings in complexity. As by-products of this work, we obtain a closed-form expression of the multiuser efficiency (ME) of power-mismatched MMSE filters in the large-system limit, and we extend the analysis of the symbol-by-symbol maximum a posteriori probability (MAP) multiuser detector in the large-system limit to the case of nonconstant user powers and nonuniform symbol prior probabilities.