Performance Improvement of Iterative Multiuser Detection for Large Sparsely Spread CDMA Systems by Spatial Coupling

Kudekar et al. proved that the belief-propagation (BP) performance for low-density parity check codes can be boosted up to the maximum a posteriori (MAP) performance by spatial coupling. In this paper, spatial coupling is applied to sparsely spread code-division multiple-access systems to improve the performance of iterative multiuser detection based on BP. Two iterative receivers based on BP are considered: 1) one receiver is based on exact BP and 2) the other on an approximate BP with Gaussian approximation. The performance of the two BP receivers is evaluated via density evolution (DE) in the dense limit after taking the large-system limit, in which the number of users and the spreading factor tend to infinity while their ratio is kept constant. The two BP receivers are shown to achieve the same performance as each other in these limits. Furthermore, taking a continuum limit for the obtained DE equations implies that the performance of the two BP receivers can be improved up to the performance achieved by the symbol-wise MAP detection, called individually optimal detection, via spatial coupling. Numerical simulations show that spatial coupling can provide a significant improvement in bit-error rate for finite-sized systems especially in the region of high system loads.