  Kudekar et al. proved that the belief-propagation (BP) performance for
low-density parity check (LDPC) 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
(CDMA) systems to improve the performance of iterative multiuser detection
based on BP. Two iterative receivers based on BP are considered: One receiver
is based on exact BP and 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.
