  Large multiple-input multiple-output (MIMO) appears in massive multi-user
MIMO and randomly-spread code-division multiple access (CDMA)-based wireless
systems. In order to cope with the excessively high complexity of optimal data
detection in such systems, a variety of efficient yet sub-optimal algorithms
have been proposed in the past. In this paper, we propose a data detection
algorithm that is computationally efficient and optimal in a sense that it is
able to achieve the same error-rate performance as the individually optimal
(IO) data detector under certain assumptions on the MIMO system matrix and
constellation alphabet. Our algorithm, which we refer to as LAMA (short for
large MIMO AMP), builds on complex-valued Bayesian approximate message passing
(AMP), which enables an exact analytical characterization of the performance
and complexity in the large-system limit via the state-evolution framework. We
derive optimality conditions for LAMA and investigate performance/complexity
trade-offs. As a byproduct of our analysis, we recover classical results of IO
data detection for randomly-spread CDMA. We furthermore provide practical ways
for LAMA to approach the theoretical performance limits in realistic,
finite-dimensional systems at low computational complexity.
