  Practical systems often suffer from hardware impairments that already appear
during signal generation. Despite the limiting effect of such input-noise
impairments on signal processing systems, they are routinely ignored in the
literature. In this paper, we propose an algorithm for data detection and
signal estimation, referred to as Approximate Message Passing with Input noise
(AMPI), which takes into account input-noise impairments. To demonstrate the
efficacy of AMPI, we investigate two applications: Data detection in large
multiple-input multiple output (MIMO) wireless systems and sparse signal
recovery in compressive sensing. For both applications, we provide precise
conditions in the large-system limit for which AMPI achieves optimal
performance. We furthermore use simulations to demonstrate that AMPI achieves
near-optimal performance at low complexity in realistic, finite-dimensional
systems.
