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 massive 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.

中文翻译：

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具有输入噪声的系统中的最佳数据检测和信号估计

实际系统经常遭受在信号生成期间已经出现的硬件损伤。尽管这种输入噪声损伤对信号处理系统的影响有限，但它们在文献中经常被忽略。在本文中，我们提出了一种用于数据检测和信号估计的算法，称为具有输入噪声的近似消息传递 (AMPI)，它考虑了输入噪声损伤。为了证明 AMPI 的功效，我们研究了两个应用：大规模多输入多输出 (MIMO) 无线系统中的数据检测和压缩感知中的稀疏信号恢复。对于这两种应用，我们在大系统限制中提供了精确的条件，AMPI 可以在这些条件下实现最佳性能。