Approximate Message Passing (AMP) is an efficient iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions, such as sparse systems. In AMP, a so-called Onsager term is added to keep estimation errors approximately Gaussian. Orthogonal AMP (OAMP) does not require this Onsager term, relying instead on an orthogonalization procedure to keep the current errors uncorrelated with (i.e., orthogonal to) past errors. \LL{In this paper, we show the generality and significance of the orthogonality in ensuring that errors are "asymptotically independently and identically distributed Gaussian" (AIIDG).} This AIIDG property, which is essential for the attractive performance of OAMP, holds for separable functions. \LL{We present a simple and versatile procedure to establish the orthogonality through Gram-Schmidt (GS) orthogonalization, which is applicable to any prototype. We show that different AMP-type algorithms, such as expectation propagation (EP), turbo, AMP and OAMP, can be unified under the orthogonal principle.} The simplicity and generality of OAMP provide efficient solutions for estimation problems beyond the classical linear models. \LL{As an example, we study the optimization of OAMP via the GS model and GS orthogonalization.} More related applications will be discussed in a companion paper where new algorithms are developed for problems with multiple constraints and multiple measurement variables.

翻译：近似信件通訊( AMP) 是某些高维线性系统( 包括非 Gausian 分布系统, 如 稀少的系统) 的有效迭代参数估计技术 。 在 AMP 中, 添加所谓的 Onsager 术语以保持 Gaussian 左右的估计错误 。 Orthogonal AMP (OAMP) 不需要这个 Onsaster 术语, 而要依靠一个正方位化程序来保持当前错误与( e., orthogonal to) 过去的错误不相干 。\ LLL{ 在本文中, 我们展示了 orthogoal- 线性, 以确保错误“ 自动独立和相同分布 Gausian ” (AIIDG)。} 此 IDGAIDGP 属性对于 OAMP 的吸引力性功能来说是必不可少的, 将保留在 secontroduction 程序上, 通过 Gram- Schmidt( GS) 或thocoalalalalalalalalalalal 解算法 的解算算算方法, 我们在任何原型的OMP- 中, 可以对 OMP- 和透算法进行不同的 AMP- 或透性分析研究。