Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. However, AMP only applies to independent identically distributed (IID) transform matrices, but may become unreliable for other matrix ensembles, especially for ill-conditioned ones. To handle this difficulty, orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP requires high-complexity linear minimum mean square error estimator. To solve the disadvantages of AMP and OAMP/VAMP, this paper proposes a memory AMP (MAMP), in which a long-memory matched filter is proposed for interference suppression. The complexity of MAMP is comparable to AMP. The asymptotic Gaussianity of estimation errors in MAMP is guaranteed by the orthogonality principle. A state evolution is derived to asymptotically characterize the performance of MAMP. Based on the state evolution, the relaxation parameters and damping vector in MAMP are optimized. For all right-unitarily-invariant matrices, the optimized MAMP converges to OAMP/VAMP, and thus is Bayes-optimal if it has a unique fixed point. Finally, simulations are provided to verify the validity and accuracy of the theoretical results.

翻译：近似信息传递( AMP) 是某些高维线性系统使用非加西安分布的低成本迭代参数测算技术。 然而, AMP 仅适用于独立分布相同的(IID) 变异矩阵, 但对其他矩阵组合, 特别是条件不完善的组合, 可能变得不可靠。 要处理这一难题, Otherogonial/ Vactor AMP (OAMP/ VAMP) 是针对一般右- 单一易变矩阵的。 然而, Bays- 优化 OAMP/ VAMP 需要高兼容性线性线性最小平均平方误测算器。 要解决 AMP 和 OAMP/ VAMMP 的缺点, 本文建议为其他矩阵设置一个耐久模匹配过滤器来抑制干扰。 MAMMP 的复杂性与 AMP 相仿。 IMP 估算错误的无孔调, 原则保证了 mAMP 的精确度, 州进化为MAMP 和 MAMP 最优级级级的校准度, 级级校准的校正的校准度校准值是MAMP 的校正的校正的校正 。