内存 AMP (Memory AMP)

from arxiv, 43 pages, 13 figures, submitted to IEEE Trans. on Information Theory for possible publication. [Memory AMP inherits the strengths of AMP and OAMP/VAMP such as low complexity, Bayes optimality and applicability to unitarily-inavariant matrices, while avoiding the weakness of AMP (e.g. limited to IID matrices) and OAMP/VAMP (e.g. needs high-complexity LMMSE).]

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 (e.g., perform poorly or even diverge) for other matrix ensembles, especially for ill-conditioned ones. Orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices to handle this difficulty. However, the Bayes-optimal OAMP/VAMP (BO-OAMP/VAMP) requires a high-complexity linear minimum mean square error (MMSE) estimator. This limits the application of OAMP/VAMP to large-scale systems. To solve the disadvantages of AMP and BO-OAMP/VAMP, this paper proposes a memory AMP (MAMP) framework under an orthogonality principle, which guarantees the asymptotic IID Gaussianity of estimation errors in MAMP. We present an orthogonalization procedure for the local memory estimators to realize the required orthogonality for MAMP. Furthermore, we propose a Bayes-optimal MAMP (BO-MAMP), in which a long-memory matched filter is proposed for interference suppression. The complexity of BO-MAMP is comparable to AMP. A state evolution is derived to asymptotically characterize the performance of BO-MAMP. Based on state evolution, the relaxation parameters and damping vector in BO-MAMP are optimized. For all right-unitarily-invariant matrices, the state evolution of the optimized BO-MAMP converges to the same fixed point as that of the high-complexity BO-OAMP/VAMP and is Bayes-optimal if its state evolution 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) 是用于某些高维线性系统的一种低成本迭代性迭接性参数估测技术, 且非加西语分布式。然而, AMP 仅适用于独立分布相同的( IID) 变异矩阵, 但可能变得不可靠( 例如, 表现不佳或甚至不同) 用于其他矩阵组合, 特别是条件不完善的组合。为了解决 AMP 和 BO- OMP/ VAMP 的劣势。本文提议在直径原则下为一般右- 整体性直径干涉矩阵配置。然而, 巴伊- 最佳 OAMP/ VAMP (BO- MA) (BOAMP/ VAMP) (BOMP) (OMP) (OM) (OMA) (BAMA) (BOMA) (BOM) ( Outral- MA) ( Oral- MA) ( IM) ( IM) ( IMA) ( IM) ( IM IM) ( IM IMD) ( IMD) ( IMD) ( IMD) ( IM) ( 的 IMD) (目前 IM) ( IM) ( IMD) ( IM IM) ( IM) ( IM) ( IM) ( IM) ( IM) ( IM) ( IM) ( IM) ( IM) ( IM) ( ) ( IM) ( IM) ( IM IM ) ( IM) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( IM) ( IM) ( IM ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ) ) ( ) ( ) ( ) ( ) ( ) ) ) ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ) (