Approximate message passing (AMP) algorithms break a (high-dimensional) statistical problem into parts then repeatedly solve each part in turn, akin to alternating projections. A distinguishing feature is their asymptotic behaviours can be accurately predicted via their associated state evolution equations. Orthogonal AMP (OAMP) was recently developed to avoid the need for computing the so-called Onsager term in traditional AMP algorithms, providing two clear benefits: the derivation of an OAMP algorithm is both straightforward and more broadly applicable. OAMP was originally demonstrated for statistical problems with a single measurement vector and single transform. This paper extends OAMP to statistical problems with multiple measurement vectors (MMVs) and multiple transforms (MTs). We name the resulting algorithms as OAMP-MMV and OAMP-MT respectively, and their combination as augmented OAMP (A-OAMP). Whereas the extension of traditional AMP algorithms to such problems would be challenging, the orthogonal principle underpinning OAMP makes these extensions straightforward. The MMV and MT models are widely applicable to signal processing and communications. We present an example of MIMO relay system with correlated source data and signal clipping, which can be modelled as a joint MMV-MT system. While existing methods meet with difficulties in this example, OAMP offers an efficient solution with excellent performance.

翻译：近似消息传递（AMP）算法将一个（高维）统计问题分解为多个子问题，再依次迭代求解各子问题，类似于交替投影。其显著特征在于，对应状态演化方程可精确预测其渐近行为。正交AMP算法（OAMP）近期被提出以避免传统AMP算法中计算所谓的"Onsager项"的需求，具有两大优势：OAMP算法的推导既简洁又具有更广泛的适用性。OAMP最初针对单个测量向量和单变换的统计问题而设计。本文将其扩展至多测量向量（MMV）和多变换（MT）的统计问题，分别提出OAMP-MMV和OAMP-MT算法，并将二者的结合称为增强型OAMP（A-OAMP）。尽管传统AMP算法在此类问题中的扩展面临挑战，但OAMP的正交性原理使得这些扩展得以简化。MMV与MT模型在信号处理及通信领域具有广泛的应用价值。本文以包含相关信源数据与信号裁剪的MIMO中继系统为例，该系统可建模为联合MMV-MT系统。尽管现有方法在处理该实例时面临困难，而OAMP则提供了具有优异性能的高效解决方案。