用于多测量向量和/或多变换问题的正交近似消息传递
Orthogonal AMP for Problems with Multiple Measurement Vectors and/or Multiple Transforms
AI总结：
本文将正交近似消息传递（OAMP）扩展至多测量向量和多变换问题，提出OAMP-MMV、OAMP-MT及增强型A-OAMP，并在MIMO中继示例中验证其高效性和优异性能。
摘要：
近似消息传递（AMP）算法将一个（高维）统计问题分解为若干部分，然后依次反复求解每个部分，类似于交替投影。其一个显著特征是其渐近行为可以通过相关的状态演化方程精确预测。正交近似消息传递（OAMP）是近年来为规避传统AMP算法中计算所谓Onsager项的需要而提出的，具有两个明显优势：OAMP算法的推导既直接又具有更广泛的适用性。OAMP最初是在具有单一测量向量和单一变换的统计问题上得到验证的。本文将OAMP扩展到具有多测量向量（MMVs）和多变换（MTs）的统计问题。我们将所得算法分别命名为OAMP-MMV和OAMP-MT，并将它们的组合称为增强型OAMP（A-OAMP）。尽管将传统AMP算法扩展到此类问题会具有挑战性，但支撑OAMP的正交原理使这些扩展变得直接。MMV和MT模型广泛适用于信号处理和通信领域。我们给出了一个具有相关源数据和信号限幅的MIMO中继系统示例，该系统可以建模为联合MMV-MT系统。虽然现有方法在该示例中遇到困难，但OAMP提供了一种性能优异的高效解决方案。
英文摘要：
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.
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