Machine learning (ML) and tensor-based methods have been of significant interest for the scientific community for the last few decades. In a previous work we presented a novel tensor-based system identification framework to ease the computational burden of tensor-only architectures while still being able to achieve exceptionally good performance. However, the derived approach only allows to process real-valued problems and is therefore not directly applicable on a wide range of signal processing and communications problems, which often deal with complex-valued systems. In this work we therefore derive two new architectures to allow the processing of complex-valued signals, and show that these extensions are able to surpass the trivial, complex-valued extension of the original architecture in terms of performance, while only requiring a slight overhead in computational resources to allow for complex-valued operations.

翻译：机器学习（ML）与张量方法在过去数十年间始终是科学界的研究热点。在前期工作中，我们提出了一种新型基于张量的系统辨识框架，该框架在降低纯张量架构计算负荷的同时，仍能实现卓越的性能表现。然而，该衍生方法仅适用于实值问题，无法直接应用于大量涉及复数值系统的信号处理与通信问题。为此，本文推导出两种新架构以处理复数值信号，并证明这些扩展方法在性能上能够超越原始架构的简单复数值扩展版本，同时仅需少量计算资源开销即可实现复数值运算。