# Complex-valued Adaptive System Identification via Low-Rank Tensor Decomposition

arXiv: https://arxiv.org/abs/2306.16428 · HTML: https://mlsanity.com/paper/2306.16428/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 42 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 6 of 6)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains](https://mlsanity.com/paper/1804.06128/) (2018)
- [Nonlinear system identification with regularized Tensor Network B-splines](https://mlsanity.com/paper/2003.07594/) (2020)
- [Non-Linear Digital Self-Interference Cancellation for In-Band Full-Duplex Radios Using Neural Networks](https://mlsanity.com/paper/1711.00379/) (2017)
- [Nonlinear System Identification via Tensor Completion](https://mlsanity.com/paper/1906.05746/) (2019)
- [Matrix output extension of the tensor network Kalman filter with an application in MIMO Volterra system identification](https://mlsanity.com/paper/1708.05156/) (2017)

## Abstract (arXiv)

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.