Tensor-computing-based Spectrum Usage Framework for 6G

In this paper, we coin a new concept of tensor-computing, which is based on tensor theory and designed for future sixth generation (6G) wireless communication systems. Two different types of tensors, namely spectrum-tensor and system-tensor, are defined and analysed to develop a new spectrum usage framework for 6G. The spectrum-tensor encapsulates high dimensional spectrum big data into the format of a compact tensor. The system-tensor summarizes key system performance, including data rate, bandwidth, delay, spectral efficiency, and energy efficiency, into a multi-dimension tensor. The concepts of spectrum-tensor and system-tensor enable unique tensor-based computing and analysis with the help of high efficiency tensor-computing tools, such as tensor completion and tensor decomposition. In the new spectrum usage framework, a value-based spectrum fusion scheme is designed. The maximum system value is achieved under the constraint that the individual value of single user should be guaranteed. The proposed tensor-computing framework builds a bridge between 6G wireless functions with real-world high dimension data processing tools, such as TensorFlow and Tensor Processing Unit (TPU). The authors hope this paper will shine a beam of tensor theory in and open a new research field of tensor-computing for future 6G wireless communications.