A Novel Framework for Wireless Digital Communication Signals via a Tensor Perspective

In this paper, we introduce a novel signal characteristic, which is ubiquitous in the vast majority of communication signals. That is, a modulated signal is of an inherent low-rank structure following a reshaping operation. We first use a toy model to develop a framework for modelling this signal characteristic, and theoretically prove the impact on the signals' rank structure by additive white Gaussian noise and inter-symbol interference, which is of great concern in the wireless communication field. Subsequently, the model is generalized to multi-input-multi-output signals, and tensor rank is taken into account. Using multi-linear algebra, we prove that the low-rankness of a reshaped signal only depends on the structure of its embedding subspace, and that its rank measure is upper bounded by the multi-rank of the basis tensor. As an application, we propose a novel adaptive sampling and reconstruction scheme for generic software-defined radio based on the low-rank structure. Numerical simulations demonstrate that the proposed method outperforms compressed sensing-based method, particularly when the modulated signal does not satisfy the sparsity assumption in the time and frequency domains. The results of practical experiments further demonstrate that many types of modulated signals can be effectively reconstructed from very limited observations using our proposed method.