Tensor decomposition-based 3D positioning with a single-antenna receiver in 5G millimetre wave systems

Exploiting a single-antenna receiver to realise three-dimensional (3D) positioning in a millimetre-wave (mmWave) system is considered. The primary motivation is that the massive antenna arrays will be deployed in the fifth-generation (5G) base stations shortly soon, which not only tremendously promote the data transmission rate, but also enable the user equipment to realise high-precision positioning with a single antenna. Based on the sparsity of the mmWave channel, the tensor decomposition is proposed to be utilised as an effective mathematical tool to realise 3D positioning. Specifically, the authors model the received signals as a third-order tensor for the inherent third-order low-rank tensor structure of the mmWave channel with a single-antenna receiver and then, the positioning parameters (including the angles of departure and the time of arrival) are estimated from the corresponding factor matrices via CAMDECOMP/PARAFAC (CP) decomposition. Moreover, Cramér-Rao bounds (CRBs) on 3D position uncertainty are derived. Numerical results demonstrate that the proposed method based on CP decomposition realises nearly the same positioning accuracy as the state-of-the-art compressed sensing-based algorithm in the 5G mmWave systems with lower computation complexity, and the root mean square errors of the 3D positioning results obtained via the proposed approach are close to their CRBs.