Channel Parameter Estimation and Location Sensing in mmWave Systems Under Phase Noise via Nested PARAFAC Analysis

In this paper, channel parameter estimation and location sensing under phase noise (PN) are achieved based on nested tensor decomposition. The PN has two effects on the received signal, i.e., common phase error (CPE) and inter-carrier interference (ICI). Using the multi-dimensionality of millimeter wave channels, the received training signal is formulated as a nested parallel factor (PARAFAC) tensor model. Resorting to the compression and line search, CPE and compound channel are iteratively estimated by fitting the outer PARAFAC model in the first stage. In the second stage, a closed-form algorithm and an iterative-form algorithm are respectively developed to fit the inner PARAFAC model. Specifically, the closed-form one leverages the spatial smoothing and forward-backward, and the iterative-form one utilizes the unitary transformation. Channel parameter estimation and location sensing of mobile station and scatterers are achieved in the third stage. The Cram$\acute{\text{e}}$r-Rao bounds (CRBs) of CPE and channel parameters are also derived to provide benchmarks. Compared with existing algorithms, the proposed algorithms exhibit performance close to CRBs, and show improved performance with low computational complexity. Besides, the proposed algorithms can cope with more challenging cases where line-of-sight (LOS) path does not exist and non-LOS paths are spatially correlated even with significant ICI.