Multipoint channel charting is a machine learning framework in which multiple massive MIMO (mMIMO) basestations (BSs) collaboratively learn a multi-cell radio map that characterizes the network environment and the users' spatial distribution pattern. The method utilizes large amounts of highdimensional channel state information (CSI) that is passively collected from spatiotemporal samples by the multiple distributed BSs. At each BS, a high-resolution multi-path channel parameter estimation algorithm extracts features hidden in the acquired CSI. Each BS then constructs a local dissimilarity matrix based on the extracted features for its collected samples, and feeds it to a centralized entity which performs feature fusion and manifold learning to construct a multi-cell channel chart. The objective is to chart the radio geometry of a cellular system in such a way that the spatial distance between two users is correlated with their CSI feature distance. The proposed multipoint charting method is capable of unravelling the topology of a Manhattangrid system, and the neighbor relations between CSI features from different spatial locations are captured almost perfectly

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To perform multi-user multiple-input and multipleoutput transmission in millimeter-wave (mmWave) cellular systems, the high-dimensional channels need to be estimated for designing the multi-user precoder. Conventional grid-based Compressed Sensing (CS) methods for mmWave channel estimation suffer from the basis mismatch problem, which prevents accurate channel reconstruction and degrades the precoding performance. This paper formulates mmWave channel estimation as an Atomic Norm Minimization (ANM) problem. In contrast to grid-based CS methods which use discrete dictionaries, ANM uses a continuous dictionary for representing the mmWave channel. We consider a continuous dictionary based on sub-sampling in the antenna domain via a small number of radio frequency chains. We show that mmWave channel estimation using ANM can be formulated as a Semidefinite Programming (SDP) problem, and the channel can be accurately estimated via off-the-shelf SDP solvers in polynomial time. Simulation results indicate that ANM can achieve much better estimation accuracy compared to grid-based CS, and significantly improves the spectral efficiency provided by multi-user precoding.

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