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In this paper, we propose a joint spatial division and multiplexing (JSDM) beamforming based on a neighbor scheme for frequency division duplex (FDD) massive multi-input multi-output (MIMO) systems. The neighbor-based JSDM (N-JSDM) can fully utilize signal space, leading to higher spectral efficiency over the conventional JSDMs. The reason is that for the neighbor scheme, neighbors and non-neighbors are classified adaptively by the angles of departure (AoD), and the prebeamformer is designed to mitigate the non-neighbors' interference by the statistical channel state information. The effective channel matrix after the prebeamformer then becomes a band matrix, from which the downlink training length (DTL) and the channel feedback length are much smaller than the number of antennas. Moreover, an optimal prebeamformer which is proved to be able to achieve the same system capacity as the full CSI …