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We propose a novel method for massive multiple-input multiple-output (massive MIMO) in frequency division duplexing (FDD) systems. Due to the large frequency separation between uplink (UL) and downlink (DL) in FDD systems, channel reciprocity does not hold. Hence, in order to provide DL channel state information to the base station (BS), closed-loop DL channel probing, and channel state information (CSI) feedback is needed. In massive MIMO, this typically incurs a large training overhead. For example, in a typical configuration with M ≃200 BS antennas and fading coherence block of T ≃ 200 symbols, the resulting rate penalty factor due to the DL training overhead, given by max{0, 1 - M/T }, is close to 0. To reduce this overhead, we build upon the well-known fact that the angular scattering function of the user channels is invariant over frequency intervals whose size is small with respect to the carrier …