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Channel feedback is essential in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. Unfortunately, prior work on multiuser MIMO has shown that the feedback overhead scales linearly with the number of base station (BS) antennas, which is large in massive MIMO systems. To reduce the feedback overhead, we propose an angle-of-departure (AoD) adaptive subspace codebook for channel feedback in FDD massive MIMO systems. Our key insight is to leverage the observation that path AoDs vary more slowly than the path gains. Within the angle coherence time, by utilizing the constant AoD information, the proposed AoDadaptive subspace codebook is able to quantize the channel vector in a more accurate way. From the performance analysis, we show that the feedback overhead of the proposed codebook only scales linearly with a small number of dominant (path) AoDs instead of the large number of BS antennas. Moreover, we compare the proposed quantized feedback technique using the AoD-adaptive subspace codebook with a comparable analog feedback method. Extensive simulations show that the proposed AoD-adaptive subspace codebook achieves good channel feedback quality, while requiring low overhead.