  Channel feedback is essential in frequency division duplexing (FDD) massive
multiple-input multiple-output (MIMO) systems. Unfortunately, previous work on
multiuser MIMO has shown that the codebook size for channel feedback should
scale exponentially with the number of base station (BS) antennas, which is
greatly increased in massive MIMO systems. To reduce the codebook size and
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 AoD-adaptive subspace codebook is able to quantize
the channel vector in a more accurate way. We also provide performance analysis
of the proposed codebook in the large-dimensional regime, where we prove that
to limit the capacity degradation within an acceptable level, the required
number of feedback bits only scales linearly with the number of resolvable
(path) AoDs, which is much smaller than the number of BS antennas. Moreover, we
compare quantized channel feedback using the proposed AoD-adaptive subspace
codebook with analog channel feedback. Extensive simulations that verify the
analytical results are provided.
