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We study the problem of providing channel state information (CSI) at thetransmitter in multi-user massive MIMO systems operating in frequency divisionduplexing (FDD). The wideband MIMO channel is a vector-valued random processcorrelated in time, space (antennas), and frequency (subcarriers). The basestation (BS) broadcasts periodically beta_tr pilot symbols from its M antennaports to K single-antenna users (UEs). Correspondingly, the K UEs send feedbackmessages about their channel state using beta_fb symbols in the uplink (UL).Using results from remote rate-distortion theory, we show that, as snr reachesinfty, the optimal feedback strategy achieves a channel state estimation meansquared error (MSE) that behaves as Theta(1) if beta_tr < r and asTheta(snr^(-alpha)) when beta_tr >=r, where alpha = min(beta_fb/r, 1), where ris the rank of the channel covariance matrix. The MSE-optimal rate-distortionstrategy implies encoding of long sequences of channel states, which wouldyield completely stale CSI and therefore poor multiuser precoding performance.Hence, we consider three practical one-shot CSI strategies with minimumone-slot delay and analyze their large-SNR channel estimation MSE behavior.These are: (1) digital feedback via entropy-coded scalar quantization (ECSQ),(2) analog feedback (AF), and (3) local channel estimation at the UEs anddigital feedback. These schemes have different requirements in terms ofknowledge of the channel statistics at the UE and at the BS. In particular, thelatter strategy requires no statistical knowledge and is closely inspired by aCSI feedback scheme currently proposed in 3GPP standardization.

FDD Massive MIMO Channel Training Optimal Rate Distortion Bounds and the Efficiency of one-shot Schemes