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

TL;DR

This paper analyzes optimal rate-distortion bounds for FDD massive MIMO channel training and evaluates the efficiency of practical one-shot feedback schemes at high SNR, considering channel correlation and feedback delay.

Contribution

It derives theoretical bounds for feedback performance in massive MIMO and compares them with practical one-shot schemes, including a standard-inspired method, under high SNR conditions.

Findings

Optimal feedback achieves different MSE decay rates depending on pilot length.

Three practical one-shot schemes are analyzed for high SNR performance.

The local estimation feedback scheme requires no prior channel statistics.

Abstract

We study the problem of providing channel state information (CSI) at the transmitter in multi-user massive MIMO systems operating in frequency division duplexing (FDD). The wideband MIMO channel is a vector-valued random process correlated in time, space (antennas), and frequency (subcarriers). The base station (BS) broadcasts periodically beta_tr pilot symbols from its M antenna ports to K single-antenna users (UEs). Correspondingly, the K UEs send feedback messages about their channel state using beta_fb symbols in the uplink (UL). Using results from remote rate-distortion theory, we show that, as snr reaches infty, the optimal feedback strategy achieves a channel state estimation mean squared error (MSE) that behaves as Theta(1) if beta_tr < r and as Theta(snr^(-alpha)) when beta_tr >=r, where alpha = min(beta_fb/r, 1), where r is the rank of the channel covariance matrix. The MSE-optimal rate-distortion strategy implies encoding of long sequences of channel states, which would yield completely stale CSI and therefore poor multiuser precoding performance. Hence, we consider three practical one-shot CSI strategies with minimum one-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 and digital feedback. These schemes have different requirements in terms of knowledge of the channel statistics at the UE and at the BS. In particular, the latter strategy requires no statistical knowledge and is closely inspired by a CSI feedback scheme currently proposed in 3GPP standardization.