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.
翻译:我们研究在多用户大规模MIMO系统频率分解(FDD)中运行的多用户大规模MIMO系统发送器中提供频道状态信息的问题。宽频MIMO频道是一个在时间、空间(antennas)和频率(subcarriers)上矢量估值随机进程。基站(BS)定期从M天线端向K单一ANTENNA用户(Ues)广播Be_tr 试点符号。与此相对,KUes在上行(UL)中使用 bea_fb 符号发送关于频道状态的反馈信息。使用远程率扭曲理论的结果,我们表明,随着Snr 抵达时,最佳反馈战略在时间、空间(antnnantr < r) 和 Theta(snr) (nnr) (al-an-an-an-an-antennannexannex) 用户端端点(k-r) 用户端点(al-fb/r,1) 用户级(al-rational-deal-ral-ral-ral-ral-ral-rational-ral-rational-ral relational reflation) commess reflation reflational reflation reflational relational refal refal) 战略要求。因此,在C-lutal-s-s-s-s-lational-slational-sal-s-s-lational-lational-slational-lational-sal-lational-deal-s-s-s-s-s-s-s-deal-sal-sal-s-sal-deal-sal-deal-deal-deal-deal-deal-deal-sal-deal-sal-sal-sal-slal-slal-sal-sal-sal-sal-sal-sal-sal-sal-sal-sal-sal-deal-deal-deal-lal-slal-lal-lal-sal-lal-sal-