Degrees of Freedom of the Network MIMO Channel With Distributed CSI

Abstract

Abstract-In this work, we discuss the joint precoding with finite rate feedback in the so-called network MIMO where the TXs share the knowledge of the data symbols to be transmitted. We introduce a distributed channel state information (DCSI) model where each TX has its own local estimate of the overall multi-user MIMO channel and must make a precoding decision solely based on the available local CSI. We refer to this channel as the DCSI-MIMO channel and the precoding problem as distributed precoding. We extend to the DCSI setting the work from Jindal in [1] for the conventional MIMO Broadcast Channel (BC) in which the number of Degrees of Freedom (DoFs) achieved by Zero Forcing (ZF) was derived as a function of the scaling in the logarithm of the Signal-to-Noise Ratio (SNR) of the number of quantizing bits. Particularly, we show the seemingly pessimistic result that the number of DoFs at each user is limited by the worst CSI across all users and across all TXs. This is in contrast to the conventional MIMO BC where the number of DoFs at one user is solely dependent on the quality of the estimation of his own feedback. Consequently, we provide precoding schemes improving on the achieved number of DoFs. For the two-user case, the derived novel precoder achieves a number of DoFs limited by the best CSI accuracy across the TXs instead of the worst with conventional ZF. We also advocate the use of hierarchical quantization of the CSI, for which we show that considerable gains are possible. Finally, we use the previous analysis to derive the DoFs optimal allocation of the feedback bits to the various TXs under a constraint on the size of the aggregate feedback in the network, in the case where conventional ZF is used.

Generalized degrees-of-freedom of the 2-user case MISO broadcast channel with distributed CSIT

“…The first one is the Centralized CSIT setting where both TXs share the CSIT information, which has been shown in Theorem 2 to be an outerbound. The second one is the naive distributed Zero-Forcing, where the discrepancies between TXs are not taken into account such that each TX implicitly assumes that the other TX has the same channel estimate [5]. In Fig.…”

“…The gap between the outer bound and the simulations comes from the fact that the GDoF metric does not take into account the finite gaps, since they do not increase as function of P (see (8)). The naive distributed Zero-Forcing is limited by the worst CSIT quality estimate, α (2) = 0, and thus the CSIT at the best TX is useless for this naive ZF and it matches the performance of the setting with no CSIT [5]. 15 …”

“…While it was suggested in the past literature that Distributed CSIT scenarios can severely impact on performance in comparison with classical limited-yetcentralized CSIT ones [5], a crucial and interesting problem is how TXs can cooperatively combat the lack of mutual CSI consistency in order to reduce the gap with respect to the centralized system performance.…”

Survey of Large-Scale MIMO Systems

“…Although fully multi-cell scheduling schemes, like the coordinated joint processing in network MIMO, can achieve large performance gains, they are not practical due to prohibitive costs. That is, not only the full CSI but also data streams intended for different mobile users at different cells need to be shared among the eNBs [105]. Instead, another feasible solution is to improve the overall network performance by allowing beamforming vectors from different eNBs to be coordinated for the sake of implementation [106].…”

On the impact of control channel reliability on coordinated multi-point transmission

“…To the best of our knowledge, this work, partly included in [17], is the first one that analyzes the impact of control channel unreliability in CoMP systems. In addition, in this work, different transmission schemes are investigated under different CoMP network architectures [18][19][20][21], considering unreliable control channels.…”