The downlink training yields rather modest performance gains due to the high degree of channel hardening effect in co-located large-scale multi-input multi-output (MIMO) systems. However, in distributed large-scale MIMO systems, the potential benefits of the downlink training become larger, since there is a high probability that each user is very close to only a part of remote antenna units and is effectively served by them which results in less channel hardening effect. In this paper, we study the benefits of the beamforming training (BT) scheme (users estimate the channel state information by using the received training symbols, which are processed by linear beamforming in advance) in distributed large-scale MIMO systems. We derive accurate and tractable closed-form analytical expressions for the spectral efficiency (SE) of the BT scheme in distributed large-scale MIMO systems with maximum ratio transmission and zero-forcing (ZF) beamforming. Based on these expressions, we analyze the benefits of the BT scheme and investigate how the number of transmit antennas and the length of coherence interval affect the SE of the BT scheme in the co-located and distributed large-scale MIMO systems. The analytical results show that the BT scheme is more suitable for distributed large-scale MIMO systems with ZF beamforming, and a less number of transmit antennas and longer coherence interval can improve the performance gain of BT scheme.
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Li et al. (2018) studied this question.