Effects of channel aging in massive MIMO systems

Abstract

MIMO communication may provide high spectral efficiency through the deployment of a very large number of antenna elements at the base stations. The gains from massive MIMO communication come from the use of multi-user MIMO on the uplink and downlink, but with a large excess of antennas at the base station compared to the number of served users. Initial work on massive MIMO did not fully address several practical issues associated with its deployment. This paper considers the impact of channel aging on the performance of massive MIMO systems. The effects of channel variation are characterized as a function of different system parameters assuming a simple model for the channel time variations at the transmitter. Channel prediction is proposed to overcome channel aging effects. The analytical results on aging show how capacity is lost due to time variation in the channel. Numerical results in a multicell network show that massive MIMO works even with some channel variation and that channel prediction could partially overcome channel aging effects.

Deterministic Equivalent Performance Analysis of Time-Varying Massive MIMO Systems

“…In fact, the channel varies between when it is learned via estimation and when it is used for precoding or detection due to the relative movement between the antennas and the scatterers. Although it is main cause for the inevitably imperfect channel state information CSIT that should be taken seriously into account, an effort for characterizing the impact of delayed CSIT in massive MIMO has been addressed only in [24]- [26]. Especially, in [24], an application of the deterministic equivalent analysis was presented by considering linear techniques in the uplink and downlink in terms of maximum ratio combining (MRC) detector and maximum ratio transmission (MRT) precoder, respectively.…”

“…Although it is main cause for the inevitably imperfect channel state information CSIT that should be taken seriously into account, an effort for characterizing the impact of delayed CSIT in massive MIMO has been addressed only in [24]- [26]. Especially, in [24], an application of the deterministic equivalent analysis was presented by considering linear techniques in the uplink and downlink in terms of maximum ratio combining (MRC) detector and maximum ratio transmission (MRT) precoder, respectively. Moreover, in [25], the optimal linear receiver in the case of cellular massive MIMO has been derived by exploiting the correlation between the channel estimates and the interference from other cells, while in [26], the uplink analysis of a cellular network with zero-forcing (ZF) receivers that holds for any finite as well as infinite number of BS antennas has been provided.…”

“…Note that this work extends substantially our conference papers [1], [2] by elaborating more on the effect of channel aging, providing an overall and thorough presentation of the analyses of both the uplink and downlink channels, and presenting the lengthy proofs, which have theoretical and practical interest regarding the large RMT. Hence, in the spirit of deterministic equivalents, developed in [10] for cellular networks, which employ the large MIMO concept, i.e., the number of users and BS antennas become larger at the same speed, we provide a deeper study in both the uplink and the downlink by considering a MMSE receiver and a RZF precoder under the assumption of imperfect CSI at the BS due to its delayed knowledge and pilot contamination as in [24]. It should be pointed out that our analysis is not just a straightforward extension of [24], which unfortunately brings too many typos, but it encompasses much more complex tools to deal with the more mathematically complex expressions of MMSE and RZF.…”

“…Hence, in the spirit of deterministic equivalents, developed in [10] for cellular networks, which employ the large MIMO concept, i.e., the number of users and BS antennas become larger at the same speed, we provide a deeper study in both the uplink and the downlink by considering a MMSE receiver and a RZF precoder under the assumption of imperfect CSI at the BS due to its delayed knowledge and pilot contamination as in [24]. It should be pointed out that our analysis is not just a straightforward extension of [24], which unfortunately brings too many typos, but it encompasses much more complex tools to deal with the more mathematically complex expressions of MMSE and RZF. Nevertheless, not only do we provide more details with comparison to [10], [24] in order to shed light into the mathematical analysis, but we also use a mixture of both approaches from the very start of defining the models to the end for providing the most advantageous analysis in terms of mathematical convenience and engineering insight.…”

“…It should be pointed out that our analysis is not just a straightforward extension of [24], which unfortunately brings too many typos, but it encompasses much more complex tools to deal with the more mathematically complex expressions of MMSE and RZF. Nevertheless, not only do we provide more details with comparison to [10], [24] in order to shed light into the mathematical analysis, but we also use a mixture of both approaches from the very start of defining the models to the end for providing the most advantageous analysis in terms of mathematical convenience and engineering insight. Note that the approximations (deterministic equivalents) are accurate even for realistic system dimensions, as simulations show.…”