and directional couplers at the BS, for the conventional MIMO system. A practical study in [104] proposes a method for the massive MIMO system, where an additional RF transceiver is used as the reference to exchange calibration pilots with other BS antennas’ transceivers. However, the method in [104] is sensitive to the placement of the reference transceiver. The underlying concept in [104, 108] is to relatively calibrate BS antennas based on the ratio of the Tx RF response to the Rx RF response, thus it is often termed as relative calibration. The design of the calibration matrix based on the relative calibration has been widely used in the context of the massive MIMO system [57, 76, 104].
2.5
Summary
Massive MIMO is still in its infancy, and despite its potentials, various crucial issues hinder the implementation of the massive MIMO system in practice. This, on the other hand, brings not only challenges but also opportunities and enormous open topics for researchers. For example, as we discussed earlier, the CSI acquisition has become the central activity of any massive MIMO systems design, and the effect of imperfect CSI can cause the degraded performance of the systems. Hence, it would be meaningful to complement and extend the existing research directions in the conventional MIMO to the massive MIMO, by taking into account the imperfections of the challenging channel estimation due to the large-scale antenna deployment, such as the effect of the pilot contamination and channel ageing. In addition, the estimate of the effective channel can be contaminated by various factors, such as the channel estimation error, channel reciprocity error and spatial correlation. In particular, it is of great interest to investigate the effect of the channel reciprocity error or the spatial channel correlation, in the sense that it is relatively difficult to deal with these practical limitations when the large scale BS antenna array is involved. Also, to the best of the author’s knowledge, there have been no effective solution approaches to compensate for the performance loss caused by the compound effect of both channel reciprocity and channel estimation errors. Such approaches, if available, can certainly help to convince many people of the huge potentials of the massive MIMO systems.
Chapter
3
Massive MIMO Uplinks with Imperfect
Channel Estimation and Spatial
Correlation
D
ETAILED analysis of the MRC in massive MIMO uplinks under imperfect channel estimation is presented in [1]. It is also suggested that other combining schemes can be further studied. In this direction, selection combining schemes can be considered. In this chapter, we consider a practical scenario of the massive MIMO uplink in the presence of a realistic spatial channel correlation and imperfect channel estimation at the receiver side. We propose a novel antenna selection combining scheme, which exploits the sparsity of the channel matrix for the effective selection of a limited number of antennas. The basic idea is to reduce the effective number of antennas that are used for combining. Consequently, the resulting effective channel matrix becomes sparse, in the sense that the corresponding entries to non-selected antennas are set to zero. This sparse channel matrix can be obtained by some approximation techniques that will be discussed later in this chapter.3.1. Related Work on UL Combining with Imperfect CSI and Channel Correlation 30
3.1
Related Work on UL Combining with Imperfect CSI
and Channel Correlation
For the massive MIMO uplinks, the impact of spatial correlation or imperfect channel estimation has been investigated in [1, 45]. More specifically, in [1], it is shown that uplink combining schemes, such as MRC, can have a reasonable performance, with knowledge of CSI for the entire combining branches. However, the price to pay for such performance gain is the significantly increased implementation overhead and the complexity of the transceiver design for massive MIMO systems, due to the extensive usage of a large number of full radio frequency transceivers that combined with the large scale BS antennas [12, 16, 91]. In [12], it is argued that cost-efficient antenna selection strategies can be employed to reduce the complexity and overhead of imple- mentation, as well as to effectively maintain a reasonably high performance. For the uplink, the diversity selection combining, such as CSC where the BS selects the anten- nas with stronger received signal power for combining, of UL receive antennas has been extensively studied in the literature, such as [17, 98], considering conventional MIMO systems. For example, the effect of imperfect channel estimation on the CSC systems is presented in [17], but not for the large scale antenna array network.
An analysis of the MRC in massive MIMO uplinks under imperfect channel estimation is given in [1]. Exploiting sparsity, the work in [109] investigates antenna/relay selection for MIMO channels. However, this work of [109] does not take into account spatial channel correlation, as well as the impacts of imperfect CSI acquisition. Considering the modelling of the spatially correlated channel and imperfect channel estimation, the model in [7, 81] is considered as a good approximation for spatial channel correlation, and channel estimation error model in [82, 87] is widely used to capture the aggregated effect of the imperfections in channel estimation algorithms. For the practical training- pilot-based estimation schemes, such as MMSE scheme, the model in [44, 110] has been shown to be accurate for realistic system dimensions.
One of the main contributions of this chapter is to propose an effective antenna selection combining scheme for spatially correlated massive MIMO uplinks under the imperfect channel estimation, by applying a sparsely structured channel gain vector at the BS side,
which, to the best of the authors’ knowledge, has not been studied in the literatures.