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Sparse Bayesian learning, beamforming techniques and asymptotic analysis for massive MIMO

Abstract : Multiple antennas at the base station side can be used to enhance the spectral efficiency and energy efficiency of the next generation wireless technologies. Indeed, massive multi-input multi-output (MIMO) is seen as one promising technology to bring the aforementioned benefits for fifth generation wireless standard, commonly known as 5G New Radio (5G NR). In this monograph, we will explore a wide range of potential topics in multi-user MIMO (MU-MIMO) relevant to 5G NR, 1) Sum rate maximizing beamforming (BF) design and robustness to partial channel state information at the transmitter (CSIT) 2) Asymptotic analysis of the various BF techniques in massive MIMO and 3) Bayesian channel estimation methods using sparse Bayesian learning. While massive MIMO has the aforementioned benefits, it makes the acquisition of the channel state information at the transmitter (CSIT) very challenging. Since it requires large amount of uplink (UL) pilots for channel estimation phase. Moreover, each antenna has associated with a radio frequency (RF) chain which in turn leads to high power consumption and hardware complexity at the base station (BS) side. One promising technology to overcome these issues is to utilize a hybrid beamforming (HBF) system. In HBF, the number of RF chains at the transmitter side is reduced significantly compared to number of antennas. Hence, it involves a two stage beamforming scheme. With the analog BF generates multiple beams in the spatial domain and thereby providing BF gain. The digital BF is used at the baseband for multiplexing the different user streams across the beams generated by the analog BF. Analog beamforming is implemented at the RF chain using phase shifters. One of our main focus in thesis is to propose efficient phase shifter design which can attain performance very close to that of the fully digital BF systems. For this purpose, we proposed an efficient scheme for analog phasor design using the technique of deterministic annealing. Fully digital BF scheme becomes a special case of our HBF design and further for the performance analysis, we focus on fully digital BF schemes itself. In a fully digital massive MIMO system, it is important to consider low complexity BF solutions. With this direction in mind, we proposed a low complexity but close to optimal (linear minimum mean square error-LMMSE) BF solution termed as reduced order zero forcing (ZF). However, it is quite incomplete if we stop with the various BF designs, we do require extensive theoretical analysis to evaluate the spectral efficiency (SE) behaviour of the massive MIMO system which we consider in the next part of the thesis. In the past decade, several academic research has been conducted on the asymptotic/large system analysis of massive MIMO systems. Large system analysis helps to avoid tedious Monte-Carlo simulations to evaluate the SE and provide simplified rate expressions as a function of the very few parameters such as channel second-order statistics, antenna dimensions and channel estimation error variance, etc. However, the majority of the existing research focus on simplified Rayleigh channel models or multiple of identity channel covariance matrices for different users to simplify the analysis. Moreover, those works which exploit distinct spatial channel covariance matrices for users lead to highly cumbersome expressions which are not intuitive and hence not much of use. Motivated by the above issues, we propose a stochastic geometry inspired randomization of the user covariance subspaces (which indeed has strong intuitive justification under large system dimensions and for millimeter wave or massive MIMO systems). Our simplifications indeed lead to very intuitive and elegant rate expressions and hence that forms one of the landmark contributions in this thesis. We provide large system results for an upper bound of the expected weighted sum rate and several other suboptimal BF schemes under partial CSIT. Moreover, we analyze the SE under different channel estimation schemes such as least squares, LMMSE and subspace projected channel estimate. However, it has to be noted that the LMMSE or subspace projected channel estimates which give superior performance need the knowledge of the user covariance subspace (low rank). Note that we do not consider explicitly an estimation method for this subspace information. But we remark that our variational Bayesian inference techniques which form the final part of the thesis can be an efficient and accurate method to estimate the pathwise components in the MIMO channel. These pathwise information can be finally utilised to form an accurate estimate of the user channel covariance subspace. Finally, we also looked at a Bayesian approach to sparse signal recovery problem. The sparse states can be considered to be either static or dynamic (where the temporal correlation is chosen to be modeled as an autoregressive process). Sparse Bayesian learning (SBL) algorithm focuses on formulating an appropriate hierarchical prior which can be modeled effectively the sparsity properties of the underlying signal. We consider a joint sparse signal plus hyperparameter (associated with the prior) estimation algorithm, which relies on variational Bayesian inference based methods. Here the motivation is to achieve lower complexity without sacrificing much on the signal recovery performance. One of the several applications of the SBL algorithm is in massive MIMO or milli meter wave channel estimation where the underlying wireless channel is sparse in angular or Doppler or delay domains. Apart from this, several applications exist in diverse fields (not only communication systems) such as data science or medical imaging, and hence this topic we considered assumes greater relevance. A majority of the topics considered here indeed form a relevant contribution to massive MIMO research community both by the proposition of new innovative algorithms and theoretical analysis. However, much remains to be pursued and we hope that this throws up a few open questions too which can inspire at least a few others to follow the road not taken yet.
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Contributor : Christo Kurisummoottil Thomas <>
Submitted on : Friday, February 12, 2021 - 2:27:51 PM
Last modification on : Wednesday, February 17, 2021 - 10:34:59 AM
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Christo Kurisummoottil Thomas. Sparse Bayesian learning, beamforming techniques and asymptotic analysis for massive MIMO. Engineering Sciences [physics]. Sorbonne University; EURECOM, 2020. English. ⟨tel-03140016⟩

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