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Downlink Multi-user Single-cell Transmission
In the last decade, an impressive number of works have been focused on the downlink transmission where one single transmitter (TX) serves multiple receivers (RXs). In the information-theoretic community, this trans- mission scenario is well known as the broadcast channel (BC) [5, 6]. This scenario has been heavily investigated both in the information theoretic society and in the industry, and is now relatively well understood. The capacity of the Gaussian multiple-input multiple-out (MIMO) channel has been obtained [7, 8] and shown to be achieved by a non-linear scheme called dirty-paper coding (DPC) in which the interference are subtracted on the TX side [9]. In addition, the performance of linear precoding has been evaluated [10, 11] and it has become clear that linear precoding is a practically interesting transmission scheme with lower complexity than DPC but good performance. Efficient algorithms have also been developed in order to maximize the performance with regards to different figures-of-merit while having a low complexity [12, 13]. However, the performance improvement can only be obtained at the cost of an accurate knowledge of the channel state at both the TX and the RXs [14, 15].
To translate these theoretic gains into practical performance, it has then been investigated how to estimate and feedback the channel state in realistic scenarios. Methods to obtain accurate feedback at the TX at low cost have been developed [16] while the impact of having imperfect channel state information (CSI) at the TX has been evaluated [15]. It has also be shown how channel dependent scheduling could help improve the performance and make the transmission more robust to imperfect CSIT [17, 18]. A comprehensive study of multiuser-MIMO transmissions with linear precoding is provided in [19].
Even with the novel developed schemes, obtaining perfect CSIT remains unrealistic due to the changing nature of the channel. Therefore, transmission methods being more robust to imperfect CSIT have been provided, optimizing either the average performance over the CSIT errors [20] or optimizing the worst case behavior [21, 22]. Another line of work aiming at exploiting delayed CSIT has been triggered by the work [23] where it was shown that even completely outdated CSIT (not correlated with the current channel state) could help improve the performance over a setting without
CSIT. Since then, many works have study how to exploit delayed CSIT (See [24–26] among others).
Finally, using TXs with a very large number of antennas, so-called massive MIMO, has been recently advocated in [27] as a solution to improve further the performance while easing the requirements in terms of signal processing and CSI. It is now considered a promising method and is the focus of the research of an increasingly large community. It is investigated both by companies developing prototypes of such TXs and by the academic world (see [28–30], among others).
Multi-cell Processing
Although the progresses and innovations done regarding the single-cell transmission have lead to great performance improvements, they remain fundamentally limited by the inter-cell interference. Thus, TX cooperation has appeared recently as the key to further performance improvements [4].
One conventional method to reduce inter-cell interference is by coordinating resource allocation via flexible and coordinated scheduling. Different frequency allocations schemes have been proposed with the goal to adapt to the interference generated in order to improve the transmission efficiency [31–34].
The Distributed Channel State Information Setting
As it was mentioned in the previous section, a large body of literature has been focused on the problem of TX cooperation with imperfect CSIT. However, it is usually assumed that the channel estimate, although imperfect, is the same at all the TXs involved in the joint processing. This means
that either the precoding is done in a central node or that the precoding is distributed across the TXs with the channel estimate being perfectly shared between the TXs. This CSIT scenario will be called hereafter the centralized CSIT case. This assumption comes partly from the legacy of previous works where all the transmit antennas were colocated so that this assumption was justified, and partly because it makes the model simple and intuitive. However, this assumption is likely to be breached in many scenarios where the TXs are not colocated. Indeed, precoding in a centralized node can be considered only in some scenarios and requires a centralized architecture
which does not scale well with the number of cooperating TXs. With distributed precoding, the CSI acquisition is inherently acquired at each TX through a different feedback channel. Two scenarios are actually considered for the acquisition of the CSIT in wireless networks and both scenarios are illustrated in Figure 2.1.
The first one consists in direct broadcast of the local estimates from each RX to all the listening TXs. This scenario is interesting as it does not require any CSIT sharing through the backhaul network. It is however not possible in the current 3GPP LTE-A standards [74].
The alternative is an over-the-air feedback from the UE to the home base station alone, followed by an exchange of the local estimates over the backhaul, as it is currently advocated by 3GPP LTE-A standards [74]. Sharing the channel estimates without delay and without quantization requires expensive fiber-based backhaul links or dedicated wireless links which will not be available everywhere or will be too costly. In many settings, the CSI sharing will therefore not be possible without further quantization loss and without a certain delay due both to scheduling and to protocol latency.
Table of contents :
Abstract
Abr´eg´e [Fran¸cais]
Acknowledgements
Contents
List of Figures
Acronyms
Notations
1 R´esum´e [Fran¸cais]
1.1 ´ Etat de l’art pour la coop´erations des transmetteurs
1.1.1 Saturation des bandes de fr´equence
1.1.2 Transmission `a partir d’un transmetteur vers de multiples r´ecepteurs
1.1.3 Coop´eration de plusieurs transmetteurs
1.2 Les d´efis de l’obtention de l’information de canal aux transmetteurs
1.2.1 Information de canal imparfaite aux transmetteurs
1.2.2 Configuration `a information de canal distribu´ee
1.3 Publications
1.3.1 Conf´erences
1.3.2 Journaux
1.4 Pr´ecodage conjoint avec information de canal distribu´ee
1.4.1 Pr´ecodage ZF avec information de canal distribu´ee
1.4.2 Analyse du nombre de degr´es de libert´e (DoF)
1.4.3 Analyse du pr´ecodage et des canaux de feedback
1.5 Alignement d’interf´erence avec information de canal incompl`ete
1.5.1 Mod`ele d’information de canal incompl`ete et introduction du probl`eme consid´er´e
1.5.2 Analyse des sc´enarios ´etroitement faisables
1.5.3 Analyse des sc´enarios largement faisables
1.6 Conclusion et nouveaux probl`emes
2 Introduction
2.1 State of the Art for Transmitter Cooperation
2.1.1 Saturation of the Wireless Medium
2.1.2 Downlink Multi-user Single-cell Transmission
2.1.3 Multi-cell Processing
2.2 The Challenges of Obtaining CSIT
2.2.1 Imperfect CSIT
2.2.2 The Distributed Channel State Information Setting .
2.3 Contributions and Publications
2.3.1 Contributions Presented in this Thesis
2.3.2 Other Contributions
3 System Model and Problem Statement
3.1 Multi TXs Transmission
3.1.1 Received Signal
3.1.2 Precoding Schemes with Perfect CSIT
3.2 Figures of Merit: Average Rate, DoF, Generalized DoF
3.2.1 Average Rate
3.2.2 Degrees-of-Freedom
3.2.3 Generalized Number of Degrees-of-Freedom
3.3 The Distributed CSIT Configuration
3.3.1 Distributed CSIT
3.3.2 Distributed Precoding
3.4 Optimal Precoding with Distributed CSIT: A Team Decision Problem
3.5 Summary of Objectives
4 DoF of ZF with Distributed CSIT
4.1 Distributed CSIT Model
4.1.1 Quantization for Distributed CSIT
4.1.2 Distributed CSIT Model
4.2 Review of the Results in the MIMO BC with Centralized CSIT
4.3 ZF in the Two-user BC with Distributed CSIT
4.3.1 Conventional Zero Forcing
4.3.2 Robust Zero Forcing
4.3.3 Beacon Zero Forcing
4.3.4 Active-Passive Zero Forcing
4.4 ZF in the General K-Users BC with Distributed CSIT
4.4.1 Conventional Zero Forcing
4.4.2 Beacon Zero Forcing
4.4.3 Active-Passive Zero Forcing
4.4.4 Discussion of the Results
4.5 Precoding Using Hierarchical Quantization
4.5.1 Hierarchical Quantization
4.5.2 Conventional Zero Forcing with Hierarchical Quantization
4.5.3 Active-Passive Zero Forcing with Hierarchical Quantization
4.6 Simulations
4.6.1 In the Two-User Case
4.6.2 With Arbitrary Number of Users
4.7 Conclusion
5 Rate Loss of ZF With Distributed CSIT
5.1 CSIT Configuration and Precoding Schemes
5.1.1 ZF with Centralized CSIT
5.1.2 ZF with Distributed CSI
5.2 Broadcast Channel with Centralized CSIT
5.2.1 Rate Loss Analysis
5.2.2 Feedback Design
5.2.3 Simulation Results
5.3 Broadcast Channel with Distributed Limited CSI
5.3.1 Rate Loss Analysis
5.3.2 Feedback Design
5.3.3 Simulation Results
5.4 Conclusion
6 DoF of IA with Distributed CSIT
6.1 Distributed CSIT and Distributed Precoding
6.2 DoF Analysis with Static Coefficients and Distributed CSI
6.2.1 Sufficient Condition for an Arbitrary IA Scheme
6.2.2 DoF Analysis in the 3-user Square MIMO IC
6.3 Simulations
6.4 Conclusion and Outlook
7 Distance-based CSIT Allocation for Network MIMO
7.1 System Setting and Problem Statement
7.1.1 Distributed CSI at the TXs
7.1.2 Distributed Precoding
7.1.3 Optimization of the CSIT Allocation
7.2 Preliminary Results
7.2.1 A Sufficient Criterion
7.2.2 The Conventional CSIT Allocation is DoF Achieving .
7.2.3 CSIT Allocation with Distributed Precoding
7.3 Distance-Based CSIT Allocation
7.3.1 Distance-based CSIT Allocation
7.3.2 Scaling Properties of the Distance-based CSIT Allocation
7.4 Simulations
7.5 Conclusion
8 Interference Alignment with Incomplete CSIT
8.1 Incomplete CSIT Configuration and Problem Statement
8.2 Feasibility Results
8.2.1 Results from the Literature
8.2.2 Tightly-feasible and Super-feasible Settings
8.2.3 New Formulation of the Feasibility Results
8.2.4 Generalized interference channels
8.3 IA with Incomplete CSIT for Tightly-Feasible Channels
8.3.1 General Criterion
8.3.2 CSIT Allocation Algorithm
8.3.3 IA Algorithm for Incomplete CSIT Allocation
8.3.4 Example of Tightly-feasible Configuration
8.4 Interference Alignment with Incomplete CSIT for Super-Feasible Channels
8.4.1 CSIT Allocation Algorithm
8.4.2 Toy-Example of the Incomplete CSIT-Algorithm in Super-Feasible Settings
8.5 Simulations
8.5.1 Tightly-Feasible Setting
8.5.2 Performance Evaluation of the CSIT allocation Algorithm
8.6 Discussion
9 Conclusion
