Cooperative Channel Estimation and Backhaul Resource Allocation

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Impact of Limited Feedback and Backhaul on Multi-cell Processing

An accurate CSIT acquisition is crucial for both coordinated beamforming and joint processing. In an extreme case of joint processing with perfect network-wise CSI at each transmitter, transmitters at dierent location can be seen as a collocated virtual multiple antennas array serving all receivers
with interference being canceled completely. Therefore, the channel degenerates to a broadcast channel and well-known precoding algorithms from the literature can be used [31]. However, in real system, both the feedback through the wireless interface and the sharing through the coordination backhaul links are limited.

Channel feedback and sharing imperfection and/or delay

With limited feedback between receiver (RX) and transmitter (TX), each transmitter obtains imperfect and/or delayed CSI. Many works have considered how coordinated beamforming or interference alignment can cope with imperfect CSIT [7,10,32{37]. Some of these works [33,34] have studied the CSI feedback resource allocation such that certain degrees-of-freedom (DoF) can be achieved. Some of the works [7, 10, 36, 37] have focused on the robust precoder design under the imperfect CSI. A number of research eorts have also considered the eect of limited feedback and/or delay in joint processing broadcast channel setting [38{40].
As is mentioned in the previous section, many coordinated beamforming and joint processing algorithms requires dierent levels of CSI data sharing between transmitters. This CSI data sharing is mainly based on the coordination backhaul. The limited backhaul has introduced further CSI imperfection and/or delay on top of limited feedback. The eect of limited backhaul has been taken into consideration for both coordinated beamforming and joint processing in many works. In [41], limited backhaul for CSI sharing is considered in interference alignment design. In [18{20], the ca- pacity limited backhaul is considered and information theoretic analysis of system performance for joint processing is provided. In [21, 22, 42{44], they consider optimal precoder design for the joint processing with limited backhaul. Despite the error and delay for CSI introduced by limited backhaul, transmitters can benet a lot from the explicit CSI sharing over the coordination backhaul. The information sharing procedure is proactive, which indicates that TX can choose to share the information that other TXs really desire or information that facilitates to the greatest extent the transmitter cooperation. However, many works on transmitter cooperation with limited backhaul focus more on the aspect of backhaul capacity limitation, without considering the possibility that TXs can decide the information to be shared. Typically, such designs exploit the backhaul using random vector quantization or scalar quantization, with no regard for the statistical proper- ties of the local information already existing at the transmitter, and ignoring the potential benets of correlated initial channel estimates available at the transmitters. Therefore, algorithm for decentralized channel estimation with limited backhaul that optimally exploit the coordination backhaul should be considered.

Precoding under distributed channel state information setting

Apart from the channel imperfection and/or delay, another important problem introduced by limited feedback and backhaul is that after the CSI sharing procedure, transmitters can have imperfect and non-identical CSI that varies from transmitter to transmitter. This is mentioned as distributed CSIT setting in this thesis and this concept is introduced for instance in [45]. It should be noticed that for multi-cell processing, many works (see [13, 18{20, 22] among others) assume a centralized design based on a single and imperfect CSI at central unit. This assumption, which is referred in this thesis as centralized CSIT, is challenged by limited feedback and backhaul scenario.

Table of contents :

Abstract
Abrege [Francais]
Acknowledgements
Contents
List of Figures
List of Tables
Acronyms
Notations
1.1 Etat de l’art de la cooperation entre emetteurs
1.1.1 Techniques de traitement multi-cellulaires
1.1.2 Transmission centralisee et distribuee
1.2 Architecture des transmissions cooperatives
1.3 L’impact de feedback et backhaul limite sur le traitement multi-cellulaires
1.3.1 L’imperfection et/ou delai a cause du feedback et partage de canal
1.3.2 Precodage sous information de canal distribuee
1.4 Organisation de these
1.5 Contributions et publications
1.6 Cooperations des transmetteurs aux liens descendants
1.6.1 Modele de transmission
1.6.2 Beamforming coordonee aux liens descendants
1.6.3 Precodage conjoint aux liens descendants
1.7 Modele de canal pour feedback et backhaul limite
1.7.1 CSIT distribuee
1.8 Facteurs de merite du systeme
1.8.1 L’erreur quadratique moyenne a chaque emetteur
1.8.2 La moyenne d’erreur quadratique moyenne entre tous les emetteurs
1.8.3 Equilibrer la precision et la coherence entre les emetteurs
1.8.4 Debit total ergodique du systeme
1.9 L’enonce du probleme
1.9.1 Le decouplage du probleme
1.9.2 La Conception d’echange d’informations ecaces: le codage Wyner-Ziv
1.9.3 La conception de transmission cooperative: le probl eme de decision en l’equipe
1.10 Conclusion et nouveaux problemes
I Motivations and Models
2 Introduction
2.1 State of Art for Transmitter Cooperation
2.1.1 Techniques for multi-cell processing
2.1.2 Decentralized and centralized transmitter cooperation
2.2 Architecture for Transmitter Cooperation
2.3 Impact of Limited Feedback and Backhaul on Multi-cell Processing
.2.3.1 Channel feedback and sharing imperfection and/or delay
2.3.2 Precoding under distributed channel state information setting
2.4 Organization of This Thesis
2.5 Contributions and Publications
3 System Model and Problem Statement
3.1 Downlink Transmitter Cooperation
3.1.1 Transmission model
3.1.2 Downlink coordinated beamforming
3.1.3 Downlink joint processing
3.2 Channel Model for Limited Feedback and Backhaul
3.2.1 Distributed CSIT
3.3 System Figures of Merit
3.3.1 Mean square error at each transmitter
3.3.2 Average mean square error at all transmitters
3.3.3 Balancing accuracy and consistency between transmitters
3.3.4 System ergodic sum rate
3.4 Problem Statement
3.4.1 Decoupling the problem
3.4.2 Ecient information exchange design: Wyner-Ziv coding problem
3.4.3 Robust decentralized transmitter cooperation design: team decision problem
3.5 Summary of the Goals
II Ecient Information Exchange Design
4 Design of Information Exchange and Cooperation on Limited Master-Slave Backhaul
4.1 Master-Slave Model
4.1.1 Master-slave coordination
4.2 Coordination Strategy in Master-Slave Model
4.2.1 M-TX sends precoder data
4.2.2 M-TX sends CSI data
4.2.3 An equivalence result
4.3 Precoding for Master-Slave Coordination
4.4 Simulations
4.5 Conclusion
5 Cooperative Channel Estimation and Backhaul Resource Allocation
5.1 System Model and Problem Description
5.1.1 Distributed CSI model
5.1.2 Limited rate coordination model
5.1.3 Channel estimation with limited coordination
5.2 Optimal Vector Quantization Model
5.3 Reconstruction Function Design
5.4 Quantizer Design
5.4.1 Shaping matrix optimization
5.5 Coordination Backhaul Resource Allocation
5.6 Balance the Accuracy and Consistency of Estimates
5.7 Numerical Performance Analysis
5.8 Conclusion
III Robust Decentralized Precoder Design under Limited
Feedback and Backhaul
6 Robust Regularized ZF in Cooperative Broadcast Channel under Distributed CSIT
6.1 System Model
6.1.1 Transmission model
6.1.2 Distributed CSI channel model
6.1.3 Regularized zero forcing with distributed CSI
6.2 Main Theoretical Result: Deterministic Equivalent of the SINR
6.2.1 Regularized ZF precoding for centralized CSI isotropic channel
6.2.2 Regularized ZF precoding for distributed CSI with independent estimate error isotropic channel
6.2.3 Regularized ZF precoding for distributed CSI isotropic channel
6.3 Application of the Theorem
6.3.1 Naive regularized ZF
6.3.2 Robust regularized ZF
6.3.3 Robust regularized ZF with equal regularization
6.4 Optimal Power Control
6.4.1 Particular case: isotropic channel
6.5 Simulation Results
6.5.1 The eect of dierent parameters on the deterministic equivalent
6.5.2 A cellular conguration simulation
6.6 Conclusion
7 Conclusion and Future Works
Appendices
A Useful Lemmas
B Proof of Theore
B.1 Deterministic equivalent for power normalization term
B.2 Deterministic equivalent for individual interference term
B.3 Deterministic equivalent for the interference term
C Proof of Theorem
D Classical Lemmas from the Literature
E New Lemmas