Multiple antenna techniques for interference mitigation in multi-cell multi-user downlink systems

다국어 초록 (Multilingual Abstract)

The capacity of cellular networks can be boosted by enabling space division multiple access (SDMA) which transmits independent data signals to multiple co-channel users simultaneously, rather than distinguishing multiple users in frequency or time domains only. In the SDMA system where co-channel interference (CCI) is inevitable, a simple channel inversion (CI) technique was proposed to eliminate the CCI and allow independent signals to be directed to the intended
users. However, the performance of the CI is quite poor due to a power boosting effect for ill-conditioned channels. To enhance the performance of the CI, vector perturbation was introduced by Hochwald and et al., which adopts a modulo operator at both transmitter and receiver. In the vector perturbation technique, the complexity required to find a perturbation vector is problematic for a large number of users since it depends on a 2K-dimensional lattice closest-point problem where $K$ is the number of co-channel users.

In this thesis, we introduce a new algorithm which further reduces the complexity of the conventional vector perturbation schemes such as the sphere encoding (SE) and lattice-reduction (LR) algorithms by searching for the real and imaginary components of the perturbation vectors individually. This provides us significant complexity savings since the complexity of the search problem is determined by
its dimension. To minimize a performance loss induced by the
decoupled joint search, diagonal precoding is applied at the
transmitter. We first describe a method which iteratively optimizes parameters of the diagonal precoder. Since our main objective is to reduce the system cost, we also present a simple method of choosing parameters which can provide the performance almost identical to the optimized ones. It is confirmed that the proposed scheme can achieve
a significant complexity reduction compared to the conventional vector perturbation algorithms with a slight performance loss.

Despite of the invention of the above efficient algorithms, the
effectiveness of the SDMA systems in a cellular scenario is known to be quite limited due to the severity of the inter-cell interference (ICI). Thus, research on ICI mitigation has become an important and timely issue. As an initial step, we propose beamforming techniques for weighted sum-rate (WSR) maximization in multi-cell downlink transmission. We start with modeling the multi-cell system as the MISO interference channels (IC). To solve the WSR maximization
problem efficiently, we establish the relation between the WSR
maximization and the virtual signal-to-interference-plus-noise ratio (VSINR) maximization problems. The VSINR differs from the actual signal-to-interference-plus-noise ratio (SINR) in a sense that the VSINR is a function of a single beamforming vector. Since the beamforming vectors for maximizing the VSINR can be expressed in a closed-form, we try to solve the VSINR problem instead of directly solving the WSR problem. Since the parameters in the VSINR expression for the equivalence between the WSR and VSINR maximization problems depend on the beamforming vectors, we should
perform iterative process.

Since the overhead for the CSI exchange among the BSs is significant in the practical system design, we also propose a method of implementing the proposed VSINR scheme using only local CSI. To this end, we perform some approximations which result in slight performance loss. Furthermore, it is shown that the proposed VSINR approach can be applied to the joint processing (JP) systems where adjacent BSs can share the message information intended for the mobile users. The JP can be modeled as the broadcast channel (BC) with per-BS power constraint.

We also study the transceiver design for multiple-input
multiple-output (MIMO) IC where both the transmitter and receiver are equipped with multiple antennas. After investigating efficient zero-forcing (ZF) transceivers for 2-user and 3-user ICs, we propose a non-iterative regularization method under the high SNR approximation to improve the performance of the ZF schemes at low SNR. The distributed implementation of the proposed regularization method is also presented where each node is able to compute its own
precoding or decoding matrix using local channel state information.

The IC is well suited to model the multi-cell system with single
co-channel user per cell. However, as wireless spectrum utilization increases, mutually interfering BC where each link has a single transmit node and multiple receive nodes become more pervasive.

Thus, in this thesis, we study the degree-of-freedom (DOF) measure which is also known as pre-log factor or multiplexing gain for two mutually interfering broadcast channels (IBC) where the i-th BS equipped with M_i antennas (i = 1, 2) transmits messages to its corresponding K_i single antenna users. We refer to the IBC with this configuration as (M_1,K_1,M_2,K_2) IBC. The IBC differs from the multiple-input multiple-output (MIMO) IC in a sense that K_i receive antennas in cell i are disconnected and cannot cooperate with each other. We present the results of the lower and upper bounds on the DOF of the IBC. From the derived results, it is shown
that for most cases, zero-forcing (ZF) beamforming can achieve the optimal DOF of the IBC except for some special cases. Also, we identify a condition that disabling receive cooperation in the MIMO IC causes no DOF loss. It is confirmed that we cannot expect a DOF improvement by enabling in-cell receive cooperation if in at least
one of two BSs, the number of antennas is greater than or equal to that of users per cell. Furthermore, we observe a positive result that as the number of users goes to infinity, the total DOF of the IBC converges to the interference-free DOF which is the maximum achievable DOF in the absence of the inter-cell interference.

Also, the effect of the cognitive message sharing among transmit nodes on the DOF performance is studied. It is shown that if at least one of two transmitters is a cognitive BS, the DOF is not degraded by disabling receive cooperation in the MIMO IC. Additionally, the DOF for the case of more than two cells is
investigated.

목차 (Table of Contents)

• Abstract 1
• 1 Introduction 5
• 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
• 1.2 Outline and Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
• 2 System Overview 11
• 2.1 Wireless Channel: Frequency-Selective Nature . . . . . . . . . . . . . . . . . . . 11
• 2.2 Frequency-Flat Fading Channel with OFDM . . . . . . . . . . . . . . . . . . . 12
• 2.3 MIMO-OFDM System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
• 2.4 Common Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
• 3 A Decoupling Approach for Low-Complexity Vector Perturbation in Multiuser Downlink Systems 15
• 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
• 3.2 System Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
• 3.3 Decoupled Vector Perturbation Scheme . . . . . . . . . . . . . . . . . . . . . . 19
• 3.3.1 Iterative Optimization of angles . . . . . . . . . . . . . . . . . . . . 21
• 3.3.2 Non-Iterative Choice of angles. . . . . . . . . . . . . . . . . . . . . 24
• 3.4 Complexity Comparison with the Conventional Schemes . . . . . . . . . . . . . 26
• 3.5 Receive Combining for Vector Perturbation Systems . . . . . . . . . . . . . . . 27
• 3.6 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
• 3.7 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 34
• 4 Beamforming Design Based on Virtual SINR Maximization for Coordinated Multi-Cell Transmission 35
• 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
• 4.2 System Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
• 4.3 Review of VSINR-based Parameterization . . . . . . . . . . . . . . . . . . . . . 40
• 4.4 Proposed VSINR Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
• 4.5 Distributed Implementation of the Proposed VSINR Scheme . . . . . . . . . . . 45
• 4.6 JP System Based on the Proposed VSINR Approach . . . . . . . . . . . . . . . 47
• 4.6.1 Centralized Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
• 4.6.2 Decentralized Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
• 4.7 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
• 4.8 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 61
• 5 Regularized Transceiver Designs for MIMO Interference Channels 63
• 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
• 5.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
• 5.3 Coordinated Transceiver Designs based on ZF Criterion . . . . . . . . . . . . . 68
• 5.3.1 CSM for Two-User IC (K = 2) . . . . . . . . . . . . . . . . . . . . . . . 69
• 5.3.2 Enhanced Interference Alignment for Three-User IC (K = 3) . . . . . . 73
• 5.4 Regularizing the ZF transceivers . . . . . . . . . . . . . . . . . . . . . . . . . . 75
• 5.5 Distributed Implementation of the Proposed Regularization Approach . . . . . 78
• 5.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
• 5.7 Chapter Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 86
• 6 Degree of Freedom for Mutually Interfering Broadcast Channels 87
• 6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
• 6.2 System Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
• 6.3 Achievable DOF with ZF Beamforming . . . . . . . . . . . . . . . . . . . . . . 92
• 6.3.1 DOF with ZF Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . 93
• 6.3.2 Achieving the Optimal DOF with ZF Beamforming . . . . . . . . . . . 99
• 6.3.3 Sum Rate Maximizing Beamforming . . . . . . . . . . . . . . . . . . . . 101
• 6.4 Tighter Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
• 6.4.1 Lower Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
• 6.4.2 Upper Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
• 6.5 Comparison to MIMO Interference Channels . . . . . . . . . . . . . . . . . . . 109
• 6.6 DOF in the Presence of Cognitive Base Stations . . . . . . . . . . . . . . . . . 111
• 6.7 Extension to the Case of More than Two Cells . . . . . . . . . . . . . . . . . . 121
• 6.7.1 Lower Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
• 6.7.2 Upper Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
• 6.7.3 Symmetric Antenna Setting . . . . . . . . . . . . . . . . . . . . . . . . . 126
• 6.8 Applications of DOF analysis in Cellular System Design . . . . . . . . . . . . . 127
• 6.9 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 128
• 7 Conclusions 130
• Bibliography 137