John Wiley & Sons LTE Optimization Engineering Handbook Cover A comprehensive resource containing the operating principles and key insights of LTE networks perfor.. Product #: 978-1-119-15897-4 Regular price: $139.25 $139.25 Auf Lager

LTE Optimization Engineering Handbook

Zhang, Xincheng

Wiley - IEEE

Cover

1. Auflage Dezember 2017
848 Seiten, Hardcover
Wiley & Sons Ltd

ISBN: 978-1-119-15897-4
John Wiley & Sons

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A comprehensive resource containing the operating principles and key insights of LTE networks performance optimization

LTE Optimization Engineering Handbook is a comprehensive reference that describes the most current technologies and optimization principles for LTE networks. The text offers an introduction to the basics of LTE architecture, services and technologies and includes details on the key principles and methods of LTE optimization and its parameters. In addition, the author clarifies different optimization aspects such as wireless channel optimization, data optimization, CSFB, VoLTE, and video optimization.

With the ubiquitous usage and increased development of mobile networks and smart devices, LTE is the 4G network that will be the only mainstream technology in the current mobile communication system and in the near future. Designed for use by researchers, engineers and operators working in the field of mobile communications and written by a noted engineer and experienced researcher, the LTE Optimization Engineering Handbook provides an essential guide that:
* Discusses the latest optimization engineering technologies of LTE networks and explores their implementation
* Features the latest and most industrially relevant applications, such as VoLTE and HetNets
* Includes a wealth of detailed scenarios and optimization real-world case studies

Professionals in the field will find the LTE Optimization Engineering Handbook to be their go-to reference that includes a thorough and complete examination of LTE networks, their operating principles, and the most current information to performance optimization.

About the Author xvi

Preface xvii

Part 1 LTE Basics and Optimization Overview 1

1 LTE Basement 3

1.1 LTE Principle 3

1.1.1 LTE Architecture 6

1.1.2 LTE Network Interfaces 7

1.2 LTE Services 11

1.2.1 Circuit?]Switched Fallback 12

1.2.2 Voice over LTE 13

1.2.3 IMS Centralized Services 16

1.2.4 Over the Top Solutions 16

1.2.5 SMS Alternatives over LTE 17

1.2.6 Converged Communication 19

1.3 LTE Key Technology Overview 19

1.3.1 Orthogonal Frequency Division Multiplexing 20

1.3.2 MIMO 21

1.3.3 Radio Resource Management 22

2 LTE Optimization Principle and Method 24

2.1 LTE

Wireless Optimization Overview 24

2.1.1 Why LTE Wireless Optimization 24

2.1.2 Characters of LTE Optimization 24

2.1.3 LTE Joint Optimization with 2G/3G 25

2.1.4 Optimization Target 25

2.2 LTE Optimization Procedure 26

2.2.1 Optimization Procedure Overview 26

2.2.2 Collection of Mass Nerwork Measurement Data 28

2.2.3 Measurement Report Data Analysis 30

2.2.4 Signaling Data Analysis 31

2.2.5 UE Positioning 32

2.2.5.1 Timing Advance 33

2.2.5.2 Location Accuracy Evaluation 35

2.2.5.3 Location Support 36

2.2.5.4 3D Geolocation 37

2.2.6 Key Performance Indicators Optimization 42

2.2.7 Technology Evolution of Optimization 43

2.3 LTE Optimization Key Point 44

2.3.1 RF Optimization 44

2.3.1.1 RSRP/RSSI/SINR/CINR 44

2.3.1.2 External Interference 48

2.3.2 CQI versus RSRP and SINR 51

2.3.2.1 CQI Adjustment 51

2.3.2.2 SINR Versus Load 54

2.3.2.3 SINR Versus MCS 56

2.3.3 Channel Power Configuration 58

2.3.3.1 RE Power 58

2.3.3.2 CRS Power Boosting 64

2.3.3.3 Power Allocation Optimization 66

2.3.4 Link Adaption 67

2.3.5 Adaptive Modulation and Coding 69

2.3.6 Scheduler 70

2.3.6.1 Downlink Scheduler 72

2.3.6.2 Uplink Scheduler 74

2.3.7 Radio Frame 75

2.3.8 System Information and Timers 76

2.3.8.1 System Information 76

2.3.8.2 Timers 81

2.3.9 Random Access 83

2.3.10 Radio Admission Control 85

2.3.11 Paging Control 86

2.3.11.1 Paging 86

2.3.11.2 Paging Capacity 92

2.3.11.3 Paging Message Size 95

2.3.11.4 Smart Paging 95

2.3.11.5 Priority Paging 96

2.3.12 MIMO and Beamforming 97

2.3.12.1 Basic Multi?]Antenna Techniques 100

2.3.12.2 2D?]Beamforming 101

2.3.12.3 2D MIMO and Parameters 104

2.3.12.4 Massive?]MIMO 105

2.3.13 Power Control 107

2.3.13.1 PUSCH/PUCCH Power Control 107

2.3.13.2 PRACH Power Control 109

2.3.14 Antenna Adjustment 111

2.3.14.1 Antenna Position 112

2.3.14.2 Remote Electrical Tilt 113

2.3.14.3 Antenna Azimuths and Tilts Optimization 117

2.3.14.4 VSWR Troubleshooting 118

2.3.15 Main Key Performance Indicators 120

Part 2 Main Principles of LTE Optimization 123

3 Coverage Optimization 125

3.1 Traffic Channel Coverage 125

3.1.1 Parameters of Coverage 126

3.1.2 Weak Coverage 128

3.1.2.1 DL Coverage Hole 128

3.1.2.2 UL Weak Coverage 128

3.1.2.3 UL and DL Imbalance 129

3.1.3 Overlapping Coverage 129

3.1.4 Overshooting 130

3.1.5 Tx1/Tx2 RSRP Imbalance 132

3.1.6 Extended Coverage 132

3.1.7 Cell Border Adjustment 135

3.1.8 Vertical Coverage 137

3.1.9 Parameters Impacting Coverage 138

3.2 Control

Channel Coverage 138

4 Capacity Optimization 140

4.1 RS SINR 140

4.2 PDCCH

Capacity 141

4.3 PUCCH Capacity 144

4.3.1 Factors Affecting PUCCH Capacity 145

4.3.2 PUCCH Dimensioning Example 151

4.4 Number of Scheduled UEs 152

4.5 Spectral Efficiency 153

4.6 DL

Data Rate Optimization 154

4.6.1 Limitation Factor 156

4.6.2 Model of DL Data Throughput 157

4.6.3 UDP/TCP Protocol 158

4.6.4 MIMO 161

4.6.4.1 DL MIMO 161

4.6.4.2 4Tx/4Rx Performance 163

4.6.4.3 Transmission Mode Switch 163

4.6.4.4 UL MU?]MIMO 164

4.6.5 DL PRB Allocation and Utilization Mechanism 165

4.6.6 DL BLER 167

4.6.7 Impact of UE Velocity 169

4.6.8 Single User Throughput Optimization 170

4.6.8.1 Radio Analysis - Assignable Bits 171

4.6.8.2 Radio Analysis - CFI and Scheduling 171

4.6.8.3 Radio Analysis - HARQ 171

4.6.9 Avarage Cell Throughput Optimization 172

4.6.10 Cell Edge Throughput Optimization 172

4.6.11 Some Issues of DL Throughput 173

4.6.11.1 Antenna Diversity not Balanced 173

4.6.11.2 DL Grant is not Enough 173

4.6.11.3 Unstable Rate 175

4.7 UL Data Rate Optimization 175

4.7.1 Model of UL Data Throughput 176

4.7.2 UL SINR and PUSCH Data Rate 176

4.7.3 PRB Stretching and Throughput 179

4.7.4 Single User Throughput Optimization 180

4.7.4.1 Radio Analysis - Available PRBs 181

4.7.4.2 Radio Analysis--Link Adaptation 181

4.7.4.3 Radio Analysis - PDCCH 182

4.7.5 Cell Avarage and Cell?]edge Throughput Optimization 182

4.7.6 Some Issues of UL Throughput 183

4.8 Parameters Impacting Throughput 185

5 Internal Interference Optimization 188

5.1 Interference Concept 188

5.2 DL

Interference 190

5.2.1 DL Interference Ratio 191

5.2.2 Balance Between SINR and RSRP 192

5.3 UL Interference 192

5.3.1 UL Interference Detection 194

5.3.2 Generation of UL Interference 196

5.3.2.1 Cell Loading Versus Inter?]Cell Interference 196

5.3.2.2 Unreasonable UL Network Structure 197

5.3.2.3 Cross slot interference 199

5.3.3 PUSCH Tx Power Analysis 200

5.3.4 UL Effect of P0 and alpha 202

5.3.5 PRACH Power Control 204

5.3.6 SRS Power Control 206

5.3.7 Interference Rejection Combinin 209

5.4 Inter?]Cell Interference Coordination 210

5.5 UL IoT Control 210

5.5.1 UL Interference Issues and Possible Solutions 210

5.5.2 UL IoT Control Mechanism 210

5.5.3 PUSCH UL_SINR Target Calculation 212

5.5.4 UL Interference Criteria 213

6 Drop Call Optimization 216

6.1 Drop Call Mechanism 216

6.1.1 Radio Link Failure Detection by UE 217

6.1.2 RadioLink Failure Detection by eNB 220

6.1.2.1 Link Monitors in eNB 220

6.1.2.2 Time Alignment Mechanism 221

6.1.2.3 Maximum RLC Retransmissions Exceeded 224

6.1.3 RadioLink Failure Optimization and Recovery 225

6.2 Reasons of Call Drop and Optimization 227

6.2.1 Reasons of E?]RAB Drop 227

6.2.2 S1 Release 230

6.2.3 Retainability Optimization 233

6.3 RRC Connection Reestablishment 233

6.4 RRC Connection Supervision 239

7 Latency Optimization 244

7.1 User Plane Latency 244

7.2 Control Plane Latency 247

7.3 Random Access Latency Optimization 247

7.4 Attach Latency Optimization 248

7.5 Paging Latency Optimization 250

7.6 Parameters Impacting Latency 250

8 Mobility Optimization 254

8.1 Mobility Management 255

8.1.1 RRC Connection Management 256

8.1.2 Measurement and Handover Events 256

8.1.3 Handover Procedure 260

8.1.3.1 X2 Handover 261

8.1.3.2 S1 Handover 267

8.1.3.3 Key point of X2/S1 Handover 267

8.2 Mobility Parameter 269

8.2.1 Attach and Dettach 272

8.2.2 UE Measurement Criterion in Idle Mode and Cell Selection 273

8.2.3 Cell Priority 276

8.3 Intra?]LTE Cell Reselection 276

8.3.1 Cell Reselection Procedure 278

8.3.2 Inter?]Frequency Cell Reselection 279

8.3.3 Cell Reselection Parameters 282

8.3.4 Inter?]Frequency Reselection Optimization 283

8.4 Intra?]LTE Handover Optimization 285

8.4.1 A3 and A5 Handover 285

8.4.2 Data Forwarding 290

8.4.3 Intra?]Frequency Handover Optimization 291

8.4.4 Inter?]Frequency Handover Optimization 292

8.4.5 Timers for Handover Failures 296

8.5 Neighbor Cell Optimization 297

8.5.1 Intra?]LTE Neighbor Cell Optimization 297

8.5.1.1 Neighbor Relations Table 297

8.5.1.2 ANR 298

8.5.2 Suitable Neighbors for Load Balancing 299

8.6 Measurement Gap 299

8.6.1 Measurement Gap Pattern 299

8.6.2 Measurement Gap Versus Period of CQI Report and DRX 304

8.6.3 Impact of Throughput on Measurement Gap 304

8.7 Indoor and Outdoor Mobility 305

8.8 Inter?]RAT Mobility 306

8.8.1 Inter?]RAT Mobility Architecture and Key Technology 307

8.8.2 LTE to G/U Strategy 309

8.8.3 Reselection Optimization 314

8.8.3.1 LTE to UTRAN 315

8.8.3.2 UTRAN to LTE 319

8.8.4 Redirection Optimization 320

8.8.4.1 LTE to UTRAN 320

8.8.4.2 UTRAN to LTE 322

8.8.5 PS Handover Optimization 322

8.8.5.1 LTE to UTRAN 322

8.8.5.2 UTRAN to LTE 324

8.8.6 Reselection and Redirection Latency 325

8.8.7 Optimization Case Study 326

8.9 Handover Interruption Time Optimization 326

8.9.1 Control Plane and User Plane Latency 329

8.9.2 Inter?]RAT Mobility Latency 332

8.10 Handover Failure and Improvement 332

8.11 Mobility Robustness Optimization 335

8.12 Carrier Aggregation Mobility Optimization 341

8.13 FDD?]TDD Inter?]mode Mobility Optimization 345

8.14 Load Balance 346

8.14.1 Inter?]Frequency Load Balance 346

8.14.2 Inter?]RAT Load Balance 348

8.14.3 Load Based Idle Mode Mobility 349

8.15 High?]Speed Mobile Optimization 351

8.15.1 High?]Speed Mobile Feature 353

8.15.2 Speed?]Dependent Cell Reselection 354

8.15.3 PRACH Issues 356

8.15.4 Solution for Air to Ground 358

9 Traffic Model of Smartphone and Optimization 360

9.1 Traffic Model of Smartphone 360

9.1.1 QoS Mechanism 362

9.1.2 Rate Shaping and Traffic Management 366

9.1.3 Traffic Model 371

9.2 Smartphone?]Based Optimization 372

9.3 High?]Traffic Scenario Optimization 372

9.3.1 Resource Configuration 374

9.3.2 Capacity Monitoring 375

9.3.3 Special Features and Parameters for High Traffic 377

9.3.4 UL Noise Rise 379

9.3.5 Offload Solution and Parameter Settings 379

Part III Voice Optimization of LTE 383

10 Circuit Switched Fallback Optimization 385

10.1 Voice Evolution 385

10.2 CSFB Network Architecture and Configuration 386

10.2.1 CSFB Architecture 386

10.2.2 Combined Register 387

10.2.3 CSFB Call Procedure 392

10.2.3.1 Fallback Options 392

10.2.3.2 RRC Release with Redirection 393

10.2.3.3 CSFB Call Procedure 395

10.2.4 Mismatch Between TA and LA 397

10.3 CSFB Performance Optimization 402

10.3.1 CSFB Optimization 402

10.3.1.1 Main Issues of CSFB 402

10.3.1.2 CSFB Optimization Method 403

10.3.2 CSFB Main KPI 407

10.3.3 Fallback RAT Frequency Configuration Optimization 409

10.3.4 Call Setup Time Latency Optimization 411

10.3.4.1 ESR to Redirection Optimization 416

10.3.4.2 Twice Paging 416

10.3.5 Data Interruption Time 418

10.3.6 Return to LTE After Call Complete 419

10.4 Short Message Over CSFB 422

10.5 Case Study of CSFB Optimization 423

10.5.1 Combined TA/LA Updating Issue 423

10.5.2 MTRF Issue 425

10.5.3 Track Area Update Reject After CSFB 425

10.5.3.1 No EPS Bearer Context Issue 428

10.5.3.2 Implicitly Detach Issue 428

10.5.3.3 MS Identity Issue 428

10.5.4 Pseudo Base Station 428

11 VoLTE Optimization 434

11.1 VoLTE Architecture and Protocol Stack 435

11.1.1 VoLTE Architecture 435

11.1.2 VoLTE Protocol Stack 435

11.1.3 VoLTE Technical Summary 438

11.1.4 VoLTE Capability in UE 439

11.2 VoIP/Video QoS and Features 442

11.2.1 VoIP/Video QoS 442

11.2.2 Voice Codec 444

11.2.3 Video Codec 446

11.2.4 Radio Bearer for VoLTE 449

11.2.5 RLC UM 454

11.2.6 Call Procedure 457

11.2.6.1 LTE Attach and IMS Register 458

11.2.6.2 E2E IMS Flow 458

11.2.6.3 Video Phone Session Handling 462

11.2.7 Multiple Bearers Setup and Release 466

11.2.8 VoLTE Call On?]Hold/Call Waiting 467

11.2.9 Differentiated Paging Priority 468

11.2.10 Robust Header Compression 470

11.2.10.1 RoHC Feature 470

11.2.10.2 Gain by RoHC 470

11.2.11 Inter?]eNB Uplink CoMP for VoLTE 475

11.3 Semi?]

Persistent Scheduling and Other Scheduling Methods 477

11.3.1 SPS Scheduling 477

11.3.2 SPS Link Adaptation 478

11.3.3 Delay Based Scheduling 481

11.3.4 Pre?]scheduling 482

11.4 PRB and MCS Selection Mechanism 484

11.4.1 Optimized Segmentation 484

11.4.2 PRB and MCS Selection 485

11.5 VoLTE Capacity 486

11.5.1 Control Channel for VoLTE 487

11.5.2 Performance of Mixed VoIP and Data 488

11.6 VoLTE Coverage 491

11.6.1 VoIP Payload and RoHC 492

11.6.2 RLC Segmentation 492

11.6.3 TTI Bundling 498

11.6.4 TTI Bundling Optimization 502

11.6.5 Coverage Gain with RLC Segmentation and TTI Bundling 507

11.6.6 MCS/TBS/PRB Selection 509

11.6.7 Link Budget 510

11.7 VoLTE Delay 513

11.7.1 Call Setup Delay 516

11.7.1.1 Call Setup Time 516

11.7.1.2 Reasons for Long Call Setup Time 516

11.7.2 Conversation Start Delay 519

11.7.3 RTP Delay 521

11.7.4 Handover Delay and Optimization 525

11.8 Intra?]LTE Handover and eSRVCC 527

11.8.1 Intra?]Frequency Handover 527

11.8.2 Inter?]Frequency Handover 528

11.8.3 Single Radio Voice Call Continuity Procedure 529

11.8.4 SRVCC Parameters Optimization 539

11.8.4.1 Handover Parameters 539

11.8.4.2 SRVCC-Related Timer 539

11.8.5 aSRVCC and bSRVCC 543

11.8.6 SRVCC Failure 543

11.8.7 Reducing SRVCC Voice Gap and eSRVCC 545

11.8.7.1 Voice Interruption Time during SRVCC 545

11.8.7.2 eSRVCC 549

11.8.8 Fast Return to LTE 552

11.8.9 Roaming Behavior According to Network Capabilities 555

11.9 Network Quality and Subjective Speech Quality 555

11.9.1 Bearer Latency 558

11.9.2 MoS 561

11.9.2.1 Voice Quality 561

11.9.2.2 Video Quality 570

11.9.3 Jitter 571

11.9.4 Packet Loss 572

11.9.5 One Way Audio 575

11.9.6 PDCP Discard Timer Operation 576

11.10 Optimization 577

11.10.1 Distribution of Main Indicators of Field Test 580

11.10.2 Compression Ratio and GBR Throughput 584

11.10.3 RB Utilization 584

11.10.4 BLER Issue 587

11.10.5 Quality Due to Handover 589

11.10.6 eSRVCC Handover Issues 589

11.10.7 Packet Loss 592

11.10.7.1 Packet Loss due to Poor RF 592

11.10.7.2 Packet Loss due to Massive users 592

11.10.7.3 Packet Loss Due to Insufficient UL grant 592

11.10.7.4 Packet Loss due to Handover 601

11.10.7.5 Packet Loss Due to Network Issue 601

11.10.8 Call Setup Issues 601

11.10.8.1 Missed Pages 602

11.10.8.2 IMS Issues 604

11.10.8.3 Dedicated Bearer Setup Issues 609

11.10.8.4 CSFB Call Issues 612

11.10.8.5 aSRVCC Failure 612

11.10.8.6 RF Issues 612

11.10.8.7 Frequent TFT Updates 617

11.10.8.8 Encryption Issue 618

11.10.9 Call Drop 619

11.10.9.1 Call Drop 619

11.10.9.2 Radio Link Failure 622

11.10.9.3 RTP?]RTCP Timeout 624

11.10.9.4 RLC/PDCP SN Length Mismatch 626

11.10.9.5 IMS Session Drop 626

11.10.9.6 eNB/MME Initiated Drop 632

11.10.10 Packet Aggregation Level 632

11.10.11 VoIP Padding 633

11.10.12 VoIP Ralated Parameters 635

11.10.13 Video?]Related Optimization 635

11.10.13.1 Video Bit Rate and Frame Rate 637

11.10.13.2 Video MoS and Audio/Video Sync 637

11.10.14 IMS Ralated Timer 637

11.11 UE Battery Consumption Optimization for VoLTE 638

11.11.1 Connected Mode DRX Parameter 643

11.11.2 DRX Optimization 644

11.11.2.1 State Estimation 644

11.11.2.2 DRX Optimization and Parameters 644

11.11.2.3 KPI Impacts with DRX 648

11.11.3 Scheduling Request Periodicity and Disabling of Aperiodic CQI 652

11.12 Comparation with VoLTE and OTT 654

11.12.1 OTT VoIP User Experience 654

11.12.2 OTT VoIP Codec 657

11.12.3 Signaling Load of OTT VoIP 658

Part IV Advanced Optimization of LTE 663

12 PRACH Optimization 665

12.1 Overview 665

12.2 PRACH Configuration Index 669

12.3 RACH Root Sequence 673

12.4 PRACH Cyclic Shift 674

12.4.1 PRACH Cyclic Shift Optimization 674

12.4.2 Rrestricted Set 679

12.5 Prach Frequency Offset 682

12.6 Preamble Collision Probability 683

12.7 Preamble Power 684

12.8 Random Access Issues 687

12.9 RACH Message Optimization 689

12.10 Accessibility Optimization 692

12.10.1 Reasons for Poor Accessibility 692

12.10.2 Accessibility 693

12.10.3 Accessibility Analysis Tree 695

12.10.4 Call and Data Session Setup Optimization 697

12.10.5 RACH Estimation for Different Traffic Profile 698

13 Physical Cell ID Optimization 702

13.1 Overview 702

13.2 PCI Optimization Methodology 703

13.2.1 PCI Group Optimization 705

13.2.2 PCI Code Reuse Distance 705

13.2.3 Mod3/30 Discrepancy Analysis 708

13.2.4 Collision and Confusion 708

13.3 PCI Optimization 709

14 Tracking Areas Optimization 711

14.1 TA Optimization 712

14.1.1 TA Update Procedure 713

14.1.2 TA Optimization and TAU Failure 715

14.2 TA List Optimization 716

14.3 TAU Reject Analysis and Optimization 719

15 Uplink Signal Optimization 721

15.1 Uplink Reference Signal Optimization 721

15.1.1 Coding Scheme of UL RS 722

15.1.2 Correlation of UL Sequence Group 723

15.1.2.1 UL Sequence Group Hopping 725

15.1.2.2 UL Sequence Hopping 726

15.1.2.3 UL Cyclic Shift Hopping 726

15.1.3 UL Sequence Group Optimization 727

15.2 Uplink Sounding Signal Optimization 729

15.2.1 SRS Characters 730

15.2.2 Wideband SRS Coverage 736

15.2.3 Dynamic SRS Adjustment Scheme 736

15.2.4 SRS Selection Dimension and Confliction 737

15.2.5 SRS Conflict and Optimization 739

16 HetNet Optimization 741

16.1 UE Geolocation and Identification of Traffic Hot Spots 741

16.2 Wave Propagation Characteristics for HetNet 745

16.3 New Features in HetNet 746

16.4 Combined Cell Optimization 747

16.5 Cell Range Expansion Offset 748

16.6 HetNet Cell Reselection and Handover Optimization 751

17 QoE Evaluation and Optimization Strategy 752

17.1 QoE Modeling 753

17.2 Data Collecting and Processing 756

17.3 QoE?]Based Traffic Evaluation 757

17.3.1 Online Video QoE 757

17.3.1.1 Video Quality Monitoring Methods 761

17.3.1.2 RATE Adaptive Video Codecs 763

17.3.1.3 Streaming KPI and QoE 764

17.3.1.4 Video Optimization 766

17.3.2 Voice QoE 769

17.3.3 Data Service QoE 770

17.3.3.1 Web browsing 770

17.3.3.2 Online Gaming 774

17.4 QoE Based Optimization 776

18 Signaling?]Based Optimization 780

18.1 S1?] AP Signaling 780

18.1.1 NAS signaling 782

18.1.2 Inactivity Supervision 783

18.1.3 UE signaling Management 785

18.2 Signaling radio bearers 786

18.3 Signaling Storm 788

18.4 Signaling Troubleshooting Method 788

18.4.1 Attach Failure 788

18.4.2 Service Request Failure 796

18.4.3 S1/X2?]Based Handover 796

18.4.4 eSRVCC Failure 798

18.4.5 CSFB Failure 800

Appendix 802

Glossary of Acronyms 820

References 823

Index 825
XINCHENG ZHANG is a Professor and Engineer with more than 20 years' experience in wireless communications and is a technical expert for one of China's largest telecom companies, China Mobile Group Design Institute Co., Ltd