Distortion-Based Crest Factor Reduction Algorithms in Multi-Carrier Transmission Systems A Dissertation Presented to The Academic Faculty by Chunming Zhao In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Electrical and Computer Engineering Georgia Institute of Technology December 2007 Distortion-Based Crest Factor Reduction Algorithms in Multi-Carrier Transmission Systems Approved by: Professor G. Tong Zhou, Advisor Professor Ye (Geoffrey) Li School of Electrical and Computer School of Electrical and Computer Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Xiaoli Ma Professor Ming Yuan School of Electrical and Computer School of Industrial and Systems Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor J. Stevenson Kenney Date Approved: 19 October 2007 School of Electrical and Computer Engineering Georgia Institute of Technology To my grandmother, my wife, and other family members, for their love and encouragement iii ACKNOWLEDGEMENTS This dissertation has been accomplished with accompany and support of many people. It is my pleasure to express my gratitude to all of them. First and foremost, I would like to express my sincere appreciation and gratitude to my advisor, Dr. G. Tong Zhou. She taught me how to start academic pursuits step by step. From her, I learned a lot and improved a lot especially in critical thinking and algorithm developing. Without her encouragement and help I can not complete this work. My time in our group was really happy and will sit in my mind forever. Next, I would like to thank my thesis defense committee members: Dr. Xiaoli Ma, Dr. J. Stevenson Kenney, Dr. Ye (Geoffrey) Li and Dr. Ming Yuan for helping me a lot to improve the quality of the dissertation. I would also like to thank my group members: Hua Qian, Ning Chen, Chunpeng Xiao, Vince Emanuele, Thao Tran, Robert Baxley, Kun Shi and Qijia Liu, for their kind helps and valuable discussions. Sharing happiness with them make my study full of fun. Special appreciation is given to Robert Baxley for our happy collaborations related to the topic of this dissertation. Last but not least, I would like to express my gratitude to my family. I would like to thank my grandmother and my parents for their love and support. Letting them feel proud of me is the biggest power for me to work hard. I would like to thank my sister for her encouragements. Special thanks to my wife, Yao Xin, for her love and accompany. She takes care of me since I met her. iv TABLE OF CONTENTS DEDICATION ....................................... iii ACKNOWLEDGEMENTS ................................ iv LISTOFTABLES .................................... viii LISTOFFIGURES .................................... ix LISTOFABBREVIATIONS .............................. xii SUMMARY......................................... xiv I INTRODUCTION.................................. 1 1.1 Motivations................................... 1 1.2 Objective.................................... 2 1.3 Outline ..................................... 3 II BACKGROUND................................... 5 2.1 Introduction .................................. 5 2.2 OFDMSystems ................................ 5 2.3 PARDefinitioninOFDMSystems. 7 2.3.1 PARDefinitioninSISO-OFDMSystems . 7 2.3.2 PAR Definition in MIMO-OFDM Systems . 9 2.4 Performance-EvaluatingMetrics . 10 2.4.1 ErrorVectorMagnitude. 10 2.4.2 SpectralMask ............................. 12 2.4.3 Signal-to-Noise-and-Distortion Ratio . 12 2.5 Distortion-Based CFR Algorithms . 14 2.5.1 SimpleClipping ............................ 15 2.5.2 OptimalClipping ........................... 20 2.5.3 Companding .............................. 21 III MIMO-OFDMPARDEFINITION. 24 3.1 Introduction .................................. 24 3.2 SISOLinearScaling .............................. 24 v 3.3 MIMOLinearScaling ............................. 26 3.3.1 Identical Scaling Factor (ISF) Case . 26 3.3.2 Multiple Scaling Factors (MSF) Case . 28 3.3.3 EfficiencyImprovementExample. 29 3.4 Conclusions................................... 31 IV EVMANALYSISINOFDMSYSTEMS. 32 4.1 Introduction .................................. 32 4.2 EVM and its Approximated Distribution . 32 4.3 EVMAnalysisofPhaseNoise ........................ 33 4.4 EVM Analysis of Amplitude Clipping . 36 4.5 EVM Analysis of Baseband Polynomial Model for Nonlinearities of the PA 38 4.6 EVM Analysis of Gain/Phase Imbalances . 41 4.7 Conclusions................................... 43 V CONSTRAINEDCLIPPING............................ 44 5.1 Introduction .................................. 44 5.2 Proposed In-Band and Out-of-Band Processing Algorithms . ...... 45 5.2.1 In-BandProcessingAlgorithm . 47 5.2.2 Out-of-BandProcessingAlgorithm. 48 5.2.3 ClippingLevelOptimization . 49 5.2.4 Performance Results of Constrained Clipping . ..... 53 5.3 Computational Complexity Analysis of Constrained Clipping ....... 54 5.3.1 Complexity of the FFT/IFFT Units . 57 5.3.2 Complexity of Time-Domain Clipping . 57 5.3.3 ComplexityofIn-BandProcessing . 57 5.3.4 Complexity of Out-of-Band Processing . 58 5.3.5 Complexity of the Constrained Clipping Algorithm . ..... 58 5.4 Performance of Constrained Clipping in Multiple-User Environment . 59 5.4.1 EVM Definition in Multiple-User Environment . 59 5.4.2 Performance Results in Multiple-User Environment . ..... 62 5.5 Conclusions................................... 65 vi VI SNDR ANALYSIS FOR TRANSCEIVER NONLINEARITIES IN AWGN CHAN- NELS......................................... 66 6.1 Introduction .................................. 66 6.2 System Setup and SNDR for Transceiver Nonlinearities . ........ 67 6.3 Closed-FormSNDRExpression. 68 6.3.1 Closed-Form E[x z] and E[ z 2] ................... 69 ∗ | | 6.3.2 Special Case 1: Linear Transmitter Nonlinear Receiver ...... 71 6.3.3 Special Case 2: Nonlinear Transmitter Linear Receiver ...... 75 6.3.4 Special Case 3: Nonlinear Transmitter and Nonlinear Receiver . 76 6.4 SNDRMaximization.............................. 80 6.5 Comparison of Clipping and Companding Techniques . ...... 83 6.5.1 SNDRofInverseFunctions . 84 6.5.2 Comparison under Peak-Power Constraint . 87 6.5.3 Remarks ................................ 90 6.6 Conclusions................................... 91 VII CONCLUSIONS................................... 92 7.1 Contributions.................................. 92 7.2 Suggestions for Future Research . 93 REFERENCES....................................... 94 VITA ............................................ 102 vii LIST OF TABLES 2.1 Smax and EVM thresholds for various modulation schemes. 11 5.1 Example parameters for evaluation of constrained clipping. ......... 59 3 5.2 PARs at the 10− CCDFlevelforvariousΩ’s.. 62 viii LIST OF FIGURES 2.1 Illustration of the EVM definition, including the magnitude error Ek and the phase error φk. .................................. 11 2.2 Spectral mask for the WiMAX standard [4]. ..... 12 2.3 Baseband structure of linear receiver a transmitter nonlinearity g( ) in the · AWGNchannel. ................................. 13 2.4 Average EVM and its approximation under different clipping ratios. Nyquist- rate sampling and four-time over-sampling are included, N = 128. 17 2.5 PSD plots of clipped signals with different clipping ratios, N = 128. Spectral mask is also included to check the severity of the spectrum regrowth. 17 2.6 Probability that the Armstrong’s method will exceed the EVM threshold with N =256.EVMthresholdis6%. 19 2.7 Transmitter AM-AM characteristics of different compressing functions g( ), · including µ-law, A-law, NLNST and exponential transform. 22 2.8 Receiver AM-AM characteristics of different expanding functions s( ), includ- · ing µ-law, A-law, NLNST and exponential transform. 22 3.1 An ideal linear PA characteristic. The average PA input power is Pi,avg; the maximum PA input power is Pi,max. To avoid nonlinear distortions, we need P P . The PA is maximally efficient if P = P ......... 25 i,max ≤ i,sat i,max i,sat 3.2 MIMO power efficiency under the MSF and ISF configurations. ....... 29 3.3 Percent power efficiency improvement when the proper PAR metric is applied tocSLM. ..................................... 30 4.1 Relationship between λ = E[ φ ]/E[ X ] and the phase noise variance for | k| | k| various modulation schemes: QPSK, 16QAM and 64QAM, N = 2048. 35 2 4.2 Theoretical µ with different σφ values for various modulation schemes: QPSK, 16QAMand64QAM. .............................. 36 4.3 Theoretical µ as a function of the clipping ratio Ω for QPSK and 16QAM. 37 4.4 Theoretical µ with different γ values, where the cubic nonlinear coefficient is c = 0.02. .................................... 40 3 − 4.5 Theoretical µ with different c values for various modulation schemes: QPSK, | 3| 16QAMand64QAM. .............................. 40 4.6 Theoretical µ contours with different gain and phase imbalances for the QPSKmodulation................................. 42 5.1 Flow chart of the constrained clipping algorithm, which is implemented by the components inside the dashed lines. 46 ix 5.2 Simplified block diagram of the constrained clipping method with signal no- tationsateachprocessingstage. 46 5.3 Vector diagram to illustrate the in-band processing algorithm, k ( ). 49 ∈ I\M 5.4 CCDF plot of constrained clipping with different initial clipping levels Amax, N = 256 with a WiMAX spectral mask and EVM = 6%. 51 5.5 Plot of the probability that an OFDM symbol will exceed 6dB in PAR versus the initial