A Thesis entitled Performance Evaluation of 2-D Pilot Aided OFDM System under Hyper-Rayleigh Fading Channel By Haobo Zhen Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Electrical Engineering Dr. Junghwan Kim, Committee Chair Dr. Ezzatollah Salari, Committee Member Dr. Dong-Shik Kim, Committee Member Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo August 2011 Copyright 2011, Haobo Zhen This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of Performance Evaluation of 2-D Pilot Aided OFDM System under Hyper-Rayleigh Fading Channel by Haobo Zhen Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Electrical Engineering The University of Toledo August 2011 Wireless radio propagation channel is widely known as the most hostile communication channel. Modeling and simulation of wireless fading channel has been an essential issue in the design of communication system. Rayleigh fading and Rician fading model are the most commonly used small scale models in wireless communication. However, recent research shows that some WSN applications where sensor nodes deployed within cavity environment suffer from more severe fading than Rayleigh fading predicted, which is referred to as hyper-Rayleigh fading. Therefore, design of a more applicable model is necessary to describe hyper-Rayleigh fading. Two-wave with diffuse power (TWDP) model is suggested to be the proper model to represent hyper-Rayleigh fading behavior. However, little effort has been made to evaluate the anti-interference capacity of OFDM system under hyper-Rayleigh fading channel. In the thesis, the characteristic of hyper-Rayleigh fading is explored and analyzed. Furthermore, performances of OFDM system with various pilot aided channel estimation techniques under hyper-Rayleigh fading are investigated. Simulation results indicate hyper-Rayleigh fading exhibits worse fading phenomena iii than Rayleigh fading when parameters ∆ and K exceed certain values. OFDM system with 2-D channel estimation demonstrates strong resistance to multipath fading, thus can be regarded as a promising candidate of WSN applications under hyper-Rayleigh fading. iv Acknowledgements First of all, I would like to thank my advisor Dr. Junghwan Kim for his guidance, his encouragement and support to me. The thesis would not have been possible without his help. I would also like to thank Dr. Ezzatollah Salari and Dr. Dong-Shik Kim for being my committee members. I want to give my thanks to my friends and fellow students in University of Toledo, who make my life in America happy and memorable. Finally, I want to express my deep appreciation and gratitude to my parents, whose love always accompany me through difficult times and days of joy. v Table of Contents Abstract iii Acknowledgements v Table of Contents vi List of Tables viii List of Figures ix 1 Introduction………………………………………………………………………… 1 1.1 Problem Statement…………………………………………………………… 1 1.2 Thesis Contribution………………………………………………………… 3 1.3 Thesis Outline…………………………………………………………….. 4 2 Principle and Model of OFDM System………………………………………...… 6 2.1 Principle of OFDM system…………………………………………….…… 6 2.2 Model of OFDM system……………………………………………………… 9 2.2.1 Convolutional Coding………………………………………………….. 10 2.2.2 Modulation Schemes………………………………………………….. 14 2.2.3 IFFT and FFT………………………………………………………….. 23 2.2.4 Cyclic Prefix………………………………………………………….. 23 3 Characteristic and Modeling of Hyper-Rayleigh Fading Channel……………… 26 3.1 Small Scale Fading…………………………………………………………... 26 vi 3.1.1 Multipath Fading……………………………………………………….. 28 3.1.2 Doppler Effect………………………………………………………….. 29 3.1.3 Expression of Received Signal……………………………………….. 30 3.2 Typical Small Scale Fading Models…………………………………………32 3.2.1 Rayleigh Fading Model……………………………………………….. 32 3.2.2 Rician Fading Model………………………………………………….. 36 3.3 Hyper-Rayleigh Fading Model………………………………………………40 4 2-D Pilot Aided Channel Estimation in OFDM System………………………… 50 4.1 Procedure of Channel Estimation………………………………………..… 50 4.2 2-D Pilot Arrangement…………………………………………………….…. 52 4.2.1 1-D Pilot Pattern……………………………………………………….. 52 4.2.2 2-D Pilot Pattern……………………………………………………….. 56 4.3 Channel Estimation Algorithms…………………………………………….. 59 5 Simulation Results and Performance Analysis………………………………….. 63 5.1 Simulation Results with Different Modulation Schemes…………………………...63 5.2 Simulation Results under Rayleigh Fading Channels……………………… 65 5.3 Simulation Results under Rician Fading Channels………………………… 67 5.3 Simulation Results under Rician Fading Channels………………………… 70 6 Conclusion and Future Work…………………………………………………..… 76 References…………………………………………………………………………... 78 vii List of Tables 2-1 Simulation specification of OFDM system……………………………………..13 3-1 Fading scenario characterized by specular components……………………….32 3-2 Comparison between four fading models……………………………………….43 5-1 Specification of OFDM system simulation under Rayleigh fading…………….65 viii List of Figures 1-1 Wireless communication environment...…………………………………………. 2 2-1 Frequency spectrum of OFDM system sub-carriers…………………………….. 7 2-2 Model of OFDM system………………………………………………………… 9 ͥ ʞ133 145 175ʟ 2-3 Rate ͧ ͬ convolutional encoder……………………………… 11 ͥ ʞ133 171ʟ 2-4 Rate ͦ ͬ convolutional encoder ………………………..………… 11 2-5 BER performance curves of coded and uncoded OFDM systems……………. 13 2-6 BPSK constellation…………………………………………………………..… 16 2-7 8PSK constellation with Gray mapping………………………………………… 17 2-8 16PSK constellation with Gray mapping………………………………………. 18 2-9 The BER performances of OFDM system with different MPSKs……………. 19 2-10 16QAM constellation with Gray mapping……………………………………. 21 2-11 BER curves of OFDM with M-ary QAMs under AWGN……………………. 22 2-12 Cyclic prefix adding………………………………………………………….. 24 3-1 Large scale fading and small scale fading…………………………………….. 27 3-2 Illustration of Doppler shift in time varying channel…………………………… 30 3-3 Illustration of specular components and diffuse components…………………. 31 3-4 Illustration of Rayleigh fading scenario………………………………………… 33 3-5 PDFs of Rayleigh fading with different variances……………………………… 34 ix 3-6 CDFs of Rayleigh fading with various variances………………………………. 35 3-7 Illustration of Rician fading scenario……………………………………………37 3-8 PDFs of Rician fading with various V…………………………………………. 38 3-9 CDFs of Rician with various V…………………………………………………39 3-10 Illustration of hyper-Rayleigh fading scenario……………………………… 41 3-11 PDFs of TWDP fading with K=3……………………………………………… 44 3-12 PDFs of TWDP with ∆ Ɣ 1…………………………………………………… 45 3-13 Comparison of PDFs among Rayleigh, Rician and TWDP…………………… 45 3-14 Illustration of range of TWDP CDFs………………………………………… 47 3-15 CDFs of the three traces……………………………………………………… 48 4-1 Block type pilot pattern……………………………………………………… 53 4-2 Illustration of block type pilot channel estimation………………………….. 54 4-3 Comb type pilot pattern……………………………………………………….. 55 4-4 Illustration of comb type pilot channel estimation……………………………… 56 4-5 Rectangular type pilot pattern…………………………………………………. 57 4-6 Procedure of rectangular type pilot channel estimation………………………… 58 5-1 Comparison of different modulation schemes under AWGN………………… 64 5-2 Comparison of different modulation schemes with coding…………………… 64 5-3 Block type BER performances with LS and LMMSE under Rayleigh……….. 65 5-4 Comb type BER performances with LS and LMMSE under Rayleigh……….. 66 5-5 Rectangular type performances with LS and LMMSE under Rayleigh……….. 67 5-6 BER performances under Rician fading with various K-factors……………….. 68 x 5-7 Block type BER performances with LS and LMMSE under Rician………….. 69 5-8 Comb type BER performances with LS and LMMSE under Rician………….. 69 5-9 Rectangular type BER performances with LS and LMMSE under Rician…….. 70 5-10 BER performances under TWDP model with various K…………………….. 71 5-11 Block type BER performances under TWDP model with ∆Ɣ 1 , K Ɣ 6..…… 71 5-12 Comb type BER performances under TWDP model with ∆Ɣ 1 , K Ɣ 6……. 72 5-13 Rectangular type BER performances under TWDP model with ∆Ɣ 1 , K Ɣ 6 .72 5-14 Comparison of BER performances under TWDP with K=3………………….. 73 5-15 Comparison of BER performances under TWDP with K=6………………….. 74 5-16 Comparison of BER performances under various fading channels………….. 74 xi Chapter 1 Introduction 1.1 Problem Statement Fading and interference are the major performance degrading factors in wireless/mobile communications. In order to improve and testify the system’s effectiveness to resist fading, modeling and simulation of communication system under fading channel is of great significance in the design of communication system. For different propagation environment, the characteristic of fading channel is diverse and complex. Therefore, design of proper fading model in particular communication circumstance is essential in this regard. Rayleigh fading and Rician fading model are the most commonly used small scale models in wireless communication [1]. However, as wireless sensor networks (WSN) migrate into vastly different applications, conventional Rayleigh and Rician channel model don’t fit in every WSN environment. Recent research [2] [3] shows that some WSN applications where sensor nodes deployed within cavity environment suffer from more severe fading than Rayleigh fading predicted, which is referred to as hyper-Rayleigh fading. Herein, development of a more applicable fading model which