NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS

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1 NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS PERFORMANCE OF THE IEEE a WIRELESS LAN STANDARD OVER FREQUENCY-SELECTIVE, SLOW, RICEAN FADING CHANNELS y Chi-han Kao Septemer 2002 Thesis Advisor: Second Reader: R. Clark Roertson Roerto Cristi Approved for pulic release; distriution is unlimited.

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3 REPORT DOCUMENTATION PAGE Form Approved OMB No Pulic reporting urden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this urden estimate or any other aspect of this collection of information, including suggestions for reducing this urden, to Washington headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA , and to the Office of Management and Budget, Paperwork Reduction Project ( ) Washington DC AGENCY USE ONLY (Leave lank) 2. REPORT DATE Septemer TITLE AND SUBTITLE: Title (Mix case letters) Performance of IEEE a Wireless LAN Standard over Frequency-Selective, Slow, Ricean Fading Channels 6. AUTHOR(S) Kao, Chi-han 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Postgraduate School Monterey, CA SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES) N/A 3. REPORT TYPE AND DATES COVERED Master s Thesis 5. FUNDING NUMBERS 8. PERFORMING ORGANIZATION REPORT NUMBER 10. SPONSORING/MONITORING AGENCY REPORT NUMBER 11. SUPPLEMENTARY NOTES The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. 12a. DISTRIBUTION / AVAILABILITY STATEMENT 12. DISTRIBUTION CODE Approved for pulic release; distriution is unlimited. 13. ABSTRACT (maximum 200 words) With the rapidly growing demand for more reliale and higher data rate wireless communications, the Institute of the Electrical and Electronics Engineers (IEEE) working group approved a standard for 5 GHz and, wireless local area networks (WLAN) in This standard, IEEE a, supports data rates from 6 up to 54 Mps, and uses orthogonal frequency division multiplexing (OFDM) for transmission in indoor wireless environments. This thesis examines the performance of the IEEE a standard for different cominations of su-carrier modulation type and code rate and determines the signal-to-noise ratio required to otain a proaility of it error P of The channel is modeled as a frequency-selective, slow, Ricean fading channel with additive white Gaussian noise (AWGN). Contrary to expectations, for the cominations of su-carrier modulation type and code rate utilized y the IEEE a standard, some of the higher data rate cominations outperform some of the lower data rate cominations. On the other hand, the results also show significant coding gain when applying convolutional coding with Viteri decoding, and hence highlight the importance of forward error correction (FEC) coding to the performance of wireless communications systems. 14. SUBJECT TERMS IEEE a standard, WLAN, OFDM, BPSK, QPSK, QAM, proaility of it error, frequencyselective fading, flat fading, fast fading, slow fading, Ricean fading, Rayleigh fading, Viteri algorithm, convolutional code, hard-decision decoding, soft-decision decoding, coding gain. 15. NUMBER OF PAGES PRICE CODE 17. SECURITY CLASSIFICATION OF REPORT Unclassified 18. SECURITY CLASSIFICATION OF THIS PAGE Unclassified 19. SECURITY CLASSIFICATION OF ABSTRACT Unclassified 20. LIMITATION OF ABSTRACT NSN Standard Form 298 (Rev. 2-89) Prescried y ANSI Std UL i

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5 Approved for pulic release; distriution is unlimited PERFORMANCE OF THE IEEE a WIRELESS LAN STANDARD OVER FREQUENCY-SELECTIVE, SLOW, RICEAN FADING CHANNELS Chi-han Kao Lieutenant Commander, Taiwan Navy B.S., Chinese Naval Academy, 1989 Sumitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL Septemer 2002 Author: Chi-han Kao Approved y: R. Clark Roertson Thesis Advisor Roerto Cristi Second Reader John Powers Chairman, Department of Electrical and Computer Engineering iii

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7 ABSTRACT With the rapidly growing demand for more reliale and higher data rate wireless communications, the Institute of the Electrical and Electronics Engineers (IEEE) working group approved a standard for 5-GHz and, wireless local area networks (WLAN) in This standard, IEEE a, supports data rates from 6 up to 54 Mps and uses orthogonal frequency division multiplexing (OFDM) for transmission in indoor wireless environments. This thesis examines the performance of the IEEE a standard for different cominations of su-carrier modulation type and code rate and determines the signal-to-noise ratio required to otain a proaility of it error P of The channel is modeled as a frequency-selective, slow, Ricean fading channel with additive white Gaussian noise (AWGN). Contrary to expectations, for the cominations of su-carrier modulation type and code rate utilized y the IEEE a standard, some of the higher data rate cominations outperform some of the lower data rate cominations. On the other hand, the results also show significant coding gain when applying convolutional coding with Viteri decoding, and hence highlight the importance of forward error correction (FEC) coding to the performance of wireless communications systems. v

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9 TABLE OF CONTENTS I. INTRODUCTION...1 A. OBJECTIVE...1 B. RELATED RESEARCH...2 C. THESIS ORGANIZATION...2 II. MULTIPATH FADING CHANNELS...5 A. FADING CHANNELS...5 B. SMALL-SCALE FADING Time-Spreading Mechanism Due To Multipath...6 a. Frequency-Selective Fading...8. Flat Fading Time-Variant Mechanism Due To Motion...9 a. Fast Fading Slow Fading Summary of Small Scale Fading...11 C. DISTRIBUTION OF PATH AMPLITUDES Rayleigh Fading Ricean Fading...12 D. SUMMARY OF MULTIPATH FADING CHANNELS...13 III. OFDM BASED IEEE a STANDARD...15 A. IEEE a BACKGROUND...15 C. OFDM FUNDAMENTALS Single/Multi-Carrier Modulation FDM/OFDM Orthogonality...18 D. OFDM BASED a PARAMETERS Guard Interval OFDM Symol Duration and Su-Carrier Spacing Numer of Su-Carriers Error Correcting Code and Coding Rate...20 E. OFDM SIGNAL PROCESSING...21 IV. PERFORMANCE WITHOUT FEC CODING...25 A. PERFORMANCE IN AWGN BPSK/QPSK Modulation QAM Modulation with a Square Constellation...26 B. PERFORMANCE IN RICEAN FADING CHANNELS BPSK/QPSK Modulation Square QAM Modulation...35 C. UNCODED OFDM SYSTEM PERFORMANCE BPSK/QPSK Modulated OFDM QAM and 64QAM Modulated OFDM...43 vii

10 D. SUMMARY OF UNCODED OFDM PERFORMANCE...45 V. PERFORMANCE ANALYSIS WITH FEC CODING...47 A. ERROR CONTROL CODING Forward Error Correcting (FEC) Coding...47 a. Convolutional Encoding Viteri Decoding Implementation of FEC Coding Coding Gain...51 B. HARD DECISION DECODING BPSK/QPSK with HDD (6,9,12, and 18 Mps) QAM with HDD (24 and 36 Mps) QAM with HDD (48 and 54 Mps) HDD Summary...78 C. SOFT DECISION DECODING BPSK/QPSK with SDD (6 and 12 Mps) BPSK/QPSK with SDD (9 and 18 Mps) SDD summary...89 VI. CONCLUSION...91 A. FINDINGS...91 B. RECOMMENDATIONS FOR FURTHER RESEARCH...92 C. CLOSING COMMENTS...92 LIST OF REFERENCES...93 INITIAL DISTRIBUTION LIST...95 viii

11 LIST OF FIGURES Figure 1. Large and small scale fading [From Ref. 6]...5 Figure 2. Multipath Intensity Profile [After Ref. 7]...7 Figure 3. Typical frequency-selective and flat fading [After Ref. 7]...8 Figure 4. Types of the small scale fading [After Ref. 8]...11 Figure 5. Rayleigh and Ricean proaility density function [After Ref.10]...13 Figure 6. Su-channel overlapping technique for FDM and OFDM [From Ref. 4]...17 Figure 7. OFDM orthogonal spectrum with 4 su-carriers [From Ref. 11]...18 Figure 8. Convolutional Encoder with constraint length v = 7 [From Ref. 5]...20 Figure 9. OFDM PHY transceiver lock diagram [From Ref. 5]...21 Figure 10. Constellation for BPSK, QPSK, 16QAM, and 64QAM [From Ref. 5]...22 Figure 11. Effect of no cyclic extension in the guard interval [From Ref.4]...23 Figure 12. Effect of adding cyclic extension in the guard interval [From Ref. 4]...24 Figure 13. MQAM signal constellation [After Ref. 13]...26 Figure 14. Performance of BPSK/QPSK, 16QAM and 64QAM in AWGN...28 Figure 15. BPSK/QPSK performance in Ricean fading channels...33 Figure 16. BPSK/QPSK performance in Rayleigh fading channels...34 Figure 17. BPSK/QPSK performance in Ricean fading channels with 0 ζ Figure QAM performance in Ricean fading channels...38 Figure QAM performance in Ricean fading channels with 0 ζ Figure QAM performance in Ricean fading channels...39 Figure QAM performance in Ricean fading channels with 0 ζ Figure 22. BPSK/QPSK modulated OFDM in composite Rayleigh/Ricean fading channels...42 Figure QAM modulated OFDM in composite Rayleigh/Ricean fading channels..43 Figure QAM modulated OFDM in composite Rayleigh/Ricean fading channels..44 Figure 25. Coding gain of BPSK/QPSK in AWGN...51 Figure 26. Performance of BPSK/QPSK with HDD ( r = 12) over Ricean Fading...55 Figure 27. HDD ( r = 12) versus uncoded BPSK/QPSK Performance over Ricean Fading...56 Figure 28. HDD ( r = 12) versus uncoded BPSK/QPSK modulated OFDM (6 and 12 Mps) performance over a pure Rayleigh fading channel...57 Figure 29. HDD ( r = 12) versus uncoded BPSK/QPSK modulated OFDM (6 and 12 Mps) performance over a composite Rayleigh/Ricean fading channel...58 Figure 30. Performance of BPSK/QPSK with HDD ( r = 34) over Ricean Fading...59 Figure 31. Uncoded versus HDD ( r = 34) BPSK/QPSK Performance over Ricean Fading...60 Figure 32. HDD ( r = 34) versus uncoded BPSK/QPSK modulated OFDM (9 and 18 Mps) performance over a pure Rayleigh fading channel...61 ix

12 Figure 33. HDD ( r = 34) versus uncoded BPSK/QPSK modulated OFDM (9 and 18 Mps) performance over a composite Rayleigh/Ricean fading channel...62 Figure 34. Performance of 16QAM with HDD ( r = 12) over Ricean Fading...64 Figure 35. HDD ( r = 12) versus uncoded 16QAM Performance over Ricean Fading...65 Figure 36. HDD ( r = 12) versus uncoded 16QAM modulated OFDM (24 Mps) performance over a pure Rayleigh fading channel...66 Figure 37. HDD ( r = 12) versus uncoded 16QAM modulated OFDM (24 Mps) performance over a composite Rayleigh/Ricean fading channel...67 Figure 38. Performance of 16QAM with HDD ( r = 34) over Ricean Fading...68 Figure 39. Uncoded versus HDD ( r = 34) 16QAM Performance over Ricean Fading..69 Figure 40. HDD ( r = 34) versus uncoded 16QAM modulated OFDM (36 Mps) performance over a pure Rayleigh fading channel...70 Figure 41. HDD ( r = 34) versus uncoded 16QAM modulated OFDM (36 Mps) performance over a composite Rayleigh/Ricean fading channel...70 Figure 42. Performance of 64QAM with HDD ( r = 23) over Ricean Fading...72 Figure 43. Uncoded versus HDD ( r = 23) 64QAM Performance over Ricean Fading..72 Figure 44. HDD ( r = 23) versus uncoded 64QAM modulated OFDM (48 Mps) performance over a pure Rayleigh fading channel...73 Figure 45. HDD ( r = 23) versus uncoded 64QAM modulated OFDM (48 Mps) performance over a composite Rayleigh/Ricean fading channel...74 Figure 46. Performance of 64QAM with HDD ( r = 34) over Ricean Fading...75 Figure 47. Uncoded versus HDD ( r = 34) 64QAM Performance over Ricean Fading..76 Figure 48. HDD ( r = 34) versus uncoded 64QAM modulated OFDM (54 Mps) performance over a pure Rayleigh fading channel...76 Figure 49. HDD ( r = 34) versus uncoded 64QAM modulated OFDM (54 Mps) performance over a composite Rayleigh/Ricean fading channel...77 Figure 50. Uncoded, HDD, and SDD BPSK/QPSK performances with AWGN...81 Figure 51. Performance of BPSK/QPSK with SDD ( r = 12) over Ricean Fading...82 Figure 52. SDD versus HDD ( r = 12) BPSK/QPSK Performance over Ricean Fading...83 Figure 53. SDD versus HDD ( r = 12) BPSK/QPSK modulated OFDM (6 and 12 Mps) performance over a composite Rayleigh/Ricean fading channel...84 Figure 54. SDD, HDD, and uncoded BPSK/QPSK modulated OFDM performance over a composite Rayleigh/Ricean fading channel...85 Figure 55. Performance of BPSK/QPSK with SDD ( r = 34) over Ricean Fading...86 Figure 56. SDD versus HDD ( r = 34) BPSK/QPSK Performance over Ricean Fading...87 Figure 57. SDD versus HDD ( r = 34) BPSK/QPSK modulated OFDM (9 and 18 Mps) performance over a composite Rayleigh/Ricean fading channel...87 x

13 Figure 58. SDD, HDD, and uncoded BPSK/QPSK modulated OFDM performance over a composite Rayleigh/Ricean fading channel...89 xi

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15 LIST OF TABLES Tale 1. OFDM rate-dependent parameters [From Ref. 5]...15 Tale 2. Major Parameters of the a PHY [From Ref. 5]...19 Tale 3. Uncoded BPSK/QPSK modulated OFDM performance statistics for γ at 5 P = Tale 4. Uncoded 16QAM modulated OFDM performance statistics...44 Tale 5. Uncoded 64QAM modulated OFDM performance statistics...45 Tale 6. Overall uncoded OFDM system performance statistics...45 Tale 7. Weight Structure of the Convolutional Codes [After Ref. 17]...53 Tale 8. HDD ( r = 12) BPSK/QPSK modulated OFDM (6 and 12 Mps) 5 performance statistics for γ at = Tale 9. HDD ( r = 34) BPSK/QPSK modulated OFDM (9 and 18 Mps) 5 performance statistics for γ at P = Tale 10. HDD ( r = 12) 16QAM modulated OFDM (24 Mps) performance 5 statistics for γ at P = Tale 11. HDD ( r = 34) 16QAM modulated OFDM (36 Mps) performance 5 statistics for γ at P = Tale 12. HDD ( r = 23) 64QAM modulated OFDM (48 Mps) performance 5 statistics for γ at P = Tale 13. HDD ( r = 34) 64QAM modulated OFDM (54 Mps) performance 5 statistics for γ at P = Tale 14. Received average energy per it-to-noise power spectral density ratio γ 5 required for P = 10 in AWGN with frequency-selective, slow Rayleigh fading and composite Rayleigh/Ricean fading with HDD Tale 15. SDD ( r = 12) BPSK/QPSK modulated OFDM (6 and 12 Mps) 5 performance statistics for γ at P = Tale 16. SDD ( r = 34) BPSK/QPSK modulated OFDM (9 and 18 Mps) 5 performance statistics for γ at = P P xiii

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17 ACKNOWLEDGMENTS First and foremost I am grateful to my eautiful wife, Tanyi, and wonderful daughter, Jenny, for the sacrifices they made in support of my completing this thesis. Secondly I would like to thank my thesis advisors, Dr. Clark Roertson and Dr. Roerto Cristi, for their endless hours of help, suggestions, ideas and advise during the development of this thesis. Thanks go out as well to LT Gell Tiger L. Pittman III, USN, and LT Patrick A. Count, USN, for introducing me OFDM. Finally in appreciation of CDR Jim Hill, previous Code 35 Curriculum Officer and Eva Anderson, Code 35 Education Specialist, and LCDR Peter Duke, my est friend, for their assistance through my tour at the Naval Postgraduate School. xv

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19 EXECUTIVE SUMMARY The ojective of this thesis is to analyze the performance of the IEEE a WLAN standard over frequency-selective, slow, Ricean fading channels. Prior to the analysis, we discuss the issues of multipath fading and introduce four different types of small-scale fading: frequency-selective fading, flat fading, fast fading, and slow fading. We then introduce the physical layers of the IEEE a WLAN standard, the fundamentals of OFDM, and the reasons that IEEE a adopted OFDM for transmission. In order to perform the analysis, we derived analytic expressions for all sucarrier modulations used in IEEE a: BPSK, QPSK, 16QAM, and 64QAM. Actually, only two expressions are required, one for BPSK and one for square QAM, since QPSK and BPSK have the same proaility of it error and oth 16QAM and 64QAM are square QAM. After the derivation, we show that two analytic expressions yield accurate results when compared to the exact results for oth Rayleigh and Ricean fading channels. Further, we assume the channel coherence andwidth is such that we have 48 independent su-carriers for large office uildings and 24 independent sucarriers for small office uildings. In turn, we consider the performance of IEEE a over oth a pure Rayleigh fading channel and over a composite Rayleigh/Ricean fading with either 48 or 24 independent su-carriers. Next, we evaluate the performance of uncoded IEEE a over Ricean fading channels so that we can otain the coding gain later y comparing these results to those with FEC coding. As expected, the performance of uncoded BPSK/QPSK modulated OFDM is etter than uncoded 16QAM and 64QAM; however, even BPSK/QPSK does not yield performance acceptale for wireless communications. After the evaluation of uncoded IEEE a, we examine the performance of IEEE a with FEC coding, where convolutional encoding and Viteri decoding are applied. The effect of Viteri hard decision decoding (HDD) is analyzed for BPSK, QPSK, 16QAM, and 64QAM, while the effect of Viteri soft decision decoding (SDD) is analyzed for BPSK and QPSK only due to the difficulty of analyzing the proaility of it error for SDD of a inary code transmitted with non-inary modulation. xvii

20 For the performance of IEEE a with HDD, as expected, the signal-to-noise ratios required for a pure Rayleigh fading channel are more than for a composite Rayleigh/Ricean fading channel, in the range of four to seven db for 5 P = 10. Also as expected, for a specific modulation type, regardless of the channel conditions considered, as the code rate increases, the signal-to-noise ratio required to achieve a fixed proaility of it error increases. Moreover, the coding gains for all su-channel modulations range from 21 to 30 db. Contrary to expectations, however, the signal-to-noise ratio required to achieve a specific P does not monotonically decrease with decreasing it rate. This phenomenon is oserved whether the channel is modeled as a pure Rayleigh fading channel or as a composite Rayleigh/Ricean fading channel. For the performance of IEEE a with SDD for BPSK/QPSK with code rate r = 12, SDD improves performance y aout 2.5 db over HDD in AWGN and y aout 3.3 db over a composite Rayleigh/Ricean fading channel. For BPSK/QPSK with code rate r = 34, SDD improves performance y aout 5.5 db over HDD in a composite Rayleigh/Ricean fading channel. From an examination of the performance difference etween 48 and 24 independent su-carriers, we conclude that the performance difference decreases as more powerful coding technique are used. xviii

21 I. INTRODUCTION A. OBJECTIVE With the rapidly growing demand for more reliale and higher data rates in wireless communications, the IEEE working group approved a standard for a 5 GHz and wireless local area network (WLAN) in This standard, IEEE a, supports a variale it rate from 6 up to 54 Mps and selects orthogonal frequency division multiplexing (OFDM) for transmission in indoor wireless environments. With OFDM as specified y the IEEE a standard, the data signal is divided among 48 separate su-carriers. For each of the su-carriers, OFDM uses either phase-shift keying (BPSK/QPSK) or M-ary quadrature amplitude modulation (16 and 64QAM) to modulate the digital signal depending on the selected data rate of transmission. Higher data rates are achieved y comining a high-order su-carrier modulation with a high rate convolutional code, while lower data rates are otained y lowering either the su-carrier modulation order or the code rate or oth. Logically, the expectation is that lower data rates result in a continually more roust wireless communication system; that is, the target performance level for the system can e maintained as the received signal-to-noise ratio goes down simply y reducing the it rate (since oth lower-order su-carrier modulation and lower code rates are more roust). In this thesis, this assumption was investigated for the IEEE a WLAN standard. The channel was modeled as a frequency-selective, slow, Ricean fading channel with additive white Gaussian noise (AWGN); although, each su-channel was modeled as flat due to OFDM. Another ojective of this thesis was to investigate performance when applying forward error correction (FEC) channel coding using oth hard decision decoding (HDD) and soft decision decoding (SDD) in conjunction with the Viteri algorithm. However, due to the difficulty of analyzing the proaility of it error for SDD of a inary code transmitted with non-inary modulation, SDD with MQAM modulation will not e considered in this thesis. 1

22 B. RELATED RESEARCH After the European Telecommunication Standards Institute Broadand Radio Access Networks (ETSI BRAN) in Europe and the Multimedia Moile Access Communications (MMAC) in Japan followed the IEEE decision, OFDM ecame a single worldwide physical layer standard for WLAN in the 5-GHz and. Therefore, many studies focus on the performance of OFDM for different cominations of fading channels, such as frequency-nonselective, fast, Rayleigh and Ricean fading channels [1] and [2], frequency-selective, Rayleigh fading channels [3], and frequency-selective, slow, Nakagami channels [4]. Unlike the aove referenced work, this thesis investigates the performance of the IEEE a standard over frequency-selective, slow, Ricean fading channels. In this thesis, we derive analytic expressions for the proaility of it error for BPSK/QPSK, 16QAM and 64QAM in Ricean fading channels. To the est knowledge of the author, these results have not een previously pulished. Further, in addition to 48 independent su-carriers, this thesis will also examine performance with 24 independent su-carriers. The reason for investigating 24 independent su-carriers will e explained in Chapter IV. C. THESIS ORGANIZATION After the introduction, the thesis is organized into five remaining chapters. The most important issue in wireless communications, multipath fading (since it determines system performance and the data rate for transmission) is discussed in Chapter II. In this thesis, even though the channel is modeled as a frequency-selective, slow, Ricean fading channel, a thorough discussion of small scale fading is still given ecause a complete understanding of this phenomenon is essential. The IEEE a standard for WLAN Medium Access Control (MAC) and Physical Layer (PHY) specifications [5] is introduced in Chapter III, and why IEEE selected OFDM is explained. Moreover, some important OFDM concepts such as orthogonality and multicarrier techniques and the major OFDM parameters, as well as OFDM signal processing are also covered in Chapter III. The performance of OFDM without FEC coding in AWGN and Ricean fading channels is examined in Chapter IV. The analysis egins with the su-carrier modulation 2

23 schemes utilized in IEEE a standard, which are BPSK, QPSK, 16QAM, and 64QAM and then advances to composite OFDM modulation. Analytic expressions are derived for the proaility of it error for BPSK/QPSK and square MQAM in this chapter. OFDM performance with FEC coding and Viteri hard decision decoding (HDD) with BPSK, QPSK, 16QAM, and 64QAM is examined in Chapter V, ut Viteri soft decision decoding (SDD) is only considered with BPSK and QPSK. The results will e compared to those of Chapter IV in order to find the coding gain. Finally, this thesis concludes with Chapter VI and a rief review of the results otained in the previous chapters, followed y recommendations for further research. 3

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25 II. MULTIPATH FADING CHANNELS Unlike satellite communications, many wireless communications channels do not have a line-of-sight (LOS) transmission path. Instead, a signal can travel from transmitter to receiver over many reflective paths. This phenomenon is referred to as multipath propagation. Due to multipath, a signal will arrive at receiver multiple times with different amplitudes, phases, and arrival times, giving rise to the terminology multipath fading. This chapter egins with a discussion of the two main types of fading effects and their characteristics and then focuses on the small-scale fading. The last part of this chapter introduces Rayleigh and Ricean fading. A. FADING CHANNELS On wireless communications channels, the effect of multipath fading on the received signal amplitude is roken into two components; large-scale fading and smallscale fading, as shown in Figure 1. Figure 1. Large and small scale fading [From Ref. 6] Large-scale fading represents the average received signal power attenuation or the path loss over large transmitter-to-receiver (T-R) separation distances, usually hundreds or 5

26 thousands of meters. Small scale fading refers to the dramatic fluctuation in signal amplitude over very small changes in T-R distance (as small as a half-wavelength) or over a short duration (in the range of fractions of a second to several seconds). All indoor wireless communication system will experience small-scale fading. This thesis will focus on the effects of small-scale fading since IEEE a is intended for WLAN transmission in indoor environment. B. SMALL-SCALE FADING There are two mechanisms that contriute to small-scale fading: time spreading of the signal due to multipath and time variance of the channel due to motion. The time spreading of the signal leads to either frequency-selective fading or flat fading, while the time variance of the channel leads to either fast fading or slow fading. 1. Time-Spreading Mechanism Due To Multipath As mentioned aove, time dispersion will cause the transmitted signal to undergo either frequency-selective fading or flat fading. Two related parameters that characterize the time spreading mechanism need to e addressed, the coherence andwidth and maximum excess delay. Coherence andwidth B c is a statistical measure of the range of frequencies over which the channel can e considered non-distorting (equal gain and linear phase). In other words, the coherence andwidth represents the range of frequencies over which signal s frequency components are strongly amplitude correlated. It is shown in [7] that B c and T m are reciprocally related y B c 1 (2.1) T m where T m is the maximum excess delay, or the time difference of arrival etween the first and last received signal components. The maximum excess delay is defined in terms of 6

27 the multipath intensity profile (MIP), illustrated in Figure 2, where the average received power S (τ) varies as a function of time delay τ. S(τ) Figure 2. Multipath Intensity Profile [After Ref. 7] However, T m is not generally the est parameter to represent a channel, ecause the MIP can change significantly for channels with the same value of T m. A more useful parameter is the root-mean-square (rms) delay spread [7], defined σ τ τ 2 2 τ = (2.2) where τ is the mean excess delay and 2 τ is the second moment of τ. Note that a fixed relationship etween B c and σ τ does not exist. If B c is defined as the andwidth over which the frequency correlation function is greater than 0.5, then an empirical rule that is often used is [8] 1 Bc. (2.3) 5σ τ If B c is defined as the andwidth over which the frequency correlation function is greater than 0.9, then an empirical rule that is often used is [8] 1 Bc. (2.4) 50σ τ 7

28 Note that the reported values of σ τ vary depending on the size and type of the uilding, with or without a clear LOS path. For small through large office uildings, the reported values of σ τ range from 30 to 120 ns [9]. a. Frequency-Selective Fading If the coherence andwidth B c is smaller than the andwidth of the transmitted signal W, then the received signal will undergo frequency-selective fading; that is, the channel is frequency-selective if Bc < W (2.5) which implies T m > T (2.6) s since Bc 1 Tm and W 1 T s, where 1 T s = R s is the symol rate. When frequencyselective fading occurs, the received signal is distorted since different spectral components of the signal are affected differently. The typical frequency-selective fading case is illustrated in Figure 3(a). B c (a) Frequency-selective fading (B c < W) B c () Flat fading (B c > W) Figure 3. Typical frequency-selective and flat fading [After Ref. 7] 8

29 . Flat Fading If the channel coherence andwidth B c, over a andwidth that is greater than the andwidth of the transmitted signal, then the received signal will undergo flat fading; that is, the channel is flat if Bc > W (2.7) or equivalently The typical flat fading case is illustrated in Figure 3(). T m < T. (2.8) s 2. Time-Variant Mechanism Due To Motion Due to the motion of either the transmitter or the receiver, the time variance causes the transmitted signal to undergo either fast fading or slow fading. There are two parameters used to descrie the time-variant nature of the channel: Doppler spread and coherence time. The Doppler spread B d is defined as the range of frequencies over which the received Doppler spectrum is essentially non-zero. When a pure sinusoidal tone of frequency f c is transmitted over a multipath channel, the received signal spectrum will have components in the range fc fd to fc + fd, where f d is the Doppler shift given y [8] v f d = sin θ (2.9) λ where v is the relative velocity of the transmitter with respect to the receiver, λ is the signal wavelength, and θ is the spatial angle etween the direction of motion of the receiver and the direction of arrival of the signal. The value of f d depends on whether the transmitter and receiver are moving toward or away from each other. 9

30 Coherence time T c is a statistical measure of the time duration over which the channel is essentially invariant. In other words, coherence time is the time duration over which two received signals have a strong potential for amplitude correlation. Note that the coherence time and the Doppler spread are reciprocally related as [8] T c 1. (2.10) B d a. Fast Fading Fast fading descries a condition where the coherence time of the channel is less than the transmitted symol period; that is, or equivalently T c Bd < T (2.11) s > W (2.12) since Tc 1 Bd and W 1 T s, where 1 T s = R s is the symol rate. In a fast fading channel, the channel impulse response changes rapidly during the time each symol is transmitted, distorting the shape of the aseand signal. In practice, fast fading only occurs for very low data rate transmission.. Slow Fading Opposite to fast fading, slow fading descries a condition where the coherence time of the channel is greater than the transmitted symol period. In other words, the channel changes at a rate much slower than the aseand signal rate; that is, T c > T (2.13) s or equivalently Bd < W. (2.14) 10

31 3. Summary of Small Scale Fading From Equations (2.5) through (2.8) and Equations (2.11) through (2.14), four types of the small scale fading can e characterized as shown in Figure 4, where B c is coherence andwidth, W is aseand signal andwidth, T m is the maximum excess delay, T s is symol time, T c is the coherence time, and B d is the Doppler spread. Small-Scale Fading (Based on multipath delay spread) Flat Fading Bc > W Tm < Ts Frequency Selective Fading Bc < W Tm > Ts Small-Scale Fading (Based on Doppler spread) Fast Fading Tc < Ts Bd > W Slow Fading Tc > Ts Bd < W Figure 4. Types of the small scale fading [After Ref. 8] C. DISTRIBUTION OF PATH AMPLITUDES In a multipath environment, the received signal amplitude is modeled as a random variale. Typical models are the Rayleigh, Ricean, and Nakagami-m distriutions. In this thesis, two widely used models for fading channels, the Rayleigh and Ricean fading channel model, are assumed. 11

32 1. Rayleigh Fading A well-accepted model for small-scale rapid amplitude fluctuations is the Rayleigh model, which is used when there is no line-of-sight (LOS) etween transmitter and receiver and all of the received signal power is due to multipath. For Rayleigh fading channels, the received amplitude is modeled as a Rayleigh random variale with the proaility density function (pdf) [10] 2 a c a c fa ( a ) exp, 0 c c = a 2 2 c σ 2σ (2.15) where 2 2σ represents the received diffuse, or non-los, signal power. 2. Ricean Fading The Ricean model is used when there is a LOS etween transmitter and receiver ut a sustantial portion of the received signal power is also due to multipath. Note that when there is a LOS ut none of the received signal power is due to multipath, the channel is non-fading. For Ricean fading channels, the received amplitude is modeled as a Ricean random variale with pdf [10] ( a 2 α 2 c ) a + c α ac fa ( a ) exp I 2 2 0, 0 c c = a 2 c σ 2σ σ where I () is the zeroth-order modified Bessel function of the first kind, 0 received direct, or LOS signal power, and received signal power for a Ricean fading channel is () 2 α is the (2.16) 2 2σ is the non-los signal power. The average S t = a c = α + 2σ. (2.17) Note that when α 0, the Ricean proaility density function for a c reduces to the Rayleigh proaility density function since I ( ) power reduces to 0 0 = 1, and the average received signal 2 2σ. The Rayleigh and Ricean proaility density function are illustrated in Figure 5, where the Ricean low SNR curve is plotted with α = 2 and 2 σ = 1, 12

33 Ricean medium SNR curve is plotted with α = 4 and is plotted with α = 8 and 2 σ = 1. 2 σ = 1, and Ricean high SNR curve 0.6 Rayleigh Ricean low SNR Ricean medium SNR Ricean high SNR f(a) a Figure 5. Rayleigh and Ricean proaility density function [After Ref.10] D. SUMMARY OF MULTIPATH FADING CHANNELS In this chapter, we discussed multipath fading and introduced different types of small scale fading channels: frequency-selective fading, flat fading, fast fading, and slow fading. Multipath fading can cause inter-symol interference (ISI), where the received signal consists of multiple versions of the transmitted waveforms. There are several ways to minimize ISI, and OFDM is one of the antidotes. In the next chapter, we explain why OFDM is roust over frequency-selective fading channels. 13

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35 III. OFDM BASED IEEE a STANDARD A. IEEE a BACKGROUND IEEE a was adopted as a WLAN standard in Septemer Misleading y its name, many readers naturally think of a as the first IEEE PHY standard for WLANs. Actually, the first IEEE standard adopted for WLANs was approved in June 1997 and specifies the medium access control (MAC) and three physical layers (PHY): frequency hopping spread spectrum ( FHSS), direct sequence spread spectrum ( DSSS) and diffuse infrared ( IR). The IR standard operates at aseand and the FHSS and DSSS standards operate in the 2.4 GHz and. In terms of data rates, DSSS originally supported oth 1 Mps and 2 Mps, while the other two support 1 Mps with 2 Mps optional. With the growing demand for higher it rates, a high-data-rate DSSS proposal, , was selected for standardization in July 1998, and extends the data rate to 11 Mps. While developing , a was also eing developed. The development was motivated y the U.S. Federal Communications Commission (FCC), which released 300 MHz of spectrum in the 5.2 GHz and in January The rate-dependent parameters of a, which utilizes BPSK, QPSK, 16-QAM, and 64-QAM as su-carrier modulation schemes in comination with rate1 2, 23, and 34 convolutional codes to otain a variale data it rate from 6 up to 54 Mps are listed in Tale 1. Tale 1. OFDM rate-dependent parameters [From Ref. 5] 15

36 B. WHY OFDM? Recall from Chapter II that a channel is referred to as frequency-selective if the coherence andwidth B c is less than the signal andwidth W. When this happens, the received signals are distorted and overlapped in time causing ISI and degrade system performance. There are several ways to minimize ISI. One is to reduce the symol rate, ut then the data rate is also reduced. Another technique is to utilize equalizers, ut equalization is processor intensive. Finally, the effects of a frequency-selective channel can e mitigated y OFDM, and OFDM has none of the drawacks of the previous techniques. OFDM is a special case of multi-carrier transmission, where a high-it-rate data stream is split into a numer of low-it-rate data streams that are transmitted simultaneously over a numer of su-carriers. For the IEEE a standard, there are 48 data su-carriers; hence, the symol rate for one su-carrier is R = R 48. Thus, the andwidth for each su-carrier is reduced y a factor of 48 as compared with the and-width the signal requires when only a single carrier frequency is used. As a result, B W = W C SC 48, and the channel for each su-carrier will e flat, or frequencynonselective, which reduces ISI and avoids multipath in frequency-selective channels. SC S C. OFDM FUNDAMENTALS In addition to its OFDM s aility to avoid ISI while achieving high data rates, OFDM has other enefits, such as roustness to RF interference and high spectral efficiency. In what follows, we discuss several fundamental OFDM concepts. 1. Single/Multi-Carrier Modulation Single carrier modulation uses a single carrier frequency to transmit all data symols sequentially. Compared to multi-carrier modulation, single-carrier modulation has several advantages. For example, it avoids excessive peak-to-average power ratio prolems, and it is much less sensitive to frequency offsets and phase noise. The main disadvantage of single carrier modulation is that it is susceptile to multipath fading or 16

37 interference ecause it uses only one carrier frequency. If the multipath distortion or interference causes the frequency response to have a null at the carrier frequency, then the entire link experiences severe performance degradation. Unlike single-carrier modulation, multi-carrier modulation uses multiple sucarriers to transmit data in parallel. For example, OFDM-ased IEEE a utilizes 48 su-carries to transmit data. Given the same multipath distortion or interference as that of single-carrier modulation, only a small portion of the su-carriers in the OFDM system is distorted, not the entire system. Therefore, the use of the multi-carrier OFDM can reduce RF interference and multipath distortion. 2. FDM/OFDM Multi-carrier transmission is nothing more than a parallel data system. For other parallel data systems, such as frequency-division multiplexing (FDM) techniques, each su-carrier is modulated with spectrally separate symols to avoid inter-carrier interference (ICI), or cross-talk, from adjacent su-carriers; however, this complete separation in spectrum leads to waste of the availale andwidth. Unlike FDM, OFDM uses orthogonal overlapped su-channels. The difference etween FDM and OFDM is illustrated in Figure 6. As shown in Figure 6, orthogonal OFDM saves almost 50 percent of the availale andwidth compared to FDM. Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5 Guard Bands Bandwidth f Ch. 1 Ch. 5 andwidth savings f Figure 6. Su-channel overlapping technique for FDM and OFDM [From Ref. 4] 17

38 3. Orthogonality The reason that su-channels can overlap with OFDM without causing ICI is that the individual cu-carriers are orthogonal. In mathematics, two vectors perpendicular to each other are orthogonal and their dot product is equal to zero. In communications, orthogonality means two signals are uncorrelated, or independent, over one symol duration. In OFDM, orthogonality prevents the su-channel demodulators from seeing frequencies other than their own, which is achieved y precisely selecting the su-carrier spacing such that each su-carrier is located on all the other su-carriers spectra zero crossing points. When sampling at the su-carrier frequencies, the su-carriers will not interfere each other (as shown in Figure 7). Note that for etter oservation, the orthogonal spectrum of an OFDM signal with four su-carriers only is shown in Figure 7. Figure 7. OFDM orthogonal spectrum with 4 su-carriers [From Ref. 11] D. OFDM BASED a PARAMETERS So far, we have explained why OFDM has the aility to comat multipath fading while achieving high data rates. We have also discussed several important concepts that 18

39 make OFDM roust in RF interference and maintain high spectral efficiency. In this section, we investigate the details of the OFDM ased IEEE a standard. The major parameters of the OFDM PHY are listed in Tale 2. Tale 2. Major Parameters of the a PHY [From Ref. 5] 1. Guard Interval The most important parameter in a PHY is the guard interval T GI, ecause it determines not only the choice of the other parameters, ut also the effectiveness of comating ISI. In order to eliminate ISI, the T GI should e much larger than the expected multipath delay spread. From [9], the reported values of rms delay spread can e up to 200 ns for a large office uilding and up to 300 ns for various factory environments. As we can see in Tale 2, the guard interval T GI for each OFDM symol is 0.8 µs, which is much greater than 300 ns. 2. OFDM Symol Duration and Su-Carrier Spacing As mentioned aove, the T GI should e chosen much larger than the expected multipath delay spread in order to comat ISI; however, the T GI cannot e chosen too large, either. When T GI increases, the OFDM effective symol duration decreases and 19

40 data rates drop. To limit the relative amount of power and time spent on the guard interval, the total symol duration chosen in a is 4 microseconds. This in turn determines the su-carrier spacing of khz, which is the inverse of the symol duration minus the guard time. 3. Numer of Su-Carriers In addition to the 48 data su-carriers, each OFDM symol has an additional four pilot su-carriers, which provide a reference to minimize frequency and phase shifts of the signal during transmission. Therefore, there are a total of 52 su-carriers for each OFDM symol. 4. Error Correcting Code and Coding Rate To correct for su-carriers in deep fades, a applies FEC coding across the su-carriers with variale code rates. Convolutional coding is used with industry standard rate 12, constraint length 7 encoded with generator polynomials (133, 171). The convolutional encoder is shown in Figure 8. Higher coding rates of 23 and 34 are otained y puncturing the rate 12 code. The rate 12 code is used with BPSK, QPSK, and 16-QAM to give rates of 6, 12, and 24 Mps, respectively. The rate 23 code is used with 64-QAM only to otain a data rate of 48 Mps. The rate 34 code is used with BPSK, QPSK, 16-QAM, and 64-QAM to give rates of 9, 18, 36, and 54 Mps, respectively. Output Input 20 Output Figure 8. Convolutional Encoder with constraint length v = 7 [From Ref. 5]

41 E. OFDM SIGNAL PROCESSING This section gives a general description of how the IEEE a PHY is implemented. The IEEE a PHY transmitter and receiver lock diagram is shown in Figure 9 [5]. Figure 9. OFDM PHY transceiver lock diagram [From Ref. 5] In the transmitter, the serial inary input data are encoded y a rate 12 constraint length 7, convolutional encoder. The code rate can e increased to 23 or 34 y puncturing the coded output its. The coded output its are next interleaved and mapped. Interleaving is a technique for handling urst errors. The interleaver randomizes urst errors and the convolutional decoder can easily correct random errors. After interleaving, the coded inary data are converted into PSK or QAM symols y mapping onto respective constellation points. The constellations for BPSK, QPSK, 16QAM, and 64QAM are all shown in Figure

42 Figure 10. Constellation for BPSK, QPSK, 16QAM, and 64QAM [From Ref. 5] In order to facilitate coherent reception, 4 pilot tones are added to each 48 data symols to make one OFDM symol. Each OFDM symol is, after serial-to-parallel conversion, modulated onto 52 su-carriers y applying an inverse fast Fourier transform (IFFT). To make the system immune to multipath fading, a cyclic extension is added to 22

43 the guard interval. As discussed earlier, a key parameter in the OFDM system is the 800 ns guard time, which is much longer than the maximum reported rms delay spread, 300 ns, in [9]. Since the guard interval is longer than the delay spread, ISI is eliminated; however, it is shown in [12] that this guard interval has to e a cyclic extension of the OFDM symol in order to maintain orthogoanlity. Three su-carriers in one OFDM symol duration with no cyclic extension added in the guard time was illustrated in Figure 11. As we can see, there is not an integer numer of cycles for each su-carrier over the OFDM symol duration, thus there will e cross-talk, or ICI, among su-carriers in the frequency domain. Figure 11. Effect of no cyclic extension in the guard interval [From Ref.4] On the contrary, y adding the cyclic extension in the guard time, each su-carrier will have an integer numer of cycles over the OFDM symol duration, and there will e no cross-talk among su-carriers. This is shown in Figure

44 Figure 12. Effect of adding cyclic extension in the guard interval [From Ref. 4] After adding the cyclic extension, windowing is applied to smooth the transition region etween symols and to narrow the output spectrum. Further, the symols are modulated onto sine and cosine carriers and are up-converted to the 5-GHz and, then amplified and transmitted through the antenna. Most of the processes done in the transmitter are reversed in the receiver, except for adding a low noise amplifier (LNA) and automatic gain control (AGC). The LNA minimizes the effective system noise temperature of the receiver. The AGC estimates the power of the received pilot tone, and controls the power of the received signal. Now that we have examined multipath fading, the IEEE a standard, and OFDM, we are ready to investigate the performance of the IEEE a WLAN standard over frequency-selective, slow, Ricean fading channels in the following chapters. 24

45 IV. PERFORMANCE WITHOUT FEC CODING This chapter examines the performance of uncoded OFDM transmitted over Ricean fading channels. The analysis egins with the su-carrier modulation schemes utilized in the IEEE a standard: BPSK, QPSK, 16QAM, and 64QAM. The overall OFDM modulation scheme is then analyzed. In this chapter, analytic expressions for the performance of all su-carrier modulation schemes used in the IEEE a standard are derived. A. PERFORMANCE IN AWGN 1. BPSK/QPSK Modulation As mentioned aove, the performances of all four su-carrier modulation schemes used in the IEEE a standard are derived in this chapter. Actually, only two expressions are required, one for BPSK and one for square QAM, since QPSK and BPSK have the same proaility of it error [7] 2E P = Q N (4.1) 0 where E N 0 is the ratio of average energy per it-to-noise power spectral density. Note that E = A T, where 2 c symol Q() is the Q-function, defined as 2 A c is the received signal power and T is the it duration. The which can e approximated as 2 1 -λ Q ( z ) = exp dλ 2π z 2 (4.2) 2 1 -z Q ( z) exp for z 2. 2π z 2 (4.3) 25

46 2. QAM Modulation with a Square Constellation In terms of a set signal constellations as shown in Figure 13, MQAM can e categorized as either rectangular QAM or square QAM. For example, in Figure 13 M=8 (lue line) is rectangular QAM and M=16 (red line) is square QAM. Of course, the square QAM can e considered a special case of rectangular QAM. Figure 13. MQAM signal constellation [After Ref. 13] Rectangular QAM can e thought of as a M i - PAM signal on the in-phase ( I ) signal component and a M q - PAM signal on the quadrature (Q ) signal component where M = Mi Mq; therefore, the proaility of symol error for rectangular QAM can e expressed as s r si ( error on error on ) P = P I Q = P P sq = P + P P P si sq si sq. (4.4) Since the I and Q components can e modeled as independent random processes, Equation (4.4) can e rewritten as 26

47 P = P + P P P (4.5) s si sq si sq where Ps i and respectively. P are the proaility of symol error for M - PAM and M - PAM, s q i q For a square QAM, M i = M q, rewritten as P si = P, and sq 2 M = M i, thus Equation (4.5) can e P = P P (4.6) 2 s 2 s. i si The proaility of symol error for M i - PAM is given y [13] P si 2( M 1) ( 6log M ) E = Q 2 M i ( Mi 1) N0 i 2 i ( M ) 2 1 3qE = Q M ( M 1) N 0 (4.7) = log 2 is the numer of its per symol. For example, q = 4 implies where q ( M) 16QAM, and q = 6 implies 64QAM. Sustituting Equation (4.7) into Equation (4.6), we otain the proaility of symol error for square QAM as 1 3qE 1 3qE Ps = 4 1 Q 1 1 Q. M ( M 1) N 0 M ( M 1) N 0 (4.8) The proaility of it error P is now otained y dividing Equation (4.8) y q to otain M 3qE 1 3qE P Q 1 1 Q q ( M 1) N 0 M ( M 1) N 0 (4.9) since P s and P are related as P P q. Note that for square QAM, q 4. With s Equation (4.1) and (4.9), we plot performance of BPSK/QPSK, 16QAM and 64QAM in AWGN versus E N 0 as shown in Figure 14. As expected, the performance of BPSK/- 27

48 QPSK is superior to the performance of 16QAM, and the performance of 16QAM is superior to that of 64QAM BPSK/QPSK 16QAM 64QAM BER E/No [db] Figure 14. Performance of BPSK/QPSK, 16QAM and 64QAM in AWGN B. PERFORMANCE IN RICEAN FADING CHANNELS The proaility of it error of all su-carrier modulation formats we have considered are functions of E = A T, where A c is simply modeled as a constant 2 c parameter. In fading channels, the received signal amplitude fluctuates and can no longer e modeled as a parameter ut must e modeled as a random variale a c. Consequently, E = a T is also a random variale; therefore, Equation (4.1) and Equation (4.9) are 2 c now conditional proailities P ( a ) proaility of it error for all su-carrier modulations. c. In this case, we need to otain the average 28