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1 NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS PERFORMANCE ANALYSIS OF THE EFFECT OF PULSED- NOISE INTERFERENCE ON WLAN SIGNALS TRANSMITTED OVER A NAKAGAMI FADING CHANNEL by Andrea Toumani March 004 Thei Advior: Second Reader: R. Clark Roberton Donald Wadworth Approved for public releae; ditribution i unlimited

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3 REPORT DOCUMENTATION PAGE Form Approved OMB No Public reporting burden for thi collection of information i etimated to average 1 hour per repone, including the time for reviewing intruction, earching exiting data ource, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comment regarding thi burden etimate or any other apect of thi collection of information, including uggetion for reducing thi burden, to Wahington headquarter Service, Directorate for Information Operation and Report, 115 Jefferon Davi Highway, Suite 104, Arlington, VA 0-430, and to the Office of Management and Budget, Paperwork Reduction Proect ( ) Wahington DC AGENCY USE ONLY (Leave blank). REPORT DATE March TITLE AND SUBTITLE: Title (Mix cae letter) Performance Analyi of the Effect of Puled-noie Interference on WLAN Signal Tranmitted over a Nakagami Fading Channel. 6. AUTHOR Andrea Toumani 7. PERFORMING ORGANIZATION NAME AND ADDRESS Naval Potgraduate School Monterey, CA SPONSORING /MONITORING AGENCY NAME AND ADDRESS35 N/A 3. REPORT TYPE AND DATES COVERED Mater Thei 5. FUNDING NUMBERS 8. PERFORMING ORGANIZATION REPORT NUMBER 10. SPONSORING/MONITORING AGENCY REPORT NUMBER 11. SUPPLEMENTARY NOTES The view expreed in thi thei are thoe of the author and do not reflect the official policy or poition of the Department of Defene or the U.S. Government. 1a. DISTRIBUTION / AVAILABILITY STATEMENT 1b. DISTRIBUTION CODE Approved for public releae; ditribution i unlimited. 13. ABSTRACT (maximum 00 word) Thi thei examine the performance of wirele local area network (WLAN) ignal, pecifically, the ignal of IEEE 80.11a tandard. The ignal i ubect to puled-noie amming, when either the deired ignal alone or the deired ignal and the amming ignal are ubect to Nakagami fading. A expected, the implementation of forward error correction (FEC) coding with oft deciion decoding (SDD) and maximum-likelihood detection improve performance a compared to uncoded ignal. In addition, the combination of maximum-likelihood detection and error correction coding render puled-noie amming ineffective a compared to barrage noie amming. When the amming ignal encounter fading a well, we aume that the average amming power i much greater than the AWGN power. For uncoded ignal, a amming ignal that experience fading actually improve performance when the parameter of the information ignal m i le than or equal to one. Surpriingly, for larger value of m a amming ignal that experience fading work in favor of the information ignal only for mall ignal-tointerference ratio (SIR). When SIR i large, performance when the amming ignal experience fading i wore relative to performance when the amming ignal doe not experience fading. For error correction coding with SDD, we invetigate only continuou amming ince it i by far the wort-cae. Moreover, while we conider a range of fading condition for the amming ignal, we examine only Rayleigh fading of the information ignal. The coded ignal, when the amming ignal experience evere fading, perform better relative to the cae when the amming ignal doe not experience fading. 14. SUBJECT TERMS IEEE 80.11a, WLAN, FEC, SDD, OFDM, BPSK, QPSK, MQAM, AWGN, Nakagami, oft deciion decoding, convolutional code, puled-noie amming, probability of bit error 17. SECURITY CLASSIFICATION OF REPORT Unclaified 18. SECURITY CLASSIFICATION OF THIS PAGE Unclaified i 19. SECURITY CLASSIFICATION OF ABSTRACT Unclaified 15. NUMBER OF PAGES PRICE CODE 0. LIMITATION OF ABSTRACT NSN Standard Form 98 (Rev. -89) Precribed by ANSI Std UL

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5 Approved for public releae; ditribution i unlimited PERFORMANCE ANALYSIS OF THE EFFECT OF PULSE-NOISE INTERFERENCE ON WLAN SIGNALS TRANSMITTED OVER A NAKAGAMI FADING CHANNEL Andrea Toumani Lieutenant Junior Grade, Hellenic Navy B.S., Hellenic Naval Academy, 1996 Submitted in partial fulfillment of the requirement for the degree of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING and MASTER OF SCIENCE IN SYSTEMS ENGINEERING from the NAVAL POSTGRADUATE SCHOOL March 004 Author: Andrea Toumani Approved by: R. Clark Roberton Thei Advior Donald Wadworth Co-Advior Dan C. Boger Chairman, Department of Information Science John P. Power Chairman, Department of Electrical and Computer Engineering iii

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7 ABSTRACT Thi thei examine the performance of wirele local area network (WLAN) ignal, pecifically, the ignal of IEEE 80.11a tandard. The ignal i ubect to pulednoie amming, when either the deired ignal alone or the deired ignal and the amming ignal are ubect to Nakagami fading. A expected, the implementation of forward error correction (FEC) coding with oft deciion decoding (SDD) and maximumlikelihood detection improve performance a compared to uncoded ignal. In addition, the combination of maximum-likelihood detection and error correction coding render puled-noie amming ineffective a compared to barrage noie amming. When the amming ignal encounter fading a well, we aume that the average amming power i much greater than the AWGN power. For uncoded ignal, a amming ignal that experience fading actually improve performance when the parameter of the information ignal m i le than or equal to one. Surpriingly, for larger value of m a amming ignal that experience fading work in favor of the information ignal only for mall ignal-tointerference ratio (SIR). When SIR i large, performance when the amming ignal experience fading i wore relative to performance when the amming ignal doe not experience fading. For error correction coding with SDD, we invetigate only continuou amming ince it i by far the wort-cae. Moreover, while we conider a range of fading condition for the amming ignal, we examine only Rayleigh fading of the information ignal. The coded ignal, when the amming ignal experience evere fading, perform better relative to the cae when the amming ignal doe not experience fading. v

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9 TABLE OF CONTENTS I. INTRODUCTION...1 A. OBJECTIVE...1 B. RELATED RESEARCH... C. THESIS ORGANIZATION... II. III. IV. THEORY REVIEW...5 A. INTRODUCTION...5 B. NAKAGAMI FADING MODEL...5 C. WAVEFORM CHARACTERISTICS Single Carrier Modulation Type...6. Forward Error Correction (FEC) Orthogonal Frequency-Diviion Multiplexing (OFDM)...9 D. SUMMARY...11 PERFORMANCE ANALYSIS WITH FEC AND SDD FOR SIGNALS TRANSMITTED OVER A NAKAGAMI FADING CHANNEL WITH PULSED-NOISE JAMMING...13 A. INTRODUCTION...13 B. BPSK/QPSK Without SDD With FEC and SDD...16 C. 16QAM/64QAM Without FEC and SDD With FEC and SDD...33 D. OFDM SYSTEM PERFORMANCE BPSK/QPSK QAM/64QAM...38 E. SUMMARY...40 PERFORMANCE ANALYSIS WITH FEC AND SDD, NAKAGAMI FADING CHANNELS, AND FADED PULSED-NOISE JAMMING...41 A. INTRODUCTION...41 B. BPSK/QPSK Without FEC With FEC and SDD Comparion of BPSK/QPSK with and without FEC and SDD...56 C. 16QAM/64QAM...57 D. SUMMARY OF FADED JAMMING...60 V. CONCLUSION...63 A. INTRODUCTION...63 B. FINDINGS...63 C. RECOMMENDATIONS FOR FURTHER RESEARCH...64 vii

10 D. CLOSING COMMENTS...64 LIST OF REFERENCES...67 INITIAL DISTRIBUTION LIST...69 viii

11 LIST OF FIGURES Figure 1. The Nakagami probability denity function [After Ref. 8.]...6 Figure. Contellation for BPSK, QPSK, 16QAM, and 64QAM [From Ref. 10.]...7 Figure 3. Convolutional encoder withν = 7 and r = 1/, where the empty boxe denote hift regiter [After Ref. 10.]....9 Figure 4. Tranmitter and receiver block diagram for the OFDM PHY [After Ref. 10.] Figure 5. BPSK/QPSK for SNR = 10 db and p = 0.5 [After Ref. 4.]...14 Figure 6. BPSK/QPSK for SNR = 10 db, and m = 1 [After Ref. 4.] Figure 7. BPSK/QPSK for SNR = 10 db, m = 5, and p = 0.5 [After Ref. 4.]...16 Figure 8. BPSK/QPSK ( r = 1/) with FEC and SDD for ignal tranmitted over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 10 db)...6 Figure 9. BPSK/QPSK ( r = 1/) with FEC and SDD for ignal tranmitted over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 16 db)...6 Figure 10. BPSK/QPSK ( r = 1/) with FEC and SDD over a Nakagami fading channel with continuou noie amming (SNR = 10 db)...7 Figure 11. BPSK/QPSK ( r = 3/4) with FEC and SDD over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 10 db)...8 Figure 1. BPSK/QPSK ( r = 3/4) with FEC and SDD over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 16 db)...9 Figure 13. BPSK/QPSK ( r = 3/4) v. r = 1/ with FEC and SDD over a Nakagami fading channel with continuou noie amming (SNR = 10 db)...9 Figure 14. BPSK/QPSK ( r = 1/) with FEC and SDD over a Nakagami fading channel with continuou noie amming (SNR = 10 db) v. uncoded performance Figure 15. BPSK/QPSK ( r = 3/4) with FEC and SDD over a Nakagami fading channel with continuou noie amming (SNR = 10 db) v. uncoded performance Figure QAM tranmitted over a Nakagami fading channel with puled-noie amming, SNR = 10 db, and p = 0.5 [After Ref. 4.]...3 Figure QAM tranmitted over a Nakagami fading channel with puled-noie amming, SNR = 0 db, and p = 0.5 [After Ref. 4.]....3 Figure QAM ( r = 1/) with FEC and SDD tranmitted over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 10 db) Figure QAM ( r = 1/) with FEC and SDD tranmitted over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 16 db) Figure 0. 16QAM ( r = 1/) with FEC and SDD tranmitted over a Nakagami fading channel with continuou noie amming (SNR = 10 db)...35 ix

12 Figure 1. 64QAM ( r = 3/4) with FEC and SDD tranmitted over a Nakagami fading channel with m = 1 (Rayleigh fading), and SNR = 6 db...36 Figure. OFDM BPSK ( r = 1/) with FEC and SDD (SNR = 10 db) Figure 3. OFDM BPSK ( r = 1/) with FEC and SDD (SNR = 16 db) Figure 4. OFDM 16QAM ( r = 1/) with FEC and SDD (SNR = 10 db) Figure 5. OFDM 16QAM ( r = 3/4) with FEC and SDD (SNR = 16 db) Figure 6. Performance of BPSK/QPSK ( m = 1/ ) when the amming ignal experience Nakagami fading...44 Figure 7. Performance of BPSK/QPSK ( m = 1) when the amming ignal experience Nakagami fading...45 Figure 8. Performance of BPSK/QPSK ( m = ) when the amming ignal experience Nakagami fading...46 Figure 9. Performance of BPSK/QPSK ( m = 3 ) when the amming ignal experience Nakagami fading...46 Figure 30. Performance of BPSK/QPSK with FEC and SDD for m = 1, SNR = 0 db, and r = 1/....5 Figure 31. Performance of BPSK/QPSK with FEC and SDD for m = 1, SNR = 30 db, and r = 1/ Figure 3. Comparion of BPSK/QPSK with FEC and SDD for m = 1, and r = 1/ Figure 33. Performance of BPSK/QPSK with FEC and SDD for m = 1, SNR = 0 db, and r = 3/ Figure 34. Performance of BPSK/QPSK with FEC and SDD for m = 1, SNR = 30 db, and r = 3/ Figure 35. Comparion of coded and uncoded BPSK/QPSK for m = 1, SNR = 30 db, and r = 1/ Figure 36. Comparion of coded and uncoded BPSK/QPSK for m = 1, SNR = 30 db, and r = 3/ Figure 37. Performance of 16QAM ( m = 1/ )...58 Figure 38. Performance of 16QAM ( m = 1) Figure 39. Performance of 16QAM ( m = 3 ) Figure 40. Performance of 64QAM ( m = 1) x

13 LIST OF TABLES Table 1. Rate-dependent parameter [From Ref. 10.]...8 Table. Weight Structure of the Bet Convolutional Code [After Ref. 10.]...17 Table 3. Croover point of curve for different m...47 Table 4. 4 Performance difference (db) between different m for P b = xi

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15 ACKNOWLEDGMENTS Thi thei would not have been poible without the initial idea, the clear explanation and the contant advice of Profeor R. Clark Roberton. I gratefully acknowledge hi mentorhip, and the endle hour he pent anwering every quetion of mine. I alo want to expre my incere appreciation to Profeor Donald Wadworth for hi guidance and aitance erving a my co-advior. Finally, I want to thank my wife Maria, for her piritual upport and undertanding a thi work matured. xiii

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17 EXECUTIVE SUMMARY The obective of thi thei wa to invetigate the performance of the effect of pule-noie amming on wirele local area network (WLAN) ignal tranmitted over a Nakagami fading channel. Signal tranmiion over a mobile channel i ubect to fading caued by multipath propagation due to reflection, diffraction, and cattering procee. The Nakagami model of a fading environment i generalized to model different fading condition. The analyi of both fading and interference are eential to deign a robut communication ytem, epecially for military application, where hotile amming i expected. Beginning the analyi when the amming ignal doe not encounter fading, we found that the ignal without forward error correction (FEC) perform poorly when the ignal propagate over a evere fading channel. When FEC with oft deciion decoding (SDD) i implemented, the probability of bit error i improved dramatically. Thi behavior i exhibited for all modulation type and data rate the IEEE 80.11a tandard pecifie. Thee reult are for a ingle carrier. The IEEE 80.11a 5-GHz WLAN tandard that we examined implement orthogonal frequency-diviion multiplexing (OFDM). A will be explained in Chapter II, OFDM can tranform a frequency-elective channel to a flat-fading one uing orthogonal ub-carrier. The fading effect of a flat-fading channel can be mitigated, and thi explain the preference given to OFDM ytem when high data rate are required. To continue with the performance analyi for the combined OFDM ignal, we aumed independent Nakagami fading for each ub-carrier. Each ub-carrier i aumed to be ubect to Nakagami fading with different m, where m i aumed to be uniformly ditributed over a pecific range. The finding demontrate the dominance of the negative effect of the more evere condition, ince the overall performance i dominated by the ubcarrier tranmitted over channel with mall value of m. However, thi approach doe not examine in depth the ditribution of m for the ub-carrier. Thu, it i wort-cae and give only a peimitic idea of how an OFDM ignal perform. xv

18 After the evaluation for an unfaded amming ignal, the analyi continue and examine the cae for when the amming ignal experience fading a well. The fading of the interference actually improve the WLAN performance when the deired ignal i ubect to Rayleigh or more evere fading or when ignal-to-interference (SIR) ratio i mall, independent of the fading of the deired ignal. Surpriingly, for milder fading of the deired ignal, fading of the amming ignal increae bit error. When FEC with SDD i implemented the reult are imilar. xvi

19 I. INTRODUCTION A. OBJECTIVE Wirele local area network (WLAN) offer increaed data rate and reliable performance even when affected by evere fading condition. Thee characteritic have made them popular for both commercial and military application. WLAN are able to operate at high data rate, and their analyi will help achieve an undertanding of their limitation and capabilitie. The IEEE 80.11a tandard i a repreentative of a WLAN and i adopted for many wirele application, both military and commercial. Thi tandard upport variable bit rate from ix to 54 Mbp and pecifie four modulation type: binary phae-hift keying (BPSK), quadrature phae-hift keying (QPSK), 16 quadrature amplitude modulation (16QAM), and 64QAM. Furthermore, it employ forward error correction (FEC) with oft deciion decoding (SDD) and orthogonal frequency-diviion multiplexing (OFDM). OFDM wa choen a a mean to overcome the effect of frequency-elective fading condition. The cope of thi thei wa to invetigate the performance of the IEEE 80.11a WLAN waveform tranmitted over frequency-elective, lowly fading Nakagami channel. In order to take into account the wort-cae cenario, the deired ignal i aumed to be ubect to pule-noie amming. The amming ignal i alo aumed to be affected by the fading channel. We make three aumption for the receiver: a. the receiver detect the ignal coherently, b. the receiver local ocillator know the amplitude of the received ignal (maximal-ratio detection), and c. for FEC with SDD, the receiver maximize the conditional probability denity function of the received code equence f ( r v ), given the correct code equence v for equally likely code equence (maximum-likelihood receiver). The effect of puled-noie amming wa alo conidered, and the amming ignal wa alo aumed to encounter fading. Since we aume that the informational ignal i 1 r

20 affected by fading, it i reaonable to aume the ame for the amming ignal. Thi thei attempt to addre the cae when the amming ignal i ubect to fading or not. B. RELATED RESEARCH Numerou work have dealt with the performance of OFDM ignal propagating through fading channel. The fading model that have been analyzed vary from Rayleigh and Ricean [1,] to the more general Nakagami [3]. In [4] Koa introduced puled-noie amming with FEC and SDD but did not conider SDD for non-binary modulation. Thi thei analyze the performance of IEEE 80.11a receiver with FEC and SDD for both binary and non-binary modulation. A for the analyi when the amming ignal experience fading, Oetting in [5] treat the performance of pread pectrum ytem when both the envelope of the deired and the amming ignal fade with a Ricean ditribution. Reference [6] and [7] extended the analyi to accommodate Nakagami fading. All thee work focu on frequency-hift keying (FSK) modulation. However, they do not addre either the coherent modulation type pecified by the IEEE 80.11a tandard or FEC with SDD, and thi i the focu and novelty of thi thei. Taking into account FEC with SDD, we obtain reult that are more generally applicable and will benefit thoe utilizing a IEEE 80.11a 5- GHz WLAN ytem. C. THESIS ORGANIZATION Apart from the introductory chapter, thi thei comprie four more chapter with the following organization. Chapter II preent the neceary background theory. It include the Nakagami probability denity function and the characteritic of the IEEE 80.11a waveform. The analyi of the next two chapter aume the information ignal i experiencing puled-noie amming and Nakagami, or a pecial cae of Nakagami, fading. Additionally, all modulation type and code rate pecified by the tandard are examined. In Chapter III we review the performance of an uncoded ignal for a ingle carrier, after the reult of [4]. Then the analyi i extended to accommodate FEC with SDD. Thi chapter conclude with an aumption concerning the effect of fading on the com-

21 bined OFDM ignal, and the reulting performance i dicued. Chapter IV i the bulk of thi thei. It tructure i imilar to Chapter III, with the difference that the amming ignal i aumed to experience fading a the information ignal doe. The analyi begin by invetigating the performance of an uncoded ignal for a ingle carrier and continue with the tudy of FEC with SDD. Chapter V ummarize all finding and comment the mot important reult. Finally, we conclude with recommendation for further reearch. 3

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23 II. THEORY REVIEW A. INTRODUCTION Before proceeding to the analyi, it i prudent to review ome background. Initially, we preent the characteritic of the Nakagami fading channel. We preent the Nakagami denity function and explain the reaon it i elected to model the fading channel. Then, we look at the characteritic of the IEEE 80.11a ignal. Specifically, we tate the different modulation type the tandard pecifie and the correponding data rate, a well a dicuing briefly convolutional coding and OFDM. B. NAKAGAMI FADING MODEL The ditribution we elected to model the fading channel i the Nakagami ditribution. The reaon i it flexibility and accuracy in matching experimental data. Changing the m parameter of the ditribution, we can model a wide variety of fading condition. The Rayleigh fading channel i a pecial cae with m = 1, one-ided Gauian fading i a pecial cae with m = 1/, and non-fading i a pecial cae that occur when m approache infinity. The Nakagami- m denity function i a function of two parameter, r and Ω, and i given by [8] a: mr m 1 Ω m fr () r = r e Γ( m) Ω m, (.1) where Ω i defined a Ω= ER [ ]. (.) Γ( m) i the Gamma function defined a 1 ( ) m t m t e dt, m 0 Γ = (.3) 0 and the m parameter i expreed a 5

24 Ω 1 m=, m. (.4) E[( R Ω) ] In Figure 1 we ee the probability denity function of the Nakagami ditribution for different value of m. Figure 1. The Nakagami probability denity function [After Ref. 8.]. C. WAVEFORM CHARACTERISTICS 1. Single Carrier Modulation Type The modulation type implemented by IEEE 80.11a tandard for a ingle carrier are BPSK, QPSK, 16QAM, or 64QAM. Thee four type were elected for two propertie they have in common. Firt, they are bandwidth efficient, a critical feature for a WLAN ytem, where increaed data rate are required. Second, they can be eaily implemented, reducing the cot of hardware. By definition the ignal of MPSK and MQAM are very imilar. We know that for a rectangular ignal contellation the power pectral denity, tranmiion bandwidth, and pectral efficiency of MQAM are identical to thoe of MPSK [9]. The contellation for 16QAM and 64QAM pecified by the IEEE 6

25 80.11a tandard are quare and are hown in Figure [10]. Like MPSK, MQAM utilize both the in-phae and the quadrature component of the carrier. Both MPSK and MQAM Figure. Contellation for BPSK, QPSK, 16QAM, and 64QAM [From Ref. 10.]. 7

26 demodulate the two component of the carrier independently and can be thought of a two independent M-ary pule amplitude modulation (MPAM) ignal. Due to thi, it i eay to implement a receiver for each of thee modulation type uing the ame hardware. In Chapter III and IV, we invetigate the performance obtained with each of the modulation type.. Forward Error Correction (FEC) In order to overcome performance degradation due to multipath fading, the IEEE 80.11a tandard employ FEC. With FEC, redundant bit are added to the raw data tream. The IEEE 80.11a tandard pecifie the convolutional encoder of Figure 3, which ue ix linear hift-regiter tage [10]. In general a convolutional code take k input bit and generate n coded output bit. The ratio r = k/ n i defined a the code rate and i indicative of the number of redundant bit in the bit tream. The code rate pecified by the tandard depend on the modulation type and the deired data rate. Table 1 give the modulation type each code rate i combined with and the achieved data rate. Table 1. Rate-dependent parameter [From Ref. 10.]. Data rate (Mbp) Modulation Code Rate 6 BPSK 1/ 9 BPSK 3/4 1 QPSK 1/ 18 QPSK 3/4 4 16QAM 1/ 36 16QAM 3/ QAM / QAM 3/4 Another parameter that pecifie the convolutional code i the contraint length ν. According to [11], ν i the maximum number of coded bit that can be affected by a ingle information bit. The convolutional encoder employed by IEEE 80.11a for 8

27 r = 1/ ha a contraint length ν = 7 and i hown in Figure 3. The le redundant code rate of /3, and 3/4 are derived from it through puncturing. Puncturing implie that ome of the encoded bit are omitted o that the number of the tranmitted bit i reduced, and the code rate i increaed. The omitted bit are replaced by dummy zero bit. Thee dummy bit are accounted for by the decoder. Output data A Input data Output data B Figure 3. Convolutional encoder withν = 7 and r = 1/, where the empty boxe denote hift regiter [After Ref. 10.]. 3. Orthogonal Frequency-Diviion Multiplexing (OFDM) OFDM i a ignaling technique that tranmit the data bit on a number of orthogonal carrier frequencie or ub-carrier. If the number of available ub-carrier frequencie are N, the data rate for an individual ub-carrier i R R N overall data rate [1]. Thu, the required bandwidth for each ub-carrier i reduced by a factor of N. The orthogonality of the carrier frequencie i another feature of OFDM that minimize the overall ignal bandwidth. The bandwidth of the individual ub-carrier ignal overlap each other, yielding an overall bandwidth aving. The IEEE 80.11a tandard pecifie 5 ub-carrier, 48 of which are ued for tranmitting information bit and the ret for tranmitting pilot tone. Beide reduced ignal bandwidth, OFDM i effective when the ignal i tranmitted over a fading channel. If the IEEE 80.11a tandard pecified only one carrier, the 9 bc = b, where b R i the

28 high data rate would caue the noie equivalent bandwidth (W ) of the ignal to exceed the coherence bandwidth of the channel ( f ) c [9]. In thi cae W > ( f) c, and the channel i aid to be frequency-elective. A a reult, the ditortion of the ignal i ignificant. For each ub-carrier of an OFDM ignal, the noie equivalent bandwidth W c i reduced by N and i le than the coherence bandwidth of the channel W = W N < ( f). Hence, the channel i characterized a flat-fading for each individual ub-carrier. While the ue of N ub-carrier reduce the bandwidth, it increae bit duration or ymbol duration, depending on the modulation type, a: c c T bc = NT. (.5) b If we let N get very large, the bit duration of each carrier may become larger than channel coherence time T > ( t), and the channel i then characterized a fat fading. In a bc c fat fading channel, the channel impule repone change rapidly within the bit duration. Thi caue frequency diperion due to Doppler preading, which lead to ignal ditortion [13]. To avoid the latter, the channel mut remain lowly fading and that limit the maximum allowable value of N. Figure 4 illutrate the generation of an OFDM ignal, where we ee the tranmitter and receiver block diagram. On the tranmitter ide, the information bit are firt convolutionally encoded by the encoder of Figure 3. Then, a block interleaver, defined by a two-tep permutation, interleave the coded bit. The firt permutation enure that adacent coded bit are mapped onto nonadacent ub-carrier. The econd enure that adacent coded bit are mapped alternatively onto le and more ignificant bit of the contellation of Figure [10]. Spreading the bit over time prevent the important bit of a block of ource bit from being corrupted when there i a deep fade or noie burt. After the interleaver tage, data are mapped. They are divided into group of one, two, four, or ix bit and converted into complex number repreenting BPSK, QPSK, 16QAM, or 64QAM contellation point, repectively. The invere fat Fourier tranform (IFFT) tranform thee ymbol into a complex baeband ignal. The moothne of the 10

29 tranition from ymbol to ymbol i done by windowing, narrowing the output pectrum. Next, the OFDM ymbol modulate the two orthogonal carrier, i upconverted, amplified and tranmitted. Figure 4. Tranmitter and receiver block diagram for the OFDM PHY [After Ref. 10.]. D. SUMMARY In thi chapter, we addreed Nakagami-m ditribution and explained the reaon we elected it to model the fading channel. Then, we tated the characteritic of the IEEE 80.11a tandard ignal: modulation type of a ingle ub-carrier, error correction coding, and orthogonal frequency-diviion multiplexing. In the next chapter, we will invetigate in detail the effect of fading and puled-noie amming on a WLAN ignal. 11

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31 III. PERFORMANCE ANALYSIS WITH FEC AND SDD FOR SIGNALS TRANSMITTED OVER A NAKAGAMI FADING CHANNEL WITH PULSED-NOISE JAMMING A. INTRODUCTION In the previou chapter, we examined all the neceary background required to undertand the baic principle of the IEEE 80.11a wirele local area network tandard. Now it i time to ee how thee principle are applied in practice by proceeding to the performance analyi. We examined the different modulation type eparately for the coded and uncoded cae. In [3] and [4], whoe work wa continued in thi thei, the analyi included the performance of coded ignal, decoded with both hard deciion decoding (HDD) and oft deciion decoding (SDD). Since thi thei wa concentrated olely on the actual characteritic of the IEEE 80.11a wirele local area network tandard, in addition to no coding, we examined only SDD. Epecially for M-ary QAM, we addreed pecific aumption made to analyze non-binary ignal with SDD. Latly, we expanded our reult to the combined OFDM ignal and examined the effect of fading when all 48 ub-carrier are conidered one ignal. In all cae we aumed the ignal experienced frequency-elective, low Nakagami fading and pulednoie amming. B. BPSK/QPSK Thee two modulation type were examined together ince they are both analyzed in the ame way. A QPSK ignal i a pecial cae of M-ary PSK that enoy double the data rate of BPSK, ince both the in-phae and the quadrature component of the carrier are utilized. 1. Without SDD The material of thi ection ha been derived in [4] and the probability of bit error rate i retated here: 13

32 P = ( p) bbpsk / QPSK 1 1 p Γ ( m+ 0.5) 1+ m SNR + SIR / 1 π Γ ( m + 1) 1+ m 1+ k k = 0 i= 1 m+ i m+ i 1 + m(snr + SIR / p) 1 1 ( ) ( SNR + SIR / p) k m k k 1 p Γ ( m+ 0.5) m+ i m m SNR SNR k = 0 i= 1 m+ i 1 π ( m 1) Γ + + SNR + m m. (3.1) In Figure 5 we can ee the performance of BPSK/QPSK for different value of m. The obviou characteritic concerning the effect of m i that, a it increae, we approach the non-fading cae. For mall value of m, fading i evere and there i coniderable performance reduction. Figure 5. BPSK/QPSK for SNR = 10 db and p = 0.5 [After Ref. 4.]. 14

33 In Figure 6 we plot the probability of bit error for the Rayleigh fading channel ( m = 1) uing different value of p, the fraction of time the ammer i on. We note the ammer i more effective when the amming i continuou. Thi i obviou for mall SIR, while for larger SIR the value of p doe not play any role. Figure 6. BPSK/QPSK for SNR = 10 db, and m = 1 [After Ref. 4.]. In Figure 7 the m parameter i larger ( m = 5 ), indicating much better fading condition than Rayleigh (uually pecifying a line-of-ight (LOS) between the worktation and the acce point). The reult are very different compared to thoe obtained for Rayleigh fading. For mid-range value of SIR, the effectivene of the ammer i improved for mall p. Thi i conitent with the reult obtained when there i no fading. In all three figure, when m i mall the bit error rate i too large, and thi explain why convolutional coding i ued in the IEEE 80.11a tandard, which i dicued in the next ection. 15

34 Figure 7. BPSK/QPSK for SNR = 10 db, m = 5, and p = 0.5 [After Ref. 4.].. With FEC and SDD In [14], Proaki give the widely accepted upper bound on the probability of bit error ( P b ), ince the exact olution cannot be derived, a 1 P < B P. (3.) k b d d d= dfree In the above inequality, k i the number of information bit encoded per clock cycle and the numerator of the code rate r, d i the weight of the path, d free repreent the minimum Hamming ditance between all pair of complete convolutional code equence, i the um of all poible bit error that can occur when a path of weight d i elected, and P d repreent the probability that the decoder will elect a path of weight d. The value of B d cannot in general be computed, but have been determined by extenive computer earch for optimal performance for a contraint length ν and code B d 16

35 rate r convolutional code. After [10], in Table the value of code pecified by the IEEE 80.11a tandard. B d are hown for the Table. Weight Structure of the Bet Convolutional Code [After Ref. 10.]. Code Rate d free B d free B d free + 1 B d free + B d free + 3 B d free + 4 1/ / / According to [1], the um in Inequality (3.) i dominated by the firt five non-zero term of the ummation. From thi point on, the analyi diverge depending on whether we are dealing with SDD or HDD. To continue with SDD, we expand the approach of [4] in order to accommodate the cae when the receiver ha no information whether a bit i ammed or not. Conequently, we have to find P d o a to be able to evaluate Inequality (3.). For optimum performance the ue of a maximum-likelihood receiver i required. A maximumlikelihood receiver maximize the conditional probability denity function of the received r code equence f ( r v ) given the correct code equence v for equally likely code equence. For the BPSK/QPSK ignal, the output of the demodulator for each bit r l i modeled a a Gauian random variable with mean r = a cl and variance σ l. If the correct path i the all-zero path and the a decoding error occur when [14] th r path differ from the correct path in d bit, then d a r > 0. (3.3) σ l= 1 cl l l In the preceding equation the index l run over the et of d bit in which the path differ from the correct path, r l i the demodulator output, 17 th r a c l i the amplitude of

36 the received ignal and i modeled a a random variable due to the effect of the fading channel, and σ l i the power of the noie for each bit, which we mut know in order to ditinguih between bit that are ammed and thoe that are not. The probability P d i imply P d d ac r l l = Pr > 0. (3.4) l= 1 σ l We define z l a r =. (3.5) σ cl l l Obviouly, after thi tranformation of random variable z l remain a Gauian random variable with mean z = a σ and variance l c l l a σ. We now introduce z a the um cl l of d independent random variable d z = z, (3.6) l= 1 where z i a Gauian random variable ince it i the ummation of independent Gauian l random variable. The mean of z i d z = a σ and the variance i l= 1 cl l d ac σ l l. l= 1 Combining Equation (3.4) and (3.6), we get P d = P( z > 0). (3.7) r Expreing P d in term of the Q-function, we can write d a c l l 1 σ = l d ac l d z a c l= 1 σ l l l= 1 σ l z Pd = Q = Q = Q σ. (3.8) 18

37 In order to take into account puled-noie amming, we plit the um of a σ over the cl l d bit: P d = Q + i d acl ac l l= 1 l= i+ 1 σt σo. (3.9) The firt part of the um in the argument of the Q-function correpond to i ammed bit, while σ t repreent the total noie power (AWGN plu amming noie). The latter part of the um correpond to d noie power σ o i preent. If we expre i unammed bit where only the AWGN i d ac l ac l l= 1 l= i+ 1 σt σo h = +, (3.10) then we ee that P d i conditional on h. To obtain the unconditional P d, we integrate Pd ( h ) multiplied by the probability denity function of h ( fh ( h )) over the value for which h i valid: P = P ( h) f ( h) dh. (3.11) d d H 0 In order to proceed, we mut find f ( h ). We know the Nakagami- m probability denity function i given by H m mac m m 1 ac Ac ( c) = ( ) c Γ m a c f a a e. (3.1) Firt, we expand Equation (3.1) in order to compute the probability denity function of a quared random variable. Next, we mut obtain the pdf of the um of i independent quared random variable, which i given by [3] a 19

38 mi mb1 1 m mi 1 b fb 1(1) b b1 e = Γ( mi) b (3.13) where the random variable b 1 i defined a i b1 = a, (3.14) l= 1 cl and b i the average power of the ignal. Analogouly, the pdf of the um of d i independent quared random variable i where md ( i) mb md ( i) 1 b 1 m fb( b) = b e Γ( md ( i) ) b, (3.15) d b = a. (3.16) l=+ i 1 Subtituting Equation (3.14) and (3.16) into Equation (3.10), we get t o cl b1 b h = h1 h σ + σ = +. (3.17) Next, we mut find the pdf of h 1 and h. From Equation (3.17), We know that b1 db1 h1 =, = σ t. (3.18) σ dh1 t 1 fh1(1) h = db fb 1(1) b 1 (3.19) b1 = f ( h1) dh1 Subtituting Equation (3.13) and (3.18) into Equation (3.19), we get mi m σt 1 h mi mi 1 b σ t 1 m fh1(1) h = ( ) h1 e Γ( mi) b. (3.0) 0

39 Following the ame methodology, we obtain the pdf of h a md ( i ) m σ o h md ( i) md ( i) 1 b σ o 1 m fh( h) = ( ) h e Γ( md ( i) ) b. (3.1) The lat tep i to find the pdf of the um of h1+ h. It i given by the convolution of the two eparate pdf. However, we will take advantage of the relevant property of the Laplace tranformation, tating that convolution i equivalent to multiplication in the Laplace domain. Thu, we multiply the two pdf after their tranformation into the Laplace domain. Since the pdf i non-zero only for poitive argument, h1 { } L f ( h1) F ( ) f ( h1) e dh1 (3.) H1 H1 H1 0 = = where L { i} indicate the Laplace tranform operator. Subtituting Equation (3.0) into (3.), we get 0 mi m σt 1 h mi mi 1 b h1 σ t 1 m FH1 () = ( ) h1 e e dh1 Γ( mi) b (3.3) which can be implified to Uing the Laplace tranform pair mi mσ t h1 mi 1 mi + 1 b t Γ( mi) 0 m FH1 () = ( σ ) h1 e dh1 b. (3.4) we et u 1 t at = 1 L e for u > 0, (3.5) u Γ ( u) ( + a) t = h1 c, (3.6) u = mi, (3.7) and mσ t a= +, (3.8) b c 1

40 which allow u to get Similarly, F mi m mi 1 H1() = ( σ t ) mi b mσ t + b. (3.9) which can be evaluated to yield h { } L f ( h) F ( ) f ( h) e dh (3.30) H H H 0 = = F md ( i) m () = ( σ ) md ( i) H o md ( i) b mσ o + b 1. (3.31) The pdf of h in the Laplace domain i the product of L { f h } and { f h } H1 ( 1) { f ( h) } = F ( ) = { f ( h1) } { f ( h) } H H H1 H L ( ) H : L L L. (3.3) Hence, ubtituting Equation (3.9) and (3.31) into Equation (3.3), we get F mi m( d i) m 1 m 1 ( ) = ( σ ) ( σ ) + + b b mi m( d i) H t o mi b b mσ t mσo m( d i) (3.33) which can be implified to F md mi m( d i) m ( σt ) ( σo) H () = mi m( d i) b mσ t mσ o + + b b. (3.34) To write Equation (3.34) in term of SNR and SIR we define and b SNR = (3.35) σ o b SIR =, (3.36) σ

41 where σ o i the power of the AWGN and Combining both power, we get the total power σ i the noie power of the amming ignal. σ = σ + σ. (3.37) t o The reulting ignal-to-noie plu interference ratio i b b SNIR = = = σ σ + σ σ b t o o 1 σ + b (3.38) which can be written Now we can rewrite Equation (3.34) a 1 SNIR = SNR SIR 1 1 SNR + SIR = ( ) 1. (3.39) F Hc ( + ) 1 1 mi md ( i) md SNR SIR SNR m () = mi m m ( SNR + SIR ) SNR md ( i). (3.40) The invere Laplace tranform of the equation above i too complicated to calculate directly. Alternatively, we ue the methodology [9] of the numerical invere of the two-ided Laplace tranform. The latter i defined a { } The invere two-ided Laplace tranform i given by x L f X( x) = FX( ) = fx( x) e dx. (3.41) c x L { FX() } = fx() x = FX() e d π. (3.4) where c mut be within the trip of convergence of F ( ) [9]. By ucceive change of variable we get c X 3

42 cx π / ce fx( x) = Re { FX( c+ ctan φ) } co( cxtan φ) π 0 { } Im F ( c+ ctan φ) in( cxtan φ) ec φ dφ. (3.43) Rewriting Equation (3.43) in term of the notation ued, we have cx π / 0 X ce fh( h) = Re { FH( c+ ctan φ) } co( cxtan φ) π { } Im F ( c+ ctan φ) in( cxtan φ) ec φ dφ. (3.44) H Up to thi point we have evaluated Pd ( i ). Next, we find P d independent of i. The probability of electing a path that i a Hamming ditance d from the correct path when i of the d bit are ammed for BPSK/QPSK i the um of the probability that one bit i ammed and d 1 are not, plu the probability of two bit are ammed and d are not, etc., and i expreed a d P = P( i bit ammed) P ( i), (3.45) d r d i= 0 where Pd ( i ) i found by ubtituting Equation (3.44) in Equation (3.11). The probability Pr ( i bit ammed) i d i Pr ( i bit ammed) = p (1 p) i d i. (3.46) where p i the fraction of time the ammer i on. Now Equation (3.45) i written a d d i d i Pd = p (1 p) Pd( i) i= 0 i. (3.47) We have almot concluded the analyi, but we mut take into account two more thing. The firt i the aumption that the average amming power remain contant, independent of p. Thi tatement implie that intantaneou amming power increae when the ammer i on. Thu, SIR i replaced with 4

43 SIR SIR =. (3.48) p The econd thing i the relation between the average energy of the uncoded data bit Eb and the coded one E. The uncoded data rate R b i r time the coded data rate R, b c b c R = rr. (3.49) b b c In addition, the average tranmitted power i the ame whether coded or uncoded bit are tranmitted. Hence, P= E R = E R (3.50) bc bc b b and R E = E = re. (3.51) b bc b b Rb c Thi mean that the power of coded bit i r time the power of uncoded bit. To compenate for thi, we mut multiply the expreion for uncoded bit power (SNR and SIR) by the code rate r. In light of Equation (3.47) and the conideration of the previou two paragraph, we can now numerically evaluate Equation (3.11). With the value in Table for B d, we can then calculate Equation (3.). For the code rate r = 1/, which i ued for data rate of ix Mbp (BPSK) and 1 Mbp (QPSK), we get Figure 8 and 9 for different value of SNR (10 db and 16 db, repectively). The point of interet in the Figure are, firtly, the fact that a SIR increae the probability of error converge to the value correponding to no amming. Second, it i obviou that the amming ignal i far more efficient when employing continuou amming ( p = 1). Taking a a reference the performance for P b 4 = 10, the comparion between the curve for p = 1 and p = 0.5 yield a difference of even db for SNR = 10 db. What i more, the performance for p = 0.1 i mall even for mall value of SIR. Undoubtedly, maximum-likelihood detection with SDD deprive the ammer of uing puled-noie technique. Puled-noie amming technique are preferred when attacking a communi- 5

44 Figure 8. BPSK/QPSK ( r = 1/) with FEC and SDD for ignal tranmitted over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 10 db). Figure 9. BPSK/QPSK ( r = 1/) with FEC and SDD for ignal tranmitted over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 16 db). 6

45 cation ytem not employing FEC and SDD, a wa hown in Figure 7. However, for the IEEE 80.11a wirele local area network tandard, FEC with SDD i pecified. To examine the effect of the Nakagami fading channel, we examine Figure 10, which demontrate ytem performance for different value of the m parameter. Baed on the finding from the two previou figure, where the wort-cae cenario for the receiver i for p = 1, we plot the probability of bit error only for continuou noie amming. Initially, we oberve that, a m increae, the performance of the receiver improve. A m approache infinity, the performance approache the AWGN limit. The difference in performance for mall value of SIR i minor. In other word, when the amming power i large, the fading condition play a minor role. Converely, a SIR increae and we encounter mall amming power, the reult are the oppoite. For large SIR, the fading condition determine to a large extent the overall performance. A mall increae of m from 1/ to 1 improve the bit error rate by a magnitude of 3 10 when SNR = 10 db. Figure 10. BPSK/QPSK ( r = 1/) with FEC and SDD over a Nakagami fading channel with continuou noie amming (SNR = 10 db). 7

46 The next plot how the difference in performance introduced by changing the code rate. Here, we ue r = 3/4, pecified for data rate of nine Mbp (BPSK) and 18 Mbp (QPSK). In Figure 11 we ee the performance for m = 1 and SNR = 10 db, while in Figure 1 we have increaed the ignal-to-noie ratio to 16 db. The general characteritic oberved for the r = 1/ code are repeated when a r = 3/4 code i ued. To compare the performance obtained with the two code, in Figure 13 the performance for both r = 1/ and r = 3/4 code with continuou noie amming are plotted. Generally, when the code rate i large, we get higher data rate. Alternatively, if we are atified with the data rate, we may reduce the coded bit duration and achieve le bandwidth expanion. On the other hand, we loe in performance when we ue a higher code rate. Figure 11. BPSK/QPSK ( r = 3/4) with FEC and SDD over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 10 db). 8

47 Figure 1. BPSK/QPSK ( r = 3/4) with FEC and SDD over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 16 db). Figure 13. BPSK/QPSK ( r = 3/4) v. r = 1/ with FEC and SDD over a Nakagami fading channel with continuou noie amming (SNR = 10 db). 9

48 In order to gain ome perceptive on the performance improvement, in Figure 14 and 15, we compare BPSK/QPSK tranmitted over a Nakagami fading channel in the preence of puled-noie amming with and without FEC and SDD. In Figure 14, for r = 1/ and SNR = 10 db, FEC with SDD provide ignificant performance improvement. The advantage depending on m begin at different SIR. For m = 1/, FEC with SDD i better for value of SIR larger than four db, while for m = 5 the correponding value i around db. In Figure 15 the code rate i r = 3/4and the overall performance i poorer than r = 1/. The cro-over point where the coding gain i poitive after 15 db ( m = 1/) and four db ( m = 5 ), repectively. Finally, it i remarkable that the nominal P b = 10 4 cannot be achieved without coding even when the fading condition are light ( m = 5 ) for SNR = 10 db. On the other hand, FEC and SDD make thi feaible even under the everet fading condition. Figure 14. BPSK/QPSK ( r = 1/) with FEC and SDD over a Nakagami fading channel with continuou noie amming (SNR = 10 db) v. uncoded performance. 30

49 . Figure 15. BPSK/QPSK ( r = 3/4) with FEC and SDD over a Nakagami fading channel with continuou noie amming (SNR = 10 db) v. uncoded performance. C. 16QAM/64QAM The bandwidth efficient M-ary QAM i ued for even higher data rate between 4 and 54 Mbp. 1. Without FEC and SDD For a econd time we borrow the reult from [4], and we preent reult that verify the ame general trend of improved performance for higher value of m. Again, we ue the uual range of 1/ to 5 for m and aume the ammer i on for 50% of the time ( p = 0.5). In Figure 16 for 16QAM we have a poorer bit error rate a compared to Figure 5 for BPSK and QPSK. A expected, 16QAM perform better than 64QAM, and a larger ignal-to-noie ratio (SNR = 0 db) i ued for the 64QAM ignal performance hown in Figure

50 Figure QAM tranmitted over a Nakagami fading channel with puled-noie amming, SNR = 10 db, and p = 0.5 [After Ref. 4.]. Figure QAM tranmitted over a Nakagami fading channel with puled-noie amming, SNR = 0 db, and p = 0.5 [After Ref. 4.]. 3

51 . With FEC and SDD The approach followed for the SDD demodulation for BPSK with FEC doe not apply for the MQAM cae. Demodulating a binary ignal with SDD mean that the demodulator output i non-binary. Uing a metric that provide enough reolution to eparate the variou level, like the Euclidean ditance, the decoder decide which path i correct. When non-binary modulation i ued, we cannot do the ame. A a reult, we aume that the quantization i applied to the demodulated ymbol. During the converion from ymbol to bit, the reulting bit inherit the quantized level of the parent ymbol. Moreover, the proce of deinterleaving pread the bit in time, and we can reaonably continue our analyi baed on the approach for binary ignal. The main difference we hould bear in mind i to ue the proper formula for the probability of bit error for M-ary QAM in Equation (3.9). According to [9], the probability of bit error in AWGN for quare M-ary QAM contellation i P b 4( M 1) 3qSNR = Q q M M 1, (3.5) where q i the number of bit per ymbol, and M i the number of poible combination of q bit. The relation between q and M i q= log M. By analogy with Equation (3.9), valid for BPSK with FEC and SDD, we get P d i d 3q ac σ l t + ac σ l o 4( M 1) l= 1 l= i+ 1 = Q q M M 1. (3.53) Following the methodology ued for BPSK and etting M = 16 and q = 4, we get Figure 18, 19, and 0 for 16QAM. In Figure 18 and 19 the ignal experience Rayleigh fading for different value of p. Next, in Figure 0 the amming i continuou, and we again ue the range for m (1/, 5). A expected, the performance i wore than for BPSK, but now data rate i higher. For r = 1/ with 16QAM, we have 4 Mbp, while for r = 3/4 with 16QAM, we get 36 Mbp. 33

52 Figure QAM ( r = 1/) with FEC and SDD tranmitted over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 10 db). Figure QAM ( r = 1/) with FEC and SDD tranmitted over a Nakagami fading channel ( m = 1) with puled-noie amming (SNR = 16 db). 34

53 Figure 0. 16QAM ( r = 1/) with FEC and SDD tranmitted over a Nakagami fading channel with continuou noie amming (SNR = 10 db). The neceary alteration of Equation (3.53) for 64QAM, the lat modulation technique we are examining, i to et M = 64 and q = 6. Again, we achieve higher data rate, but the performance i even wore compared to all previou cae. For r = /3 with 64QAM we have 48 Mbp, while for r = 3/4 with 64QAM we get 54 Mbp. In Figure 1 we ee the probability of bit error for r = 3/4. The combination of 64QAM and the larger value of the poible code rate ha the pooret performance and will be ued only in very favorable condition of fading and ignal-to-noie ratio. That i the reaon we ue the relatively high value of SNR = 6 db. 35

54 Figure 1. 64QAM ( r = 3/4) with FEC and SDD tranmitted over a Nakagami fading channel with m = 1 (Rayleigh fading), and SNR = 6 db. D. OFDM SYSTEM PERFORMANCE Having invetigated the performance of every combination of modulation and code rate utilized by the IEEE 80.11a tandard, we now examine the other ignificant characteritic of the IEEE 80.11a waveform, orthogonal frequency-diviion multiplexing (OFDM). We conider that all 48 data ub-carrier are tranmitted parallel. It i likely that each ub-carrier may encounter different fading. The quetion that rie i how hall we handle and combine the bit error rate of each ub-carrier that wa derived in the previou ection. We anwer that quetion by haring the approach of [3] and [4]. Since the IEEE 80.11a i a protocol for WLAN indoor tranmiion, by default the fading environment i a variable one. Open or cloed door contribute greatly to that variability. Multiple reflection on the wall and the obect of a room are alo reponible. Additionally, there are other diffraction and cattering factor that obviouly affect an indoor communication link. 36

55 The Nakagami ditribution i a great aide in our effort, becaue by changing the m parameter we model different fading channel. Suppoing that both evere and mild fading condition are likely to occur imultaneouly for different ub-carrier, we treat each ub-carrier a being independent and ubect to Nakagami fading with different m. Auming that all value of m are probable in a pecific range, we model m a a uniformly ditributed random variable. Ranging m from 1/ to 5 i a reaonable aumption, and we mut calculate the bit error rate 48 time and take the average. 1. BPSK/QPSK The reult for the uncoded ignal are preented in [4]. In Figure we can ee the difference of the combined OFDM ignal, compared to a ingle BPSK/QPSK with FEC and SDD. We plot the bit error rate againt the extreme of m (1/, 5). The overall picture we get i the domination of the evere fading in the combined ignal. Thi finding i confirmed in Figure 3 where we have increaed SNR to 16 db. The performance trend for the average of the 48 ub-carrier i cloer to the m = 1/ curve for mot value of SIR. Figure. OFDM BPSK ( r = 1/) with FEC and SDD (SNR = 10 db). 37