NAVAL POSTGRADUATE SCHOOL THESIS

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1 NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS SIMULATION PERFORMANCE OF MULTIPLE-INPUT MULTIPLE-OUTPUT SYSTEMS EMPLOYING SINGLE- CARRIER MODULATION AND ORTHOGONAL FRE- QUENCY DIVISION MULTIPLEXING by Halil Derya Saglam December 004 Thei Advior: Co-Advior: Murali Tummala Roberto Criti 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 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, 5 Jefferon Davi Highway, Suite 04, Arlington, VA 0-430, and to the Office of Management and Budget, Paperwork Reduction Project ( ) Wahington DC AGENCY USE ONLY (Leave blank). REPORT DATE December TITLE AND SUBTITLE: Simulation Performance of Multiple-Input Multiple-Output Sytem Employing Single-Carrier Modulation And Orthogonal Frequency Diviion Multiplexing 3. REPORT TYPE AND DATES COVERED Mater Thei 5. FUNDING NUMBERS 6. AUTHOR(S) Halil Derya Saglam 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Potgraduate School Monterey, CA SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES) N/A 8. PERFORMING ORGANIZATION REPORT NUMBER 0. SPONSORING/MONITORING AGENCY REPORT NUMBER. 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. a. DISTRIBUTION / AVAILABILITY STATEMENT b. DISTRIBUTION CODE Approved for public releae; ditribution i unlimited 3. ABSTRACT (maximum 00 word) Thi thei invetigate the imulation performance of multiple-input multiple-output (MIMO) ytem utilizing Alamoutibaed pace-time block coding (STBC) technique. The MIMO communication ytem uing STBC technique employing both ingle-carrier modulation and orthogonal frequency diviion multiplexing (OFDM) are imulated in Matlab. The phyical layer part of the IEEE 80.6a tandard i ued in contructing the imulated OFDM cheme. Stanford Univerity Interim (SUI) channel model are elected for the wirele channel in the imulation proce. The performance reult of the imulated MIMO ytem are compared to thoe of conventional ingle antenna ytem. 4. SUBJECT TERMS. Multiple-Input Multiple-Output (MIMO), Orthogonal Frequency Diviion Multiplexing (OFDM), Space-Time Block Coding (STBC), Stanford Univerity Interim (SUI) Model, Spatially Correlated MIMO Channel, Spatial Diverity, Alamouti Scheme, Maximal Ratio Combining 5. NUMBER OF PAGES PRICE CODE 7. SECURITY CLASSIFICA- TION OF REPORT Unclaified 8. SECURITY CLASSIFICA- TION OF THIS PAGE Unclaified 9. SECURITY CLAS- SIFICATION OF AB- STRACT Unclaified 0. LIMITATION OF ABSTRACT NSN Standard Form 98 (Rev. -89) Precribed by ANSI Std UL i

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5 Approved for public releae; ditribution i unlimited SIMULATION PERFORMANCE OF MULTIPLE-INPUT MULTIPLE-OUTPUT SYSTEMS EMPLOYING SINGLE-CARRIER MODULATION AND OR- THOGONAL FREQUENCY DIVISION MULTIPLEXING Halil Derya Saglam Lieutenant Junior Grade, Turkih Navy B.S., Turkih Naval Academy, 999 Submitted in partial fulfillment of the requirement for the degree of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL December 004 Author: Halil Derya Saglam Approved by: Murali Tummala Thei Advior Roberto Criti Co-Advior John Power Chairman, Department of Electrical and Computer Engineering iii

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7 ABSTRACT Thi thei invetigate the imulation performance of multiple-input multipleoutput (MIMO) ytem utilizing Alamouti-baed pace-time block coding (STBC) technique. The MIMO communication ytem uing STBC technique employing both ingle-carrier modulation and orthogonal frequency diviion multiplexing (OFDM) are imulated in Matlab. The phyical layer part of the IEEE 80.6a tandard i ued in contructing the imulated OFDM cheme. Stanford Univerity Interim (SUI) channel model are elected for the wirele channel in the imulation proce. The performance reult of the imulated MIMO ytem are compared to thoe of conventional ingle antenna ytem. v

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9 TABLE OF CONTENTS I. INTRODUCTION... A. OBJECTIVE AND METHODOLOGY... B. RELATED RESEARCH... C. ORGANIZATION OF THE THESIS... II. III. IV. MIMO SYSTEMS AND ALAMOUTI SCHEME...5 A. MULTIPLE-INPUT MULTIPLE-OUTPUT (MIMO) SYSTEMS...5. Single-Input Single-Output (SISO) Sytem...5. Single-Input Multiple-Output (SIMO) Sytem Multiple-Input Single-Output (MISO) Sytem Multiple-Input Multiple-Output (MIMO) Sytem...7 B. ALAMOUTI SCHEME...8. Maximal Ratio Combining (MRC) Scheme for Sytem...9. Alamouti Scheme for Sytem Alamouti Scheme for Sytem... C. SUMMARY...3 MIMO CHANNEL MODELS...5 A. STANFORD UNIVERSITY INTERIM (SUI) CHANNELS FOR THE IEEE 80.6a STANDARD...5 B. GENERATING CORRELATED MIMO CHANNELS...7. Uncorrelated MIMO Channel...7. Correlated MIMO Channel LOS Component...9 C. GENERATING CORRELATED FREQUENCY-SELECTIVE MIMO CHANNELS...0 D. SUMMARY... ALAMOUTI-BASED SCHEMES OVER FREQUENCY-SELECTIVE CHANNELS...3 A. SPACE-TIME BLOCK CODING-SINGLE CARRIER (STBC-SC) SYSTEMS OVER FREQUENCY-SELECTIVE CHANNELS...4. SISO Sytem over Frequency-Selective Channel...4. SIMO Sytem over Frequency-Selective Channel MISO Sytem over Frequency-Selective Channel MIMO Sytem over Frequency-Selective Channel...7 B. SPACE-TIME BLOCK CODING-ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING (STBC-OFDM) SYSTEMS OVER FREQUENCY-SELECTIVE CHANNELS...9. SISO-OFDM Sytem over Frequency-Selective Channel...9 a. Channel Encoding...30 b. Symbol Mapping...30 c. Invere Fat Fourier Tranform (IFFT) Operation...3 vii

10 d. Cyclic Prefix Addition...33 e. Digital-to-Analog Converion and RF Modulation...34 f. RF Demodulation and Digital to Analog Converion...34 g. Cyclic Prefix Removal and FFT Operation...34 h. Demapping and Decoding SIMO-OFDM Sytem over Frequency-Selective Channel MISO-OFDM Sytem over Frequency-Selective Channel MIMO-OFDM Sytem over Frequency-Selective Channel...38 C. SUMMARY...39 V. SIMULATION RESULTS...4 A. PERFORMANCE OF SYSTEMS USING ALAMOUTI SCHEMES...4 B. PERFORMANCE OF MIMO-SC SYSTEMS OVER SUI CHANNELS...43 C. PERFORMANCE OF MIMO-OFDM SYSTEMS OVER SUI CHANNELS...49 D. SUMMARY...54 VI. CONCLUSION...57 A. SUMMARY OF THE WORK DONE...57 B. SIGNIFICANT RESULTS AND CONCLUSIONS...57 C. SUGGESTIONS FOR FUTURE WORK...58 APPENDIX A. SUI CHANNEL PARAMETERS...6 APPENDIX B. MATLAB CODE EXPLANATION...63 A. SIMULATION PARAMETERS...63 B. CONDUCTED ITERATIONS...65 C. EXPLANATIONS OF THE SUB-FUNCTIONS...66 LIST OF REFERENCES...69 INITIAL DISTRIBUTION LIST...73 viii

11 LIST OF FIGURES Figure. Schematic of a SISO Sytem (After Ref..)...5 Figure. Schematic of a SIMO ytem (After Ref..)...6 Figure 3. Schematic of a MISO Sytem (After Ref..)...7 Figure 4. Schematic of a MIMO Sytem (After Ref..)...8 Figure 5. Maximal Ratio Combining for a Sytem (After Ref. 4.)...0 Figure 6. Alamouti Scheme for a Sytem (After Ref. 4.)...0 Figure 7. Alamouti Scheme for a Sytem (After Ref. 4.)... Figure 8. The Frequency Repone Plot of Different SUI Channel Model...7 Figure 9. Conceptual Diagram for Generating a Correlated MIMO Channel Baed Figure 0. on SUI Channel Model... Schematic of a SIMO-SC Sytem Utilizing MRC over Frequency- Selective Channel...5 Figure. Schematic of a STBC-SC Sytem over Frequency-Selective Channel..6 Figure. Schematic of a STBC-SC Sytem over Frequency-Selective Channel..8 Figure 3. Block Diagram of a SISO-OFDM Scheme...30 Figure 4. Gray coded (a) BPSK, (b) QPSK and (c) 6-QAM contellation (From Ref. 0.)...3 Figure 5. Allocation of Subcarrier before the IFFT Block (ee Table 6)...3 Figure 6. OFDM Symbol Time Structure (From Ref. 0.)...33 Figure 7. Schematic of a SIMO-OFDM Sytem Utilizing MRC...36 Figure 8. Schematic of a MISO-OFDM Sytem Utilizing STBC...37 Figure 9. Figure 0. Schematic of a MIMO-OFDM Sytem Utilizing STBC...39 The BER Performance Comparion of the Alamouti Scheme to the MRC Scheme over Rayleigh Fading Channel (The imulation parameter are given in Table 7)...43 Figure. SUI Channel Impule Repone on a Sampling Grid with a Sampling Frequency f =.857 MHz...44 Figure. Schematic of Generation of 9-ymbol Block...45 Figure 3. The BER Performance of the SISO-SC Sytem over Different SUI Channel (The imulation parameter are given in Table 8)...46 Figure 4. Schematic of Generation of 9-ymbol Block for each Tranmit Antenna...47 Figure 5. The BER Performance Comparion of Single-Carrier Scheme over the SUI- Channel (The imulation parameter are given in Table 9)...48 Figure 6. The BER Performance of the MISO Single-Carrier Sytem over Correlated Channel (The imulation parameter are given in Table 0)...50 Figure 7. The BER Comparion of SISO-OFDM with Variou CP Size to SISO-SC over the SUI- Channel (The imulation parameter are given in Table )..53 Figure 8. The BER Comparion of all Scheme over the SUI- Channel (The imulation parameter are given in Table 3)...55 Figure 9. A Conceptual Diagram of the Iteration for the Outer Function...66 ix

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13 LIST OF TABLES Table. Tranmiion Sequence of the Alamouti Scheme... Table. Notation for the Received Signal in Alamouti Scheme... Table 3. SUI Channel Characterization (After Ref. 3.)...6 Table 4. Tranmiion Sequence for STBC...7 Table 5. The Sequence and the Location of the Received Signal for a STBC Sytem...9 Table 6. Allocation of OFDM Subcarrier in the IEEE 80.6a Standard...3 Table 7. Parameter for Alamouti and MRC Single-Carrier Simulation...4 Table 8. Parameter for SISO Sytem Simulation over SUI Channel...45 Table 9. Parameter for Simulation of the Single-Carrier Sytem over SUI- Channel...47 Table 0. Parameter for Simulation of the MISO Sytem over Correlated SUI- Channel...49 Table. OFDM Symbol Duration for Variou Guard Ratio...5 Table. Parameter for Simulation of the SISO-SC and SISO-OFDM Sytem over the SUI- Channel Model...5 Table 3. Parameter for Simulation of the all Single-Carrier and OFDM Sytem over the SUI- Channel...54 Table 4. Parameter of the SUI Channel Model...6 Table 5. The Variable Repreenting the Simulation Parameter...64 xi

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15 LIST OF ACRONYMS AND ABBREVIATIONS AWGN BER CSI db FFT IFFT ISI MIMO MISO MRC OFDM PSK QAM RF SC SIMO SISO STBC SUI Additive White Gauian Noie Bit Error Rate Channel State Information decibel Fat Fourier Tranform Invere Fat Fourier Tranform Inter Symbol Interference Multiple Input Multiple Output Multiple Input Single Output Maximal Ratio Combining Orthogonal Frequency Diviion Multiplexing Phae Shift Keying Quadrature Amplitude Modulation Radio Frequency Single Carrier Single Input Multiple Output Single Input Single Output Space Time Block Coding Stanford Univerity Interim xiii

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17 ACKNOWLEDGEMENTS I thank my wife Cigdem for being in my life and for the upport and love he ha given during my tudie at NPS. Thank go out a well to Ruth and Bobby Moorhatch. The upport and love you gave u will never be forgotten. Finally, I want to thank my advior Prof. Murali Tummala for hi guidance and patience during the development of thi thei. xv

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19 EXECUTIVE SUMMARY Future military and commercial wirele communication ytem are required to provide higher data rate and reliable communication. Two major challenge in ytem deign are the limited pectrum and the fading caued by multipath component in the wirele channel. To obtain higher data rate, larger bandwidth are required. To keep the ame reliability under evere channel condition, a higher tranmitted power level i neceary. The emerging multiple-input multiple-output (MIMO) communication technologie have the potential to improve the performance without increaing the bandwidth or the tranmitted power. MIMO ytem exploit patial diverity by employing multiple antenna at either ide of the communication link. MIMO ytem may add robutne to future military communication ytem under battlefield condition. Due to it robutne under frequency elective channel, orthogonal frequency diviion multiplexing (OFDM) ha been adopted in everal wirele communication tandard, uch a the IEEE 80.a local area network (LAN) tandard and the IEEE 80.6a metropolitan area network (MAN) tandard. The combination of OFDM and MIMO technologie i a potential candidate for future wirele ytem. When the patial diverity gain provided by a MIMO ytem i added to robutne to fading provided by the OFDM ytem, the performance of the reulting ytem i ignificantly enhanced compared to the conventional ingle antenna and ingle-carrier ytem. The main objective of thi thei wa to invetigate MIMO and MIMO-OFDM ytem. The pace coding technique and the decoding algorithm tudied in thi thei are baed on the widely accepted Alamouti cheme. The Alamouti cheme wa originally propoed for flat fading channel. The extended cheme, pace-time block coding (STBC), ha been developed for frequency-elective, multipath channel. The STBC technique i invetigated for ytem employing both ingle-carrier and OFDM modulation. Sytem with two tranmit antenna and a ingle receive antenna are the mot invetigated cheme utilizing the Alamouti and the STBC MIMO technique. By extending the xvii

20 exiting reult for thi cae, in thi thei, we developed the input-output relation and decoding equation for the other poible antenna combination, uch a one tranmitting and two receiving antenna, and two tranmitting and two receiving antenna. The widely ued Stanford Univerity Interim (SUI) channel model were elected to repreent the wirele channel. The ue of multiple antenna at both end of a communication ytem reult in multiple channel between the tranmitter and the receiver. The multiple channel of MIMO ytem are contructed uing the SUI channel model. In practice, the pacing between antenna and the environment effect (angle of arrival and angle of departure of the electromagnetic wave) may caue correlation between thee multiple channel. We invetigated the patial correlation effect on both frequency-flat and frequency-elective MIMO channel. The MIMO ytem with ingle-carrier and OFDM modulation were imulated in Matlab. Simulation reult are preented in the form of the bit error rate (BER) curve. A performance comparion among the variou MIMO ytem i reported. The mot ignificant reult of the imulation wa that the ytem employing higher number of antenna at either ide of the communication link performed better than the one with fewer antenna. In the work reported here, the bet performing ytem wa the MIMO-OFDM ytem with two tranmitting and two receiving antenna. In a imulation uing the SUI- channel model, at a BER of 4 0, MIMO-OFDM performed db better than the conventional ingle antenna ytem employing ingle-carrier modulation; the total tranmitted power wa kept at the ame level in each cheme. xviii

21 I. INTRODUCTION One of the bigget challenge in wirele communication i to operate in a timevarying multipath fading environment under limited power contraint. The other challenge i the limited availability of the frequency pectrum. Future commercial and military wirele ytem will be required to upport higher data rate with reliable communication under pectrum limitation and multipath fading environment. Military communication ytem mut maintain reliable communication under the condition of hotile jamming and other interference without increaing emitted power or requiring larger bandwidth. In order to improve the reliability without increaing the emitted power, time, frequency or pace diverity could be exploited. In time diverity, the received ignal i ampled at a higher rate, thu providing more than one ample per tranmitted ymbol. In frequency diverity, the ame information i ent over a number of carrier []. Both diverity technique require larger bandwidth. To exploit pace diverity, the ame information i tranmitted or received through multiple antenna. Employing multiple antenna at the receiver and/or the tranmitter improve the quality of a wirele communication link without increaing the tranmitted power or bandwidth []. Therefore, the deign and implementation of multiple-input multiple-output (MIMO) communication ytem i an attractive reearch area. Orthogonal frequency diviion multiplexing (OFDM) i a widely ued method in wirele communication ytem. Due to it effectivene in multipath channel condition, OFDM ha been adopted by everal wirele communication tandard, uch a the IEEE 80.a local area network (LAN) tandard and the IEEE 80.6a metropolitan area network (MAN) tandard. The combination of OFDM and MIMO ytem preent better olution by adding more diverity gain to the conventional OFDM ytem employing a ingle antenna at both the receiver and the tranmitter [3]. The robutne to fading provided by OFDM i enhanced by the patial diverity of MIMO ytem, and the reulting performance of MIMO-OFDM ytem i ignificantly improved.

22 A. OBJECTIVE AND METHODOLOGY The main objective of thi thei wa to invetigate MIMO and MIMO-OFDM ytem and compare their performance to the conventional ingle antenna ytem. The firt tep to achieve thi goal wa to tudy the fundamental of MIMO ytem by invetigating their performance in a communication ytem. In thi thei, the publihed technique for the ytem with ingle-carrier modulation and with OFDM were invetigated. Several communication ytem with variou number of antenna utilizing both inglecarrier modulation and OFDM were developed in Matlab. The developed ytem were imulated uing the widely ued Stanford Univerity Interim (SUI) channel model. B. RELATED RESEARCH Due to their efficiency in providing an improved performance without increaing the bandwidth or the emitted power, MIMO ytem are the ubject of coniderable reearch effort. Probably the mot attractive cheme from the tand point of implementation and performance i the Alamouti tranmit diverity cheme [4] baed on maximal ratio combining (MRC) [5]. Numerou tudie have been performed to invetigate it performance and led to the development of everal variation [6, 7]. The cheme wa originally developed for flat fading channel. Subequently, it ha been extended to frequency elective channel cae [8, 9] and renamed a the pace-time block coding (STBC) technique. Later, the extended cheme ha been elected to be a part of the IEEE 80.6a tandard [0]. Channel modeling i another reearch area in MIMO ytem. The IEEE 80.6 Broadband Wirele Acce Working Group propoed SUI channel model for ytem imulation []. The preented channel model have been widely ued by many reearch tudie. C. ORGANIZATION OF THE THESIS Thi thei i organized into ix chapter. Chapter II introduce the input-output relation in MIMO ytem and Alamouti tranmit diverity cheme deigned for flat fading channel. Chapter III introduce the SUI channel model. The uncorrelated MIMO channel baed on SUI modeling and their extenion to correlated MIMO channel are

23 alo dicued. Chapter IV introduce the STBC cheme that ue both ingle-carrier modulation and OFDM. Chapter V preent the imulation reult of the communication ytem developed in Matlab. Chapter VI provide a ummary of the work, the concluion and uggetion for future tudie. Appendix A lit the SUI channel parameter. Appendix B provide an explanation of the Matlab imulation. 3

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25 II. MIMO SYSTEMS AND ALAMOUTI SCHEME The goal of thi chapter i to introduce a widely ued pace coding technique called the Alamouti cheme. An overview of the input-output relation of MIMO ytem i preented to decribe the pace coding algorithm at the tranmitter and the decoding proce at the receiver in the Alamouti cheme. A. MULTIPLE-INPUT MULTIPLE-OUTPUT (MIMO) SYSTEMS In order to develop the input-output relation of ingle-input multiple-output (SIMO), multiple-input ingle-output (MISO) and MIMO ytem, the ingle-input ingle-output (SISO) ytem i decribed firt.. Single-Input Single-Output (SISO) Sytem The chematic diagram of a SISO ytem i hown in Figure. The time-variant channel impule repone from the tranmitter to the receiver i denoted a h(, t) it repreent the repone at time t with an impule applied at time t τ where τ, which indicate that in a general etup, the ytem i time-varying. The input-output relation for a SISO ytem i given by τtotal ( ) = ( τ, ) ( τ ) τ = ( τ, ) ( ) (.) 0 r t h t x t d h t x t where x( t ) i the tranmitted ignal and r ( t) denote the received ignal at time t. The upper limit of the integralτ total i the duration of the impule repone. The operator denote the convolution operation []. h ( τ, t) Tranmitter x( t ) r( t) Receiver Figure. Schematic of a SISO Sytem (After Ref..) 5

26 . Single-Input Multiple-Output (SIMO) Sytem A SIMO ytem ha a ingle tranmit antenna and multiple ( M ) receive antenna. Figure illutrate the chematic of a SIMO ytem. Tranmitter x( t) hm r h ( τ t), ( τ, t) M r rm r ( ) r t ( t) r Receiver Figure. Schematic of a SIMO ytem (After Ref..) The channel ( ) ingle tranmit antenna to the receive antenna are given by h τ, t, i =,,, M, repreent the impule repone from the i r M r receive antenna. The received ignal at the repective ( ) = ( τ, ) ( ) ( ) = ( τ, ) ( ) r t h t x t r t h t x t ( ) = ( τ ) ( ) r t h, t x t. M r M r Repreenting the ignal at the receiver antenna in a vector form, we have the received ignal vector Similarly, the channel vector i given by ( t) r ( t) r ( t) r ( t) T M. r (.) r = (.3) ( t) h ( t) h ( t) h ( t) T = M r h. (.4) Therefore, we can expre the input-output relationhip of a SIMO ytem a ( t) = ( τ, t) x ( t) r h (.5) where the operator denote the element-by-element convolution. 6

27 3. Multiple-Input Single-Output (MISO) Sytem Figure 3 depict a imple MISO ytem with multiple ( M ) tranmit antenna and a ingle receive antenna. Input-output relationhip of a MISO ytem can be developed on the line of a SIMO ytem a dicued above. The multiple tranmitted ignal ( ) x τ, t, j =,,, M, are convolved with the channel impule repone j ( ) t j t h τ, t, j =,,, M. The receiving antenna receive a uperpoition of the multiantenna tranmiion through the channel []. Accordingly, the received ignal can be expreed a ( ) = ( ) ( τ, ) + ( ) ( τ, ) + + ( ) ( τ, ) r t x t h t x t h t x t h t. (.6) Uing the vector notation for the received ignal equation (.6), we can write the inputoutput relation for a MISO ytem a T = Mt where ( t) x ( t) x ( t) x ( t) ( ) = h( τ, ) x( ) Mt r t t t (.7) x i the tranmiion vector, and the channel vector i denoted a ( t) h ( t) h ( t) h ( t) h. = Mt t Mt Tranmitter x ( t) M t h ( τ t), r ( t) Receiver xm t ( t) hm t ( τ, t) Figure 3. Schematic of a MISO Sytem (After Ref..) 4. Multiple-Input Multiple-Output (MIMO) Sytem After dicuing the input-output relation for the SIMO and the MISO ytem, we now proceed to develop the MIMO ytem relation. A imple MIMO ytem i illutrated in Figure 4. The received ignal at the firt receive antenna i expreed by 7

28 ( ) = ( ) ( τ, ) + + ( ) ( τ, ) r t x t h t x t h t. (.8), Mt, Mt Thi i analogou to the MISO ytem input-output relation. The received ignal at the M r -th receive antenna i given by ( ) = ( ) ( τ, ) + + ( ) ( τ, ) r t x t h t x t h t. (.9) M r M r, Mt M r, Mt The general input-output relation for a MIMO ytem in matrix-vector notation i given by T = Mt where ( t) x ( t) x ( t) x ( t) ( t) = ( τ, t) ( t) r H x (.0) x i the M tranmiion vector, ( t) r ( t) r ( t) r ( t) T = Mt r i the M r M channel matrix given by t r t H i the M receive vector, and ( τ,t) h, ( τ, t) h, ( τ, t) h, M ( τ, t) t h, ( τ, t) h, ( τ, t) h, M ( τ, t) t H( τ, t) =. (.) hm,( τ, t) h,(, ), (, ) r M τ t h r M r M τ t t x ( t ) hm r h ( τ t ),, ( τ t),, r ( t) Tranmitter xm t M t ( t) h 8 ( τ t ), M t, h r t ( τ t) M, M, M r r M r ( t) Figure 4. Schematic of a MIMO Sytem (After Ref..) B. ALAMOUTI SCHEME Receiver The Alamouti tranmit diverity technique wa propoed in 998 [4]. The technique i generally referred to a the Alamouti cheme in the literature. Alamouti cheme i one of the firt pace coding cheme developed for the MIMO ytem. Since the cheme ha a imple tranmit coding technique and a imple decoding implementation, it gained coniderable interet.

29 The Alamouti cheme wa developed for ytem under flat fading condition, i.e., over frequency independent channel. Therefore, while dicuing the cheme, the indice of delay τ and time t of the channel are dropped. The channel are denoted a hi, i =,, repreenting ingle-tap impule repone. Prior to developing the Alamouti cheme, we firt need to preent the input-output relation of the SIMO ytem uing a maximal ratio combining cheme.. Maximal Ratio Combining (MRC) Scheme for Sytem Maximal ratio combining (MRC) cheme i developed for the ytem having multiple receive antenna, i.e., multiple channel. The cheme i baed on the aumption that the receiver ha perfect channel knowledge. The tranmitted information i etimated by proceing the channel tate information (CSI) and the received ignal [5]. The channel information may be obtained by inerting known pilot ymbol. The receiver etimate the channel information by interpolating the ample of the received pilot ymbol [4]. Figure 5 illutrate a ytem employing MRC. The impule repone of the channel from the tranmit antenna to the receive antenna i denoted by h and to the receive antenna i denoted by h. Auming that the channel have flat fading, received ignal with additive noie are expreed by r = h + n r = h + n 9 (.) where i the tranmitted information ymbol and n and n denote the complex noie component. The MRC ue the CSI and the received ignal r and r to compute the etimated value of. The MRC obtain an etimate of uing the relation [4] = h r + h r. (.3) The combining cheme compenate for the phae hift in the channel by multiplying the received ignal with the complex-conjugate of the correponding channel [5]. Subtituting (.) into (.3), we can rewrite the etimate of a ( ) = h + h + h n + h n. (.4)

30 The contructed complex value i the maximum likelihood etimate of the tranmitted ymbol [4]. The etimate of the tranmitted ymbol i motly dependent upon the magnitude of the channel h and h, i.e., MRC i reitant to phae change of the channel. h r r Maximal Ratio Combining h Channel State Information Figure 5. Maximal Ratio Combining for a Sytem (After Ref. 4.). Alamouti Scheme for Sytem The Alamouti cheme for a ytem with two tranmit antenna and a ingle receive antenna i hown in Figure 6. Two conecutive ymbol and are tranmitted imultaneouly during the firt ymbol period (at time = t). During the next ymbol period (at time = t + T), and are tranmitted from antenna and, repectively, where the aterik indicate complex conjugation. The tranmiion equence i hown in Table. 4 3 h h 4 3 Alamouti encoder h r 3 r Alamouti decoder h r 4 r Channel State Information Figure 6. Alamouti Scheme for a Sytem (After Ref. 4.) 0

31 Time Tranmit Antenna- Tranmit Antenna- t Table. t+t Tranmiion Sequence of the Alamouti Scheme The received ignal at time t, which i the uperpoition of the two incoming ignal, can be expreed by ( ) Table ), but the decoding cheme will be different. r = r t = h + h + n (.5) where n i the additive complex noie component. Auming that the channel i contant acro two conecutive ymbol period, we can expre the received ignal at time t+t a ( ) r = r t + T = h h + n (.6) where n i the additive complex noie component. Two conecutive received ignal and the CSI are employed at the Alamouti decoder. The etimate of the tranmitted ymbol are computed by [4] = h r + h r h r h r =. Subtituting (.5) and (.6) into (.7), we can rewrite the decoder equation a ( ) ( ) = h + h + h n + h n h h h n h n = +. + Thi outcome how that the Alamouti decoder compenate the phae change of the channel in a manner imilar to that in the MRC cheme. 3. Alamouti Scheme for Sytem (.7) (.8) We can extend the Alamouti cheme to a ytem by adding one more receiving antenna. A chematic of the Alamouti cheme for a ytem i illutrated in Figure 7. The tranmiion equence i identical to the one in the ytem (ee

32 4 3 h 4 3 Alamouti encoder r r Alamouti decoder h Channel State Information Figure 7. Alamouti Scheme for a Sytem (After Ref. 4.) Auming that the channel i contant acro conecutive ymbol period, the received ignal can be expreed by r = h + h + n,, r = h + h + n,, r = h + h + n 3,, 3 r = h + h + n 4,, 4 where ni, i =,,3,4, are the complex noie component. Table lit the notation for the received ignal at the receive antenna. The channel impule repone hi, j, i, j =,, repreent the four poible path in the cheme. (.9) Time Receive Antenna- Receive Antenna- t r r t+t r 3 r 4 Table. Notation for the Received Signal in Alamouti Scheme The Alamouti decoder contruct the etimate of and uing the CSI, the received ignal and the decoding equation given by [4]

33 = h r + h r + h r + h r,, 3,, 4 = h r h r + h r h r.,, 3,, 4 Subtituting (.9) into (.0), we can rewrite the decoder equation a ( ) ( ) = h + h + h + h + h n + h n + h n + h n,,,,,, 3,, 4 h h h h h n h n h n h n =, +, +, +., +,, 3 +,, 4 (.0) (.) Clearly, we can ee that the etimate motly depend on the magnitude of the channel o that the cheme i reitant to phae change. C. SUMMARY Thi chapter dicued the input-output relation in MIMO ytem, the MRC cheme for ytem and the Alamouti cheme for and ytem. In all cae, only flat channel model are ued to introduce the decoding proce. In the next chapter, MIMO channel model for the frequency elective cae are introduced. 3

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35 III. MIMO CHANNEL MODELS Building a channel model i important for invetigating the performance of wirele communication ytem. Channel parameter are extracted from meaurement including path lo, Ricean K-factor, delay pread and Doppler pread for SISO ytem and patial correlation for MIMO ytem. The Stanford Univerity Interim (SUI) channel are widely ued channel model baed on uch meaurement. In the literature, mot imulation, epecially the IEEE 80.6a tandard-baed OFDM ytem imulation, are conducted uing the SUI channel model. Generation of the SUI channel for SISO ytem and the patial correlation effect on correlated MIMO channel are dicued in thi chapter. A. STANFORD UNIVERSITY INTERIM (SUI) CHANNELS FOR THE IEEE 80.6a STANDARD The IEEE 80.6 Broadband Wirele Acce Working Group propoed channel model for fixed broadband ytem in the year 00. Thee channel model are known a Stanford Univerity Interim (SUI) channel model becaue of the contribution of the Stanford Univerity in the development proce. The detailed channel generation i decribed in []. Three different terrain categorie are defined in the SUI channel model. The maximum path lo category i hilly terrain with moderate-to-heavy tree denitie (Category A). The minimum path lo category i typically flat terrain with light tree denitie (Category C). The intermediate path lo category i Category B. The SUI channel model define two model for each terrain type, thu leading up to a total of ix categorie. Each channel model i characterized by a time delay, a Ricean K-factor and a Doppler pread in addition to the path lo behavior. The broad parameterization of the SUI channel i ummarized in Table 3. From thi claification, we can eaily ee that the SUI- channel i the leat evere channel model with a low delay pread ( 0.4 µ for the nd tap and 0.9 µ for the 3 rd tap), a low Doppler pread (0.4 Hz, 0.3 Hz, 0.5 Hz for the t, nd and 3 rd tap, repectively) and a high K-factor (8 db for the t tap). The mot evere channel i certainly the SUI-6 model with a high delay pread ( 4 µ for the nd tap and 5

36 0 µ for the 3 rd tap), a high Doppler pread ( Hz,.5 Hz,.5 Hz, for the t, nd and 3 rd tap, repectively) and K = 0, i.e., no direct path component but only a fading component (ee Appendix A for detail of all SUI model parameter). SUI-Model Terrain Type Delay Spread Ricean K Factor Doppler SUI- C Low High Low SUI- C Low High Low SUI-3 B Low Low Low SUI-4 B Moderate Low High SUI-5 A High Low Low SUI-6 A High Low High Table 3. SUI Channel Characterization (After Ref. 3.) Each of the ix SUI channel i modeled a a 3-tap dicrete ytem with nonuniform delay, i.e., multipath fading exit for each SUI model. The SUI channel are alo modeled for different antenna type. Each channel ha parameter defined for an omni-directional antenna and for a 30 directional antenna. The detailed parameter for the omni-directional and for the 30 directional antenna cae are given in Appendix A. The latet IEEE 80.6 Broadband Wirele Acce Working Group report [] contain a complimentary Matlab code for generating channel for the SUI-3 model. In thi thei, to create a imulation environment, an expanded verion of Matlab code (containing all ix SUI channel) wa developed baed on the code in []. After generating the SUI channel model in Matlab, the frequency repone of the channel model were invetigated. The frequency repone plot of five different SUI channel are hown in Figure 8. The frequency range wa choen to be in term of the ubcarrier index 0-55 in accordance with the fat Fourier tranform (FFT) ize of the IEEE 80.6a tandard. The frequency repone wa normalized uch that the maximum magnitude wa. By oberving the fluctuation of the magnitude value, the SUI- 6

37 channel magnitude repone change moothly between 0.9 and.0 where a the SUI-5 channel magnitude repone varie rapidly between 0.5 and.0. A a reult, the higher the SUI channel index, the more frequency elective i the channel. Magnitude Magnitude Magnitude Magnitude Magnitude SUI- SUI- SUI-3 SUI-4 SUI Subcarrier Figure 8. The Frequency Repone Plot of Different SUI Channel Model B. GENERATING CORRELATED MIMO CHANNELS Since there are multiple antenna at both end of MIMO ytem, the preence of patial correlation ha an effect on the channel. The ideal cae i that all channel in a MIMO ytem are independent, i.e., uncorrelated with each other. In reality, however, the phyical configuration of the antenna (antenna pacing) and operating environment parameter (angle of arrival and angle of departure of the electromagnetic wave) caue patial correlation on the antenna array of a MIMO ytem. A MIMO ytem performance i reduced by thi patial correlation. An analyi of patial correlation i dicued in [4].. Uncorrelated MIMO Channel Conider a ytem with M t tranmit and 7 M r receive antenna. Auming that all the channel are flat and uncorrelated (i.e., each path i repreented by a ingle complex tap weight), the MIMO channel can be modeled to be zero mean and circularly ymmet-

38 ric with unit variance. The uncorrelated channel i an identically and independently ditributed channel, denoted a Hw with dimenion M r M t. The propertie of H w are E E { Hw i, j } { Hw i, j } = 0 = { Hw H i, j wm, n } E = 0 if i m or j n where E{ } denote the expectation operator [].. Correlated MIMO Channel In practice, MIMO channel can differ from H w becaue of the patial correlation. A more practical MIMO channel can be expreed a [] / / r w t (3.) H = R H R (3.) where M R r i the r r M receive correlation matrix and R t i the M t M t tranmit correlation matrix. The correlation matrice matrice and have the following propertie: form []: R r and R = R R / / r r r R R R / / t = t t. 8 R t are poitive emi-definite Hermitian The correlation matrice for a ytem can be generated in the following (3.3) ρr R r = ρr, (3.4) ρt R t = ρt (3.5) where ρr and ρ t denote the receive and tranmit correlation coefficient. The patial fading coefficient i dependent upon the ditance between the antenna, the wavelength and the geometry of the phyical environment and take value between 0 and. When the tranmit and receive correlation coefficient are both equal to zero, the correlation matrice Rr and uncorrelated channel Rt become identity matrice, and then the MIMO channel will be equal to the H w. The computation of the correlation coefficient i preented in

39 detail in [4]. In thi thei, the environmental parameter (antenna pacing, angle of arrival and angle of departure of the electromagnetic wave) were not taken into account to compute the correlation coefficient. The correlation coefficient parameter were choen arbitrarily. 3. LOS Component In the preence of a line-of-ight (LOS) component, MIMO channel have a fixed and a random component. The MIMO channel with a LOS component can be repreented a [] where K / ( + K ) H i the LOS and ( K ) K H = H + H w (3.6) + K + K / + Hw i the random uncorrelated fading component. The element of H have unit power. The Ricean K-factor in (3.6) i the ratio of the LOS component power to the fading component power. When K = 0, the channel become pure Rayleigh faded channel, i.e., there i no LOS component. When K =, all we have i the LOS component, and there i no fading component. Then the channel become flat []. In the preence of both patial correlation and LOS component, to achieve a complete MIMO channel, only the fading component i computed uing (3.), and the fixed LOS component i added to the fading component uing (3.6). The generation of the correlated SIMO and MISO channel are imilar to the MIMO channel. Conider a ytem with a ingle tranmit and two receive antenna. The uncorrelated SIMO channel H w i a row vector. Since we have a ingle tranmit antenna, there i no tranmit correlation, i.e., ρ t = 0. The tranmit covariance matrix R t i then an identity matrix. From (3.), the correlated SIMO channel can be expreed a where H = R H (3.7) / Rr i the quare-root of the receive correlation matrix R r. / r For the MISO cae, conider a ytem with two tranmit antenna and a ingle receive antenna. The uncorrelated MISO channel 9 w Hw will be a column vector. Since

40 there are multiple antenna only at the tranmitter, the receive correlation matrix identity matrix. The correlated MISO channel i expreed by where w / t R r i an H = H R (3.8) / Rt i the quare-root of the tranmit correlation matrix R t. In the preence of a LOS component, the fixed component of the MISO and the SIMO channel are added to the correlated fading component of the MISO and the SIMO channel, repectively. The complete MISO or SIMO channel i achieved by the relation given in (3.6). C. GENERATING CORRELATED FREQUENCY-SELECTIVE MIMO CHANNELS The generation of the SUI channel for SISO ytem and correlated flat MIMO channel have been dicued o far. The uncorrelated channel Hw in (3.) ha ingle-tap complex component for the flat channel cae. The frequency elective channel have multi-tap component. To tudy the correlated frequency elective MIMO channel, conider a ytem with two tranmit and two receive antenna operating over the MIMO channel generated by the SUI model. Each tap i characterized by a delay pread, a power level, a Doppler pread and a Ricean K-factor. Therefore, a SUI channel ha a fixed and a fading component for each tap. The fading component include the delay pread, the Doppler pread and the power level. The fixed component i generated with the pecified Ricean K-factor for the given SUI model []. In a MIMO channel for a ytem baed on SUI channel modeling, the fading and fixed component can be expreed a repectively, where ( ) ij h k i the channel repone between the i-th( i =, ) tranmit antenna and the j-th (, ) ( ) ( ) ( 3) ( ) ( ) ( 3) ( ) ( ) ( 3) ( ) ( ) ( 3) ( ) ( ) ( 3) ( ) ( ) ( 3) ( ) ( ) ( 3) ( ) ( ) ( 3) h h h h h h H w = (3.9) h h h h h h h h h h h h H =, (3.0) h h h h h h j = receive antenna for the k-th( k =,,3) tap. Auming that all 0

41 tap correlation are equal, the correlated fading component of the MIMO channel i expreed by where H ( k ) w ij ( k ) = ( k ) Hˆ R H R (3.) / / ij r w ij t i the uncorrelated channel matrix for the k-th tap. To achieve the complete MIMO channel, the LOS component will be added to the correlated fading component. Then the MIMO channel i given by H ( ) ( ) ˆ ij k = K Hij k + H ij ( k ) (3.) + K + K where H ( k ) i the fixed component between the i-th ( i =, ) ij j-th ( j =, ) receive antenna for the k-th (,,3) MIMO channel i illutrated in Figure 9. D. SUMMARY tranmit antenna and the k = tap. Generation of a correlated In thi chapter, the generation of SUI channel for SISO ytem, uncorrelated MIMO channel and patial correlation effect on flat and frequency elective MIMO channel were dicued. It wa demontrated that the channel become more frequency elective a the SUI index increae. In the next chapter, we will develop the input-output relation for the Alamouti cheme baed STBC ytem over frequency elective multi-tap channel.

42 Power level Ricean K-factor Delay pread Doppler pread ρt ρr Generate the fixed Component H eq. (3.0) Generate the fading Component H w eq. (3.9) Compute the correlation matrice / R r eq. (3.4) eq. (3.5) / R t ue prop. in eq. (3.3) Compute the correlated fading component Ĥ eq. (3.) Compute the complete MIMO channel H eq. (3.) Figure 9. Conceptual Diagram for Generating a Correlated MIMO Channel Baed on SUI Channel Model

43 IV. ALAMOUTI-BASED SCHEMES OVER FREQUENCY- SELECTIVE CHANNELS The tranmitted ignal experience different type of fading depending upon the relationhip between the ignal parameter (bandwidth, ymbol period, etc.) and the channel parameter (Doppler pread, delay pread, etc.). When the bandwidth of the channel i greater than the bandwidth of the tranmitted ignal, the received ignal experience a flat fading channel. A flat channel i approximated a a ingle-tap weight with zero delay. When the bandwidth of the channel i greater than the bandwidth of the tranmitted ignal, the received ignal experience a frequency elective channel or a multipath fading channel. Over frequency elective channel, multiple verion of the tranmitted ignal having faded amplitude arrive at the receiver at lightly different time intant. Frequency elective channel are modeled by multiple tap dicrete ytem with different delay parameter [5]. Alamouti tranmit diverity cheme, which wa dicued in Chapter II, wa originally propoed for flat channel. The pace coding technique i performed over a ymbol pair, i.e., two conecutive ymbol (ee Table ). The decoding equation (.7) and (.0) are developed for flat channel. The frequency-flat channel in thee equation are repreented a one-tap complex weight. The extenion of the Alamouti cheme to frequency-elective channel wa invetigated in [8] and [9]. The extended cheme i called pace-time block coding (STBC), ince pace coding i performed over block of ymbol. The cheme preented in [8] and [9] i for the ytem with two tranmit antenna and a ingle receive antenna ( ). In thi thei, the cheme i further extended to and ytem uing the original Alamouti cheme. OFDM ha emerged a an attractive alternative cheme to conventional modulation cheme due to it effectivene in reducing the effect of frequency elective channel [7]. The combination of MIMO ytem and OFDM modulation i one of the widely dicued area in the MIMO reearch. Different pace coding technique in MIMO- OFDM ytem have been invetigated by many author [6, 7, 6]. In thi work, we have elected the STBC cheme a the pace coding cheme for MIMO-OFDM ytem to 3

44 tudy it imulation performance and compare it performance to that of STBC-SC ytem. The STBC cheme i choen a an optional technique in the OFDM phyical layer pecification of the IEEE 80.6a tandard. In thi chapter, we dicu the STBC coding technique for the MIMO ytem with both ingle-carrier modulation and OFDM. Input-output relation and the decoding equation are preented for SISO, SIMO, MISO and MIMO ytem. A. SPACE-TIME BLOCK CODING-SINGLE CARRIER (STBC-SC) SYS- TEMS OVER FREQUENCY-SELECTIVE CHANNELS Before dicuing the STBC cheme, in order to get familiar with the notation, the dicrete-time SISO ytem relation over frequency elective channel are introduced firt.. SISO Sytem over Frequency-Selective Channel Conider that a block of ymbol i tranmitted from a ingle antenna by auming that the channel characteritic do not change during the period of tranmiion. The tranmitted block of ymbol i expreed by ( ) ( ) ( ) S = N (4.) where N i the block ize. The tranmitted ymbol block will experience a frequency elective channel. The channel can be repreented a a dicrete-time filter given by where ( ) h q = h + h q + h q (4.) P 0 P q i the unit delay operator and n,,, received ignal can be expreed a h n = P are the filter coefficient. The ( ) = ( ) ( ) = ( ) + ( ) + ( ) r t h q t h t h t h t P. (4.3) 0 P The noie component of the received ignal i omitted here for convenience. The maximum likelihood etimate of the tranmitted ymbol block i computed by where h ( q) ( ) = ( ) ( ) = ( ) + ( + ) + + ( + ) t h q r t h r t h r t h r t P (4.4) 0 P repreent a non-caual realization of the filter given in (4.) [8].. SIMO Sytem over Frequency-Selective Channel The chematic of a SIMO ytem over frequency elective channel i illutrated in Figure 0 for a realization. The tranmitted block of ymbol i identical to the 4

45 SISO cae (ee Eq. (4.)). Since there are two receive antenna, we have two channel filter given by ( ) ( ) h q = h + h q + + h q P 0 P h q = h + h q + + h q P 0. P The tranmitted ignal i paed through thee two channel filter, and the received ignal are expreed by ( t ) h ( q ) h ( ) = ( ) ( ) r t h q t ( ) = ( ) ( ) r t h q t. ( q ) ( ) r t r ( t) Maximal Ratio Combining (4.5) (4.6) ( t) Figure 0. Channel State Information Schematic of a SIMO-SC Sytem Utilizing MRC over Frequency- Selective Channel The etimate of the tranmitted ignal block i computed on the line of the maximal ratio combining cheme. The multiplication operation in the decoding equation (.3) i turned into a filter operation for the frequency elective channel. Accordingly, the etimate of the tranmitted ymbol block i given by [8] ( ) ( ) ( ) ( ) ( ) t = h q r t + h q r t. (4.7) Notice that the conjugate of the filter h ( q) and h ( q) 5 in (4.7) are non-caual filter. By ubtituting (4.5) into (4.7), the etimate of the tranmitted ignal block in (4.7) can be rewritten a ( ) ( ) ( ) ( ) ( ) 0 P 0 h r ( t + ) + + h r ( t + P). t = h r t + h r t h r t + P + h r t + P (4.8)

46 3. MISO Sytem over Frequency-Selective Channel The Alamouti cheme for a ytem over flat channel wa dicued in Chapter II. The flat-channel implementation wa baed on applying the Alamouti encoding cheme over a ymbol pair, i.e., two conecutive ymbol. The cheme can be extended to the frequency-elective channel cae by utilizing the STBC technique. A chematic of a MISO ytem utilizing STBC i illutrated in Figure. The tranmitted block of ymbol are given by S S ( ) ( ) ( ) ( ) ( ) ( ) = N = N where S and S are the imultaneouly tranmitted block of ymbol from antenna and antenna, repectively. The Alamouti pace-time encoding cheme i performed over thee two ymbol block. The firt antenna tranmit a complex-conjugated and ymbol-inverted verion of S, and the econd antenna tranmit a complex-conjugated verion of S in the econd tranmiion burt. The tranmitted block of ymbol in the (4.9) econd burt are given by ( ) ( ) ( ) * S = = N 3 S S ( ) ( ) ( ) N * 4 = S = (4.0) where S 3 and S4 are tranmitted from antenna and, repectively. The tranmiion ymbol block equence for the STBC for a ytem i hown in Table 4. ( t) Figure. ( t) STBC Encoder ( ) = ( ) t t 3 ( ) = ( ) t t 4 ( t) ( t) h ( q ) h ( q ) r ( t) r ( t) STBC Decoder Channel State Information ( ) ( ) t t Schematic of a STBC-SC Sytem over Frequency-Selective Channel 6

47 Time Tranmit Antenna- Tranmit Antenna- t tranmiion burt S S nd tranmiion burt S * 3 = S S = * 4 S Table 4. Tranmiion Sequence for STBC The notation of the channel for a ytem i identical to the one for the ytem (ee Eq. (4.5)). Auming that the channel characteritic remain contant during conecutive tranmiion of ymbol block, the received ignal are given by [8] where r ( t ) and r ( ) ( ) = ( ) ( ) + ( ) ( ) r t h q t h q t ( ) = ( ) ( ) + ( ) ( ) r t h q t h q t 3 4 t denote the received ignal during the t and nd tranmiion (4.) burt, repectively. The STBC decoder etimate the tranmitted block of ymbol uing the decoding equation given by [4, 8] where h ( q) and h ( q) ( ) = ( ) ( ) + ( ) ( ) t h q r t h q r t ( ) = ( ) ( ) ( ) ( ) t h q r t h q r t repreent the non-caual realization of the channel filter. 4. MIMO Sytem over Frequency-Selective Channel After dicuing the SISO, SIMO and MISO ytem over frequency-elective (4.) channel, we now proceed to develop the MIMO ytem relation. A chematic of a MIMO ytem utilizing STBC i illutrated in Figure. The patial encoding cheme i identical to the MISO ytem utilizing STBC. The tranmitted block of ymbol were introduced in Equation (4.9) and (4.0). The four MIMO channel for the ytem are expreed a 7

48 ( ) ( ) ( ) ( ) h q = h + h q + + h q P,, 0,, P h q = h + h q + + h q P,,0,,P h q = h + h q + + h q P,,0,,P h q = h + h q + + h q P,,0,,. P (4.3) ( t ) ( t ) STBC Encoder ( ) = ( ) t t 3 ( ) = ( ) t t 4 ( t ) ( t ) h h h ( q ) ( q ) ( q ) h ( q ) r3 r4 ( t) ( t) r ( t) r ( t) STBC Decoder ( ) ( ) t t Channel State Information Figure. Schematic of a STBC-SC Sytem over Frequency-Selective Channel Auming that the channel characteritic remain contant over two tranmiion burt, the received ignal are given by ( ) = ( ) ( ) + ( ) ( ) r t h q t h q t,, ( ) = ( ) ( ) + ( ) ( ) r t h q t h q t,, ( ) = ( ) ( ) + ( ) ( ) r t h q t h q t 3, 3, 4 ( ) = ( ) ( ) + ( ) ( ) r t h q t h q t 4, 3, 4. The equence and the location of the received ymbol block in (4.4) are given in Table 5. The STBC decoder etimate the tranmitted block of ymbol by uing the decoding equation [4, 8] where ( ) ( ) = ( ) ( ) + ( ) ( ) + ( ) ( ) + ( ) ( ) t h q r t h q r t h q r t h q r t,, 3,, 4 ( ) = ( ) ( ) ( ) ( ) + ( ) ( ) ( ) ( ) t h q r t h q r t h q r t h q r t,, 3,, 4. (4.4) (4.5) h i, j q, i =, ; j =,, repreent the non-caual realization of the channel filter. The equation in (4.5) are imilar to the flat channel Alamouti decoding equation previouly introduced in (.0). The multiplication operation in the flat channel cae i now replaced by the filter operation. 8

49 Receive Antenna- Receive Antenna- t tranmiion burt r ( t ) r ( t ) nd tranmiion burt r3 ( t ) r4 ( t ) Table 5. The Sequence and the Location of the Received Signal for a STBC Sytem B. SPACE-TIME BLOCK CODING-ORTHOGONAL FREQUENCY DIVI- SION MULTIPLEXING (STBC-OFDM) SYSTEMS OVER FREQUENCY- SELECTIVE CHANNELS In the previou ection, we dicued the ingle-carrier MIMO ytem utilizing STBC over frequency-elective channel. The combination of STBC and OFDM i dicued in thi and the following ection. OFDM ha emerged a an attractive and alternative cheme to the conventional modulation cheme due to it effectivene in reducing the effect of frequency-elective channel [7]. In OFDM, the entire ignal bandwidth i divided into a number of orthogonal ubcarrier band, and then the ignal i tranmitted in thee narrowband over a number of ubcarrier. The OFDM and STBC parameter were elected from the IEEE 80.6a tandard [0]. The IEEE 80.6a tandard include the STBC cheme a an optional pecification for ytem employing OFDM.. SISO-OFDM Sytem over Frequency-Selective Channel A block diagram of a SISO-OFDM ytem i hown in Figure 3. A detailed explanation of each block i given in the following dicuion. The phyical layer part of the IEEE 80.6a tandard i ued in decribing the SISO-OFDM cheme here. 9

50 [ 0] x[ 0] Channel coding Symbol Mapping... [ N ] IFFT... x[ N ] Cyclic Prefix Addition D/A Converter RF Modulation x( t) 00 (meage to be ent) (pilot inertion) h( q ) Decoder Symbol Demapping [ 0]... FFT x[ 0]... Cyclic Prefix Removal A/D Converter RF Demodulation r ( t) 00 (received meage) [ N ] (etimation proce) x[ N ] Figure 3. Block Diagram of a SISO-OFDM Scheme a. Channel Encoding The information bit equence i firt encoded by the channel encoder. Error control coding i ued to rearrange the tranmitted information to increae it reitance to noie. The IEEE 80.6a tandard ue concatenated forward error correction (FEC), which i baed on the erial concatenation of a Reed-Solomon outer code and a rate compatible Trelli coded modulation (TCM) inner code. Between the outer and the inner code, employing an interleaver i optional. Since our main focu in thi thei wa to tudy the MIMO and MIMO-OFDM ytem, the imulation only ued the convolutional encoder to keep it imple. The encoder had a rate of ½, contraint length 7 and generator polynomial in octal form 7 and 33 [0]. b. Symbol Mapping The channel encoded bit are mapped to I and Q ymbol coordinate uing a gray code ymbol map depending on the modulation cheme. Figure 4 how ome of the contellation introduced in IEEE 80.6a tandard. 30

51 (a) (b) (c) Figure 4. Gray coded (a) BPSK, (b) QPSK and (c) 6-QAM contellation (From Ref. 0.) c. Invere Fat Fourier Tranform (IFFT) Operation Mapped ymbol are next input to the IFFT block. The FFT ize i equal to the number of ubcarrier. In the IEEE 80.6a tandard, two type of OFDM cheme are included, OFDM with 56 ubcarrier and OFDMA (for higher data rate and multiple acce) with 048 ubcarrier. In thi thei, the OFDM with 56 ubcarrier wa choen for imulation purpoe. Three type of ubcarrier are defined in the OFDM technique of IEEE 80.6a tandard: data carrier for information tranmiion, pilot carrier deigned to extract the channel information at the receiver, and guard carrier (alo called null carrier) placed on the either edge of the pectrum to avoid interference from adjacent band. The aignment of ubcarrier in the IEEE 80.6a tandard i given in Table 6. Thee carrier allocation will be ued in organizing the information and pilot ymbol before the IFFT operation. Figure 5 illutrate the ubcarrier organization prior to IFFT operation according to the carrier allocation given in Table 6. 3

52 Size of FFT 56 # of information ubcarrier 9 # of pilot ubcarrier 8 # of null ubcarrier (including the DC ubcarrier) 56 # of lower frequency guard ubcarrier 8 # of higher frequency guard ubcarrier 7 Frequency indice of null ubcarrier (including the DC ubcarrier) 8, 7,, 0, 0 + 0, + 0,, + 7 Frequency indice of pilot ubcarrier 84, 60, 36,,,36,60,84 Table 6. Allocation of OFDM Subcarrier in the IEEE 80.6a Standard 8 null ubcarrier information ymbol DC ubcarrier 8 pilot ubcarrier 7 null ubcarrier IFFT Figure 5. Allocation of Subcarrier before the IFFT Block (ee Table 6) The output of the IFFT block in dicrete time can be expreed by = = 0,... (4.6) NFFT j π fkn x[ n] ke n NFFT NFFT k = 0 3

53 where k i the k-th ymbol entering to the IFFT block and f k i the k-th ubcarrier frequency. The index of ubcarrier frequency in (4.6) i choen to be 0 to N intead of 8 to + 8, for convenience. The length of the IFFT output i called the ueful time T b. d. Cyclic Prefix Addition Multipath delay pread caue interymbol interference (ISI), and the ISI bring about performance degradation. To deal with thi problem, a guard time i introduced for each OFDM ymbol. The guard time i choen to be larger than the expected delay pread o that multipath component from one ymbol would not interfere with thoe from the next ymbol. In the IEEE 80.6a tandard, optional guard length T g are FFT pecified with repect to the ueful timet b. The optional guard ratio Tg T are b 4, 8, 6 and 3. The deired length of the guard interval i derived from thi ratio. The addition of cyclic prefix (CP) i hown in Figure 6. Conider that the guard ratio i choen to be 6. The output of the IFFT block ha a length of 56; therefore, the guard length will be 6. The CP i formed by taking the lat 6 ample of the IFFT output and concatenating them to the beginning of the ymbol equence in (4.6). The reulting new equence i [ ] [ ] [ ] [ ] [ ] [ ] [ ] xcp = x 40 x 4 x 54 x 55 x 0 x x 55. (4.7) The total interval after adding the CP i referred to a the ymbol time T. Figure 6. OFDM Symbol Time Structure (From Ref. 0.) 33