Proposed Algorithm for MIMO-OFDM Systems on Fast-Time ... · I declare that the thesis entitled...

Proposed Algorithm for MIMO-OFDM Systemson Fast-Time Varying Multipath fading channel

A Thesis submitted to Gujarat Technological University

for the Award of

Doctor of Philosophyin

Electronics and Communication Engineering

by

Darshankumar Chandrakant Dalwadi(Enrollment No. : 129990911012 )

under supervision of

Dr. Himanshu B. Soni

GUJARAT TECHNOLOGICAL UNIVERSITYAHMEDABAD

July - 2018

c©[Darshankumar Chandrakant Dalwadi]

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DECLARATION

I declare that the thesis entitled Proposed Algorithm for MIMO-OFDM Systems on Fast-Time Varying Multipath fading channel, submitted by me for the degree of Doctor ofPhilosophy is the record of research work carried out by me during the period from October2012 to April 2018 under the supervision of Dr Himanshu B. Soni and this has not formedthe basis for the award of any degree, diploma, associateship, fellowship, titles in this or anyother University or other institution of higher learning.

I further declare that the material obtained from other sources has been duly acknowledgedin the thesis. I shall be solely responsible for any plagiarism or other irregularities, if noticedin the thesis.

Signature of the Research Scholar: . . . . . . . . . . . . . . . . . . . . . . Date: . . . . . . . . . . . . . . . . . . . . . .

Name of Research Scholar: Darshankumar Chandrakant Dalwadi

Place: Vallabh Vidyanagar

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CERTIFICATE

I certify that the work incorporated in the thesis Proposed Algorithm for MIMO-OFDMSystems on Fast-Time Varying Multipath fading channel submitted by DarshankumarChandrakant Dalwadi was carried out by the candidate under my supervision/guidance.To the best of my knowledge: (i) the candidate has not submitted the same research work toany other institution for any degree/diploma, Associateship, Fellowship or other similar titles(ii) the thesis submitted is a record of original research work done by the Research Scholarduring the period of study under my supervision, and (iii) the thesis represents independentresearch work on the part of the Research Scholar.

Signature of Supervisor: . . . . . . . . . . . . . . . . . . . . . . . . . . . Date: . . . . . . . . . . . . . . . . . . . . . . . . . . .

Name of Supervisor: Dr. Himanshu B. Soni


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Course-work Completion Certificate

This is to certify that Mr.Darshankumar Chandrakant Dalwadi enrolment no. 129990911012is a PhD Scholar enrolled for PhD program in the branch Electronics and CommunicationEngineering of Gujarat Technological University, Ahmedabad.(Please tick the relevant option(s)

� He/She has been exempted from the course-work (successfully completed during M.PhilCourse)

� He/She has been exempted from Research Methodology Course only (successfully com-pleted during M.Phil Course)

� He/She has successfully completed the PhD course work for the partial requirement forthe award of PhD Degree. His/Her performance in the course work is as follows-

Grade Obtained in Research Methodology(PH001)

Grade Obtained in Self Study Course(Core Subject) (PH002)

AB AA

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It is certified that PhD thesis titled Proposed Algorithm for MIMO-OFDM Systems onFast-Time Varying Multipath fading channel, by Darshankumar Chandrakant Dal-wadi has been examined by us. We undertake the following:

(a) Thesis has significant new work knowledge as compared already published or areunder consideration to be published elsewhere. No sentence, equation, diagram, table,paragraph or section has been copied verbatim from previous work unless it is placedunder quotation marks and duly referenced.

(b) The work presented is original and own work of the author (i.e. there is no plagiarism).No ideas, processes, results or words of others have been presented as author’s ownwork.

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(d) There is no falsification by manipulating research materials, equipment or processes,or changing or omitting data or results such that the research is not accurately repre-sented in the research record.

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Name of Research Scholar: Darshankumar C. Dalwadi


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PhD THESIS Non-Exclusive License toGUJARAT TECHNOLOGICAL UNIVERSITY

In consideration of being a PhD Research Scholar at GTU and in the interests of the facilita-tion of research at GTU and elsewhere, I, Darshankumar Chandrakant Dalwadi havingEnrollment No. 129990911012 hereby grant a non-exclusive, royalty free and perpetuallicense to GTU on the following terms:

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(f) I represent that my thesis is my original work, does not infringe any rights of others,including privacy rights, and that I have the right to make the grant conferred by thisnon-exclusive license.

(g) If third party copyrighted material was included in my thesis for which, under theterms of the Copyright Act, written permission from the copyright owners is required,I have obtained such permission from the copyright owners to do the acts mentionedin paragraph (a) above for the full term of copyright protection.

(h) I retain copyright ownership and moral rights in my thesis, and may deal with the copy-right in my thesis, in any way consistent with rights granted by me to my Universityin this non-exclusive license.

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(i) I further promise to inform any person to whom I may hereafter assign or licensemy copyright in my thesis of the rights granted by me to my University in this non-exclusive license.

(j) I am aware of and agree to accept the conditions and regulations of PhD including allpolicy matters related to authorship and plagiarism.

Signature of the Research Scholar: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Name of Research Scholar: Darshankumar C. Dalwadi

Date: . . . . . . . . . . . . . . . . . . . . . . . . . . Place: Vallabh Vidyanagar

Signature of Supervisor: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Date: . . . . . . . . . . . . . . . . . . . . . . . . . . Place: Vallabh Vidyanagar

Seal

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Thesis Approval Form

The viva-voce of the PhD Thesis submitted by Darshankumar Chandrakant Dalwadi (En-rollment No. 129990911012) entitled Proposed Algorithm for MIMO-OFDM Systems onFast-Time Varying Multipath fading channel was conducted on . . . . . . . . . . . . . . . . . . . . . . . . .(day and date) at Gujarat Technological University.(Please tick any one of the following option)

� The performance of the candidate was satisfactory. We recommend that he/she be awardedthe PhD degree.

� Any further modifications in research work recommended by the panel after 3 monthsfrom the date of first viva-voce upon request of the Supervisor or request of IndependentResearch Scholar after which viva-voce can be re-conducted by the same panel again (brieflyspecify the modification suggested by the panel).

� The performance of the candidate was unsatisfactory. We recommend that he/she shouldnot be awarded the PhD degree (The panel must give Justifications for rejecting the researchwork ). .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Name and Signature of Supervisor with Seal 1) (External Examiner 1) Name and Signature

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ABSTRACT

We have discussed the issue of PAPR in OFDM system based on low complexity scramblingapproach and raised cosine filter with interleaver method. We have minimized the value ofPAPR in OFDM system. In low complexity technique, we have present the novel PAPRminimization technique which is based on the combination of probabilistic approach andcoded approach. In the proposed algorithm the out-of-band radiation is reduced as well ascomplexity of physical system is low. In the extended work, we have solve the problem in3-GPP LTE physical layer system in which to achieve the lowest PAPR value with respectto OFDM system with multiple interleaver. We have targeted uplink of the LTE system inwhich we have used the OFDM system with multiple interleaver to minimize the probabilityof error as well as to reduce the PAPR based on various shaping filter coefficient.

As further extension of the work, the proposed estimation technique of MIMO-OFDM sys-tem with respect to time varying mobile velocity. We have evaluated the channel with respectto the SKF and DKF method for linear channel estimation. For known mobile velocity, pro-posed algorithm outperforms compared to conventional algorithm. We have further extendedthe work with respect to the nonlinear channel estimation. When mobile velocity is rapidlychange or unknown then nonlinear Kalman filter performs better compared to SKF and DKFmethod.

In the same line of research, we have proposed adaptive fuzzy cubature Kalman filter equal-ization technique on MIMO-OFDM system with velocity of the mobile is time varying. Thismethod is based on various membership function. In this case we have considered the dif-ferent mobile velocity. This approach is more adaptive compared to other technique. As perthe requirement, we have select the membership function and track the channel which min-imize the BER. The proposed method is suitable for non linear channel estimation in whichamplitude of the channel and Doppler shift parameters are simultaneously estimated. Theproposed method does not occupy the whole bandwidth and due to this BER outperformscompared to other methods.

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AcknowledgmentFirstly, I would like to express my sincere gratitude to my Ph.D. supervisor, Dr. HimanshuSoni, Principal, G. H. Patel College of Engineering and Technology, Vallabh Vidyanagar forhis continuous support and kind guidance throughout the tenure of my research. He alwaysraised his bar high, to expand the horizon of my research endeavor and meet the desiredobjectives within a stipulated amount of time. He always remains as a source of inspirationand provided a good environment to cultivate new ideas and explore them in the field ofinterest. I am very much obliged to him for his profound approach, motivation and spendingvaluable time to mold this work and bring a hidden aspect of research in a light.

I extend the special thanks to my Doctorate Progress Committee (DPC) members, Dr. Tan-may Pawar, Head of Electronics Engineering Department, BVM, Vallabh Vidyanagar andDr. Jignesh N. Sarvaiya, Head of Electronics Engineering Department, SVNIT, Surat, fortheir valuable comments, useful suggestions and encouragement to visualize the problemfrom the different perspective.Their humble approach and the way of appreciation for goodwork have always created the amenable environment and boost-up my confidence to pushthe limit.

I am very much thankful to Charutar Vidya Mandal for facilitating me enough space andresources to complete my work with pleasant experience and ease of comfort.

I have no words to express my feeling for my mother, my father and my wife Hardika forstanding with me all the time and carried out all the social responsibilities and made merelieve to spend ample amount of time for my research.

During this time, I always remain blessed by my grandfather Principal C. H. Prajapati. Theyhave provide the proper direction in my whole life. They kept me calm and aligned with mywork despite of all the up-down and fluctuation in life. I blow down my head to the feet ofmy grandfather.

I am very much thankful to my son Hitarth, my relatives, friends, colleagues, faculty mem-bers of BVM, and my students for all their support and help during my research.

Finally, I express my broad sense of gratitude to the almighty for his grace and blessing.

Darshankumar C. Dalwadi

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Table of Content

ABSTRACT x

Acknowledgment xi

List of Abbreviations xvi

List of Symbols xviii

List of Figures xix

List of Tables xxi

1 Introduction 11.1 General Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Multipath Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Types of Small scale fading . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 MIMO-OFDM Transmitter Model . . . . . . . . . . . . . . . . . . . . . . 41.5 MIMO-OFDM Receiver Model . . . . . . . . . . . . . . . . . . . . . . . . 41.6 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.6.1 Research Gaps and Motivation of Work . . . . . . . . . . . . . . . 81.7 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.8 Objective and Scope of work . . . . . . . . . . . . . . . . . . . . . . . . . 91.9 Contribution of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.10 Organization of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Literature Survey 122.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.1 Introduction to MIMO-OFDM System . . . . . . . . . . . . . . . . 122.2 MIMO-OFDM System Model . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 System Model of MIMO-OFDM Transmitter . . . . . . . . . . . . 132.2.2 System Model of MIMO-OFDM Receiver . . . . . . . . . . . . . . 14

2.3 Literatures for OFDM with PAPR minimization technique . . . . . . . . . 14

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2.4 Literatures for the estimation of channel in MIMO-OFDM system . . . . . 16

3 PAPR Minimization technique for MIMO-OFDM System 183.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 System Model of Proposed low complexity PAPR minimization technique . 19

3.2.1 Block diagram of low complexity PAPR minimization technique . . 193.3 System Model of Proposed PAPR minimization technique based on inter-

leaver method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.1 Block diagram of proposed method . . . . . . . . . . . . . . . . . 21

3.4 Interpolation of OFDMA signal using interleaver technique . . . . . . . . . 223.4.1 Interpolation of OFDMA signal without interleaver technique . . . 233.4.2 Interpolation of OFDMA signal with proposed interleaver technique 24

3.5 Simulation Results of low complexity PAPR minimization technique . . . . 243.5.1 Simulation parameters and results . . . . . . . . . . . . . . . . . . 25

3.6 Simulation Results of PAPR minimization technique based on interleavermethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.6.1 Simulation parameters and results . . . . . . . . . . . . . . . . . . 31

3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 Channel Estimation technique using Linear and Non linear Kalman filter 374.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Estimation of channel based on linear Kalman filter method . . . . . . . . . 38

4.2.1 Block diagram of MIMO-OFDM transmitter . . . . . . . . . . . . . 384.2.2 Block diagram of MIMO-OFDM receiver . . . . . . . . . . . . . . 38

4.3 Mathematical model of channel estimation technique . . . . . . . . . . . . 394.3.1 Estimation of channel based on MMSE equalizer . . . . . . . . . . 394.3.2 Estimation of channel based on Kalman filter . . . . . . . . . . . . 41

4.4 Estimation of channel based on Modified Kalman filter . . . . . . . . . . . 424.4.1 Mathematical model of Modified Kalman Filter . . . . . . . . . . . 42

4.5 Simulation Results of MIMO-OFDM system with linear Kalman filter . . . 444.5.1 Simulation parameters and results . . . . . . . . . . . . . . . . . . 44

4.6 Simulation Results of MIMO-OFDM with MKF method . . . . . . . . . . 494.6.1 Simulation parameters and results . . . . . . . . . . . . . . . . . . 50

4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

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5 Channel estimation technique using Fuzzy based Adaptive Kalman filter tech-nique 565.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.2 System Model of MIMO-OFDM Transmitter and Receiver . . . . . . . . . 57

5.2.1 System Model of MIMO-OFDM transmitter . . . . . . . . . . . . . 575.2.2 System Model of MIMO-OFDM receiver . . . . . . . . . . . . . . 585.2.3 Mathematical model of MIMO-OFDM channel estimation . . . . . 59

5.3 Channel estimation based on FAKF technique . . . . . . . . . . . . . . . . 595.3.1 Mathematical model of proposed FAKF technique . . . . . . . . . . 605.3.2 Fuzzy membership function . . . . . . . . . . . . . . . . . . . . . 605.3.3 Performance analysis of various parameters . . . . . . . . . . . . . 62

5.4 Simulation Results of MIMO-OFDM system with FAKF technique . . . . . 645.4.1 Simulation parameters and results . . . . . . . . . . . . . . . . . . 64

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6 MIMO-OFDM Channel estimation using Adaptive Fuzzy Cubature Kalmanfilter 706.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706.2 Mathematical Model of MIMO-OFDM Transmitter and Receiver . . . . . . 71

6.2.1 System Model of MIMO-OFDM transmitter . . . . . . . . . . . . . 716.2.2 System Model of MIMO-OFDM receiver . . . . . . . . . . . . . . 726.2.3 Mathematical model of MIMO-OFDM channel estimation . . . . . 73

6.3 Estimation of channel based on AFCKF technique . . . . . . . . . . . . . . 736.3.1 Mathematical model of proposed Adaptive Fuzzy Cubature Kalman

Filter technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.3.2 Fuzzy membership function . . . . . . . . . . . . . . . . . . . . . 756.3.3 Implementation algorithm of basic CKF method . . . . . . . . . . . 766.3.4 Performance analysis of various parameters . . . . . . . . . . . . . 77

6.4 Proposed Equalization technique of MIMO-OFDM system . . . . . . . . . 786.4.1 Mathematical model of proposed equalization technique . . . . . . 78

6.5 Simulation Results of MIMO-OFDM system with AFCKF method . . . . . 806.5.1 Simulation parameters and results . . . . . . . . . . . . . . . . . . 80

6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7 Conclusion and Future Scope 867.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

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7.2 Future Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

References 88

List of Publications 91

List of Courses Attended 92

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List of Abbreviations

ACF Auto Correlation FunctionADC Analog (to) Digital ConverterAFCKF Adaptive Fuzzy Cubature Kalman FilterBER Bit Error RateBPSK Binary Phase Shift KeyingCCDF Complementary Cumulative Distribution FunctionCCF Cross Correlation FunctionCFO Carrier Frequency OffsetCKF Cubature Kalman FilterCOFDM Coded Orthogonal Frequency Division MultiplexingCP Cyclic PrefixCSI Channel State InformationDAC Digital (to) Analog ConverterDKF Double Kalman FilterDOSi Degree Of SimilarityEM Expected MaximizationFAKF Fuzzy Adaptive Kalman FilterFFT Fast Fourier TransformGPP Generation Partnership ProjectGSM Global System (for) MobileIFFT Inverse Fast Fourier TransformISI Inter Symbol InterferenceKF Kalman FilterLFDMA Localized Frequency Division Multiple AccessLMS Least Mean SquareLS Least SquareLTE Long Term EvolutionMC-CDMA Multicarrier Code Division Multiple AccessMIMO Multiple Input Multiple OutputMKF Modified Kalman FilterMMSE Minimum Mean Square ErrorMSE Mean Square ErrorOFDM Orthogonal Frequency Division MultiplexingOFDMA Orthogonal Frequency Division Multiple AccessOSTBC Orthogonal Space Time Block CodePAPR Peak (to) Average Power Ratio

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PDF Probability Density FunctionQAM Quadrature Amplitude ModulationQPSK Quadrature Phase Shift KeyingRC Raised CosineSC-FDMA Single Carrier Frequency Division Multiple AccessSFBC Space Frequency Block CodeSISO Single Input Single OutputSKF Single Kalman FilterSNR Signal (to) Noise RatioSQNR Signal (to) Quantization Noise RatioSTC Space TimeSTC Space Time CodeTSK Takagi Sugeno KangUTRAN Univesal Terrestrial Radio Access Network

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List of Symbols

Symbol Description

Gt(n) Transmitter MatricesRt(n) Receiver MatricesHt(n) Channel Matricesaw Phase factorA[k] IFFT inputa[q] IFFT outpute[k] Error at kth instantK Number of tapsRys CCF between received and input sequenceRyy ACF between of received sequenceE(e[k])2 Mean Square Errorxk+1 Next state value at Kth instantuk Known input at Kth instantyk Output at Kth instantKk Kalman gainDk Derivativeik Innovation sequencegk+1 Next state predicted valuehb,at (m) Channel impulse responsef b,aD,t Maximum Doppler Shiftrd Radius of poleQb,at (n) Normal noise

Sp Process noise covarianceSq Measurement noise covarianceL(x) Low speed PDFM(x) Medium speed PDFH(x) High speed PDFωdT Fading ratefd Doppler frequency

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List of Figures

1.1 Multipath Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Based on Multipath time delay spread . . . . . . . . . . . . . . . . . . . . 31.3 Based on Doppler spread . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 MIMO-OFDM Transmitter Model . . . . . . . . . . . . . . . . . . . . . . 41.5 MIMO-OFDM Receiver Model . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Block diagram of MIMO-OFDM transmitter . . . . . . . . . . . . . . . . . 132.2 Block diagram of MIMO-OFDM receiver . . . . . . . . . . . . . . . . . . 15

3.1 Block diagram of low complexity PAPR minimization technique . . . . . . 203.2 Proposed PAPR minimization technique . . . . . . . . . . . . . . . . . . . 223.3 Low complexity PAPR minimization technique for BPSK . . . . . . . . . . 273.4 Low complexity PAPR minimization technique for 8-QAM . . . . . . . . . 273.5 Low complexity PAPR minimization technique for 32-QAM . . . . . . . . 283.6 Low complexity PAPR minimization technique for 128-QAM . . . . . . . . 293.7 Comparative analysis of low complexity PAPR minimization technique . . . 303.8 Proposed PAPR Minimization technique with other technique for 8-QAM/OFDM 333.9 Proposed PAPR Minimization technique with other technique for 32-QAM/OFDM 333.10 Proposed PAPR Minimization technique with other technique for 128-QAM/OFDM 343.11 Proposed PAPR Minimization technique with interleaver using RC filter for

8-QAM/OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.12 Proposed PAPR Minimization technique with interleaver using RC filter for

32-QAM/OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.13 Proposed PAPR Minimization technique with interleaver using RC filter for

128-QAM/OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.1 Block diagram of MIMO-OFDM transmitter . . . . . . . . . . . . . . . . . 384.2 Block diagram of MIMO-OFDM receiver . . . . . . . . . . . . . . . . . . 394.3 Block diagram of Kalman filter algorithm . . . . . . . . . . . . . . . . . . 424.4 Comparison of MMSE and Kalman filter . . . . . . . . . . . . . . . . . . . 45

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4.5 MSE V/S SNR for MIMO-OFDM Channel Estimation (Predictor) . . . . . 464.6 MSE V/S SNR for MIMO-OFDM Channel Estimation (Estimator) . . . . . 464.7 BER V/S SNR for MIMO-OFDM Channel Estimation . . . . . . . . . . . 474.8 MSE V/S SNR for MIMO-OFDM System (Predictor)-QPSK . . . . . . . . 474.9 MSE V/S SNR for MIMO-OFDM System (Estimator)-QPSK . . . . . . . . 484.10 BER V/S SNR for MIMO-OFDM System-QPSK . . . . . . . . . . . . . . 484.11 MSE V/S SNR for MIMO-OFDM with MKF technique (Predictor) . . . . . 504.12 MSE V/S SNR for MIMO-OFDM with MKF technique (Estimator) . . . . 514.13 BER V/S SNR for MIMO-OFDM with MKF technique . . . . . . . . . . . 514.14 MSE V/S SNR for MIMO-OFDM Channel Estimation (Predictor) - QPSK . 534.15 MSE V/S SNR for MIMO-OFDM Channel Estimation (Estimator) - QPSK 534.16 BER V/S SNR for MIMO-OFDM Channel Estimation - QPSK . . . . . . . 54

5.1 System Model of MIMO-OFDM transmitter . . . . . . . . . . . . . . . . . 575.2 System Model of MIMO-OFDM receiver . . . . . . . . . . . . . . . . . . 585.3 Flowchart of proposed fuzzy adaptive Kalman filter method . . . . . . . . . 605.4 Membership value v/s Velocity of the mobile . . . . . . . . . . . . . . . . . 625.5 MSE V/S SNR for MIMO-OFDM Estimation (Predictor) - BPSK . . . . . . 655.6 MSE V/S SNR for MIMO-OFDM Estimation (Estimator) - BPSK . . . . . 655.7 BER V/S SNR for MIMO-OFDM Estimation - BPSK . . . . . . . . . . . . 665.8 MSE V/S SNR for MIMO-OFDM Channel Estimation (Predictor) - QPSK . 685.9 MSE V/S SNR for MIMO-OFDM Channel Estimation (Estimator) - QPSK 685.10 BER V/S SNR for MIMO-OFDM Channel Estimation - QPSK . . . . . . . 69

6.1 System Model of MIMO-OFDM transmitter . . . . . . . . . . . . . . . . . 716.2 System Model of MIMO-OFDM receiver . . . . . . . . . . . . . . . . . . 726.3 Membership value v/s Velocity of the mobile . . . . . . . . . . . . . . . . . 776.4 MSE V/S SNR for MIMO-OFDM with AFCKF technique (Predictor-QPSK) 806.5 MSE V/S SNR for MIMO-OFDM with AFCKF technique (Estimator-QPSK) 816.6 BER V/S SNR for MIMO-OFDM with AFCKF technique - QPSK . . . . . 826.7 MSE V/S SNR for MIMO-OFDM with AFCKF technique (Predictor-8-QAM) 836.8 MSE V/S SNR for MIMO-OFDM with AFCKF technique (Estimator-8-QAM) 846.9 BER V/S SNR for MIMO-OFDM with AFCKF technique - 8-QAM . . . . 84

xx

List of Tables

3.1 Simulation Parameters and it’s Value . . . . . . . . . . . . . . . . . . . . . 253.2 Simulation results of various modulation techniques . . . . . . . . . . . . . 263.3 Simulation Parameters and its Value . . . . . . . . . . . . . . . . . . . . . 313.4 Simulation results for PAPR minimization using RC filter . . . . . . . . . . 32

4.1 Simulation Parameters and it’s Value . . . . . . . . . . . . . . . . . . . . . 494.2 Simulation Parameters and its Value . . . . . . . . . . . . . . . . . . . . . 524.3 Simulation results for MIMO-OFDM system with SKF, DKF and MKF . . 52

5.1 Simulation Parameters and it’s Value . . . . . . . . . . . . . . . . . . . . . 665.2 Simulation results for MIMO-OFDM with FAKF, SKF & DKF . . . . . . . 67

6.1 Simulation Parameters and its Value . . . . . . . . . . . . . . . . . . . . . 826.2 Simulation results for MIMO-OFDM with AFCKF, FKF, SKF & DKF . . . 836.3 Simulation Parameters and its Value . . . . . . . . . . . . . . . . . . . . . 85

xxi

Chapter 1

Introduction

1.1 General Overview

During the past decades, wireless communication has benefited from substantial advance-ment in the technology and it is considered as the key enabling technique of innovativefuture consumer products. For the sake of satisfying the requirements of various applica-tions, significant technological achievements are required to ensure that wireless deviceshave appropriate architectures suitable for supporting a wide range of services delivered tothe users.

In current wireless communication technique, the large amount of data rate is required. Thisrequirement is fulfill by MIMO-OSTBC system. In most of the literature, channel is consid-ered as flat and time invariant. However for fast fading rate, MIMO-OSTBC system neededan improved equalizer which remove the inter symbol interference. To reduce this problem,MIMO system combined with OFDM technique. The main advantages of MIMO-OFDMsystem are lower complexity, antenna diversity, removal of ISI and higher data rate. Toachieve the maximum capacity and diversity gain, the channel state information must be per-fectly known. But in most practical scenario, it is difficult to known the perfect CSI at thereceiver side. So, efficient estimation technique is required in MIMO-OFDM system whichminimize the bit error rate.

This chapter is organize as follows: Section 1.2 described the various multipath propagationcondition like reflection, diffraction and scattering. Section 1.3 described the types of smallscale fading. Section 1.4 and 1.5 described the system model of MIMO-OFDM transmitterand receiver respectively. Section 1.6 described the literature review. Section 1.7 describedthe problem statement. Section 1.8 described the objective and scope of work. Section 1.9described the contribution of thesis. Section 1.10 described the organization of thesis.

1

Chapter 1. Introduction

1.2 Multipath Propagation

In wireless communication system, the radio channel is used between base station and mo-bile station. The signal transmitted from the tower and received to the mobile via differentpropagation paths. In some cases, a Line of Sight situation occurred between transmitter andreceiver. There are several propagation mechanisms between base station and mobile sta-tion like reflection or diffraction of signals by different objects in the environment: houses,mountains, windows, walls, etc. The propagation paths between transmitter and receiver isvery large. As shown in figure 1.1, each of the paths has a different amplitude, differenttime delay, different phase shifts, direction of departure from the transmitter, and directionof arrival.

Figure 1.1: Multipath Propagation

1.3 Types of Small scale fading

Small scale fading means the fluctuation of the signal amplitude at the receiver side due tointerference received from different multipath components. With respect to the relationshipbetween the signal parameters and the channel parameters, the signal transmitted from basestation will faced different types of fading. Signal parameters include bandwidth, symbolperiod etc. Channel parameters include rms delay spread, Doppler spread etc. Figure 1.2and figure 1.3 shows the types of Small Scale Fading. Based on multipath time delay spread,

2

1.3. Types of Small scale fading

there are two types of small scale fading: 1) Flat Fading and 2) Frequency Selective Fading.Based on Doppler spread, there are two types of small – scale fading: 1) Fast Fading and 2)Slow Fading.

Figure 1.2: Based on Multipath time delay spread

Figure 1.3: Based on Doppler spread

3


1.4 MIMO-OFDM Transmitter Model

A MIMO-OFDM system is the system with no. of transmitter antennas are Nt and numberof receiver antennas are Nr and number of subcarriers are Nc to be considered. Figure 1.4shows MIMO-OFDM transmitter model. According to the properties of the orthogonal spacetime block coder, let transmitted signal is given by,

Gt(n) = [Gt,1(n), Gt,2(n), Gt,3(n), ......., Gt,m(n)]T (1.1)

The orthogonal space time block coder is given by,

D(Gt(n)) =L∑

m=1

(AmRe[Gt,m(n)] + jBmIm[Gt,m(n)]) (1.2)

Where (Am, Bm) are mth fixed time slot × no. of tx antenna matrices.

Figure 1.4: MIMO-OFDM Transmitter Model

1.5 MIMO-OFDM Receiver Model

Figure 1.5 shows the MIMO-OFDM receiver model. The received signal can be expressedas,

Rt(n) = D(Gt(n))Ht(n) + Pt(n) (1.3)

4

1.6. Literature review

For n = 0,1,2,.....,Nc − 1, where Rt(n) is the receiver matrices with no. of slot × no. of rxantenna and Ht(n) is the frequency response of channel and Pt(n) is the noise with no. ofslot × no. of rx antenna.

Figure 1.5: MIMO-OFDM Receiver Model

1.6 Literature review

In IEEE 802.11n and IEEE 802.11ac, OFDM is seen as possible technique at physical layerwith multiple input and multiple output. OFDM is adopted by 3GPP-LTE system to improvethe wireless broadband connectivity [6]. OFDM is used in applications such as audio broad-casting, digital television, wireless networking and in wireless broadband connectivity [6].In OFDM one of the problems is high peak values of the signals in the time domain dueto the number of subcarriers are accumulated through an IFFT block. Because of this highPAPR value, it reduces the SQNR of ADC and DAC and also reduces the efficiency of thetransmitter [1]. So at the transmitter side, it is required to reduce the high PAPR value.

In the research work [1], alternative multisequence scheme considered to minimize the PAPRin MIMO-OFDM system. The authors have developed a space frequency block coding struc-ture to combine the signals at different transmitter antenna. In the prescribed work, authors

5


have considered space frequency block code which limit the performance of OFDM systemwhen frequency selective channel is considered. In [2], authors have incorporated compand-ing nonlinear transform technique to minimize PAPR in OFDM signals. In this method, thepeak power is minimized by compressing the transmitted signal, and expanded the receivedsignal. In this technique, out of band radiation is generated due to nonlinear operation at thetransmitter side. In the work [3], authors have proposed the adaptive clipping level controlmethod to minimize the PAPR in OFDM. But this method causes out of band radiation and inband distortion. However, filtering after clipping can eliminate the radiation but it increasethe value of peak power. In [4], authors have proposed the effective PAPR minimizationtechnique of SFBC-OFDM for multinode cooperative transmission. This work is limited toSISO system. Authors have not considered the effect of multiple antenna at transmitter andreceiver side. In the work [5], authors have addressed the PAPR minimization techniquebased on exponential companding for OFDM systems. Companding is a non linear processand due to this out of band radiation is developed which limit the performance of OFDMsystem. In [6] author has used the localized frequency division multiple access approach toreduce the high PAPR value. In this approach, the signal reconstruction becomes complex.So, efficient PAPR reduction technique is required to reduce the PAPR value and also reducethe complexity of signal reconstruction at the uplink of 3GPP- LTE system.

In current wireless communication technique, the large amount of data rate is required. Thisrequirement is fulfill by MIMO-OSTBC system. In most of the prior work, channel is con-sidered as flat and time invariant. However for fast fading rate, MIMO-OSTBC systemneeded an improved equalizer which remove the inter symbol interference. To reduce thisproblem, MIMO system combined with OFDM technique. The main advantages of MIMO-OFDM system are lower complexity, antenna diversity, removal of ISI and higher data rate.To achieve the maximum capacity and diversity gain, the channel state information must beperfectly known. But in most practical scenario, it is difficult to known the perfect CSI at thereceiver side. So, efficient estimation technique is required in MIMO-OFDM system whichminimize the bit error rate.

For estimating the channel, various methods have been adopted. In [7], performance eval-uation of MC-CDMA system under the Rayleigh channel is explained by the author. Theestimation of channel is based on the Kalman filter of MC-CDMA system. In [7], authorspresent that for low to moderate fading rate, decision directed detectors are preferred and forhigher fading rate, pilot assisted detectors are preferred. However, in this case only linearestimation is considered which is based on Kalman filter and MC-CDMA system. The non

6

1.6. Literature review

linear estimation of channel has not been considered. In the research work [8], authors haveproposes a decoding technique for Alamouti’s STC method over time-selective channels. Inthis, authors have not considered the multicarrier system and estimation is also based onlinear equalization only. In [9], authors have proposed tracking of the channel and detectionof symbol for MIMO-OFDM system under the time-varying fading channel. The proposedmethod is based on expectation maximization algorithm. However, this method requires thenumerous iteration to achieve optimum results. The authors [10] have address the problem ofjoint CFO and estimation for MIMO-OFDM systems. The estimation of channel is based onextended Kalman filtering. However, this method is based on only first order approximationof non linear estimation. In [11], authors have proposed TSK fuzzy approach to estimatingthe channel for MIMO-OFDM. In the proposed algorithm, the computational complexity islower because the inverse matrix required by the MMSE receiver is not required. However,in this work time varying channel condition has not been considered. In [12], authors haveaddresses the CKF method which deals with nonlinear state-space models. However, authorshave not addresses the issues of fading rates i.e. time varying channel condition has not beenconsidered by the authors.

In most of the literature [7,9,11,12], estimation of channel is based on overhead symbols.The overhead method is not efficient when channel variation is faster. We have used decisionmaking technique of estimation of channel which is not require any overhead symbols. Whenchannel variation is fast, we have minimize the estimated error as well as bit error rate. Wehave developed the equalizer which minimize the bit error rate in the fast fading environment.We have jointly estimated the Doppler frequency shift parameters and channel frequencyresponse based on fuzzy based adaptive filter. The fuzzy based method is depend on thefuzzy membership function. As per the membership function, we have estimate the channel.We have considered the various types of membership function which represent the differentmobile velocity.

The authors [21] have address the channel estimation based on autoregressive model. Buthere author considered the linear approximation i.e. different mobile velocity has not beenconsidered. In [22], channel estimation is based on slow fading channel. Here author consid-ered the single antenna system. The multi antenna system has not been considered. In [23],the author address the blind channel estimation technique for OFDM systems over frequencyselective fading channels. Here, algorithm is based on slow fading channel. The author hasnot considered the fast channel variation.

7


1.6.1 Research Gaps and Motivation of Work

As per the literature discussed in the previous section following research, the gap has beenidentified.

1. In 3-GPP LTE uplink OFDM system, the PAPR reduced due to RC filter and multipleinterleaver method. This method has not been explored in the available literature anddue to this limited performance of OFDM system in terms of PAPR and BER.

2. In case of estimating the channel, the most of the reported work considered the knownvelocity of the mobile. The unknown velocity of the mobile is not well addressed inthe prior work which is required to investigate in detail with a various setting of thesystem.

3. Performance evaluation of MIMO-OFDM system for time varying velocity of thechannel based on non linear estimation is not well investigated in the available lit-erature.

4. The non linear estimation approach for tracking has not been explored with respect tofuzzy based adaptive cubature Kalman filter method.

5. To investigate the performance of fuzzy based adaptive cubature Kalman filter basedon various membership function i.e. to considered the different mobile velocity.

1.7 Problem Statement

When the mobile is moving with its known velocity then state equation can be described aslinear model. For the case when channel variation is slower (like 5 km/h, 10 km/h etc.), thechannel is estimated by the Kalman filter method. But when the channel variation is faster i.e.when the mobile is moving with unknown velocity (like range from 40 km/h to 160 km/h),then state equation can be described as nonlinear model. In this case channel is estimatedby the fuzzy based adaptive cubature Kalman filter method. Because the basic Kalman filtermethod is suitable for only linear estimation. When the channel variation is faster then thebasic Kalman filter method do not track the channel accurately due to its linearity. In the caseof nonlinear estimation of channel we have proposed fuzzy based adaptive cubature Kalmanfilter method which accurately tracks the channel variation. We have make the comparativeanalysis of the BER performance of proposed method and conventional method.

8

1.8. Objective and Scope of work

1.8 Objective and Scope of work

Our research work has been mainly directed to complete following defined major objectivesto fill the research gap mentioned earlier.

1. To reduce the high PAPR value of OFDM using proposed algorithm.

2. To estimate the channel state using linear estimation method (Mobile velocity is known)-KF method.

3. To estimate the channel state using non linear estimation method (Mobile velocity isunknown)-Higher order statistics of the KF method.

4. To estimate the channel state using Non linear KF method.

5. To estimate the channel state using proposed fuzzy based Adaptive Kalman and Cuba-ture Kalman filter method.

6. To accurately estimate the channel compared to existing methods.

1.9 Contribution of Thesis

The major findings of our work and contribution to this thesis have been presented as follows.

1. We have developed PAPR reduction technique for COFDM systems with probabilisticapproach. We have derived the new analytical expression for PAPR reduction tech-nique using proposed method for BPSK, QPSK and M-ary QAM modulation. Wehave present the novel PAPR reduction technique that is based on the combination ofprobabilistic approach and coded approach. In the low complexity PAPR minimizationtechnique, we have change the order of the input of OFDM block. In the proposed al-gorithm the out-of-band radiation is reduced as well as complexity of physical systemis low.

2. We have demonstrated discrete technique with shaping filter for PAPR minimization inOFDM system using multiple interleaver. The proposed algorithm solve the problemin 3-GPP LTE physical layer system in which to achieve the lowest PAPR value withrespect to OFDM system with multiple interleaver. We have targeted uplink of the LTE

9


system in which OFDM system used with multiple interleaver to minimize the prob-ability of error as well as to reduce the PAPR using various shaping filter coefficient.We have also compared the simulation results for OFDM system with Interleaver andwithout Interleaver.

3. We have estimate the channel and track the MIMO-OFDM system based on SKFmethod to improve the estimation of channel compare to conventional estimationmethod. We have considered Rayleigh fading channel with first order statistics. Inthis technique, we have achieved lowest BER compare to conventional method.

4. We have also estimate the channel and track the MIMO-OFDM system based on DKFmethod. As we increase the Kalman filter order, the performance of BER is degraded.Because second order Kalman filter tends to the non-linear estimation. If mobile sta-tion velocity is constant or known then single order Kalman filter is suitable. But ifmobile station velocity is varied or unknown then Kalman filter is not suitable. Wehave consider the unknown mobile velocity scenario.

5. We have evaluated the channel based on variation in the mobile velocity. If mobilevelocity is varied or unknown, the proposed method improves the BER performancecompare to other method. We have compared the proposed non linear Kalman filtermethod with the SKF & DKF method. From simulation results, it is revealed that theproposed estimation method based on non linear Kalman filter outperforms the BERcompare to other method.

6. We have proposed the novel noise adjustment technique for MIMO-OFDM system onfast time varying multipath fading channel using fuzzy based method. If mobile stationvelocity is very fast then proposed method is used. We have proposed the methodwith respect to Rayleigh fading channel. We have also compare the proposed AFCKFand FAKF method with the SKF, DKF and Nonlinear Kalman filter method. In theproposed method, the lowest value of bit error rate is achieved compare to conventionalmethod.

1.10 Organization of thesis

We have organized our work into seven chapters, and here we are presenting details insightof the work chapter wise.

10

1.10. Organization of thesis

In the first chapter, we have given a brief introduction to problems and challenges involvedin MIMO-OFDM wireless communication system. We have presented literature related tothe problem and research gaps. We have also discussed the problem statement, objectivesand our contribution to this thesis.

In the second chapter, we have briefly discuss the methods and solutions presented by exist-ing literature in the domain of research. We will also describe how our finding is differentthan available solutions and how it addresses a problem in a more better way.

In the third chapter, we have present our proposed PAPR minimization technique for MIMO-OFDM system. We will also discuss simulation results of the proposed scheme for variousperformance metrics with the existing schemes.

In the fourth chapter, we have explained the proposed non linear estimation method basedon Modified Kalman filter. We will also compare the MKF method with linear estimationmethod. We will also discuss the simulation results of the proposed scheme with the existingschemes.

In the fifth chapter, we have extended our work based on fuzzy based adaptive algorithm.When mobile velocity is varied, the performance evaluation of proposed algorithm is better.The bit error rate is reduced based on the selection of various membership function. We willconsider the criteria related to membership function like low speed users and medium speedusers. We will present the various simulation results of proposed method and also give thecomparative analysis.

In the sixth chapter, we have discussed our proposed fuzzy based adaptive Cubature Kalmanfilter method. When mobile station varies with high speed, the proposed algorithm produceslowest value of bit error rate compared to other algorithm. We will present the mathematicalmodel and simulation results of proposed method.

In the seventh chapter, we have discussed conclusion and future scope of the work.

11

Chapter 2

Literature Survey

2.1 Introduction

In this chapter we have discussed the literature survey. The literature survey is mainly dividedinto two categories: (i) In first category we have discussed the literature survey of PAPRminimization technique and (ii) In second category we have discussed the literature surveyof estimation of channel for MIMO-OFDM system.

This chapter is organize as follows: In section 2.2 we have discussed the system model ofMIMO-OFDM with mathematical equation. In section 2.3 we have discussed the variousliterature for OFDM with PAPR minimization technique. In section 2.4, we have discussedthe literature for estimation of channel for MIMO-OFDM system.

2.1.1 Introduction to MIMO-OFDM System

In present situation, there is a huge demand of high data rates in wireless communication.In MIMO system, the high data rate is achieved by sending the data in a simulcast mannerfrom various antennas. OSTBC technique provides the channel coding and antenna diversity.Most of the literature is based on flat fading and time invariant channel condition. Practicallycharacteristic of the channel is frequency selective and time variant. In the case of frequencyselective fading efficient equalizer is required which remove the ISI effect. This problem canbe overcome by OFDM technique, which is used with MIMO system. Combined MIMOand OFDM system, which is called as MIMO-OFDM system, is mostly used in currentgeneration wireless system. This system is used to provide high data rate and diversity.

12

2.2. MIMO-OFDM System Model

2.2 MIMO-OFDM System Model

In this section we have discussed the block diagram of MIMO-OFDM transmitter and re-ceiver with mathematical model.

2.2.1 System Model of MIMO-OFDM Transmitter

Figure 2.1 shows the basic MIMO-OFDM transmitter model. Digital data is applied to thedifferent modulator. Using serial to parallel converter the data is divided into several parallelstreams. Then after data is fed to the IFFT block in which frequency domain signal is con-verted in to the time domain signal. Then adding cyclic prefix into the time domain signaland then convert the parallel data stream into the serial data stream and finally with the helpof DAC, the analog signal is generated which is passed to the wireless channel.

Figure 2.1: Block diagram of MIMO-OFDM transmitter

As shown in figure 2.1, the message bits are initially modulated by modulator and then it isencoded by an orthogonal space time block coder and then it is fed to the OFDM modulator.In the orthogonal space time block coder scheme, the data is transmitted in no. of parts, thendata is provided to the no. of antennas and number of times. For the orthogonal space timeblock coder, let transmitted signal is given by,

13

Chapter 2. Literature Survey


Where Gt(n) is the transmitted signal.


D(Gt(n)) =L∑

m=1


Where (Am, Bm) are mth fixed time slot × number of transmitter antenna matrices.

2.2.2 System Model of MIMO-OFDM Receiver

Figure 2.2 shows the MIMO-OFDM receiver model with channel estimation. The receivedsignal from wireless channel are applied to the ADC which convert analog signal into digitalsignal. Then after cyclic prefix are removed and then remaining signal is applied to theserial to parallel converter which gives parallel data stream. With the help of FFT block timedomain signal is converted into the frequency domain and then it is applied to the parallelto serial converter which convert back into serial data stream. The various demodulationtechniques which demodulate the signal and finally we receive the original signal.

The received signal is given by,

Rt(n) = D(Gt(n))Ht(n) + Pt(n) (2.3)


2.3 Literatures for OFDM with PAPR minimization technique

In an OFDM system the one of the problem is high peak values of the signals in the timedomain due to the number of subcarriers are accumulated through an IFFT block. Becauseof this high PAPR value, it reduces the SQNR of ADC and DAC while reduces the efficiency

14

2.3. Literatures for OFDM with PAPR minimization technique

Figure 2.2: Block diagram of MIMO-OFDM receiver

of the power amplifier in the transmitter. So, the main objective in the OFDM system is toreduce this PAPR value.

In the research work [1], alternative multisequence scheme considered to minimize the PAPRin MIMO-OFDM system. The authors have developed a space frequency block coding struc-ture to combine the signals at different transmitter antenna. In the prescribed work, authorshave considered space frequency block code which limit the performance of OFDM systemwhen frequency selective channel is considered.

In the [2], authors have incorporated nonlinear companding transform technique to reducePAPR in OFDM signals. In this method, the peak power is reduced by compressing thetransmitted signal, and expanded the received signal. But in this technique, radiation isgenerated due to nonlinear operation at the transmitter side.

In the [3], authors have proposed the adaptive clipping level control method to reduce thePAPR in OFDM. But this method causes radiation and distortion. However, filtering afterclipping can eliminate the radiation but it increase the value of peak power.

In the work [4], authors have proposed the effective PAPR reduction technique of SFBC-OFDM for multinode cooperative transmission. But this work is limited to SISO system i.e.

15

Chapter 2. Literature Survey

one transmit antenna and one receive antenna. Authors have not considered the effect ofmultiple antenna at transmitter and receiver side.

In the work [5], authors have addressed the PAPR reduction technique based on exponentialcompanding for OFDM systems. Companding is a non linear process and due to this out ofband radiation is developed which limit the performance of OFDM system.

In [6] author has used the localized frequency division multiple access approach to reducethe high PAPR value. In this approach, the signal reconstruction becomes complex. So,efficient PAPR reduction technique is required to reduce the PAPR value and also reduce thecomplexity of signal reconstruction at the uplink of 3GPP- LTE system.

2.4 Literatures for the estimation of channel in MIMO-OFDM system

In MIMO-OFDM system, there are two types of estimation method for each subcarrier: (i)Blind channel estimation techniques and (ii) Pilot assisted channel estimation techniques.In blind channel estimation techniques, pilot samples are not used and due to this it’s morespectrally efficient but it’s having higher computational complexity. Pilot assisted channelestimation technique is based on the MMSE, the LS or the LMS technique. In that MMSEalgorithm performs better in time-varying channel condition. Channel equalization is theimportant part of the channel estimation.

The objective of Channel equalization is to reconstruct the original signal. It also removesthe degradation caused by the channel. The wireless channel is time-variant, in this types ofchannel, non-linear distortion is occurred. The linear equalization is not performed well inthis condition, for that efficient equalization techniques are required which should be bothadaptive and non-linear.

In [7], authors have evaluate the performance of adaptive MC-CDMA systems in Rayleighchannel condition. The channel estimation is based on the Kalman filter of MC-CDMAsystem. In [7], authors present that for low to moderate fading rate, decision directed detec-tors are preferred and for higher fading rate, pilot assisted detectors are preferred. However,in this case only linear estimation is considered which is based on Kalman filter and MC-CDMA system. The non linear estimation has not been considered.

In [8], authors have proposes a decoding technique for Alamouti’s ST coded transmissionsover time-selective channels that arise due to Doppler shifts and CFO. In this, authors have

16

2.4. Literatures for the estimation of channel in MIMO-OFDM system

not considered the multicarrier system and estimation of channel is also based on linearequalization only.

In [9], authors have proposes tracking of the channel and detection of symbol for MIMO-OFDM systems over the time-varying fading channel. The proposed method is based onEM algorithm. However, this method requires the numerous iteration to achieve optimumresults.

The authors [10] have address the problem of joint CFO and estimation of channel forMIMO-OFDM system.The estimation of channel is based on extended Kalman filtering.However, this method is based on only first order approximation of non linear estimation.

In [11], authors have proposed TSK fuzzy approach to estimate the channel for MIMO-OFDM systems. In the proposed algorithm, the computational complexity is lower becausethe inverse matrix required by the MMSE receiver is not required. However, in this worktime varying channel condition has not been considered.

In [12], authors have addresses the CKF method which deals with nonlinear state-spacemodels. However, authors have not addresses the issues of fading rates i.e. time varyingchannel condition has not been considered by the authors.

The authors [21] have address the channel estimation based on autoregressive model. Buthere author considered the linear approximation i.e. different mobile velocity has not beenconsidered. In [22], channel estimation is based on slow fading channel. Here author consid-ered the single antenna system. The multi antenna system has not been considered. In [23],the author address the blind channel estimation technique for OFDM systems over frequencyselective fading channels. Here, algorithm is based on slow fading channel. The author hasnot considered the fast channel variation.

17

Chapter 3

PAPR Minimization technique for MIMO-OFDMSystem

3.1 Introduction

In IEEE 802.11n and IEEE 802.11ac, OFDM is seen as possible technique at physical layerwith multiple input and multiple output. OFDM is adopted by 3GPP-LTE system to im-prove the wireless broadband connectivity [6]. OFDM is used in applications such as audiobroadcasting, digital television, wireless networking and in wireless broadband connectivity[6].

The 3GPP is an international standardization body working on 3G UTRAN and on the GSM[6] as well as on the current 4G wireless network. The latest standard is being developedin 3GPP is widely known as LTE or Evolved UTRAN [6]. In earlier it was decided that theLTE radio access should be based on SC-FDMA in the uplink and OFDMA in the downlink.SC-FDMA is also known as Discrete Fourier Transform Spread OFDMA [6].

In an OFDM system the one of the problem is high peak values of the signals in the timedomain due to the number of subcarriers are accumulated through an IFFT block [1-2].Because of this high PAPR value, it reduces the SQNR of ADC and DAC while reducesthe efficiency of the power amplifier in the transmitter [3-4]. So, the main objective in theOFDM system is to minimize this high PAPR value [5-6].

In section 3.2, we have presented a PAPR minimization technique for Coded OFDM systemswith scrambler approach. We have estimated the channel using BPSK, QPSK and M-QAMmodulation technique. We have derived the new analytical expression for PAPR minimiza-tion technique using proposed method for BPSK, QPSK and M-QAM modulation. In thissection we have present the PAPR minimization technique that is based on the combinationof probabilistic approach and coded approach. In the low complexity PAPR minimization

18

3.2. System Model of Proposed low complexity PAPR minimization technique

technique, we have change the order of the input of OFDM block. In the proposed algorithmthe out-of-band radiation is reduced as well as complexity of physical system is low.

In section 3.3, we have targeted uplink of the LTE system in which we have proposed thealgorithm in which OFDM system used with multiple interleaver to minimize the PAPRvalue using various shaping filter coefficient and to improve bit error rate. The proposedalgorithm minimize the PAPR value as we increase the shaping coefficient and the overallOFDM systems does not suffers from high PAPR.

Our work is organized as follows. Section 3.2 defines system model and mathematical ex-pression of proposed work based on low complexity PAPR minimization method. Section3.3 defines the system model. Section 3.4 defines the mathematical expression of proposedwork based on interleaver method. Section 3.5 defines the simulation results of low com-plexity PAPR minimization method. Section 3.6 defines the simulation results of interleavermethod. Section 3.7 defines the summary of work.

3.2 System Model of Proposed low complexity PAPR minimization tech-nique

In this section, we have present the novel PAPR minimization technique which is based onthe combination of probabilistic approach [1] and coded approach [2]. In the low complexityPAPR minimization technique, we have change the order of the input of OFDM block. In theproposed algorithm the out-of-band radiation is reduced as well as complexity of physicalsystem is low. As we increase the number of subblocks, the PAPR value is reduced.

3.2.1 Block diagram of low complexity PAPR minimization technique

Figure 3.1 shows the block diagram of low complexity PAPR minimization technique. Asshown in figure 3.1, using serial to parallel converter input data stream is divided into numberof parts based on number of blocks. Then frequency domain data is converted into timedomain using number of N - point IFFT. This data is multiplied with number of phase factorand then applied to the adder.

19

Chapter 3. PAPR Minimization technique for MIMO-OFDM System

Figure 3.1: Block diagram of low complexity PAPR minimization technique

The output data y is given by,

y = IFFT

(W∑w=1

awY w

)=

W∑w=1

(aw · IFFT{Y w}) =W∑w=1

(awyw) (3.1)

As shown in Algorithm - 1, the parameter values of no. of block and phase factors are setin the step 1 to 3. In step 4, PAPR is calculated using equation 3.1. In step 5, current PAPRvalue is compared with the minimum PAPR value. Step 6 present the number of iterationbased on number of blocks.

The proposed PAPR minimization technique is low complexity technique. The computa-tional burden of the system is less. The Computational burden of the Systems are givenbelow:

1. The number of multiplications required to calculate PAPR is W only (Minimum valueis W=2).

2. The number of adder required is one.

3. Minimum value of phase factor is 2.

20

3.3. System Model of Proposed PAPR minimization technique based on interleaver method

Algorithm 1 Low complexity PAPR Minimization AlgorithmStep 1 : Division

1: Divide the input block into W blockStep 2 : Phase factor setting

2: Set the phase factor value aw = 1 for w = 1:W3: Find PAPR using equation 3.1, and put the PAPR value as PAPRminimum

Step 3: Set the total no. of block4: Set W = 2

Step 4: Evaluate PAPR5: Find PAPR using equation 3.1 for aw=-1

Step 5: PAPR comparison6: If PAPR>PAPRminimum, go back aw to 1, otherwise modify PAPRminimum = PAPR

Step 6: No. of iteration7: If w<W, increment w and jump to step number 4. Else quit with optimum value of phase

factors, a

3.3 System Model of Proposed PAPR minimization technique based oninterleaver method

In this section, we have present a novel discrete spreading scheme with shaping filter methodto minimize the PAPR in OFDM system using multiple interleaver. In proposed algorithm,the N point discrete transform and RC filter is used to minimize the PAPR value. In the pro-posed algorithm as we increased the shaping coefficient the PAPR performance is improved.The proposed algorithm is minimize the PAPR for OFDM system with multiple interleaverapproach.

3.3.1 Block diagram of proposed method

Figure 3.2 shows the proposed PAPR minimization technique with interleaver. Digital datais applied to the interleaver, then after it is given to the M-QAM modulator. The data isdivided into several parallel data streams. After that proposed discrete spreader and Raisedcosine filter are jointly used to handle the data and then data is applied to the IFFT block.Then cyclic prefix are added into the time domain signal and then convert the parallel streaminto the serial stream and finally digital signal is converted into the analog signal using DACand then passes to the wireless channel.

21


Figure 3.2: Proposed PAPR minimization technique

In current uplink 3-GPP LTE system single carrier-FDMA technique is used. In the work,we have used OFDM system with multiple interleaver which minimized the bit error ratewith respect to various modulation techniques like 8-QAM, 16-QAM, 32-QAM, 64-QAMand 128-QAM.

Algorithm 2 Proposed PAPR Minimization Algorithm with interleaver approachStep 1 : Set the FFT size and data block sizeStep 2 : Set the number of OFDM block for iterationStep 3: Set the input dB value and modulation techniqueStep 4: Evaluate CCDF value of OFDMA systemStep 5: Evaluate CCDF value of LFDMA systemStep 6: Evaluate CCDF value of OFDMA with interleaver systemStep 7: Plot the graph of CCDF versus dB value for different modulation technique

3.4 Interpolation of OFDMA signal using interleaver technique

In this section, we have discussed the mathematical model of PAPR minimization techniquebased on interleaver method. We have also present the comparative analysis of interpolationin terms of interleaver and without interleaver method.

22

3.4. Interpolation of OFDMA signal using interleaver technique

Algorithm 3 Proposed PAPR Minimization Algorithm with discrete spreader and RCfilter approach

Step 1 : Set the FFT size and data block sizeStep 2: Find the spreading factor value: S = FFT size/No. of subcarriers per userStep 3: Set the length of RC filter and Oversampling factorStep 4: Set the RC filter coefficient value from 0.2 to 1.0Step 5 : Set the number of OFDM block for iterationStep 6: Set the input dB value and modulation techniqueStep 7: Evaluate CCDF value for various filter coefficientStep 8: Plot the graph of CCDF versus dB value for different filter coefficient

3.4.1 Interpolation of OFDMA signal without interleaver technique

In the discrete technique for OFDMA without interleaver, the input transmitted signal A[k]

given as,

A[k] =

{A[k], k = 0, 1, 2, ..., P − 1

0, k = P, P + 1, ..., Q− 1(3.2)

The IFFT output sequence a[q] with q = S.p + s for s = 0,1,2,...,S-1 can be expressed asfollows []:

a[q] = a[Sp+ s] =1

Q

Q−1∑k=0

A[k]ej2πqQ =

1

S

1

P

P−1∑k=0

A[k]ej2πSp+sSP

k (3.3)

For s = 0, equation 3.3 becomes

a[q] = a[Sp] =1

S

1

P

P−1∑k=0

A[k]ej2πpPk =

1

Sa[p] (3.4)

For s 6= 0,

A[k] =P−1∑r=0

x[r]e−j2πrQk (3.5)

such that equation 3.3 becomes a[q] = a[Sp+ s]

=1

S

(1− ej2π

sS

).1

P

P−1∑r=0

a[r]

1− ej2π{(p−r)P

+ sSP }

(3.6)

23


From equation 3.4 and 3.6, it is noticed that without interleaver OFDMA signal is the 1/Sscaling of the original signal.

3.4.2 Interpolation of OFDMA signal with proposed interleaver technique

In the OFDMA signal with interleaver method, the mapping of subcarrier starts with the vth

subcarrier, discrete symbol given as,

A[k] =

{X[(k − v)/S], k = S · p1 + v, p1 = 0, 1, 2, ..., P − 1

0, otherwise(3.7)

The IFFT output signal is given by,

A[k] =

{X[(k − v)/S], k = S · p1 + v, p1 = 0, 1, 2, ..., P − 1

0, otherwise

a[q] = a[Ps+ p]

= 1Q

Q−1∑k=0

A[k]ej2πqQk

= 1S· 1P

P−1∑p1=0

A[p1]ej2π( qQp1+

qQv)

= 1S·(

1P

P−1∑p1=0

A[p1]ej2π p

Pp1

)· ej2π

qQv

= 1Sej2π

qQv · a[p]

(3.8)

Compared with equation 3.8, we can seen that the phase rotation is about ej2πqv/Q

So, compared to equation 3.6 and 3.8, the interpolation of OFDMA signal with interleavermethod is less complex than the without interleaver method.

3.5 Simulation Results of low complexity PAPR minimization technique

In this work, we have presented a PAPR minimization technique for Coded OFDM system.We have evaluate the channel with respect to the BPSK, QPSK and M-QAM Modulationtechnique. We have present the novel PAPR minimization technique which is based on thecombination of probabilistic approach [1] and coded approach [2]. In the low complexityPAPR minimization technique, we have change the order of the input of OFDM block. In

24

3.5. Simulation Results of low complexity PAPR minimization technique

the proposed algorithm the out-of-band radiation is reduced as well as complexity of physicalsystem is low.

We have calculate the complementary cumulative distribution function value of proposedmethod. We have also considered the effect of number of OFDM subblocks. As we increasedthe number of subblocks then PAPR value is minimized. We have also compared the CCDFvalue of OFDM signal with number of subblocks and without subblocks.

3.5.1 Simulation parameters and results

The simulation parameters are mentioned in table 3.1.

Table 3.1: Simulation Parameters and it’s Value

Name of Parameters ValueTypes of Modulation BPSK,QPSK,M-QAM

No. of bits per Symbol 1,2,3,4,5,6,7FFT Size 256

No. of subblocks 1,2,4,8,16Subcarriers 64

OFDM blocks 3000Oversampling factor 4

Code rate 1/2,1/3,1/4

As per the simulation parameters listed in Table 3.1. We have considered various types ofmodulation technique like BPSK, QPSK and M-QAM. The total no. of subcarriers per userare 64. We have evaluated CCDF value for different no. of subblocks like 1,2,4,8 and 16.We have also considered the various code rate like 1/2, 1/3 etc.

The simulation results of various modulation techniques are mentioned in table 3.2.

In the Figure 3.3, it has been observed that as we increase the number of subblocks, theCCDF value has been decreased. As we increased the number of subblocks from 1 to 16, theCCDF value has been decreased. It is seen that, for number of subblock is 2 and input 10dB the CCDF value is around 10−3. The same CCDF value 10−3 is achieved at 7 dB inputfor number of subblock is 16. So, there is a 3 dB improvement achieved when the numberof subblock increase from 2 to 16. The lowest value of CCDF is achieved for number ofsubblock is 16.

25


Table 3.2: Simulation results of various modulation techniques

Modulation Technique N-Point FFT No. of Subblock CCDF at 7 dB

BPSK/OFDM 256

W/O Red. 0.61171 0.60432 0.41474 0.19678 0.041

16 0.0013

QPSK/OFDM 256

W/O Red. 0.83631 0.8122 0.72734 0.54478 0.2477

16 0.048

16-QAM/OFDM 256

W/O Red. 0.86971 0.852 0.7184 0.53538 0.2523

16 0.055

32-QAM/OFDM 256

W/O Red. 0.87631 0.85232 0.7094 0.55438 0.2723

16 0.0517

64-QAM/OFDM 256

W/O Red. 0.8781 0.84172 0.70234 0.53138 0.262

16 0.0483

128-QAM/OFDM 256

W/O Red. 0.881 0.8542 0.7274 0.53978 0.2713

16 0.0443

26

3.5. Simulation Results of low complexity PAPR minimization technique

Figure 3.3: Low complexity PAPR minimization technique for BPSK

Figure 3.4: Low complexity PAPR minimization technique for 8-QAM

27


Figure 3.4 shows the CCDF graph for 8-QAM OFDMA system. It is noticed that, for numberof subblock is 2 and input 9 dB the CCDF value is around 10−2. The same CCDF value 10−2

is achieved at 7 dB input for number of subblock 16. So, there is a 2 dB improvementachieved when the number of subblock increase from 2 to 16. We have achieved lowestvalue of CCDF when number of subblock is 16.


Figure 3.5 shows the plot of CCDF for 32-QAM OFDMA system. It is revealed that, fornumber of subblock is 2 and input 8.5 dB the CCDF value is around 10−1. The same CCDFvalue 10−1 is achieved at 7 dB input for number of subblock 16. So, there is a 1.5 dBimprovement achieved when the number of subblock increase from 2 to 16. Compared thefigure 3.4 and 3.5, as we increase the M-ary number from 8 to 32, the performance of CCDFis degraded. It is clearly seen that CCDF value is increased from 10−2 to 10−1 for 32-QAMcase.

Figure 3.6 shows the CCDF graph for 128-QAM OFDMA system. It is seen that, for numberof subblock is 2 and input 8 dB the CCDF value is > 10−1. The same CCDF value > 10−1

is achieved at 6.8 dB input for number of subblock 16. So, there is a 1.2 dB improvementachieved when the number of subblock increase from 2 to 16. Compared the figure 3.5 and

28

3.6. Simulation Results of PAPR minimization technique based on interleaver method


3.6, as we increase the M-ary number from 32 to 128, the performance of CCDF is degraded.It is clearly seen that CCDF value is increased for 128-QAM case.

Figure 3.7 shows the comparative analysis of low complexity PAPR minimization methodwith respect to BPSK, QPSK and M-QAM modulation technique. It is noticed that CCDFvalue is increased, as we increase the M-ary number. It is also noticed that as the number ofsubblock increased from 1 to 16, the CCDF value is decreased.

3.6 Simulation Results of PAPR minimization technique based on in-terleaver method

In this section, we have evaluated the performance of novel discrete spreader scheme withshaping filter which minimizes the peak to average power ratio in OFDM system using mul-tiple interleaver. We have calculated received power value with respect to the various tech-niques like OFDMA, Localized FDMA (used in 3-GPP LTE) and OFDM system with inter-leaver (proposed technique). In this section we have discussed the results with respect to thevarious modulation technique like 8-QAM/OFDM, 32-QAM/OFDM and 128-QAM/OFDM.

29


Figure 3.7: Comparative analysis of low complexity PAPR minimization tech-nique

The simulation results are divided into two categories: In the first category we have com-pare the proposed OFDM system with interleaver technique with the OFDMA and localizedFDMA (used in 3-GPP LTE) technique. Figure 3.8 to figure 3.10 represents ComplementaryCumulative Distribution Function value versus input decibel value for 8-QAM, 32-QAM and128-QAM types of modulation techniques respectively. Simulation results show that in pro-posed OFDM system with interleaver technique, the peak to average power ratio is very lowcompare to the other techniques.

In second category we have simulate the proposed technique for PAPR minimization forOFDM system with interleaver using shaping filter. Figure 3.11 to figure 3.13 representsCCDF value versus input decibel value for 8-QAM, 32-QAM and 128-QAM types of mod-ulation techniques respectively using shaping filter coefficient 0.2, 0.4, 0.6, 0.8 and 1.0.Simulation results show that as we increased the filter coefficient from 0.2 to 1.0, the PAPRvalue decreases. We have achieved the lowest level of PAPR value in the proposed algorithm.

The simulations parameters are mentioned in table 3.3. Simulation results regarding pro-posed algorithm of shaping filter for OFDM system with multiple interleaver for differentmodulation technique are mentioned in table 3.4.

30




Table 3.3: Simulation Parameters and its Value

Name of Parameters ValueTypes of Modulation 8-QAM to 128-QAM

No. of bits per Symbol 3,4,5,6,7FFT Size 256

Subcarriers 64OFDM blocks 7000

Spreading factor 4Oversampling factor 8RC filter coefficient 0.2,0.4,0.6,0.8,1.0

RC filter length 6Number of interleavers 64

As per the simulation parameters listed in Table 3.3. We have considered various types ofmodulation technique like 8-QAM, 16-QAM, 32-QAM, 64-QAM and 128-QAM. The totalno. of subcarriers per user are 64. We have evaluated CCDF value for two different cate-gories: In category I, we have compared the proposed interleaver method with conventionwithout interleaver method. In category II, we have considered the various RC filter coef-ficient value like 0.2, 0.4, 0.6, 0.8 and 1.0. The simulation results of various modulationtechniques are mentioned in table 3.4.

Figure 3.8 shows the graph of CCDF value versus SNR for 8-QAM modulation technique.In the Figure 3.8, it has been observed that in the proposed method of interleaver, the value ofCCDF is decreased compared to the conventional method. At 8 dB, for OFDMA the value ofCCDF is around 10−1 and for LFDMA the value of CCDF is 10−2. The same value of CCDF10−2 is achieved when SNR is 3.5 dB for OFDMA with interleaver approach. So, there isa improvement of 4.5 dB in the case of proposed method compared to LFDMA method. Inthe proposed method CCDF outperforms compare to other method.

Figure 3.9 shows the simulation plot of CCDF value versus SNR for 32-QAM modulationtechnique. It has been noticed that we have achieved lowest CCDF value in the proposedmethod compared to the conventional method. At 6 dB, for OFDMA the value of CCDFis around 0.909 and for LFDMA the value of CCDF is 10−1. The same value of CCDF

31


Table 3.4: Simulation results for PAPR minimization using RC filter

Modulation Technique Filter Coefficient CCDF at 5 dB

8-QAM/OFDM

0.2 0.99570.4 0.99230.6 0.89230.8 0.12561 0.0134

16-QAM/OFDM

0.2 0.99610.4 0.99440.6 0.89450.8 0.24561 0.0156

32-QAM/OFDM

0.2 0.99740.4 0.78960.6 0.17890.8 0.01121 0.0014

64-QAM/OFDM

0.2 0.99810.4 0.99480.6 0.89780.8 0.67981 0.5478

128-QAM/OFDM

0.2 0.99230.4 0.87450.6 0.66780.8 0.23761 0.1456

10−1 is achieved when SNR is 3 dB for OFDMA with interleaver approach. So, there is aimprovement of 3 dB in the case of proposed method compared to LFDMA method.

Figure 3.10 shows the graph of CCDF value versus SNR for 128-QAM modulation tech-nique. It has been revealed that as we increase the M-ary number the value of CCDF is alsoincreased. Compared to figure 3.8 and 3.9, in the figure 3.10 we have achieved higher valueof CCDF. But it is cleared that in the case of proposed method, we have achieved lowestvalue of CCDF compared to conventional method.

Figure 3.11 shows the graph of CCDF versus SNR for proposed interleaver method with RCfilter of 8-QAM method. It has been observed that in the proposed method of interleaverwith RC filter coefficient, the value of PAPR has been decreased as we increased the shaping

32


Figure 3.8: Proposed PAPR Minimization technique with other technique for8-QAM/OFDM

Figure 3.9: Proposed PAPR Minimization technique with other technique for32-QAM/OFDM

33


Figure 3.10: Proposed PAPR Minimization technique with other techniquefor 128-QAM/OFDM

Figure 3.11: Proposed PAPR Minimization technique with interleaver usingRC filter for 8-QAM/OFDM

34


coefficient value from 0.2 to 1.0. For 0.4 shaping coefficient value, we have achieved CCDFvalue is 10−2 at 7 dB. The same 10−2 CCDF value is achieved at 5 dB with shaping coefficient1.0. So, there is a improvement of 2 dB as we increase the shaping coefficient from 0.4 to1.0. The lowest value of PAPR is achieved for shaping coefficient value of 1.0.


Figure 3.12 shows the simulation plot of CCDF versus SNR for proposed interleaver methodwith RC filter of 32-QAM method. It has been noticed that for 0.6 shaping coefficient value,we have achieved CCDF value is 10−3 at 6 dB. The same 10−3 CCDF value is achieved at4.8 dB with shaping coefficient 1.0. So, there is a improvement of 1.2 dB as we increase theshaping coefficient from 0.6 to 1.0.

Figure 3.13 shows the graph of CCDF versus SNR for proposed interleaver method with RCfilter of 128-QAM method. It has been noticed that for 0.6 shaping coefficient value, wehave achieved CCDF value is 10−2 at 6.4 dB. The same 10−2 CCDF value is achieved at5.4 dB with shaping coefficient 1.0. So, there is a improvement of 1 dB as we increase theshaping coefficient from 0.6 to 1.0.

35



3.7 Summary

In this section, we have discussed the various types of PAPR minimization technique. Wehave compared the proposed PAPR minimization technique with the conventional technique.In the part I, we have proposed low complexity PAPR minimization technique which is basedon the combination of probabilistic approach and coded approach which reduced the PAPRvalue efficiently. The complexity of proposed method is lower. In the part II, we haveproposed PAPR minimization technique with interleaver and RC filter approach. We haveminimized the PAPR value for uplink of the 3-GPP LTE physical system. In the interleaverbased approach, the interpolation of OFDMA signal is less complex than without interleavermethod. In the RC filter approach, as we increased the RC filter coefficient then PAPR valueis reduced.

36

Chapter 4

Channel Estimation technique using Linear andNon linear Kalman filter

4.1 Introduction

The Kalman filter is a mathematical tools that can be used for stochastic estimation. TheKalman filter is named after Rudolph E. Kalman, who is describing a recursive solution tothe problem of discrete linear filtering. The Kalman filter is a set of equations that described apredictor and corrector type estimator. It is used to minimizes the estimated error covariance.This chapter describes the basics of Kalman filter with respect to its mathematical expression.

In section 4.2, we have presented a estimation of channel and tracking of MIMO-OFDM sys-tem based on linear Kalman filter to improve the performance of system compared to otherestimation technique. In this section, we have considered that mobile station is stationaryin nature i.e. mobile station is not moving. We have evaluate the channel with respect toRayleigh channel model. From simulation results, it is revealed that the proposed techniqueoutperforms the BER compare to conventional technique. We have achieved lowest BERcompared to other method.

In section 4.3, we have presented a estimation of channel for MIMO-OFDM system based onMKF method to improve the performance of system compared to other estimation technique.In this section, we have considered that mobile station is moving with low speed. We haveevaluate the channel with respect to Rayleigh channel model. We have achieved the lowestBER particularly when the mobile station is moving with low speed.

Our work is organized as follows. Section 4.2 defines estimation of channel based on linearKF method. Section 4.3 defines estimation of channel based on MKF method. Section 4.4defines the simulation results of linear KF method. Section 4.5 defines the simulation resultsof MKF method. Section 4.6 defines the summary of work.

37

Chapter 4. Channel Estimation technique using Linear and Non linear Kalman filter

4.2 Estimation of channel based on linear Kalman filter method

In this section, we have presented estimation of channel and tracking of MIMO-OFDMsystem based on linear Kalman filter to improve the performance of system compared toconventional technique. We have considered the time invariant Rayleigh channel model. Wehave also compared the proposed technique with the conventional technique. From Theoreti-cal analysis and simulation results, it is revealed that the proposed technique outperforms theBER compare to other technique. We have achieved lowest BER compared to other method.

4.2.1 Block diagram of MIMO-OFDM transmitter

Figure 4.1 shows the block diagram of MIMO-OFDM transmitter.

Figure 4.1: Block diagram of MIMO-OFDM transmitter

We have evaluate the channel with respect to different modulation technique. We have con-sider the OSTBC coder with respect to 2 transmitter and 2 receiver antenna. The OSTBCcoder provides the transmitter diversity. In this case Channel state information is known tothe receiver. We have consider various types of channel like Rayleigh flat fading channel andRayleigh frequency selective slow fading channel.

4.2.2 Block diagram of MIMO-OFDM receiver

Figure 4.2 shows the block diagram of MIMO-OFDM receiver.

At the receiver side, we have estimate the channel of MIMO-OFDM system. We have esti-mate the channel under following condition: (i) In first case, we have considered Rayleigh

38

4.3. Mathematical model of channel estimation technique

Figure 4.2: Block diagram of MIMO-OFDM receiver

flat fading channel, when the mobile is not moving. In this case we have considered station-ary model. (ii) In second case, we have considered Rayleigh frequency selective slow fadingchannel. In this case mobile is moving with slow speed. We have proposed the algorithmwhich minimized the BER compared to other method.

4.3 Mathematical model of channel estimation technique

In this section, we have mentioned the mathematical model of the conventional method andproposed method. The conventional method of channel estimation is based on the MMSEequalizer. The proposed method of channel estimation is based on the Kalman filter.

4.3.1 Estimation of channel based on MMSE equalizer

In Minimum Mean Square Error equalizer, we have find a set of coefficients c[k] whichminimizes the error between desired signal and the equalized signal c[k]× y[k], i.e. [6] [7],

E(e [k])2 = E(s [k] − c [k]× y [k])2 (4.1)

39


E(e [k])2 = E(s [k] − cTy

) (s [k] − cTy

)T(4.2)

E(e [k])2 = E(s [k])2 − cTRys− Rsyc + cTRyyc (4.3)

where, e[k] is the error, c is column vector of the equalization coefficients, y is column vectorof the received samples, K is the no. of taps, Rys = E(ys[k]) is the cross correlation betweenreceived and input sequence , Rsy = E(s[k]yT ) is the cross correlation between receivedand input sequence and Ryy = E(yyT ) is the auto-correlation of the received sequence. Forsolving the MMSE criterion, we need to find a set of coefficients which minimizes E(e[k])2.

We have to find the optimum value of equalization coefficients in the following way:

∂/∂c [E(s[ k])2 − cTRys− Rsyc + cTRyyc

]= 0 (4.4)

− Rsy + Ryyc = 0 (4.5)

c = Ryy−1Rsy (4.6)

Simplifying above equation we get,

Rsy = E(s [k] yT

)(4.7)

Rsy = E(

s [k] (hs [k] + n)T)

(4.8)

Rsy = hTE(s2 [k]

)+ E (s [k] n) (4.9)

Rsy = h (4.10)

Ryy = E(yyT

)(4.11)

40

4.3. Mathematical model of channel estimation technique

Ryy = E(

(hs [k] + n) (hs [k] + n)T)

(4.12)

Ryy = E(hhT

)E(s2 [k]

)+ hE (s [k] n) + E (n [k] s [k]) hT + E

(n2)

(4.13)

Ryy = E(hhT

)+ E

(n2)

(4.14)

Note:

1. E(s2[k]) = 1 is the variance of the input signal.

2. E(s[k]n[k]) = 0 means there is no correlation between input signal and noise.

4.3.2 Estimation of channel based on Kalman filter

Kalman filter is used to estimate the various states of the linear system. The lowest value ofestimation error is achieved in Kalman filter.

Algorithm 4 Estimation of channel based on KF AlgorithmStep 1: State Equation formula:xk+1 = Axk + Buk + process noise (wk) where A, B and C represents the transition,input and measurement matrix respectivelyStep 2 : Measurement equation formula:yk = Cxk + measurement noise (zk)Step 3: KF equations are as follows: (Estimator Equation)

Kk = APkCT (CPkC

T + Sz)−1 (4.15)

xk+1 = (Axk +Buk) +Kk (yk+1 − Cxk) (4.16)

Pk+1 = APkAT + Sw − APkCTS−1z CPkA

T (4.17)

Where, Kk is the gain of Kalman, xk+1 is the estimator which represent next state, Pk+1 isthe estimator error covariance, A, B and C are matrices, k is the time index, u is the knowninput, y is system output, Sw and Sz are the process and measurement noise respectively.

41


Figure 4.3 shows the estimation of the channel based on Kalman Filter. There are two typesof formulas are used: (i) Predictor formula and (ii) Corrector formula.

Figure 4.3: Block diagram of Kalman filter algorithm

4.4 Estimation of channel based on Modified Kalman filter

In this section, we have discussed the estimation of channel of MIMO-OFDM system basedon the proposed MKF technique. In the case of linear model analysis, the Kalman filter isthe possible solution. For non linear channel condition, we have adopt MKF technique. Inthe MKF case, channel variation is nonlinear in nature.

4.4.1 Mathematical model of Modified Kalman Filter

When the mobile station is stationary, the Kalman filter algorithm gives the lowest value ofbit error rate compared to conventional MMSE equalizer. But when the mobile station isvarying with respect to low to medium speed, the MKF algorithm gives the lowest value ofBER for MIMO-OFDM system. Here, in this section we have discussed the mathematicalexpression of MKF.

The term hk(gk) is the single stage predicted output mk and mk − hk(gk) is the innovationsequence and it is defined as:

42

4.4. Estimation of channel based on Modified Kalman filter

Algorithm 5 Modified Kalman filter AlgorithmStep 1: State equation formula:

gk+1 = f (gk, vk) + pk (4.18)

Step 2: Output equation formula:

mk = hk(gk) + qk (4.19)

Step 3: Calculate the following derivative matrices:

Dk = f ′(gk, vk) (4.20)

Fk = hk′(gk) (4.21)

Step 4: Execute the following KF equation:Kalman gain is given as:

Kk = PkFTk (FkPkF

Tk + Sq)

−1 (4.22)

Predicted system value is given as:

gk+1 = f(gk, vk) +Kk[mk − hk(gk)] (4.23)

Error covariance is given as:

Pk+1 = Dk(I −KkFk)PkDT + Sp (4.24)

43


ik = (mk − hk(gk)) (4.25)

The weighted innovation, Kk[mk − hk(gk)] acts as a correction to the predicted estimate gkto form the estimation gk, the weighting matrix Kk is commonly referred to as Kalman gainmatrix.

4.5 Simulation Results of MIMO-OFDM system with linear Kalmanfilter

In this section, we have simulated the proposed linear Kalman filter for MIMO-OFDM sys-tem with different modulation technique. We have calculated MSE value of proposed tech-nique which is compared with conventional technique. In this section we have discussed thesimulation results of MSE V/S SNR and BER V/S SNR of MIMO-OFDM system with andwithout Kalman filter. We have compared the proposed Kalman filter technique with con-ventional MMSE technique. We have also evaluated the higher order Kalman filter methodon MIMO-OFDM system.


The simulation results are divided into two category: In first category we have compare theproposed Kalman filter technique with conventional MMSE technique. Figure 4.4 representsthe BER V/S SNR plot for MIMO-OFDM system with and without Kalman filter. Simulationresults show that in proposed Kalman filter technique, the BER value is lowered comparedto without Kalman filter technique.

In second category we have compare the first order and second order statistics of the Kalmanfilter. Figure 4.5, 4.6 and 4.7 shows the simulation results of this category. As the KF orderincreased, the BER is also increased. But higher order Kalman filter is applicable in nonlinear analysis of the channel. First order Kalman filter is applicable for linear analysis. Sodue to non linearity in the channel the BER is also increased. When the mobile velocity isunknown; it is varying with the time for that non linearity of the channel is considered. Forthat second order Kalman filter is applicable.

44

4.5. Simulation Results of MIMO-OFDM system with linear Kalman filter

Figure 4.4: Comparison of MMSE and Kalman filter

Figure 4.4 shows estimation of channel with respect to MMSE equalizer and Kalman filterestimation. From figure 4.4, we say that the lowest value of BER is achieved in Kalmanfilter method. At SNR value 20 dB, BER value is 10−3 in the MMSE channel estimation. Inthe case of Kalman filter method BER is 10−5 at 20 dB SNR. So, compare to conventionalMMSE equalizer method there is an improvement in the case of proposed KF method.

Figure 4.5 shows the MSE V/S SNR graph for MIMO-OFDM with predicted KF method.The predictor and corrector equations are mentioned in figure 4.3. Based on that formula,MSE value is predicted. As the SNR increased, the MSE value is decreased. It is noticedthat, at SNR 10 dB the value of MSE is 10−2 for SKF case and 10−1 for DKF case. The MSEvalue outperforms in the case of first order Kalman filter method due to linear Kalman filterestimation.

Figure 4.6 shows the MSE V/S SNR plot for MIMO-OFDM with estimated Kalman filter.The estimator equations are mentioned in section 4.3. Based on that formula MSE value iscalculated. It is revealed that, at SNR 10 dB the value of MSE is 10−3 for SKF case and 10−1

for DKF case. As the SNR increased, the MSE value is decreased.

Figure 4.7 shows the BER V/S SNR graph for MIMO-OFDM with increasing the order ofthe KF method. As the order of the KF increased, the BER value is also increased because

45


Figure 4.5: MSE V/S SNR for MIMO-OFDM Channel Estimation (Predictor)

Figure 4.6: MSE V/S SNR for MIMO-OFDM Channel Estimation (Estima-tor)

46

4.5. Simulation Results of MIMO-OFDM system with linear Kalman filter

Figure 4.7: BER V/S SNR for MIMO-OFDM Channel Estimation

as the order of the filter increased, the nonlinearity of the channel is also increased and dueto this BER is increased.

Figure 4.8: MSE V/S SNR for MIMO-OFDM System (Predictor)-QPSK

47


Figure 4.9: MSE V/S SNR for MIMO-OFDM System (Estimator)-QPSK

Figure 4.10: BER V/S SNR for MIMO-OFDM System-QPSK

Figure 4.8 shows the MSE V/S SNR graph for MIMO-OFDM with predicted KF method forQPSK modulation. The predictor and corrector equations are mentioned in figure 4.3. As

48

4.6. Simulation Results of MIMO-OFDM with MKF method

the SNR value increased, the MSE value is decreased.

Figure 4.9 shows the MSE V/S SNR graph for MIMO-OFDM with estimated KF method forQPSK modulation. The estimator equations are mentioned in section 4.3. The MSE value isoutperformed in the proposed algorithm.

Figure 4.10 shows the BER V/S SNR graph for MIMO-OFDM with increasing the order ofthe KF method. The digital modulation technique in this case is QPSK. As the order of theKF increased, the BER value is also increased.



Name of Parameters ValueModulation Technique BPSK, QPSK

System BW 2 MHzFFT Size 256

Subcarriers 64OFDM blocks 7000

No. of the antenna 2 TX, 2 RXOrder of the Kalman filter 1,2

As per the simulation parameters listed in Table 4.1. We have considered various types ofmodulation technique like BPSK and QPSK. The total no. of subcarriers per user are 64. Wehave evaluated BER for single order and double order Kalman filter. We have consideredRayleigh channel.

4.6 Simulation Results of MIMO-OFDM with MKF method

In this section, we have estimated the channel of proposed Modified Kalman filter for MIMO-OFDM system with different modulation technique. We have calculated MSE value and BERof proposed MKF method, SKF and DKF techniques. In this section we have discussed thesimulation results with respect to various modulation techniques. We have compared theproposed MKF technique with SKF and DKF techniques.

49



In this section, we have discussed the simulation results of proposed MKF technique. Wehave also compared the proposed MKF technique with SKF and DKF technique. Figure4.11, 4.12 and 4.13 shows the simulation results of proposed MKF technique, SKF and DKFtechnique. From the simulation results, it is cleared that in case of proposed method the BERvalue is lowered compared to SKF and DKF technique.

Figure 4.11: MSE V/S SNR for MIMO-OFDM with MKF technique (Predic-tor)

Figure 4.11 shows the MSE V/S SNR graph for MIMO-OFDM with predicted KF. As theSNR increased, the MSE value is decreased. The lowest value of MSE is achieved in thecase of proposed MKF technique. At the 10 dB SNR value the MSE value is around 10−3

for proposed MKF technique and around 10−2 for SKF and 10−1 for DKF technique.

Figure 4.12 shows the MSE V/S SNR graph for MIMO-OFDM with estimated KF. As theSNR increased, the MSE value is decreased. The lowest value of MSE is achieved in thecase of proposed MKF technique. At the 10 dB SNR value the MSE value is around 10−4

for proposed MKF technique and around 10−3 for SKF and 10−1 for DKF technique.

Figure 4.13 shows the BER V/S SNR graph for MIMO-OFDM with proposed MKF, SKFand DKF techniques. As the order of the Kalman filter increased, the BER value is also

50


Figure 4.12: MSE V/S SNR for MIMO-OFDM with MKF technique (Esti-mator)

Figure 4.13: BER V/S SNR for MIMO-OFDM with MKF technique

51


increased because as the order of the filter increased, the nonlinearity of the channel is alsoincreased. But in proposed MKF technique BER value is decreased, as we increase thenonlinearity in the channel. At the 10 dB SNR value the BER value is around 10−4 forproposed MKF technique and around 10−3 for SKF and 10−2 for DKF technique. So, theproposed MKF technique is better in terms of nonlinearity of the channel.



Name of Parameters ValueTypes of Modulation BPSK, QPSK

No. of bits per Symbol 1, 2System BW 2 MHz

FFT Size 256Subcarriers per user 64

OFDM blocks 7000No. of Antenna 2TX, 2RX

Types of Kalman filter MKF, SKF, DKF

Table 4.3 shows the simulation results of MIMO-OFDM System with SKF, DKF and MKFbased channel estimation.

Table 4.3: Simulation results for MIMO-OFDM system with SKF, DKF andMKF

SNR (dB) BER (SKF) BER (DKF) BER (MKF)3 0.045 0.065 0.0254 0.040 0.060 0.0205 0.037 0.055 0.0186 0.031 0.050 0.0157 0.023 0.045 0.0108 0.016 0.040 0.0099 0.008 0.038 0.006

10 0.0045 0.035 0.00511 0.0040 0.030 0.00312 0.0035 0.025 0.00113 0.0020 0.002 0.000714 0.0025 0.009 0.000415 0.0009 0.001 0.0001

52


Figure 4.14: MSE V/S SNR for MIMO-OFDM Channel Estimation (Predic-tor) - QPSK

Figure 4.15: MSE V/S SNR for MIMO-OFDM Channel Estimation (Estima-tor) - QPSK

53


Figure 4.16: BER V/S SNR for MIMO-OFDM Channel Estimation - QPSK

Figure 4.14 shows the MSE V/S SNR graph for MIMO-OFDM system with predicted tech-nique. As the SNR increased, the MSE value is decreased. The lowest value of MSE isachieved in the case of proposed technique compared to SKF and DKF technique.

Figure 4.15 shows the MSE V/S SNR plot for MIMO-OFDM system with estimated tech-nique. As the SNR increased, the MSE value is decreased. The lowest value of mean squareerror is achieved in the case of proposed technique compared to SKF and DKF technique.

Figure 4.16 shows the BER V/S SNR graph for MIMO-OFDM system with proposed MKF,SKF and DKF techniques. As the order of the Kalman filter increased, the BER value isalso increased because as the order of the filter increased, the nonlinearity of the channel isalso increased and due to this nonlinearity BER value is increased. But in proposed MKFtechnique BER value is decreased, as we increase the nonlinearity in the channel. So, theproposed MKF technique is better in terms of nonlinearity of the channel.

4.7 Summary

In this section, we have discussed the MIMO-OFDM channel estimation method based onlinear and non linear Kalman filter. We have compared the proposed technique with the

54

4.7. Summary

conventional technique. In the part I, we have proposed linear Kalman filter technique whichimprove the performance of BER compared to MMSE equalizer. When mobile station isstationary, the proposed method gives the better results. In the part II, we have proposedModified Kalman filter technique which improve the performance of BER with respect tonon linear channel estimation. When mobile station is moving with low speed, the proposedMKF method outperforms the probability of error with multipath fading environment.

55

Chapter 5

Channel estimation technique using Fuzzy basedAdaptive Kalman filter technique

5.1 Introduction

In this section, we have discussed a novel equalization technique for MIMO-OFDM systembased on adaptive fuzzy algorithm. We have proposed the method with respect to Rayleighfrequency selective low to medium speed fading channel. The proposed method gives thebetter results when mobile is moving with low to medium speed. We have plot the BERversus SNR graph for proposed fuzzy adaptive Kalman filter method. We have compared theproposed fuzzy adaptive Kalman filter method with the other method. With reference to lowto medium speed moving mobile, the proposed method gives the lowest value of bit errorrate compared to other method.

In section 5.2, we have presented mathematical model of MIMO-OFDM transmitter andreceiver. We have also discussed the estimation of channel and tracking of MIMO-OFDMsystem. We have also discussed the various parameters like number of transmitter, numberof receiver and Doppler frequency shift parameters.

In section 5.3, we have presented a estimation of channel for MIMO-OFDM with fuzzy adap-tive Kalman filter method which improve the channel estimation compare to other method.In this section, we have considered that mobile station is moving with low to medium speed.We have also compared the proposed technique with the other technique. We have estimatedthe channel under Rayleigh frequency selective medium fading channel condition. Fromtheoretical analysis and simulation results, it is cleared that the proposed estimation methodoutperforms the BER compared to other technique. We have achieved lowest BER comparedto other technique.

56

5.2. System Model of MIMO-OFDM Transmitter and Receiver

Our work is organized as follows. Section 5.3 defines channel estimation based on FAKFtechnique. Section 5.4 defines the simulation results of FAKF technique. Section 5.5 definesthe summary of work.

5.2 System Model of MIMO-OFDM Transmitter and Receiver

In this section, we have presented mathematical model of MIMO-OFDM transmitter andreceiver. We have also discussed the estimation of channel and tracking of MIMO-OFDMsystem. We have discussed the various parameters like number of transmitter, number ofreceiver and Doppler frequency shift parameters.

5.2.1 System Model of MIMO-OFDM transmitter

Figure 5.1 shows the system model of MIMO-OFDM transmitter. In MIMO-OFDM system,number of transmitter, number of receiver and number of subcarriers are denoted by Nt, Nr

and Nc respectively.

Figure 5.1: System Model of MIMO-OFDM transmitter

We have evaluate the channel with respect to different modulation technique. We have con-sider the OSTBC coder with respect to 2 transmitter and 2 receiver antenna. The OSTBCcoder provides the transmitter diversity. In this case Channel state information is known tothe receiver. We have consider various types of channel like Rayleigh slow fading channeland Rayleigh frequency selective medium fading channel. For the orthogonal space timeblock coder, let transmitted signal is given by,

57

Chapter 5. Channel estimation technique using Fuzzy based Adaptive Kalman filtertechnique




D(Gt(n)) =L∑

m=1



5.2.2 System Model of MIMO-OFDM receiver

Figure 5.2 shows the system model of MIMO-OFDM receiver. The received signal is givenby,

Rt(n) = D(Gt(n))Ht(n) + Pt(n) (5.3)


Figure 5.2: System Model of MIMO-OFDM receiver

58

5.3. Channel estimation based on FAKF technique

5.2.3 Mathematical model of MIMO-OFDM channel estimation

In this section we have select second order Auto-regressive model due to its less complexityand perfectness. The mth path channel impulse response is given by,

hb,at (m) = db,a1,t−1hb,at−1(m) + db,a2,t−1h

b,at−2(m) + qb,at (m) (5.4)

For a = 1,2,3,...,Nr, b = 1,2,3,...,Nt, and m = 0,1,2,3,...,M-1, where qb,at (m) is a standardNormal process. The Doppler frequency shift parameters are defined as,

db,a1,t = 2rd cos(

2πf b,aD,tT)

(5.5)

db,a2,t = −r2d (5.6)

Where f b,aD,t is the maximum Doppler shift value and rd is the radius of the pole. Equation(5.4) must be converted into the frequency domain,

Hb,at (n) =

Nc−1∑m=0

hb,at (m)e−j2πmnNc =

M−1∑m=0

hb,at (m)e−j2πmnNc (5.7)

Hb,at (n) = db,a1,t−1H

b,at−1(n) + db,a2,t−1H

b,at−2(n) +Qb,a

t (n) (5.8)

Qb,at (n) =

M−1∑m=0

qb,at (m)e−j2πmnNc (5.9)

Due to the time varying channel, d1,t is the time varying parameter. To estimate the channel,we have to jointly measured d1,t andHb,a

t (n). The joint measurement of equation 5.4 and 5.7is a nonlinear process. It is difficult for any linear method [19] to simulcast measurement.The proposed adaptive fuzzy Kalman filter method is accurately follow the channel than theother estimation method.

5.3 Channel estimation based on FAKF technique

In this section, we have presented the novel noise adjustment technique for MIMO-OFDMsystem on time varying multipath fading channel using fuzzy based method. The investigatedparameters are bit error rate, size of the antenna and the types of modulation method. We

59


Figure 5.3: Flowchart of proposed fuzzy adaptive Kalman filter method

have proposed the method with respect to Rayleigh fading channel. We have also comparethe proposed fuzzy based adaptive method with the SKF, DKF and Nonlinear Kalman filtermethod. When mobile moving with low to medium speed, the proposed method gives thelowest value of bit error rate compare to other method.

5.3.1 Mathematical model of proposed FAKF technique

In the conventional Kalman filter, in [19] it assumes that there is a prior information of the[20] Sp and Sq. Practically in most applications Sp and Sq covariance are not known. Therole of covariance Sp and Sq in the Kalman filter algorithm is to adjust the Kalman gain insuch a way that it controls the bandwidth of the filer as the process and the measurementerrors are vary. In fuzzy based adaptive filter method, the covariance Sp and Sq are adjust insuch a way that to generate minimum error.

Figure 5.3 shows the flowchart of the proposed fuzzy model.

5.3.2 Fuzzy membership function

Consider that mobile velocity is varies with two different speed: Low Speed and MediumSpeed. Case I: For low speed users - Speed of the mobile is 0 km/h to 30 km/h The PDF is

60


Algorithm 6 Fuzzy adaptive Kalman filter AlgorithmAdjustment of measurement noise covariance SqStep 1: Calculate theoretical covariance based on following equation

Sk = HkPkHTk + Sqk (5.10)

Pk = E[(gk − gk)(gk − gk)T ] (5.11)

Step 2: Comparison between original covariance with its ideal valueIf original covariance ik has any mismatching with its ideal value, then a Fuzzy system isused to derive adjustments for SqStep 3: Fuzzy based adjustment of Measurement noise SqCompute approximated value of original covariance using following equation:

Ark =1

N

k∑j=j0

ijiTj (5.12)

Where, j0 is the staring sample inside the estimated blockCompute Degree of Similarity using following equation:

DoSik = Sk − Ark (5.13)

From equation 5.10 of Sk, it is noticed that increased in Sq will increased S, and vice versaStep 4: Apply following adaptive rules for DoSiIf DoSi ∼= 0, then maintain Sq unchangedIf DoSi > 0, then decrease SqIF DoSi < 0, then increase SqStep 5: The correction in Sq is made in this way:

Sqk(j, j) =Sqk−1(j, j)+∆Sqk (5.14)

Where ∆Sqk is the tuning factor that is either additive or subtractive from the element (j,j) of Sq. In this way we can also adjust the process noise covariance

61


Figure 5.4: Membership value v/s Velocity of the mobile

given by,

L (x) =

x−ab−a , if a ≤ x ≤ b

1, if b < x ≤ cd−xd−c , ifc < x ≤ d

(5.15)

For a=0, b=10 and x=5, we get L(x)=0.5. For c=20, d=30 and x=27 we get L(x)=0.3.

Case II: For medium speed users - Speed of the mobile is 30 km/h to 60 km/h The PDF isgiven by,

M (x) =

x−ab−a , if a ≤ x ≤ b

1, if b < x ≤ cd−xd−c , ifc < x ≤ d

(5.16)

For a=30, b=40 and x=38, we get M(x)=0.8. For c=50, d=60 and x=56 we get M(x)=0.4.

Figure 5.4 shows the fuzzy membership function for low speed and medium speed mobileusers.

5.3.3 Performance analysis of various parameters

In this section we have discussed the various parameters like speed of the mobile, fadingrate and Doppler shift parameters etc. The mobile speed is varied from 0 km/h to 60 km/h.The frequency f is 2 GHz. System bandwidth is 3.072 MHz and total 512 subchannels.Subcarrier symbol rate is 3.072M/512 = 6 KHz and number of cyclic prefix is 128. Number

62


of transmit antenna is 2 and number of receive antenna is 2. M-QAM modulation techniqueis used.There are two types of Fading rate (i) Slow fading and (2) Medium fading. For slow fadingrate, ωdT = 8.64× 10−3 Because, if mobile velocity is 30km/h then

fd =v

λcos θ (5.17)

fd =30× 1000× 900× 106

3× 108 × 3600=

15000

3600= 25Hz (5.18)

Then, ωdT = 0.026 for T = 0.166 ms (T = 1/6KHz)

For Medium fading rate, ωdT = 1.04× 10−1 Because, if mobile velocity is 60km/h then

fd =v

λcos θ (5.19)

fd =60× 1000× 900× 106

3× 108 × 3600=

6000

36= 50Hz (5.20)

Then, ωdT = 0.052 for T = 0.166 ms

The Doppler frequency shift parameters are given by,

db,a1,t = 2rd cos(

2πf b,aD,tT)

(5.21)

db,a1,t = 2× 0.998× cos

(2π

50√2

0.166m

)(5.22)

db,a1,t = 2× 0.998× cos (0.037) = 1.995 (5.23)

db,a2,t = −r2d (5.24)

63


db,a2,t = −(0.998)2 = 0.996 (5.25)

5.4 Simulation Results of MIMO-OFDM system with FAKF technique

In this section, we have present the simulation results of proposed noise adjustment techniquefor MIMO-OFDM system. We have discussed the simulation results of MIMO-OFDM withproposed FAM, SKF, DKF and nonlinear Kalman filter technique. When mobile is movingwith low to medium speed, the proposed algorithm gives the lowest value of BER comparedto other method.


The simulation results are divided into two category: In first category we have plot MSE V/SSNR for prediction and estimation technique. We have compared the proposed techniquewith other technique. Figure 5.5 and 5.6 represents the MSE V/S SNR graph for predictionand estimation technique respectively. Simulation results show that in proposed technique,the MSE value is lowered compare to other technique.

In second category we have we have plot BER V/S SNR for proposed technique. We havecompared the proposed technique with other technique. Figure 5.7 represents the BER V/SSNR graph for proposed FAKF, SKF, DKF and non linear Kalman filter method. Simulationresults show that in proposed technique, the BER value is lowered compare to other tech-nique. So, when mobile moving with low to medium speed the proposed technique giveslowest value of BER compared to other technique.

Figure 5.5 shows the MSE V/S SNR graph for MIMO-OFDM with predicted technique. Asthe SNR increased, the MSE value is decreased. At SNR 5 dB, the MSE value is 10−3, 10−2,10−1 and 0.6712 for proposed FAM method, non linear KF method, SKF and DKF methodrespectively. The MSE value is outperforms in the case of proposed technique compared toSKF, DKF and non linear KF technique.

Figure 5.6 shows the MSE V/S SNR plot for MIMO-OFDM with estimated technique. AtSNR 5 dB, the MSE value is 10−4, 10−3, 10−3 and 10−1 for proposed FAM method, nonlinear KF method, SKF and DKF method respectively. The MSE value is outperforms in thecase of proposed technique compared to SKF, DKF and non linear KF technique.

64

5.4. Simulation Results of MIMO-OFDM system with FAKF technique

Figure 5.5: MSE V/S SNR for MIMO-OFDM Estimation (Predictor) - BPSK

Figure 5.6: MSE V/S SNR for MIMO-OFDM Estimation (Estimator) - BPSK

65


Figure 5.7: BER V/S SNR for MIMO-OFDM Estimation - BPSK

Figure 5.7 shows the BER V/S SNR graph for MIMO-OFDM with proposed FAKF tech-nique and BPSK modulation. As the KF order increased, the BER value is also increasedbecause as the order of the filter increased, the nonlinearity of the channel is also increased.In the proposed FAKF method, the BER value is lowered compared to other method. Sowhen any nonlinearity is introduce that is when mobile moving with low to medium speedat that time proposed method gives lowest value of BER compared to other method.



Name of Parameters ValueModulation Technique BPSK

Mobile velocity 0 km/h to 60 km/hSystem BW 3.072 MHzSubcarriers 512

Subcarrier Symbol Rate 6 kHzNo. of cyclic prefix 128

Method FAKF, SKF, DKF, Non linear KFNo. of the antenna 2 TX, 2 RX

Order of the Kalman filter 1,2

66

5.4. Simulation Results of MIMO-OFDM system with FAKF technique

As per the simulation parameters listed in Table 5.1. We have considered various typesof modulation technique like BPSK and QPSK. The total no. of subcarriers per user are512. We have evaluated BER for FAKF, SKF, DKF and non linear KF method. We haveconsidered Rayleigh channel model.

Table 5.2 shows the simulation results of MIMO-OFDM with FAKF, SKF & DKF basedestimation.

Table 5.2: Simulation results for MIMO-OFDM with FAKF, SKF & DKF

SNR (dB) BER (FAKF) BER (SKF) BER (DKF)0 0.0176 0.0179 0.01802 0.0172 0.0176 0.01794 0.0150 0.0170 0.01746 0.0130 0.0165 0.01688 0.0025 0.0150 0.015510 0.9E-04 0.0048 0.013012 0.7E-04 3.7E-03 0.011014 0.4E-04 3.4E-03 2.8E-0316 0.9E-05 2.5E-03 9.0E-0318 0.8E-05 4.7E-04 6.0E-0420 0.3E-05 3.5E-04 5.2E-04

Figure 5.8 shows the MSE V/S SNR graph for MIMO-OFDM with predicted QSPK tech-nique. As the SNR increased, the MSE value is decreased. The lowest value of MSE isachieved in the case of proposed technique compared to SKF, DKF and non linear KF tech-nique.

Figure 5.9 shows the MSE V/S SNR plot for MIMO-OFDM with estimated QPSK technique.The lowest value of MSE is achieved in the case of proposed technique compared to SKF,DKF and non linear KF technique.

Figure 5.10 shows the BER V/S SNR graph for MIMO-OFDM with proposed FAKF methodand QPSK modulation. As the KF order increased, the BER value is also increased becauseas the order of the filter increased, the nonlinearity of the channel is also increased. In theproposed FAKF method, the BER value is lowered compared to other method. So when anynonlinearity is introduce that is when mobile moving with low to medium speed at that timeproposed method gives lowest value of BER compared to other method.

67


Figure 5.8: MSE V/S SNR for MIMO-OFDM Channel Estimation (Predictor)- QPSK

Figure 5.9: MSE V/S SNR for MIMO-OFDM Channel Estimation (Estima-tor) - QPSK

68

5.5. Summary

Figure 5.10: BER V/S SNR for MIMO-OFDM Channel Estimation - QPSK

5.5 Summary

In this section, we have discussed the MIMO-OFDM channel estimation method based onFuzzy adaptive Kalman filter. We have compared the proposed technique with the othertechnique. We have proposed FAKF technique which improve the performance of BERcompared to other technique. When mobile station is moving with low to medium speed,the proposed FAKF method gives the better results. In our work, we have considered theRayleigh low to medium speed fading channel.

69

Chapter 6

MIMO-OFDM Channel estimation usingAdaptive Fuzzy Cubature Kalman filter

6.1 Introduction

In this section, we have discussed a novel equalization technique for MIMO-OFDM systembased on adaptive fuzzy cubature Kalman filter algorithm. We have proposed the methodwith respect to Rayleigh frequency selective fast fading channel. The Doppler frequencyshift parameters and channel amplitudes are simultaneously measured by the proposed method.This is beneficial when channel variation is faster. We have plot the BER versus SNR graphfor proposed fuzzy adaptive Kalman filter method. The investigated parameters are bit errorrate, size of the antenna and the types of modulation method. We have compared the pro-posed adaptive fuzzy cubature Kalman filter method with the other method. With referenceto fast moving mobile, the proposed method gives the lowest value of bit error rate comparedto other method.

In section 6.2, we have presented mathematical model of MIMO-OFDM transmitter andreceiver. We have also discussed the estimation of channel and tracking of MIMO-OFDMsystem. We have also discussed the various parameters like number of transmitter, numberof receiver and Doppler frequency shift parameters.

In section 6.3, we have presented a estimation of channel for MIMO-OFDM system basedon adaptive fuzzy cubature Kalman filter which improve the estimation compare to othermethod. In this section, we have considered that mobile station is moving with low to veryhigh speed. We have estimated the channel under Rayleigh frequency selective fast fadingchannel condition. We have achieved the lowest BER particularly when the mobile station ismoving with very high speed.

70

6.2. Mathematical Model of MIMO-OFDM Transmitter and Receiver

Our work is organized as follows. Section 6.2 defines mathematical model of MIMO-OFDMtransmitter and receiver. Section 6.3 defines estimation of channel based on adaptive fuzzycubature Kalman filter method. Section 6.4 defines the simulation results of adaptive fuzzycubature Kalman filter method. Section 6.5 defines the summary of work.

6.2 Mathematical Model of MIMO-OFDM Transmitter and Receiver

In this section, we have presented mathematical model of MIMO-OFDM transmitter andreceiver. We have also discussed the estimation of channel for MIMO-OFDM system. Wehave discussed the various parameters like number of transmitter, number of receiver andDoppler frequency shift parameters.

6.2.1 System Model of MIMO-OFDM transmitter

Figure 6.1 shows the system model of MIMO-OFDM transmitter. In MIMO-OFDM system,number of transmitter, number of receiver and number of subcarriers are denoted by Nt, Nr

and Nc respectively.

Figure 6.1: System Model of MIMO-OFDM transmitter

As shown in figure 6.1, We have evaluate the channel with respect to different modulationtechnique. The OSTBC coder provides the transmitter diversity. In this case Channel state in-formation is known to the receiver. We have consider various types of channel like Rayleighfrequency selective slow to medium fading channel and Rayleigh frequency selective fastfading channel. For the orthogonal space time block coder, let transmitted signal is given by,

71

Chapter 6. MIMO-OFDM Channel estimation using Adaptive Fuzzy Cubature Kalmanfilter



The Orthogonal space time block coder is given by,

D(Gt(n)) =L∑

m=1



6.2.2 System Model of MIMO-OFDM receiver

Figure 6.2 shows the system model of MIMO-OFDM receiver. The received signal is givenby,

Rt(n) = D(Gt(n))Ht(n) + Pt(n) (6.3)

For n = 0,1,2,.....,Nc − 1, where Rt(n) is the receiver matrices with no. of slot × no. of rxantenna and Ht(n) is the frequency response of channel and Pt(n) is the noise with no. ofslot × no. of rx antenna. Here, we have considered Rayleigh fading channel with fast timevariation.

Figure 6.2: System Model of MIMO-OFDM receiver

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6.3. Estimation of channel based on AFCKF technique

6.2.3 Mathematical model of MIMO-OFDM channel estimation

In this section we have select second order Auto-regressive model due to its less complexityand perfectness with respect to fast fading rate of the channel. The mth path channel impulseresponse is given by,

hb,at (m) = db,a1,t−1hb,at−1(m) + db,a2,t−1h

b,at−2(m) + qb,at (m) (6.4)

For a = 1,2,3,...,Nr, b = 1,2,3,...,Nt, and m = 0,1,2,3,...,M-1, where qb,at (m) is a standardNormal process. The Doppler frequency shift parameters are defined as,

db,a1,t = 2rd cos(

2πf b,aD,tT)

(6.5)

db,a2,t = −r2d (6.6)

Where f b,aD,t is the maximum Doppler shift value and rd is the radius of the pole. Equation(6.4) must be converted into the frequency domain,

Hb,at (n) =

Nc−1∑m=0

hb,at (m)e−j2πmnNc =

M−1∑m=0

hb,at (m)e−j2πmnNc (6.7)

Hb,at (n) = db,a1,t−1H

b,at−1(n) + db,a2,t−1H

b,at−2(n) +Qb,a

t (n) (6.8)

Qb,at (n) =

M−1∑m=0

qb,at (m)e−j2πmnNc (6.9)

The proposed adaptive fuzzy cubature Kalman filter method is accurately follow the channelthan the other estimation method in terms of fast time variation of the channel.

6.3 Estimation of channel based on AFCKF technique

In this section, we have presented a novel equalization technique for MIMO-OFDM systembased on adaptive fuzzy algorithm. We have proposed the method with respect to Rayleighfrequency selective fast fading channel. The Doppler frequency shift parameters and channelamplitudes are simultaneously measured by the proposed method. This is beneficial whenchannel variation is faster. We have plot the BER versus SNR graph for proposed adaptivefuzzy cubature Kalman filter method. The investigated parameters are bit error rate, size of

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the antenna and the types of modulation method. We have compared the proposed adaptivefuzzy cubature Kalman filter method with the fuzzy Kalman filter method, SKF, DKF andNon linear Kalman filter method. With reference to moving mobile with high speed, theproposed AFCKF method gives the lowest value of bit error rate compared to other method.

6.3.1 Mathematical model of proposed Adaptive Fuzzy Cubature Kalman Filter tech-nique

A CKF is defined as nonlinear Bayesian filter. It was demonstrated by Haykin [12]. It isproposed for nonlinear estimation of the state. It is approximated as Normal distributionof a Baye’s filter. It is the more accurate Normal filter estimation then the conventionalNormal filters. The adaptive fuzzy system is incorporated in to the CKF to improve theperformance of bit error rate and channel state prediction of MIMO-OFDM system. Thefuzzy adaptive system uses fuzzy inference system of Takagi-Sugeno type, because in T-Smethod the nonlinear models is represented using interpolation between linear models. Thefuzzy rule with respect to variation in the mobile velocity is given as: (i) If mobile velocityis 10 km/h to 120 km/h then the user is low-medium speed user and (ii) If mobile velocityis > 120 km/h then the user is high speed user. In terms of mathematical form, fuzzy rule isgiven as: Rule u: If estimated velocity of previous time instant t − 1 is vt−1 Then considerits fuzzy set is Fu(vt−1)

Gt = Du,t−1Gt−1 + Pt (6.10)

rt = JtGt +Qt (6.11)

Where,

Du,t−1 =

1 0 0

0 d1,t−1(u)INtNr d2,t−1INtNr

. . .

. INtNr 0NtNr

for u = 1,2,3,...,U d1,t(u) is the mobile velocity, and Fu is fuzzy set rule. The output of thefuzzy adaptive system is given as:

Gt =U∑u=1

µu (vt−1)Du,t−1Gt−1 + Pt (6.12)

rt = JtGt +Qt (6.13)

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The fuzzy base µu(vt) is defined as,

µu (vt) =Fu (vt)U∑u=1

Fu (vt)

(6.14)

U∑u=1

µu (vt) = 1 (6.15)

If vt−1 is FuGu,t = Du,t−1Gt−1 +Ku,tet (6.16)

Where,et = rt − JtGt (6.17)

Ku,t is the fuzzy Kalman gain. Here, et denotes the error in the prediction steps. The Kalmangain Ku,t is used for minimization of the covariance E{eteTt } in the prediction error steps.

6.3.2 Fuzzy membership function

Consider that mobile velocity is varies with three different speed: Low Speed, MediumSpeed and High Speed Case I: For low speed users - Speed of the mobile is 0 km/h to 40km/h The PDF is given by,

L (x) =

1, if x ≤ ab−xb−a , if a < x ≤ b

0, if x > b

(6.18)

For a=40, b=80 and x=50, we get L(x)=0.75 and so on.

Case II: For medium speed users - Speed of the mobile is 40 km/h to 120 km/h The PDFis given by,

M (x) =

0, if x ≤ a(x−a)(m−a) , if x ∈ (a,m](b−x)(b−m)

, if x ∈ (m, b)

0, if x ≥ b

(6.19)

For a=40, b=120 and x=60, we get M(x)=0.5 and so on.

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Figure 6.3: Membership value v/s Velocity of the mobile

6.3.4 Performance analysis of various parameters

In this section we have discussed the various parameters like speed of the mobile, fading rateand Doppler shift parameters etc. The mobile speed is varied from 10 km/h to 160 km/h.The frequency f is 2 GHz. System bandwidth is 3.072 MHz and total 512 subchannels.Subcarrier symbol rate is 3.072M/512 = 6 KHz and number of cyclic prefix is 128. Numberof transmit antenna is 2 and number of receive antenna is 2. QPSK modulation technique isused.There are two types of Fading rate (i) Slow fading and (2) Fast fading. For slow fading rate,ωdT = 8.64× 10−3 Because, if mobile velocity is 10km/h then

fd =v

λcos θ (6.21)

fd =10× 1000× 900× 106

3× 108 × 3600=

15000

3600= 8.34Hz (6.22)

Then, ωdT = 8.64× 10−3 for T = 0.166 ms (T = 1/6KHz)

For fast fading rate, ωdT = 1.04× 10−1 Because, if mobile velocity is 160km/h then

fd =v

λcos θ (6.23)

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fd =160× 1000× 900× 106

3× 108 × 3600=

6000

36= 133.33Hz (6.24)

Then, ωdT = 1.39× 10−1 for T = 0.166 ms

The Doppler frequency shift parameters are given by,

db,a1,t = 2rd cos(

2πf b,aD,tT)

(6.25)

db,a1,t = 2× 0.998× cos

(2π

133.33√2

0.165m

)(6.26)

db,a1,t = 2× 0.998× cos (0.073) = 1.986 (6.27)

db,a2,t = −r2d (6.28)

db,a2,t = −(0.998)2 = 0.996 (6.29)

6.4 Proposed Equalization technique of MIMO-OFDM system

In this section we have discussed the proposed equalization technique of MIMO-OFDM sys-tem based on AFCKF method. A signal is attenuated and distorted by the channel. Equaliza-tion is used to remove distortion of the signal. Equalizer have a frequency characteristics thatis the inverse of that of the channel. This will eliminate the pulse dispersion and distortion.We have applied the fuzzy technique on cubature Kalman filter.

6.4.1 Mathematical model of proposed equalization technique

In this section we have discussed the mathematical model of proposed equalization techniqueof MIMO-OFDM system based on AFCKF method. The received signal for each subcarrier

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6.4. Proposed Equalization technique of MIMO-OFDM system

is given by,rt = O(Ht)st +Qt (6.30)

Where rt is received signal, O(Ht) is channel gain of detected and predicted part and Qt ismeasurement error

O(Ht) = O(Ht|t−1) +O(Ht|t−1) (6.31)

The received signal can again given as,

rt = O(Ht)st +Qt (6.32)

rt = O(Ht|t−1)st +O(Ht|t−1)st +Qt (6.33)

rt = O(Ht|t−1)st + Qt (6.34)

Where,Qt = O(Ht|t−1)st +Qt (6.35)

The optimal equalizer is given by,

φoptt =U∑u=1

µu(vu,t−1|t−1)φu,t (6.36)

The proposed equalization is based on Adaptive fuzzy cubature Kalman filter method. Com-pared to fuzzy Kalman filter method, the lowest value of bit error rate is achieved in proposedAFCKF method.

φu,t = OH(Hu,t|t−1)X[O(Hu,t|t−1

)OH

(Hu,t|t−1

)+Qt

](6.37)

The conventional equalizer is given by,

φct−1 = OH(Ht−1)[O(Ht−1

)OH

(Ht−1

)+Qt

]−1(6.38)

The MSE is defined as,

MSE(n) =

E

{[Ht(n)− Ht(n)

]2}E{

[Ht(n)]2} (6.39)

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6.5 Simulation Results of MIMO-OFDM system with AFCKF method

In this section we have discussed the simulation parameters of MIMO-OFDM system andsimulation results with respect to proposed adaptive fuzzy cubature Kalman filter method.We have also compared the proposed technique with FAKF, SKF and DKF technique.


In this section, we have discussed the simulation results of proposed AFCKF technique. Wehave also compared the proposed AFCKF technique with SKF and DKF method. Figure6.4, 6.5 and 6.6 shows the simulation results of proposed AFCKF technique, SKF, DKF andFuzzy adaptive KF technique. As per the simulation results, it is cleared that BER value islowered compare to other technique. When mobile speed is medium to high, the proposedtechnique gives lowest value of BER compared to other technique.

Figure 6.4: MSE V/S SNR for MIMO-OFDM with AFCKF technique(Predictor-QPSK)

Figure 6.4 shows the MSE V/S SNR graph for MIMO-OFDM with predicted QPSK tech-nique. As the SNR increased, the MSE value is decreased. At SNR 10 dB, the MSE value

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6.5. Simulation Results of MIMO-OFDM system with AFCKF method

is 10−3, 0.0124, 0.0321 and 10−1 for proposed AFCKF, FKF, SKF and DKF method respec-tively. The lowest value of MSE is achieved in the case of proposed technique.

Figure 6.5: MSE V/S SNR for MIMO-OFDM with AFCKF technique(Estimator-QPSK)

Figure 6.5 shows the MSE V/S SNR plot for MIMO-OFDM system with estimated QPSKtechnique. As the SNR increased, the MSE value is decreased. At SNR 10 dB, the MSEvalue is 10−4, 0.00232, 0.00452 and 10−1 for proposed AFCKF, FKF, SKF and DKF methodrespectively. The MSE is outperforms in the case of proposed technique.

Figure 6.6 shows the BER V/S SNR graph for MIMO-OFDM system with proposed FACKF,SKF, DKF and Fuzzy adaptive KF technique. When mobile moving with very high speed, thenonlinearity of the channel is also increased and due to this nonlinearity BER is increased.But in proposed AFCKF technique BER value is decreased, as we increase the nonlinearityin the channel. So, the proposed AFCKF technique is better in terms of nonlinearity (Whenmobile station is moving with high speed) of the channel.


Table 6.2 shows the simulation results of MIMO-OFDM with AFCKF, FKF, SKF & DKFbased estimation.

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Figure 6.6: BER V/S SNR for MIMO-OFDM with AFCKF technique - QPSK


Name of Parameters ValueTypes of Modulation QPSK


Subcarrier Symbol Rate 6 kHzNo. of cyclic prefix 128No. of the antenna 2 TX, 2 RX

Types of Kalman filter AFCKF, FAKF, SKF, DKF

Figure 6.7 shows the MSE V/S SNR graph for MIMO-OFDM with predicted technique. Asthe SNR increased, the MSE value is decreased. The lowest value of MSE is achieved inthe case of proposed method. As we increased the M-ary number, the MSE value is alsoincreased.

Figure 6.8 shows the MSE V/S SNR graph for MIMO-OFDM with estimated technique. Asthe SNR increased, the MSE value is decreased. The MSE value is outperforms in the caseof proposed technique. As we changed the M-ary no. from 4 to 8, the MSE value is also

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6.5. Simulation Results of MIMO-OFDM system with AFCKF method

Table 6.2: Simulation results for MIMO-OFDM with AFCKF, FKF, SKF &DKF

SNR (dB) BER (AFCKF) BER (FKF) BER (SKF) BER (DKF)0 0.0186 0.0187 0.0188 0.01902 0.0180 0.0182 0.0184 0.01864 0.0175 0.0177 0.0180 0.01826 0.0140 0.0145 0.0150 0.01548 0.0025 0.0050 0.0140 0.0148

10 1.0E-03 0.0045 0.0120 0.013012 0.2E-03 3.5E-03 0.0114 0.012814 1.0E-04 2.7E-03 0.01043 0.011816 0.5E-04 2.3E-03 9.0E-03 10.5E-0318 0.2E-04 2.2E-03 7.0E-03 8.2E-0320 0.1E-04 2.1E-03 5.0E-03 6.1E-03

Figure 6.7: MSE V/S SNR for MIMO-OFDM with AFCKF technique(Predictor-8-QAM)

increased.

Figure 6.9 shows the BER V/S SNR graph for MIMO-OFDM with proposed FACKF, SKF,DKF and Fuzzy adaptive KF technique. When mobile moving with very high speed, the non-linearity of the channel is also increased and due to this nonlinearity BER value is increased.

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Figure 6.8: MSE V/S SNR for MIMO-OFDM with AFCKF technique(Estimator-8-QAM)

Figure 6.9: BER V/S SNR for MIMO-OFDM with AFCKF technique - 8-QAM

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6.6. Summary

But in proposed AFCKF technique BER value is decreased, as we increase the nonlinearityin the channel. So, the proposed AFCKF method is better in terms of nonlinearity (Whenmobile station is moving with high) of the channel. Compared to figure no. 6.6, BER valueis increased because in this case we increased the M-ary no. from 4 to 8.



Name of Parameters ValueTypes of Modulation 8-QAM


Subcarrier Symbol Rate 6 kHzNo. of cyclic prefix 128No. of the antenna 2 TX, 2 RX

Types of Kalman filter AFCKF, FAKF, SKF, DKF

6.6 Summary

In this section, we have discussed the MIMO-OFDM channel estimation method based onAdaptive Fuzzy Cubature Kalman filter. We have compared the proposed technique withthe other technique. We have proposed AFCKF technique which improve the performanceof BER with respect to other estimation technique. When mobile station is moving withmedium to high speed, the proposed AFCKF method gives the better results. So, when chan-nel variation is faster, the proposed method gives the lowest value of bit error rate comparedto other method.

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Chapter 7

Conclusion and Future Scope

7.1 Conclusion

In this work, we have proposed PAPR minimization technique for OFDM system. The pro-posed algorithm is based on the combination of probabilistic approach and coded approachwhich minimized the PAPR value efficiently. The complexity of proposed method is verylow. The proposed method minimize the PAPR with respect to BPSK, QPSK and M-QAMmodulation technique. In a same line of research we have also proposed the PAPR mini-mization technique for uplink 3-GPP LTE physical system with interleaver concept. It isconcluded that the proposed algorithm minimize the PAPR value in 3-GPP LTE physicallayer system.

We have proposed the estimation of channel for MIMO-OFDM with linear Kalman filtertechnique. We have considered the time invariant Rayleigh channel model. In this case,we have considered the stationary mobile station condition. We have also compared theproposed technique with the conventional technique. The proposed technique outperformsthe bit error rate. We have achieved lowest bit error rate compared to other method. Wehave extended the work to the non linear Kalman filter in which we have considered thetime variant Rayleigh channel model. It is found that for slow fading channel, the proposedmethod outperforms the probability of error compared to other method.

We have also proposed the equalization technique for MIMO-OFDM system based on adap-tive fuzzy algorithm. We have select Rayleigh frequency selective slow to medium fadingchannel. The proposed method gives the better results when mobile is moving with low tomedium speed. We have compared the proposed fuzzy adaptive Kalman filter method withthe other method. It is verify that with reference to low to medium speed moving mobile, theproposed method gives the lowest value of mean square error compared to other method.

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7.2. Future Scope

We have extended the work of the channel estimation using adaptive fuzzy cubature Kalmanfilter algorithm. We have considered Rayleigh frequency selective fast fading channel. TheDoppler frequency shift parameters and channel amplitudes are simultaneously measured bythe proposed method. This is beneficial when channel variation is faster. The investigatedparameters are BER and the types of modulation method. We have compared the proposedadaptive fuzzy cubature Kalman filter method with the other method. It is revealed that withrespect to fast time varying multipath fading, the proposed method gives the lowest value ofbit error rate compared to other method.

7.2 Future Scope

In this thesis, we have proposed the estimation of channel for MIMO-OFDM with respectto different velocity of the mobile. There are some scopes for the expansion of the work.We have studied the performance of proposed method with respect to various mobile speed;the work can be explored for the many other environments and challenging condition. Theproposed work can be explored further and to design the embedded chip set.

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List of Publications

1. Darshankumar C. Dalwadi and Himanshu B. Soni, "A Novel Channel EstimationTechnique of MIMO-OFDM System based on Modified Kalman Filter", Indian jour-nal of science and technology, Thomson Reuters, Volume 9, issue 36, 2016, DOI:10.17485/ijst/2016/v9i36/97757

2. Darshankumar C. Dalwadi and Himanshu B. Soni, "A Novel Discrete Spreading Schemewith RC Filter for PAPR reduction in OFDM System using Multiple Interleaver", In-ternational Journal of Applied Engineering Research, Scopus Elsevier, Volume 10, No.17, 2015

3. Darshankumar C. Dalwadi and Himanshu B. Soni, "Low Complexity PAPR reductiontechnique for Coded OFDM systems with Scrambling approach", International Journalof Current Engineering and Technology, International Press Corporation USA, Vol. 4,No. 5, pp. 3294-3299, 2014

4. Darshankumar C. Dalwadi and Himanshu B. Soni, "A novel noise adjustment tech-nique for MIMO-OFDM system based on Fuzzy based adaptive method", 5th Interna-tional Conference on Advanced Computing, Networking, and Informatics - ICACNI,NIT Goa, Springer, 2017

5. Darshankumar C. Dalwadi and Himanshu B. Soni, "Channel Estimation and Trackingof MIMO-OFDM System based on Kalman Filter", IEEE sponsored 3rd Internationalconference on Electronics and Communication systems, Coimbatore, IEEE, 2016

6. Darshankumar C. Dalwadi and Himanshu B. Soni, "A Novel Equalization techniquefor MIMO-OFDM System based on Adaptive Fuzzy Algorithm", Journal of DigitalCommunications and Networks, Science Direct, Elsevier (Under review)

91

List of Courses Attended

1. "Summer project on MIMO, Massive MIMO and OFDM 4G/5G Wireless technolo-gies", Organized by Department of Electrical Engineering, IIT Kanpur, During 20th to23rd June, 2017

2. "Mobile Broadband Systems: LTE and LTE Advanced", Organized by Nirma Univer-sity, Ahmedabad, During 25th November 2015

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