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Handbook of Research on Fuzzy and Rough Set Theory in Organizational Decision Making Arun Kumar Sangaiah VIT University, India Xiao-Zhi Gao Aalto University, Finland Ajith Abraham Machine Intelligence Research Labs, USA

A volume in the Advances in Business Strategy and Competitive Advantage (ABSCA) Book Series

Published in the United States of America by IGI Global Business Science Reference (an imprint of IGI Global) 701 E. Chocolate Avenue Hershey PA, USA 17033 Tel: 717-533-8845 Fax: 717-533-8661 E-mail: [email protected] Web site: http://www.igi-global.com Copyright © 2017 by IGI Global. All rights reserved. No part of this publication may be reproduced, stored or distributed in any form or by any means, electronic or mechanical, including photocopying, without written permission from the publisher. Product or company names used in this set are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI Global of the trademark or registered trademark. Library of Congress Cataloging-in-Publication Data Names: Sangaiah, Arun Kumar, 1981- editor. | Gao, Xiao-Zhi, 1972- editor. | Abraham, Ajith, 1968- editor. Title: Handbook of research on fuzzy and rough set theory in organizational decision making / Arun Kumar Sangaiah, Xiao-Zhi Gao, and Ajith Abraham, editors. Description: Hershey, PA : Business Science Reference, [2017] | Series: Advances in business strategy and competitive advantage | Includes bibliographical references and index. Identifiers: LCCN 2016028984| ISBN 9781522510086 (hardcover) | ISBN 9781522510093 (ebook) Subjects: LCSH: Decision making--Mathematical models. | Fuzzy sets. Classification: LCC T57.95 .H355 2017 | DDC 511.3/223--dc23 LC record available at https://lccn.loc.gov/2016028984 This book is published in the IGI Global book series Advances in Business Strategy and Competitive Advantage (ABSCA) (ISSN: 2327-3429; eISSN: 2327-3437)

British Cataloguing in Publication Data A Cataloguing in Publication record for this book is available from the British Library. All work contributed to this book is new, previously-unpublished material. The views expressed in this book are those of the authors, but not necessarily of the publisher. For electronic access to this publication, please contact: [email protected].

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Chapter 13

Optimized-Fuzzy-LogicBased Bit Loading Algorithms Sankar Ganesh S. VIT University, India

Arunprakash Jayaprakash VIT University, India

Mohanaprasad K. VIT University, India

Sivanantham Sathasivam VIT University, India

ABSTRACT Next generation wireless communication systems promise the subscribers with Giga-bit-data-rate experience at low Bit Error Rate (BER) under adverse channel conditions. In order to maximize the overall system throughput of Orthogonal Frequency Division Multiplexing (OFDM), adaptive modulation is one of the key solutions. In adaptive modulated OFDM, the subcarriers are allocated with data bits and energy in accordance with the Signal to Interference Ratio (SIR) of the multipath channel, which is referred to as adaptive bit loading and adaptive power allocation respectively. The number of iterations required allocating the target bits and energy to a sub channel is optimized. The key choice of the paper is to allocate the bits with minimum number of iterations after clustering the sub channels using fuzzy logic. The proposed method exhibits a faster convergence in obtaining the optimal solution.

INTRODUCTION OFDM is considered as the most widely adopted multicarrier communication technique for very high speed data transmission in wireless local area networks (WLAN) and digital subscriber link (DSL) systems. OFDM exhibits various advantages over the conventional single carrier communication systems. The OFDM systems are robust against frequency selective channels as the multipath channels effect as flat fading channels to individual subcarriers and hence one-tap equalization is made possible. The subcarriers in OFDM are orthogonal sine pulses so that the conventional frequency division multiplexing systems, the subcarriers can be closely spaced without interference, thereby improving spectral efficiency and reducing the total bandwidth requirements. Even though the time varying channels introduce inter carrier interference (ICI), several CFO estimation and correction techniques can be used to avoid this undesirable effect. DOI: 10.4018/978-1-5225-1008-6.ch013

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 Optimized-Fuzzy-Logic-Based Bit Loading Algorithms

In spite of these advantages of OFDM, a decrease in the performance occurs under multipath channels due to the fluctuations in the frequency response of the channels. This is severe in the case of highly frequency selective channels. The set of data to be transmitted are modulated onto orthogonal subcarriers which are summed up and transmitted through the channel. The multipath channel which is frequency selective in nature attenuates the data symbols modulated at different subcarriers differently. Certain subcarriers may be attenuated heavily so that the data symbols modulated on to those subcarriers are completely lost during transmission. Channel gain for certain other subcarriers will be very high. Hence, the system performance and throughput will be very much less than the optimum value if a fixed transmission scheme is used for OFDM transmission under a highly frequency selective channel. The data symbols modulated on to subcarriers which are attenuated heavily has very low SIR and hence high bit error rate which results in a poor performance. Hence, adaptive modulation aims at leaving out the subcarriers that are attenuated heavily and allocate bits to the subcarriers according to the channel gain. The adaptation of the modulation level according to the SIR results in better BER performance and high system throughput. Several adaptive bit and power allocation loading schemes have been studied. The most powerful method to allocate bits with less energy is using Hughes-Hartogs Greedy Algorithm by (Hughes-Hartogs, 1988) but it takes a large number of iterations to converge to the optimal solution. Chow’s Algorithm proposed by (Chow, Cioffi, & Bingham, 1995) uses channel capacity approximation and converges to the solution for given target bits and performance margin. Campello’s Algorithm proposed by (Campello, 1999, 1998) is different in the way that it takes differential energy to achieve the target bits. But both these algorithms take a lot of iterations again. Simple bit loading algorithm proposed by (Nader-Esfahani & Afrasiabi, 2007) has low complexity and takes less iteration than Hughes Hartogs Greedy, Chow and Campello. It is based on grouping of sub channels based on gain. A clustering based bit loading algorithm which uses neural network for clustering the subcarriers is elaborated in (Birla, 2014). A computationally efficient bit loading algorithm for OFDM systems is proposed in (Vo, Amis, Chonavel, Siohan, & Member, 2015) which adaptively switches between Greedy algorithm and bit removing algorithm. The adaptive modulated multicarrier systems are also applied in the context of visible light communication (Hong, Member, Wu, Chen, & Member, 2016), power line communication (Gianaroli, Pancaldi, & Vitetta, 2015) and filter bank multicarrier based optical communication (Jung, Jung, & Han, 2015). The proposed algorithm has very low computation complexity and is convergent to the optimal solution; moreover, it has low algorithmic complexity for implementation purposes. Grouping concept proposed by (Wang, Cao, & Statement, 2013; Nader-Esfahani & Afrasiabi, 2007) is used in proposed fuzzy based bit loading algorithm with very low complexity and less iteration with comparable energy as compared to existing algorithms. It is observed that maximum of 15 bits can be allocated to a sub-channel but for energy optimization with less iteration maximum of 11 bits can be allocated. Fuzzy is related to ambiguity. Fuzzy based Systems are based on Soft Threshold Concept where transitions are based on ambiguity i.e. various intervals can be decided based on discretion of user. So bit loading algorithms are optimized using fuzzy logic by (Sastry, 2010). The conventional bit loading algorithms require more number of iterations to find the optimum solutions and hence become difficult to be applied for real time applications. Hence in the present study, a fuzzy theory based solution is proposed for the adaptive bit loading problem formulated as a constrained optimization problem. In this chapter, an adaptive loading and modulation scheme is proposed in which all the parameters are adapted using a fuzzy logic base system. Rest of the chapter is organized as follows. Bit loading and Fuzzy introduction is given in the

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 Optimized-Fuzzy-Logic-Based Bit Loading Algorithms

next section. The proposed clustering based loading algorithms using fuzzy and simulations results are elaborated in the subsequent section. The next section contains the comparison between existing and proposed algorithms and concludes the chapter.

BIT LOADING AND FUZZY LOGIC Bit Loading Bit Loading is a technique in which bit allocation is performed for the sub-carriers in Multicarrier Modulation. The bits allocation is based on the sub channel quality which is based on parameters like SNR. The aim of this technique is to allocate more bits to channels with high SNR or low corrupted channels and fewer bits to channels with low SNR or highly corrupted channels. Bit Loading involves allocation of parameters like Energy and the bits to a sub channel. The parameters taken into account while allocating the bits and energy are Sub-channel Gain(H), Sub-channel Noise(N), SNR gap(Γ), Target Bits(Btotal), Maximum Energy(Ptotal), Target Margin(tm). All the algorithms take few of the above mentioned parameters into account to propose an optimal solution for Bit Loading. The number of bits that can modulated on to each subcarrier depends upon the channel characteristics and SNR at that particular frequency. More power must be allocated to those subcarriers with lower SNR to transmit data. Due to an overall power limit on each subcarrier, those frequencies with high attenuation are able to carry less number of bits than a channel with a better channel gain. More bits can be allocated to that particular sub-channel which has better SNR at that frequency range in the sub-channel range (Juan Wen & Tian, 2013). The SNR for a sub-channel is given by SNRk =

H k 2

(Γ ⋅ σ ) 2

, k = 1, 2 … N

(1)

where SNR gap, Γ, represents how far is the channel from Shannon Channel Capacity. To reduce iteration complexity one of the methods is cluster or group sub-channels based on their gain response. This approach leads to group by group bit loading which just takes one iteration to allocate bits but for grouping iterations are needed. The number of groups is given by 2   H max   + 1 Number of Groups = log2   H min 2   

(2)

where |Hmax|2 and |Hmin|2 are maximum and minimum gains of the sub-channels and x denote the largest integer less than x. Figure 1 shows grouping performed based on sub-channel gains.

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 Optimized-Fuzzy-Logic-Based Bit Loading Algorithms

Figure 1. Grouping of sub-channels

Bit-Loading for kth sub-channel is performed by finding maximum and minimum bits that can be loaded in that group using maximum and minimum Channel Gain values in the equation    SNRk  BLk = log2 −1.6 ∗ + 1   ln 5 ∗ T arget BER  

(

)

(3)

The energy for kth sub-channel is given by

(

BLk

Ek = 2

   Γ ⋅ σ 2  , k = 1, 2..N  − 1 ∗   H 2   k 

)

(4)

where BL is the loaded bits in the sub-channel and σ2 is Noise Variance. Finally Bit Error rate, BER for kth sub-channel (k varies from 1,2..N)is given by,

BERk = 0.2e

 2      H   −1.6 Ek ⋅ k     2BLk −1  σ 2      



(5)

Present your perspective on the issues, controversies, problems, etc., as they relate to theme and arguments supporting your position. Compare and contrast with what has been, or is currently being done as it relates to the chapter’s specific topic and the main theme of the book (Figure 1).

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Fuzzy Logic Fuzzy is related to ambiguity. Unlike Neural networks that are based on Hard Threshold Concept i.e. output is either logic 0 or 1, Fuzzy based Systems are based on Soft Threshold Concept where transitions are based on ambiguity i.e. various intervals can be decided based on discretion of user (Sastry, 2010). The unique features of fuzzy logic make it an excellent choice for many control problems. The target control system is governed by user defined rules which is processed by the fuzzy logic system. it Hence it can be adjusted and modified easily to improve the system performance. The fuzzy logical system is not restricted to a few feedback inputs and a couple of control outputs, nor does it require information on the rate-of-change of parameters for its implementation. Both linear and non-linear systems for embedded control can be designed using fuzzy logic. The fuzzy logic can be applied effectively solve real world problems through intelligent interpretations and human like thinking. Instead of taking a crisp decision based on hard thresholds, a soft decision is taken considering different parameters simultaneously. Various methods are used for fuzzification like rank ordering, inference, intuition and threshold concept. All these help in grouping the Sub-Channels into packets based on the channel response. For our purpose we can choose either rank ordering or threshold concept for fuzzification.

CLUSTERING BASED BIT LOADING ALGORITHM USING FUZZY LOGIC Fuzzy Based Bit Loading Algorithms are based on Threshold Concept. Using various Threshold Ranges groups are made based on sub-channel quality. For simulation purpose the input data includes 64 sub-channels. The gain response is generated using a 3 tap-filter and is shown in Figure 2. The target BER is taken as 10-5. Noise variance is 0.001. The Target Bits are taken to be 300. Figure 2. Sub-channel response

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 Optimized-Fuzzy-Logic-Based Bit Loading Algorithms

Figure 3. Fuzzy based bit loading algorithm 1

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 Optimized-Fuzzy-Logic-Based Bit Loading Algorithms

Fuzzy Based Algorithm: 1 In this algorithm groups are made based on Normalized Sub-channel Gains. The thresholds are found based on the no. of groups calculated using (1). The Flowchart for the Algorithm is shown in Figure 3. The algorithm helps to reach the Bit Allocation almost near to Target Bits requirement. The Simulation Results are shown in Figure 4. For the channel response shown in Figure 2, the number of groups came out to be 10. Clearly higher bits are loaded in sub-channels of higher gain. The BER calculated using (5) is found to be of the order 10-4. The total Energy required to transmit target number of bits is found to be 2.4 Joules, calculated using (4), which converges to Hughes-Hartogs Optimal result. The algorithm takes 1 iteration for grouping, 1 for bit allocation and 5 iterations (approximately equal to Target Bits/No. of Sub-channels) to meet the target bits requirement. In all the algorithm takes 7 iterations for given Simulation Inputs.

Fuzzy Based Algorithm: 2 In this algorithm groups are made based on Normalized Sub-channel Gains. The thresholds are found based on the no. of bad channel threshold taken from user. The bad channel threshold separates low gain channels from higher gain channels. No bit should be allocated to the bad channels ideally but for meeting target bit requirement few bits are allocated. The Flowchart for the Algorithm is shown in Figure 6. The algorithm helps to reach the Bit Allocation almost near to Target Bits requirement. The Simulation Results are shown in Figure 5. For the channel response shown in Figure 2, the bad channel threshold was given as 0.05. Clearly higher bits are loaded in sub-channels of higher gain. The BER calculated using (5) is found to be of the order 10-4. The total Energy required to transmit target number of bits is found to be 1.22 Joules converging to Hughes-Hartogs Optimal result. This algorithm also takes 1 iteration for grouping, 1 for bit allocation and 5 iterations (approximately equal to Target Bits/No. of Sub-channels) to meet the target bits requirement. In all the algorithm takes 7 iterations for given Simulation Inputs.

Figure 4. Bit allocation of fuzzy based algorithm 1

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 Optimized-Fuzzy-Logic-Based Bit Loading Algorithms

Figure 5. Bit allocation of fuzzy based algorithm 2

RESULTS AND DISCUSSIONS The number of Iterations taken for allocation, grouping and to meet the target bits requirement is discussed in this section for various algorithms in Table 1. The variation on the basis of iterations and Energy utilized with target is also discussed. Compared to Fuzzy Based Algorithm 1, based on number of group threshold concept, Fuzzy Based Algorithm 2 based on bad channel threshold shows better results as energy requirement is very less when compared. Table 2 shows that at the expense of energy (not much significant change) we can make our algorithms faster by reducing the number of iterations. Hence we can preper these sub-optimal algorithms to minimize iteration complexity. The line graph in Figure 7 shows the variation of Iterations with the target Bits for the Hughes Hartogs algorithm and proposed algorithms. The results show that Hughes Hartogs algorithms takes a lot of Iterations to meet the target bit requirements. Table 1. Number of Iterations taken for loading bits by various algorithms Algorithm

Allocation

Grouping

Meeting Target Bits

Hughes-Hartogs Algorithm

N * Target Bits

-

-

Proposed Fuzzy Algorithm 1

1

1

(Target Bits)/(No. of Sub-channels)

Proposed Fuzzy Algorithm 2

1

1

(Target Bits)/(No. of Sub-channels)

Table 2. Energy and iteration comparison for given simulation input Algorithm

Energy (Joules)

Iteration

Hughes-Hartogs Algorithm

0.1789

25600

Chow Algorithm

0.8221

3264

Campello Algorithm

2.21

16064

Proposed Fuzzy Algorithm 1

2.4

7

Proposed Fuzzy Algorithm 2

1.22

7

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Figure 6. Fuzzy based bit loading algorithm 2

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Figure 7. Log (iteration) vs. target bits for the algorithms

CONCLUSION Compared to Hughes Hartogs optimal solution, clustering based algorithm using Fuzzy Logic takes a single iteration for bit allocation, one iteration for grouping and few iterations for reaching Target Bits requirement. As a result iteration complexity is reduced. The solution is almost convergent to the optimal solution with a little higher energy but substantially reduced number of iterations. The proposed algorithms are sub optimal but advantageous in terms of iterations. All the Algorithms reach BER of the order of 10-4 before Forward Error Correction.

REFERENCES Birla, N., Agarwal, N., Sankar Ganesh, S., & Babu, V. (2014). Clustering based Bit Loading Algorithms using Neural Networks. International Journal of Review in Electronics & Communication Engineering, 2(2), 2–5. Campello, J. (1998). Optimal Discrete Bit Loading for Multicarrier Modulation Systlems. IEEE Symp. Info. Theory. http://doi.org/ doi:10.1109/ISIT.1998.708791 Campello, J. (1999). Practical bit loading for DMT. IEEE International Conference on Communications. http://doi.org/ doi:10.1109/ICC.1999.765384 Chow, P. S., Cioffi, J. M., & Bingham, J. (1995). Practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels. IEEE Transactions on Communications, 43(2), 773–775. doi:10.1109/26.380108

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Gianaroli, F., Pancaldi, F., & Vitetta, G. M. (2015). A Novel Bit and Power Loading Algorithm for Narrowband Indoor Powerline Communications. doi:10.1109/ICCW.2015.7247401 Hong, Y., Member, S., Wu, T., Chen, L., & Member, S. (2016). On the Performance of Adaptive MIMOOFDM Indoor Visible Light Communications. IEEE Photonics Technology Letters, 28(8), 907–910. doi:10.1109/LPT.2016.2517192 Hughes-Hartogs, D. (1989). U.S. Patent No. 4,833,706. Washington, DC: U.S. Patent and Trademark Office. Jung, S., Jung, S., & Han, S. (2015). AMO-FBMC for Asynchronous Heterogeneous Signal Integrated Optical Transmission. IEEE Photonics Technology Letters, 27(2), 133–136. doi:10.1109/LPT.2014.2363197 Nader-Esfahani, S., & Afrasiabi, M. (2007). Simple bit loading algorithm for OFDM-based systems. Electronics Letters, 1(3), 312–316. doi:10.1049/iet-com Sastry, K. S., & Babu, D. M. P. (2010). Fuzzy logic based adaptive modulation using non data aided SNR estimation for OFDM system. International Journal of Engineering Science and Technology, 2(6), 2384–2392. Vo, T. N., Amis, K., Chonavel, T., Siohan, P., & Member, S. (2015). A Computationally Efficient Discrete Bit-Loading Algorithm for OFDM Systems Subject to Spectral-Compatibility Limits. IEEE Transactions on Communications, 63(6), 2261–2272. doi:10.1109/TCOMM.2015.2424890 Wang, D., Cao, Y., Zheng, L., & Du, Z. (2013). Iterative group-by-group bit-loading algorithms for OFDM systems. IEEE Transactions on Vehicular Technology, 62(8), 4131–4135. doi:10.1109/TVT.2013.2257908 Wen, & Tian, Q. (2013). A Fast adaptive transmit power and bit allocation in OFDM system. Advanced Materials Research, 765, 444–447.

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