Download Performance Analysis of Multiuser Downlink MIMO NOMA Wireless Communication System on Color Image Transmission and more Study Guides, Projects, Research Communications Engineering in PDF only on Docsity!
© 2017. Md. Humaun Kabir & Shaikh Enayet Ullah.. This is a research/review paper, distributed under the terms of the Creative Commons Attribution-Noncommercial 3.0 Unported License http://creativecommons.org/licenses/by-nc/3.0/), permitting all non- commercial use, distribution, and reproduction inany medium, provided the original work is properly cited.
Performance Analysis of Multiuser Downlink MIMO NOMA
Wireless Communication System on Color Image Transmission
By Md. Humaun Kabir & Shaikh Enayet Ullah
Pundra University of Science and Technology
Abstract- In this paper, a comprehensive study has been made to evaluate the performance of 2 × 2
multiantenna configured MIMO NOMA wireless communication system. The simulated system
incorporatesvarious types of signal processing techniques (Channel coding: LDPC & Convolutional,
Digital modulation: QPSK, DQPSK & 4-QAM, Signal detection: ML decoding based QR channel
decomposition aided SIC). On considering downlink transmission of encrypted color image of each
of two users in a hostile fading channel, it is noticeable from MATLAB based simulation study that the
system is very much robust and effective in retrieving transmitted color images underutilization of
LDPC channel coding and 4-QAM digital modulation techniques. The performance of the simulated
downlink MIMO NOMA wireless communication system has been evaluated in terms of bite error
rate(BER) under scenario of various receive signal to noise ratio(SNR) ranging from 0dB to 16dB.
Keywords: NOMA, MIMO, ML decoding, QR channel factorization aided SIC, LDPC.
GJCST-E Classification: C.2.
PerformanceAnalysisofMultiuserDownlinkMIMONOMAWirelessCommunicationSystemonColorImageTransmission
Strictly as per the compliance and regulations of:
Global Journal of Computer Science and Technology: E
Network, Web & Security
Type: Double Blind Peer Reviewed International Research Journal
Publisher: Global Journals Inc. (USA)
Online ISSN: 0975-4172 & Print ISSN: 0975-
Volume 17 Issue 3 Version 1.0 Year 2017
Performance Analysis of Multiuser Downlink
MIMO NOMA Wireless Communication System
on Color Image Transmission
Keywords: NOMA, MIMO, ML decoding, QR channel factorization aided SIC, LDPC.
I. Introduction
ith rapid technological advancement in both mobile and wireless communications, the number of users for affordable and powerful mobile computing devices (smartphones, iPhones, netbooks, and laptops) is increasing and leading an exponential increase in the amount of data traffic that the network operators need to accommodate within their networks. It is expected that by 2020 the global IP network will carry 6.4 EB of Internet traffic per day and 21 GB per capita. In perspective of coping with this explosion of broadband data traffic, the network operators will make use of various new solutions and technologies to be integrated for network capacity enhancement in the next generation/5G mobile networks. Some of the promising solutions include the deployment of heterogeneous small cell networks which enables dynamic cooperation between different radio access technologies, MIMO/Massive MIMO(using a large number of antennas, 100 or more)for simultaneous
serving a number of users in the same time frequency resource; Cloud radio access networks (C-RAN) offering a centralized, cooperative, clean and cloud computing architecture; Software-defined networks (SDN) and network function virtualization (NFV) that assist the mobile operators to reduce their capital expenditure (CAPEX) intensity by transferring their hardware-based network to software- and cloud based solutions. In view of increasing the spectral efficiency of the next generation/ 5G networks and reduction of inter cell interference levels, another promising solution can accepted to use non-orthogonal multiple access (NOMA) technique[1]. In consideration of supporting higher throughput transmission in next generation (5G) networks, there is a growing interest among the mobile operators to exploit vast amounts of available frequency spectrum in the mmwave band (30-300 GHz).The Non- orthogonal multiple access (NOMA), millimeter wave (mmWave), and massive multiple-input-multiple-output (MIMO) have been emerging as key technologies for the fifth generation (5G) mobile communications [2, 3].
II. Literature R eview
It is known from literature reviewing that many researchers of academic institutions and industries have been working since 2014 on suitability of NOMA as 5G compatible radio interface technology based on power- domain user multiplexing scheme. In this paper, few works are described briefly.
W
Author α: Lecturer, Department of Computer Science and Engineering, Pundra University of Science and Technology, Bogra-5800, Bangladesh. e-mail: humaun4938@gmail.com Author σ: Professor, Department of Applied Physics and Electronic Engineering, University of Rajshahi, Rajshahi-6205, Bangladesh. e-mail: enayet_apee@ru.ac.bd
(^
E
Global Journal of Computer Science and Technology
Volume XVII Issue III Version I
Year
2017
Abstract- In this paper, a comprehensive study has been made to evaluate the performance of 2 × 2 multiantenna configured MIMO NOMA wireless communication system. The simulated system incorporates various types of signal processing techniques (Channel coding: LDPC & Convolutional, Digital modulation: QPSK, DQPSK & 4-QAM, Signal detection: ML decoding based QR channel decomposition aided SIC). On considering downlink transmission of encrypted color image of each of two users in a hostile fading channel, it is noticeable from MATLAB based simulation study that the system is very much robust and effective in retrieving transmitted color images under utilization of LDPC channel coding and 4-QAM digital modulation techniques. The performance of the simulated downlink MIMO NOMA wireless communication system has been evaluated in terms of bit error rate(BER) under scenario of various receive signal to noise ratio(SNR) ranging from 0dB to 16dB.
In [4],Chenet. al. proved that NOMA combined with SU-MIMO techniques achieved system performance improvement. The impact of rank optimization on the performance of NOMA with SU- MIMO in downlink were studied and 23% for cell average throughput and 33% for cell-edge user throughput were achieved as compared to other orthogonal access system. In [5], Lan et. al. investigated the system-level throughput of NOMA with closed-loop single-user multiple-input multiple-output (SU-MIMO) in the cellular downlink and clarified the potential gains as compared to OMA. In [6] Liu et. al. studied the NOMA based downlink multi-user beamforming system, where the base station (BS) tried to transmit information to multiple user clusters and each beam served one user cluster compromising of two users simultaneously. User
Md. Humaun Kabir α^ & Shaikh Enayet Ullah σ
𝒀𝒀 1 = � 𝑌𝑌 𝑌𝑌^1112 � = � 𝐻𝐻 𝐻𝐻^11 (1,1)(2,1)^ 𝐻𝐻 𝐻𝐻^11 (1,2) (2,2)� �� 𝑋𝑋 𝑋𝑋1,11,2� + � 𝑋𝑋 𝑋𝑋2,12,2�� + � 𝑛𝑛 𝑛𝑛1,11,2� (6)
The signal received at first layer of user UE 1 is given by
𝑌𝑌 11 = 𝐻𝐻 1 (1,1)�𝑋𝑋1,1 + 𝑋𝑋2,1� + 𝐻𝐻 1 (1,2)�𝑋𝑋1,2 + 𝑋𝑋2,2� + 𝑛𝑛1,1 (7)
The signal received at second layer of userUE 1 is given by 𝑌𝑌 12 = 𝐻𝐻 1 (2,1)�𝑋𝑋1,1 + 𝑋𝑋2,1� + 𝐻𝐻 1 (2,2)�𝑋𝑋1,2 + 𝑋𝑋2,2� + 𝑛𝑛1,2 (8)
On performing QR matrix decomposition of 𝐇𝐇 1 as:
𝐇𝐇 1 = 𝐐𝐐 1 𝐑𝐑 1 (9)
𝒁𝒁 1 = 𝑸𝑸 1 𝐻𝐻^ 𝒀𝒀 1 = 𝑹𝑹 1 (𝑿𝑿 1 + 𝑿𝑿 2 ) + 𝒏𝒏 1
⇒� 𝑍𝑍 𝑍𝑍1,11,2� = �𝑅𝑅^1 (1,1) 0 𝑅𝑅 𝑅𝑅^11 (1,2) (2,2)� �� 𝑋𝑋 𝑋𝑋1,11,2� + � 𝑋𝑋 𝑋𝑋2,12,2�� + � 𝑛𝑛 𝑛𝑛1,11,2� (10)
From equation (10), the components of 𝒁𝒁 1 (𝑍𝑍1,1and 𝑍𝑍1,2 ) can be written as:
𝑍𝑍1,1 = 𝑅𝑅 1 (1,1)�𝑋𝑋1,1 + 𝑋𝑋2,1� + 𝑅𝑅 1 (1,2) (𝑋𝑋1,2 + 𝑋𝑋2,2 ) + 𝑛𝑛1,1 (11)
𝑍𝑍1,2 = 𝑅𝑅 1 (2,2)�𝑋𝑋1,2 + 𝑋𝑋2,2� + 𝑛𝑛1,2 (12)
Neglecting contribution from noise in equation (12) and the estimated transmitted symbols for both users can be written as
�𝑋𝑋1,2 + 𝑋𝑋2,2� = 𝑍𝑍1, 𝑅𝑅 1 (2,2) (13)
Substituting the value of �𝑋𝑋1,2 + 𝑋𝑋2,2�from equation (13) in equation (11) and neglecting the noise component, we can write
𝑍𝑍1,1 = 𝑅𝑅 1 (1,1)�𝑋𝑋1,1 + 𝑋𝑋2,1� + 𝑅𝑅 1 (1,2) 𝑍𝑍1, 𝑅𝑅 1 (2,2) (14)
�𝑋𝑋1,1 + 𝑋𝑋2,1� = 𝑍𝑍1, 𝑅𝑅 1 (1,1)^
− 𝑅𝑅^1
(1,2) 𝑅𝑅 1 (1,1)
𝑍𝑍1, 𝑅𝑅 1 (2,2)^
The right hand term of equation (15) is known and this equation can be written in modified form as
𝑍𝑍̂1,1 =
𝑃𝑃 2 𝑃𝑃 1 𝑺𝑺2,1=𝑺𝑺1,1^ + 2.0^ 𝐒𝐒2,1^ (17)
As the modulated symbols are normalized in such that each complex symbols has unitary power. The normalized QAM modulated signal vector is denoted by 𝐒𝐒. Then the transmitted symbol from first transmitting antenna considered as interference component for UE 1 can be estimated using ML decoding based QR channel decomposition aided SIC scheme as
𝑺𝑺�2,1 = arg min �𝑍𝑍̂̂1,1 − 2.0 𝑺𝑺��
2 (18)
Dividing equation (19)by (^) �𝑃𝑃 1 , we get
𝑍𝑍1, �𝑃𝑃 1 𝑅𝑅 1 (2,2)
𝑍𝑍1, �𝑃𝑃 1 𝑅𝑅 1 (2,2) =^ 𝑺𝑺1,2^ + 2.0^ 𝑺𝑺2,2^ (20)
The transmitted symbol from second transmitting antenna for considered as interference component for UE 1 can be estimated using ML decoding based QR channel decomposition aided SICscheme as
𝑺𝑺�2,2 = arg min �𝑍𝑍̂1,2 − 2.0 𝑺𝑺��
2 (21)
Substituting the value of 𝑺𝑺�2,2 in equation (20), the transmitted symbol from second transmitting antenna for user UE 1 as desired signal component can be estimated as:
𝑺𝑺�1,2=𝑍𝑍̂1,2-2.0 𝑺𝑺�2,2 (22)
Transmission
(^
E
Global Journal of Computer Science and Technology
Volume XVII Issue III Version I
Year
2017
components x1,1of UE 1 and x2,1of UE 2 are transmitted from first transmitting antenna and x (^) 1,2 of UE 1 and x2,2 of UE 2 are transmitted from second transmitting antenna. Each of two components of both 𝐒𝐒 1 and 𝐒𝐒 2 are needed in power scaling.The 20% of the total power P(P 1 = 0.2 P)remaining 80% of the total power P(P 2 = 0.8 P)are allocated to user UE 1 and to user UE 2 respectively. With consideration of 2×2 sized matrices,[𝑯𝑯 1 ]^ and [𝑯𝑯 2 ] (^) containing complex Rayleigh fading channel coefficients for users UE 1 and UE 2 ,the received signals at UE 1 (= 𝐘𝐘 1 ) and UE 2 (= 𝐘𝐘 2 ) are given by:
where 𝒏𝒏 1 and 𝐧𝐧 2 are the additive white Gaussian noises (AWGN) estimated based on the typically assumed receive SNR values at receivers of user UE 1 and user UE 2 respectively. In case of estimating transmitted signals for user UE 1 , equation(4) can be written in elaborate form as:
where,𝐐𝐐 1 is a 2 × 2 unitary matrix and 𝐑𝐑 1 is an 2 × 2 upper triangular matrix and multiplying both sides of equation(6) with complex conjugate transformed of 𝐐𝐐 1 , we get:.
Dividing equation (16) by �𝑃𝑃 1 , we get
where, 𝑺𝑺� 𝜖𝜖 𝑺𝑺 and ‖. ‖^2 is indicative of Frobenius norm of matrix. Equation(13) can be written in modified form as: 𝑍𝑍1, 𝑅𝑅 1 (2,2)^ =^ �𝑃𝑃^1 𝑺𝑺1,2^ +^ �𝑃𝑃^2 𝑺𝑺2,2(19)
where 𝑺𝑺� 𝜖𝜖 𝑺𝑺 and ‖. ‖^2 have already been specified.
Substituting the value of 𝑺𝑺�2,1 from equation (18) in equation (17),the transmitted symbol from first transmitting antenna for user UE 1 as desired signal component can be estimated as:
𝑺𝑺�1,1=𝑍𝑍̂̂1,1 -2.0 𝑺𝑺�2,1 (23)
In case of estimating transmitted signals for userUE 2 , equation(5) can be written in elaborate form as:
𝒀𝒀 2 = � 𝑌𝑌 𝑌𝑌^2122 � = �𝐻𝐻 𝐻𝐻^22 (1,1) (2,1)^ 𝐻𝐻 𝐻𝐻^22 (1,2)(2,2)� �� 𝑋𝑋 𝑋𝑋1,11,2� + � 𝑋𝑋 𝑋𝑋2,12,2�� + � 𝑛𝑛 𝑛𝑛2,12,2� (24)
The signal received at first layer of user UE 2 is given by
𝑌𝑌 21 = 𝐻𝐻 2 (1,1)�𝑋𝑋1,1 + 𝑋𝑋2,1� + 𝐻𝐻 2 (1,2)�𝑋𝑋1,2 + 𝑋𝑋2,2� + 𝑛𝑛2,1 (25) The signal received at second layer of user UE 2 is given by 𝑌𝑌 22 = 𝐻𝐻 2 (2,1)�𝑋𝑋1,1 + 𝑋𝑋2,1� + 𝐻𝐻 2 (2,2)�𝑋𝑋1,2 + 𝑋𝑋2,2� + 𝑛𝑛2,2 (26) On performing QR matrix decomposition of 𝐇𝐇 2 as:
𝐇𝐇 2 = 𝐐𝐐 2 𝐑𝐑 2 (27)
𝒁𝒁 2 = 𝑸𝑸 2 𝐻𝐻^ 𝒀𝒀 2 = 𝑹𝑹 2 (𝑿𝑿 1 + 𝑿𝑿 2 ) + 𝒏𝒏 2
⇒� 𝑍𝑍 𝑍𝑍2,12,2� = �𝑅𝑅^2 (1,1) 0 𝑅𝑅 𝑅𝑅^22 (1,2) (2,2)� �� 𝑋𝑋 𝑋𝑋1,11,2� + � 𝑋𝑋 𝑋𝑋2,12,2�� + � 𝑛𝑛 𝑛𝑛2,12,2� (28)
From equation (28), the components of 𝒁𝒁 2 (𝑍𝑍2,1and 𝑍𝑍2,2 ) can be written as: 𝑍𝑍2,1 = 𝑅𝑅 2 (1,1)�𝑋𝑋1,1 + 𝑋𝑋2,1� + 𝑅𝑅 2 (1,2) (𝑋𝑋1,2 + 𝑋𝑋2,2 ) + 𝑛𝑛2,1 (29)
𝑍𝑍2,2 = 𝑅𝑅 2 (2,2)�𝑋𝑋1,2 + 𝑋𝑋2,2� + 𝑛𝑛2,2 (30)
Neglecting contribution from noise in equation (30) and the estimated transmitted symbols for both users can be written as
�𝑋𝑋1,2 + 𝑋𝑋2,2� = 𝑍𝑍2, 𝑅𝑅 2 (2,2)^ (31) Substituting the value of �𝑋𝑋1,2 + 𝑋𝑋2,2�from equation (31) in equation (29) and neglecting the noise component, we can write
𝑍𝑍2,1 = 𝑅𝑅 2 (1,1)�𝑋𝑋1,1 + 𝑋𝑋2,1� + 𝑅𝑅 2 (1,2)^ 𝑍𝑍2, 𝑅𝑅 2 (2,2)^ (32)
�𝑋𝑋1,1 + 𝑋𝑋2,1� = 𝑍𝑍2, 𝑅𝑅 2 (1,1)^ −^
𝑅𝑅 2 (1,2) 𝑅𝑅 2 (1,1)
𝑍𝑍2, 𝑅𝑅 2 (2,2)^ (33) The right hand term of equation (33) is known and this equation can be written in modified form as
Dividing equation (34)by �𝑃𝑃 2 , we get
𝑃𝑃 1 𝑃𝑃 2 𝑆𝑆1,1^ +^ 𝑆𝑆2,1^ =0.5^ 𝑆𝑆1,1^ + S^ 2,1^ (35)
Then the transmitted symbol from first transmitting antenna considered as interference component for UE 2 can be estimated using ML decoding based QR channel decomposition aided SICscheme as
𝑺𝑺�1,1 = arg min �𝑍𝑍̂̂2,1 − 0.5 𝑺𝑺��
2 (36)
𝑍𝑍2, 𝑅𝑅 2 (2,2)^ =^ �𝑃𝑃^1 𝑆𝑆1,2^ +^ �𝑃𝑃^2 𝑆𝑆2,2^ (37)
Dividing equation (37)by (^) �𝑃𝑃 2 , we get
𝑍𝑍̂2,2 = 𝑍𝑍2, �𝑃𝑃 𝑅𝑅 (2,2)^ = 0.5^ 𝑆𝑆1,2^ +^ 𝑆𝑆2,2^ (38)
𝑆𝑆̂1,2 = arg min �𝑍𝑍̂2,2 − 0.5 𝑆𝑆̂� 2 (39)
d) 2D Median Filtering
e) Data Scrambling Cryptography is probably the most important aspect of communications security and is becoming
Transmission
(^
E
Global Journal of Computer Science and Technology
Volume XVII Issue III Version I
Year
2017 Year
2017
(^
E
Global Journal of Computer Science and Technology
Volume XVII Issue III Version I
where,𝐐𝐐 2 isa 2 × 2 unitary matrix and 𝐑𝐑 2 is an 2 × 2 upper triangular matrix and multiplying both sides of equation (24) with complex conjugate transformed of 𝐐𝐐 2 , we get:.
where,𝑺𝑺� 𝜖𝜖 𝑺𝑺 and equation(31) can be written in modified form as:
The transmitted symbol from second transmitting antenna considered as interference component for UE 2 can be estimated using ML decoding based QR channel decomposition aided SIC scheme as
where, 𝑺𝑺� 𝜖𝜖 𝑺𝑺 and substituting the value of �𝑆𝑆1,2 from equation (39) in equation (38), the transmitted symbol from second transmitting antenna for user UE 2 as desired signal component can be estimated as:
The transmitted symbol from first transmitting antenna for user UE 2 as desired signal component can be estimated from equation (35) as:
2D median filtering is widely used as an effective technique for removing various types of noises (salt and pepper and Gaussian) from noise contaminated image. In such filtering operation, the pixel values in the neighborhood window are generally ranked according to intensity and the middle value (the median) becomes the output value for the pixel under evaluation. In this paper, 2D Median Filtering scheme with a 3× neighborhood windowing mask is preferably used to make sorting of all the pixel values within the window and finding the median value and replacing the original pixel value with the median value [16].
Block diagram of MIMO NOMA Wireless Communication System
Transmission
Year
2017
(^
E
Global Journal of Computer Science and Technology
Volume XVII Issue III Version I
Fig.1:
BER performance of Convolutional and LDPC channel encoded MIMO NOMA wireless communication system with QPSK digital modulation scheme for image transmission
It is seen from figure 3 that the estimated BER values for both users are almost constant in convolutional channel coding. In case of LDPC channel coding, BER values decrease in higher SNR value region. Under assumption of SNR value of 10 dB in case of user#1, the estimated BER values are 0.5006 and 0.4151 in convolutional and LDPC channel coding schemes with DQPSK digital modulation which implies a system performance improvement of 0.81 dB. In case of user #2 for identical SNR value, the estimated BER values are 0.5023 and 0.4002 which is indicative of system performance improvement of 0.99 dB. For a 40%BER, a SNR improvement of around 1.8 dB is achieved in case of user #2 in comparison to user #1.
Signal to Noise ratio(dB)
BER
MIMO NOMA for user 1 with LDPC and QPSK
MIMO NOMA for user 2 with LDPC and QPSK
MIMO NOMA for user 1 with Convolutional coding and QPSK
MIMO NOMA for user 2 with Convolutional coding and QPSK
Transmission
(^
E
Global Journal of Computer Science and Technology
Volume XVII Issue III Version I
Year
2017
Fig. 2:
BER performance of Convolutional and LDPC channel encoded MIMO NOMAWireless communication system with 4-QAM digital modulation scheme.
Signal to Noise ratio(dB)
BER
MIMO NOMA for user 1 with LDPC and 4-QAM
MIMO NOMA for user 2 with LDPC and 4-QAM
MIMO NOMA for user 1 with Convolutional coding and 4-QAM
MIMO NOMA for user 2 with Convolutional coding and 4-QAM
Transmission
(^
E
Global Journal of Computer Science and Technology
Volume XVII Issue III Version I
Year
2017
Fig. 4:
Fig. 5: Transmitted and retrieved image for user #1 of MIMO NOMA wireless communication system under implementation of LDPC channel coding with 4-QAM digital modulation at SNR value of 10 dB
VI. CONCLUSION
R eferences R éférences R eferencias
- HrishikeshVenkatarman and Ramona Trestian, “5G Radio Access Networks: Centralized RAN, Cloud- RAN, and Virtualization of Small Cells”, CRC Press, an imprint of Taylor and Francis Group, Florida, USA, 2017.
- ShahidMumtaz, Jonathan Rodriguez and Linglong Dai, “mmWave Massive MIMO - A Paradigm for 5G”, Academic Press, an imprint of Elsevier, United Kingdom,2017.
- Di Zhang, Zhenyu Zhou,Chen Xu, Yan Zhang, Jonathan Rodriguez, and Takuro Sato,” Capacity
Analysis of Non-Orthogonal Multiple Access with mmWave Massive MIMO Systems”, IEEE Journal on Selected Areas in Communications, Volume 35,no.7,pp. 1606 – 1618,2017.
- Xiaohang Chen,AnassBenjebbour,Yang Lan,Anxin Li, and Huiling Jiang, “Impact of rank optimization on downlink non-orthogonal multiple access (NOMA) with SU-MIMO”,IEEE International Conference publications on Communication Systems, pp. 233 – 237, 2014.
- Yang Lan, AnassBenjebboiu, Xiaohang Chen, Anxin Li and Huiling Jiang, “Considerations on downlink non-orthogonal multiple access (NOMA) combined with closed-loop SU-MIMO”, 8th International Conference publications on Signal Processing and Communication Systems (ICSPCS) , pp. 1 – 5,
- Shimei Liu, Chao Zhang and GangmingLyu, “User selection and power schedule for downlink non- orthogonal multiple access (NOMA) system”, 2015 IEEE International Conference publications on Communication Workshop (ICCW), pp. 2561 – 2565, 2015.
- Muhammad BasitShahab, MdFazlul Kaderand Soo Young Shin, “On the power allocation of non- orthogonal multiple access for 5G wireless networks”, IEEE International Conference
Transmission
Year
2017
(^
E
Global Journal of Computer Science and Technology
Volume XVII Issue III Version I
Fig. 6: Transmitted and retrieved image for user #2 of MIMO NOMA wireless communication system under implementation of LDPC channel coding with4-QAM digital modulation at SNR value of 10 dB
In this present paper, we have made a comprehensive study on performance analysis of 5G compatible power domain user multiplexing scheme based downlink multiuser MIMO NOMA wireless communication system. Various low order digital modulation and channel coding schemes have been utilized to evaluate the system performance. On the basis of simulation results, it can beconcluded that the downlink multiuser MIMO NOMA wireless communication system is undoubtedly a robust system in perspective of signal transmission in hostile fading channel under the utilization of 4-QAM digital modulation and LDPC channel coding scheme.
This page is intentionally left blank
Transmission
Year
2017
(^
E
Global Journal of Computer Science and Technology
Volume XVII Issue III Version I
