Mid Sweden University The Department of Information Technology and Media (ITM) Author: Muhammad Ashfaq Malik E-mail address: mama0926, mius0902,
[email protected] Study programme: Simulation of Communication System, 7.5 credit points Examiner: Dr. Magnus Eriksson,
[email protected] Tutors: Dr. Magnus Eriksson,
[email protected] Scope: 0 words inclusive of appendices Date: 2011-02-07 M.Sc. project report within Computer Engineering D, course, 7.5 points MISO & MIMO SIMULINK Model WiMAX Muhammad Ashfaq Malik Muhammad Islam Mudassir Iqbal WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik Acknowledgements / Foreword 2011-02-07 Abstract The 4G track at among the technologies for mobility, broadband wireless access, and QoS (Quality of Service) is becoming the preferred technology for reliable, flexible, standardized, low cost, very efficient and convenience. The WiMAX (Worldwide interoperability for Microware Access) is an IP based (support to mobility), BWA (Broadband Wireless Access) technology which provide the performance, flexibility, reliability, standardization and Internet access by the cellular technology with long coverage and QoS. The WiMAX is a standard of IEEE 802.16, which is a wireless digital communication system. It is intended for WMAN (Wireless Metropolitan Area Network), which can provide BWA up to 30 miles for fixed station and 3 to 10 for mobile station. WiMAX in LoS (Line of Sight), it have to the air directly from transceiver, operating frequency at weather / atmospheric parameters that can reach longer distance with better signal strength and higher throughput and Non-LoS (Non-Line of Sight) is proportionally converse. The OFDM (Orthogonal Frequency Division Multiplexing) is pillar of WiMAX that multicarrier modulation, ISI (Inter-symbol Interference). WiMAX vs LTE will play the important role of LTE in the future of wireless cellular network technology that will be providing and ideal backhaul technology for 4G standards. In the eye of WiMAX vs LTE, which will be promising to deliver the internet your cell phone at the speed of your at home broadband internet. We have calculate the technical point that WiMAX implementation which use the MIMO and MISO transceiver technology improve the reception and allows the data rate as well as transmission power. The WiMAX is almost here the competing technologies, such as HSPA (High-Speed Downlink Packet Access), LTE, IEEE 802.20, IEEE 802.22 are also trying to catch up fast and the next generation WiMAX is already being designed. ii WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik Acknowledgements / Foreword 2011-02-07 The most precious goal of the project, we have compared the performance of WiMAX-MISO & MIMO by different SIMULINK models at the various parameters. In both type of transceiver technique, which we have implemented the OFDM with the various value of QPSK (Quadrate Phase Shift Keying), BPSK (Binary Phase Shift Keying) and APSK (Amplitude Phase Shift Keying). After that we have modification of the standard WiMAX-MISO & MIMO SIMULINK model, blocks which as AWGN (Additive white Gaussian noise) fading (Rician & Rayliegh) channels, Modulation and Demodulation. For the purpose of better perfection of the WiMAX-MISO & MIMO SIMULINK model, which we have got the result of the physical media transceiver. The antennas RF (Radio Frequency) has been used the STBC (Space Time Block Code) technique to transceiver the data. Our analytical report will show to us, which types of WiMAX have effective and reliable result at the low BER at the SNR series. Keywords: WiMAX (Worldwide interoperability for Microware Access), BWA (Broadband Wireless Access), WMAN (Wireless Metropolitan Area Network), OFDM (Orthogonal Frequency Division Multiplexing), ISI (Inter-symbol Interference), WiMAX-MISO & MIMO Simulink model and STBC (Space Time Block Code) technique. iii WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik Acknowledgements / Foreword 2011-02-07 Acknowledgements / Foreword All praises to ALLAH, the most compassionate most merciful. We wish to express my deepest gratitude Prof. Dr. Magnus Erikson for his interest and encouragement for this work. We would like to thank my supervisor Prof. Dr. Magnus Erikson for his supervisor, support, and invaluable help for this project and report. Muhammad Ashfaq Malik Muhammad Islam Mudaissir Iqbal iv WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik Table of Contents 2011-02-07 Table of Contents Abstract....................................................................ii Abstract....................................................................ii Acknowledgements / Foreword..................................iv Acknowledgements / Foreword..................................iv Table of Contents.......................................................v Terminology / Acronyms...........................................vii Terminology / Acronyms...........................................vii Mathematical notation...........................................................viii Introduction..............................................................9 Introduction..............................................................9 1.1 Background and problem motivation................................10 1.2 Overall aim / High-level problem statement......................11 1.3 Scope 11 1.4 Outline...............................................................................11 1.5 Contributions.....................................................................12 Theory / Related work..............................................13 Theory / Related work..............................................13 1.6 Overview of WiMAX............................................................13 Example of level 3 heading.....................................................14 1.7 Standard of WiMAX ..........................................................14 1.8 Orthogonal Frequency Division Multiplexing.....................15 Principles of OFDM...................................................................15 1.9 Orthogonal Frequency Division Multiple Access................16 Advantages of OFDMA.............................................................16 OFDMA Protocols......................................................................17 The difference and the benefit of OFDM & OFDMA..................18 1.10 Line Of Sight....................................................................18 1.11 Non-Line of Sight.............................................................18 1.12 MIMO (Multiple-Input and Multiple-Output).....................19 Receive diversity with two antennas......................................21 Receive diversity with N receive antenna..............................22 Methodology / Model................................................24 Methodology / Model................................................24 Design / Implementation..........................................31 Design / Implementation..........................................31 v WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik Table of Contents 2011-02-07 4.1.1IEEE 802.16-2004 OFDM PHY link, including Space-Time Block Coding (WiMAX-MISO)..........................31 4.1.2IEEE 802.16e-2005 OFDM PHY link, (WiMAX-MIMO) with two fading channel........................................32 4.1.3IEEE 802.16e-2005 OFDM PHY link, (WiMAX-MIMO) with single fading channel.....................................33 4.2.1Bernoulli Binary generator...............................................34 4.2.2Forward Error Correction (FEC) and Modulator Bank......35 4.2.3IFFT packaging.................................................................36 4.2.4Space Time Diversity Encoder.........................................36 4.2.5OFDM Transmitter............................................................37 4.2.6MISO Fading Channel with AWGN....................................37 4.2.7Rician Fading...................................................................38 4.2.8AWGN Channel.................................................................38 4.2.9AWGN block.....................................................................39 4.2.10OFDM Receiver..............................................................40 4.2.11Space Time Diversity Combiner....................................40 4.2.12 Orthogonal Space Time Block Combiner (OSTC)..........40 4.2.13Extract Data Carrier.......................................................41 4.2.14Demodulator and FCE Bank...........................................41 4.2.15ALAMOUTI Transmitter and Receiver.............................42 4.2.16Bit Error Rate Calculation..............................................44 Results....................................................................45 Results....................................................................45 Conclusions / Discussion...........................................50 Conclusions / Discussion...........................................50 References.............................................................52 References.............................................................52 Appendix A: Documentation of own developed program code..................................................................53 Appendix A: Documentation of own developed program code..................................................................53 Example of Appendix subheading.........................................53 Appendix B: Mathematical deductions.......................54 Appendix B: Mathematical deductions.......................54 Appendix C: User manual.........................................55 Appendix C: User manual.........................................55 Appendix D: Result of questionnaire survey..............56 Appendix D: Result of questionnaire survey..............56 vi WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik Terminology / Acronyms 2011-02-07 Terminology / Acronyms STBC 4G 3GPP TDD LOS TDM TDMA WAN WAP WCDMA Wi-Fi WiMAX WLAN WMAN NLOS OFDM OFDMA QoS IEEE MAC QAM BWA MISO MIMO GSM WMAN FDD AM FDM DSL SISO SIMO BER AWGN BPSK SNR QPSK QAM OSTBO FEC RS Space-Time Block Coding fourth Generation Third-Generation Partnership Project Time Division Duplexing Line Of Sight Time Division Multiplexing Time Division Multiple Access Wide Area Network Wireless Access Protocol Wideband Code Division Multiple Access wireless fidelity Worldwide interoperability for Microwave Access Wireless Local Area Network Wireless Metropolitan Area Network Non–Line-Of-Sight Orthogonal Frequency Division Multiplexing Orthogonal Frequency Division Multiple Access Quality of Service Institute of Electrical and Electronics Engineers Medium Access Control layer Quadrature Amplitude Modulation Broadband Wireless Access Multiple-input and Single-output Multiple-Input and Multiple-Output Global System for Mobile Communications Wireless Metropolitan Area Network Frequency-Division Duplexing Agile Modeling Frequency Division Multiplexing Digital Subscriber Line Single Input, Single Output Single Input, Multiple Output Bit Error Rate Additive White Gaussian Noise Binary Phase Shift Keying Signal-to-Noise Ratio Quadrature Phase Shift Keying Quadrature Amplitude Modulation Orthogonal Space Time Block Coding Forward Error Correction Reed-Solomon vii WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik CC IFFT FFT HDL OSTBC LTE Convolution Code Terminology / Acronyms 2011-02-07 Fast Fourier Transform High Density Lipids Orthogonal Space Time Block Combiner Long Term Evolution Mathematical notation Symbol G(x) kISI Description CRC generator polynomial Degree of Inter-symbol-interference viii WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 Introduction During the 1998, the IEEE 802.16 group was developed an air interface standard for wireless broadband. The group was report that the development of a LOS-based point-tomultipoint wireless broadband system operate on the 10 GHz to 66GHz mm wave band. The wireless network standardsbased interoperable solution is emerging for wireless broadband which the WiMAX (Worldwide Interoperability for Microwave Access) and compliance with a standard. The WMAN (Wireless Metropolitan Area Network) is the development of WiMAX standards which provide the guaranty of quality of service, security, and mobility. The OFDM (Orthogonal Frequency Division Multiplexing)-based physical layer is used for Non-LoS application with data rate 2 GHz to 11 GHz. The WiMAX solution as IEEE 802.16-2004 OFDM physical layer SIMULINK model, which is replace all prior WiMAX basics of the fixed application. When the mobile WiMAX, define to it as the IEEE 802.16e-2005 physical SIMULINK model which amendment to the IEEE 802.16-2004 standards of the characteristics add the nomadic and mobility support. We have studied the multiple collections of IEEE 802.16 standards; there are multiple physical-layer choices and multiple MAC architecture choices. In the order, we have Wireless MAN (Metropolitan Aria Network)-OFDM which based on OFDM-based physical layer and Wireless-OFDMA which based on OFDMA physical layer. Further more over, the WiMAX expand MAC architecture, duplexing and frequency band. 9 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 Table 1. The IEEE 802.16 standards 1.1 Background and problem motivation The motivation of the project is that to design the smart cellular device that embed the characteristics of power full wireless network qualities. If, we survey the public market there are need to be reduced, and a smaller set of design choices for implementation need to be defined. This requirement it may be by the WiMAX defining a limited number of system profiles and certification profiles which has IEEE 802.16-2004 or IEEE 802.16e-2005 standard to IEEE 802.16-2009, OFDM PHY based. Currently, the WiMAX Forum has two different system profiles: one based on IEEE 802.162004, OFDM PHY, called the fixed system profile; the other one based on IEEE 802.16e-2005 scalable OFDMA PHY, called the mobility system profile. More over the, the IEEE 802.16-2009 standard is Vs the prior WiMAX standards. It has to cover the air interference for fixed and mobile broadband wireless access system. Motivation of the report which has the WiMAX focus on the mobility, broadband wireless access, and QoS (Quality of Service) is becoming the preferred technology for reliability, flexibility, standardized, low cost, and very efficient and convenience. The WiMAX is an IP based (support to mobility), BWA (Broadband Wireless Access) technology which provide the performance, flexibility, reliability, standardization and Internet access by the cellular technology with long coverage and QoS. The WiMAX is a standard of IEEE 802.16, which is a wireless digital communication system. It is intended for 10 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 WMAN (Wireless Metropolitan Area Network), which can provide BWA up to 30 miles for fixed station and 3 to 10 for mobile station. WiMAX in LoS (Line of Sight), it have to the air directly from transreceiver, operating frequency at weather / atmospheric parameters that can reach longer distance with better signal strength and higher throughput and Non-LoS (Non-Line of Sight) is proportionally converse. The OFDM (Orthogonal Frequency Division Multiplexing) is pillar of WiMAX that multicarrier modulation, ISI (Inter-symbol Interference). 1.2 Overall aim / High-level problem statement The obligation of the project “WiMax (Evolution and Simulator Development)” is Development in MATLAB/ SIMULINK with using the SIMULINK IEEE 802.16-2004 OFDM PHY SIMULINK standard model. After long analytical study, we have to be Implemented of “WiMax (Evolution and Simulator Development) MISO & MIMO” based on OFDM PHY layer, SIMULINK model using the some MATLAB/SIMULIN methods and block functions, which WiMax mode land to find the result that is the more suited for our aim which one we want to develop. 1.3 Scope This is the research oriented implementation of the WiMax (MISO & MIMO)-OFDM PHY SIMULINK Model. The IEEE 802.16 group subsequently produced 802.16a, 802.16d and 802.16e, enhancement to the standard, to include Non-LOS and LOS applications in the 2GHz–11GHz band, using an orthogonal frequency division multiplexing (OFDM)-based physical layer. Additions to the MAC layer, such as support for orthogonal frequency division multiple access (OFDMA). All of the research in the field of Wireless network is a backbone of the 4G. It will be more effective, reliable, and perfect for the growth of human beings. 1.4 Outline Chapter 2 will explore to the properties and Implementation of “WiMax (Evolution and Simulator Development)-MISO & MIMO”. Chapter 3 will explain the methodology of the project Chapter 4 will describe the methods of simulink model the project implementation Chapter 5 has the result of the project Finally, we have the list of reference, where we get the ideas. 11 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 1.5 Contributions In this project, we equally participate to complete the whole project as well as its documentation and also do the group study that support to resolve the many problems those we have faced. The strategy of our study, we read the research papers and get idea from web media and also study the books than we get “WiMax (MISO & MIMO)-OFDM PHY Simulink Model”. 12 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 Theory / Related work In the report's theory study, sometimes called Related work, there may be additional facts required for the reader's understanding of the report. At this point a summary of background material in the area should be provided, i.e. standards, scientific articles, books, magazines, documents on the web, technical reports and user manuals. Explain pedagogically with clear examples and many illustrations. It should be demonstrated that you have an awareness of the context and the background of your work in addition to that carried out by you within the project. Explain the aim of the technology that you describe, and not only how the technology works. For D-level you should display an awareness of the key research within the area, in order to ensure that your work has certain news worthiness. However it is vital that you do not deviate too much from your research problem. Your assignment is not to write a textbook. It is important to find an appropriate balance between related work and your own results. The theory study should only constitute a minor portion of a thesis. Instead of “Theory” or “Related work”, the heading may very well be a specific topic, for example “The GSM standard” or ”A survey on the research field of X". If the theoretical study section is rather brief then it is possible to include it within the Introduction chapter. 1.6 Overview of WiMAX The overview of WiMAX is a standard-based wireless technology that makes available high throughput broadband connections over long distance. The WiMAX can be used for a number of several distributed or central applications, as well as including the mile to mile broadband connections, hotspots and high-speed connectivity for business customers. It has to provide WMAN (wireless metropolitan area network) connectivity at the data rate up to 70 Mbps and on the average can cover between 5-to-10 km. 13 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik Example of level 3 heading Avoid too many heading levels. References 2011-02-07 1.7 Standard of WiMAX WiMAX technology is based on the IEEE 802.16 standard, its 2nd name is WMAN (Wireless Metropolitan Area Network). The basic data on IEEE 802.16 Standard is shown below S.No. 1 2 3 4 5 Properties Status Frequency band Application MAC architecture Transmission Scheme Gross data rate Multiplexing Duplexing Channel bandwidths Air-Interface designation 802.16 Completed dec, 2001 10Gz-66GHz 2GHz-11GHz Fixed LOS Point to Multipoint mesh Singel carrier only 802.16-2004 Completed june, 2004 2GHz-11GHz for fixed Fixed Non-LOS Point to Multipoint mesh Singel carrier256 OFDMor 2,048OFDM 1Mbps-75Mbps Burst TDM/TDMA/ OFDM TDD and FDD WirelessMAN-SCa WirelessMANOFDM WirelessMANOFDMA 256 – OFDM as Fixed WiMAX 802.16e-2005 Completed dec, 2005 2GHz-6GHz for mobile app. Fixed and Mobile Non-LoS Point to Multipoint mesh Single carrier, 256 OFDM or scalable OFDM with128, 512, 1,024 or 2,048 sub carrier 1Mbps-75Mbps Burst TDM/TDMA/ OFDMA TDD and FDD WirelessMAN-SCa WirelessMAN-OFDM WirelessMAN-OFDMA Scable OFDMA as Mobile WiMAX 6 7 8 9 32Mbps134.4Mbps Burst TDM/TDMA TDD and FDD WirelessMAN-SC 10 WiMAX implementatio n None Table 2.1: WiMAX Standard 14 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 1.8 Orthogonal Frequency Division Multiplexing OFDM (Orthogonal frequency division multiplexing) is a FDM (frequency division multiplexing) modulations technique for transmitting the large amounts of digital data over a radio wave, which is divided into several parallel lower bit rates into high bit rate data stream flew, and operation in different modulation stream and sub carriers. Therefore, high data rate system of small symbol duration is inversely proportional to data rate, which is split into many parallel streams which increases the flow of data symbols for each data. More over OFDM works by splitting the system into multiple smaller subsignals on a different frequency that are transmitted to the receiver while receiving the signal continuously. OFDM reduces the large amount of crosstalk in signal broadcast 802.11a, 802.16 and WiMAX technologies which used in OFDM. Fig.2.1 Orthogonal Frequency Division Multiplexing Principles of OFDM OFDM is also a block transmission method. In this technique the complex-valued data symbols adjust a large number of strongly grouped carrier waveforms. The major benefit of this concept in a radio environment is that each of the data streams experiences an almost flat fading channel. • Signal characteristics • OFDM with a cyclic prefix • Channel noise and Doppler spread • Design of OFDM signals • Coding 15 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 1.9 Orthogonal Frequency Division Multiple Access OFDM is a modulation technique but a signal access approach and created many independent users can be used by different data streams. The earlier OFDM systems such as DSL, 802.11 / G and 802.16/WiMAX earlier versions, use the single-user OFDM. In this scheme all the sub carriers are used by a single user at a time. For example, in 802.11a/g, collocate many users which are dividing the 20MHz bandwidth by transmitting at different times after contending for the channel. WiMAX (802.16e-2005) obtain a different approach, known as OFDMA (orthogonal frequency division multiple access), in which users distribute sub carriers and time slots. OFDMA technique is more costly as compare to OFDM, such as overhead in both directions: First transmitter which needs the channel information for its users, and the second one is receiver which needs to know sub carriers it has been assigned. Figure 2.2: orthogonal frequency division multiple accesses. Advantages of OFDMA After the large study, we have observed there are following advantage of OFDMA. • OFDMA basically the mixture of FDMA and TDMA. • OFDMA is a flexible multiple-access technique. • Using the same power the OFDMA approve the same data rate to be sent. • In OFDMA Users are dynamically collected sub carriers (FDMA) in different time slots (TDMA). • It is possible to minimize interface from neighbouring cell by using different carrier in a cellular system. • Major advantage of OFDMA is reduce the transmit power and to solve the problem of peak-to-average-power ratio. 16 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 Fig. 2.3: In OFDMA, the base station allocates to each user Fig. 2.4: OFDM with 256 and OFDMA with only 64 of the 256 sub carriers OFDMA Protocols The main basic protocols of OFDMA are described in the following Mainer as • Sub-channelization • Mapping messages • Ranging 17 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 The difference and the benefit of OFDM & OFDMA The main benefits and differences have been described as following • One of the main differences is that IEEE 802.16d uses OFDM. • And IEEE 802.16e (mobile) uses OFDMA. • OFDM is better suited to fixed application and less complex than OFDMA. • OFDMA is more flexible due to managing different user device. • The operator is easier to managing the bandwidth and transmits power. Fig. 2.5: OFDM AND OFDMA 1.10 Line Of Sight Line of sight (LOS) is a fixed dish antenna point’s which is straight at the WiMax tower from a root top. Its frequency rang normally 66 GHz and radius is 30-mile. 1.11 Non-Line of Sight 18 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 Non-line of sight (Non-LOS) is a small antenna on computer which is connects to the tower and it is used to explain the radio transmission which across partially obstructed a path between the location of the signal transreceiver. Many kinds of radio transmission which is depend to unstable degrees, on line of sight between the transreceiver. Normally the common conditions which are include buildings, tress, hill, mountain and other natural object. NLOS is normally less refereed to as loose line of sight. Its frequency range is normally 2 GHz to 11 GHz and radius is 4 to 6 mile 1.12 MIMO (Multiple-Input and Multiple-Output) We can improve and make strong communication from end to end wireless communication by using the multiple power antennas mechanism. We have make logical design, which are 1 to 1, 1 to many, many to 1 and many to many. In this, we have discussed about the use of antennas MIMO. In addition of radio frequency, multiple-input and multiple-output, is used to improve the communication performance between multiple antennas at both the transceiver. MIMO can be divided into three main categories which is point out in given below. • • • Preceding Spatial multiplexing Diversity coding Further more, we have explain of MIMO channel (many to many) by using the mathematical terms as, in a 2×2 MIMO channel, probable usage of the available 2 transmit antennas can be as follows Consider that we have a transmission sequence, for example In normal transmission, we will be sending in the first time slot, in the second time slot, and so on. However, as we now have 2 transmit antennas, we may group the symbols into groups of two. In the first time slot, send and from the first and second antenna. In second time slot, send and from the first and second antenna, send and in the third time slot and so on. Notice that as we are grouping two symbols and sending them in one time slot, we need only time slots to complete the transmission – data rate will be doubled. 19 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 This forms the simple explanation of a probable MIMO transmission scheme with 2 transmit antennas and 2 receive antennas. AWGN & Receiver Diversity WiMAX with SISO, MISO, SIMO and MIMO is a series of increase the Antennas with the method Xi=x1+x2+………….+xn. Where Xi is the antennas i=1,2,3,……..n. this design strategy is to make a strong multiple antenna’s at the transceiver improves the bit error rate (BER) performance. In this technique, let us describe to understand the BER improvement with (mathematical way to) receive diversity. We are just getting started, let us limit ourselves to additive white Gaussian noise (AWGN) channel (i.e assume that the channel gains are unity). Single receive antenna case Let us start with the mathematical prove that there is one transmit antenna, sending signals with energy and one receive antenna. Since, we are taking only BPSK modulation, and the signals which are sent out are either or . 20 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 Let assume that there will be a single receive antenna having a thermal noise (either Rician or Rayliegh fading) AWGN with MEAN and VARIANCE The probability for the density function of noise is, The received signal equation is, , where is the received symbol, Is the transmitted symbol (taking values ’s and and is the Additive White Gaussian Noise (AWGN). In the scenario, BER for BPSK modulation in AWGN, that probability of bit error is, ’s) Receive diversity with two antennas Now, we consider with the two transceiver antennas each one have thermal noise (AWGN) with MEAN and VARIANCE and the noise on each antenna is independent from each other, and transmitter is sending symbols with energy The received signal is, , where , are the received symbols from receive antenna 1, 2 respectively, is the transmitted symbol (taking values ’s and ’s) and , is the Additive White Gaussian Noise (AWGN) on receive antenna 1, 2 respectively For simplicity, let us assume that the signal At the receiver, we now have and , and perform implies the was transmitted. To decode, the simplistic is to take the mean of hard decision decoding, transmitted bit is 1 and and if implies transmitted bit is 0. 21 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 Now, let us find out if there is any receive diversity gain by performing this averaging. Splitting into signal term and noise term In the discussion perspective, we have sum of Gaussian random variables, if is a Gaussian random variable with mean , variance and is another independent Gaussian random , variance , then is another variable with mean Gaussian random variable with mean , variance Furher, from the discussion on functions of Gaussian random variables, if is a Gaussian random variable with mean , variance , then is another Gaussian random , variance is another variable with mean Using the above two equations, the noise term and v riance Gaussian random variable with mean When compared with the single antenna case, we can see the variance of the noise term is scaled by a factor of 2. This implies that the effective bit energy to noise ratio in a two receive antenna case is twice the bit energy to noise ratio for single antenna So, the bit error probability for two receive antenna is, . Expressing in decibels, with two receive antennas, we need only lower bit energy . Receive diversity with N receive antenna With a general N transceiver antenna, the received symbol is, , where , ,… are the received symbols from 22 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 receive antenna 1, 2 respectively, is the transmitted symbol (taking values ’s and ’s) and , ,… is the Additive White Gaussian Noise (AWGN) on receive antenna 1, 2,… N respectively. For demodulation, we compute symbols, and if transmitted bit is 0. which is the mean of all the N received implies implies the transmitted bit is 1 and The variance of the noise term is . Effective bit energy to noise ratio in an N receive antenna case is N times the bit energy to noise ratio for single antenna. . So the bit error probability for N receive antenna is, 23 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 Methodology / Model WiMAX is the technology brand name for the implementation of the standard IEEE 802.16, which specifies the air interface at the PHY (Physical layer) and at the MAC (Medium Access Control layer). As we specifying the support of various channels, bandwidths, adaptive modulation and MATLAB coding is a pillar of our project goal. It is specifies the support for MISO & MIMO antennas to provide good Non-line-of-sight (NLOS) characteristics. The WiMAX MISO model use the standard parameter, on the other side for WiMAX MIMO we have write a code, which can take the dynamic parameter of the MIMO model that dynamic parameter automatically select the some our required parameter values, which are written in the following code as Channel Bandwidth, delay spread spectrum, Channel SNR, Modulation Scheme. //code.m file %simulate the model for different SNR values %close the model if it is open clear clc BW=input('Required channel bandwidth in MHz(max 20 MHz)='); disp('choose cyclic prefix to overcome delays spreads') disp(',1/4 for longest delay spread ,1/8 for long delay spreads ,') disp('1/16 for short delays spreads ,1/32 for very small delay spread channels') G=input('= '); channels=[1.75 1.5 1.25 2.75 2.0]; oversampling=[8/7 86/75 144/125 316/275 57/50 8/7]; for i=1:5 y(i)=rem(BW,channels(i)); if y(i)==0 n=oversampling(i); end end y=(y(1))*(y(2))*(y(3))*(y(4))*(y(5)); if y~=0 n=8/7; end if ((G~=1/4)&(G~=1/8)&(G~=1/16)&(G~=1/32)) error('you have choosed a guard period thats not valid in the ieee 802.16') end Nused=200; Nfft=256; fs=(floor((n*BW*1e6)/8000))*8000; %sampling freqency freqspacing= fs/Nfft; %freqency spacing Tb= 1/freqspacing; %usfel symbol time Tg= G*Tb ;%Guard time Ts=Tb+Tg ;%symbol time samplingttime= Tb/Nfft; %adaptive encoding and decoding depending on the channel SNR 24 WiMAX - MISO & MIMO SIMULINK Model Muhammad Ashfaq Malik References 2011-02-07 genpoly=gf(1,8); for idx=0:15 genpoly=conv(genpoly,[1 gf(2,8)^idx]); end primepoly=[1 0 0 0 1 1 1 0 1]; convvec=poly2trellis(7,[171,133]); cSNR=input('Enter the channel SNR in dB(it should be above 6.4 dB)='); if cSNR