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Effect of Combined Adaptive Modulation Technique on The Performance Of Wireless Communication System ABSTRACT Modern reliable high speed wireless data communication requires special adaptive technology to combat various negative effects that occurs in a communication channel such as multipath phenomena, fading, path loss, Doppler shift etc. Adaptive modulation and transmitter antenna diversity are the key techniques to overcome the channel driven problems. In our study we had investigated the three combined adaptive modulation schemes – adaptive modulation and selective transmitter diversity, adaptive modulation and transmit adaptive array and adaptive space time modulation. We had compared the effect of fading gain, instantaneous Signal to Noise Ratio and constellation size on system performance for the three different schemes. With the increase of fading gain the Bit Error Rate performance decreases. But with the increase of Signal to Noise ratio and constellation size the system performance increases significantly. Among all three combined schemes the adaptive modulation and transmit adaptive array is better because this scheme requires the complex valued Channel State Information to specify the antenna weighting factors, whereas others only require the predicted channel power. CHAPTER 1 1.1 Overview of Communication Communication is the transfer of information from one place to another place [1]. As a matter of fact communication is just a transfer of message and even the way two people converse is a form of communication. Distribution of the data, message from one place to another location with high reliability and security is the major role of communication system. 1.1.1 Elements of Communication System Communication System consists of the following components which acts together to accomplish information transfer or exchange. This includes input transducer, transmitter, channel, receiver and output transducer [13].
Figure1.1: Basic block diagram of communication system The above diagram represents the block diagram of communication system. Now let us explain each block in details. 1.1.2 Main Blocks of Communication Systems Input Transducer: • •
The input message by a source must be converted by a transducer to form suitable for the particular type of communication. In electrical communication, speech waves are converted to voltage variation by a microphone.
Transmitter: • •
The transmitter processes an input signal to produce a transmitted signal suited to the characteristics of the transmission channel. Signal processing for transmission always involves modulation. In addition to modulation, other functions performed by the transmission are amplification, filtering and coupling the modulated signal to the channel.
Channel: The channel can have different forms • • • •
The atmosphere or free space Coaxial cable Fiber optic Wave guide etc
Receiver: The receiver function is to extract the desired signal from the received signal at the channel output and to convert it to a form suitable for the output transducer. Speaker acts as a transducer to convert the received electric signal to voice signal. Output Transducer: The function of the output transducer is to convert the electric signal at its input into the form desired by the user. 1.1.3 Classification of Communication Systems Communication system can be categorized into two different types – Analog Communication & Digital Communication, based on types of signal it transmits between communication transmitter and receiver. Table 1.1: Different aspects of Analog and Digital Communication Topics Features
Analog Communication
Digital Communication
1. This form of communication uses analog messages. 2. An analog message is a physical quantity that varies with time usually in a smooth and continuous fashion. 3. Since the information resides in a time varying waveform, an analog communication system should deliver this wave form with a specific degree of reliability or fidelity.
1. This form of communication uses digital messages. 2. A digital message is a ordered sequence of symbols selected from a finite set of discrete elements. 3. Since the information resides in discrete symbols a digital communication system should deliver these symbols with a specified degree of accuracy in a specified amount of time.
Advantages
Topics Disadvantages
Application
1. Smaller bandwidth is required. 2. Synchronizing problem is relatively easier. 3. Infinite amount of signal resolution. 4. Analog has high density compare to digital communication.
1.Inexpensive digital circuits 2. Privacy preserved (data encryption). 3. Can merge different date and transmit over a common digital transmission system. 4.Error correction is possible by coding
Analog Communication
Digital Communication
1. Expensive analog components L & C. 2. No privacy i.e. security is high. 3. Cannot merge data from different sources. 4. No error correction capability
1. Larger bandwidth is required. 2. Synchronizing problem is relatively difficult. 3. It is unreliable as the messages cannot be recognized by signatures. 4. The establishment of Digital Communication causes degradation of the environment in some cases and also misuse of efficiency.
1. Data Transmission, Shannon Hartley Theorem. 2. Smart Transducer, Communication Security. 3.Multiplexing , Vocoder ,Channel, Flash ADC.
1.Digital Transmission, Orthogonal Frequency Division Multiplexing 2. TWAIN, GSM, 3.Digital Watermarking 4.Direct digital synthesizer, Visix, Error detection and correction 5.Robotic welding 6.Paralleled power wave 7.Networking terminology (LAN,WAN,MAC,Ethernet)
Communication system can also be categorized another two different types â€“ wired and wireless communication. Table 1.2: Different aspects of wired and wireless communication Topics
Wired communication
Wireless communication
Features
1. Radio waves are the forms of electromagnetic radiation the energy is
1. The transmission Channel is the main issue of
conveyed by waves of magnetic and electric field. 2. In a wire these waves are induced and guided by an electric current passing along with the electrical conductor but this is not the only way of propagation. 3. The radio waves are produced by radio transmitter which consists of a radio wave source connected to some form of antenna. Advantages
Topics Disadvantages
Application
communication system and conventionally it is the set of hard wired cables that connect all the lines of the wire. 2. In wireless system the cables are replaced by the free space, but only at the cost of requiring the erection of antennas that allow the line of sight communication.
1. Compressive sensing. 2. Secondary surveillance radar. 3. Sound ranging is passive method 4. Sound ranging equipment tends to be small. 5. It offers more security as data is not sent through air. 6. No worry of batteries. 7. Cheap long distance communication quick.
1. Freedom from land acquisition. 2. Ease of communication over different terrain.
Wired communication
Wireless communication
1.Limited range 2. More signal loss occurs and the signal travels down the wire. 3.A terrestrial wireless link is less secure and less reliable 4.Needs more time to send data than wireless 5.Not comfortable for user to send information
1.Bandwidth allocation is extremely limited 2.Atmospheric effects 3.Transmission needs to be clear 4.Interference and efficiency propagation 5.Restrictive costs
1.Telephone Network 2.Cable Television 3.Internet Access 4.Fiber optic Communication 5.Waveguide (Electromagnetism)
1.Cellular Telephone (Phones and Modems) 2.WiFi , Wireless microphones, remote controls IrDA 3.RFID (Radio Frequency Identification) 4.Wireless USB, Wireless sensing network, Wireless LAN
1.2 Modern Wireless Communication Systems 1.2.1 GSM GSM stands for Global System for Mobile communication [2]. It is a 2nd generation mobile phone system. At present, this is the most popular standard for mobile telephony system and according to GSM Association  This standard is used by 80% of the global mobile market. In this standard both the signaling and speech channels are digital. Which makes this standard different from the previous standardâ€™s [46]. Table 1.3: History of GSM Year
Event
198285
Conference European des Postes et Telecommunications began specifying a European digital telecommunications standard; in the 900MHz frequency band. These standards later become known as Global System for Mobile Communication (GSM).
1986
Fieldtested were held in Paris to select which digital transmission technology to use. The choice was TDMA or FDMA.
1987
A combination of TDMA and FDMA was selected as the transmission technology for GSM
1988
CEPT began producing GSM specifications for a phased implementation.
1991
The GSM 1800 standard was released
1992
Phase I specification were completed. First commercial phase I GSM networks were launched. The first international roaming agreement was established between Telecom Finland and Vodafone in UK.
Services by GSM: According to specifications, many services are offered by GSM. The most basic service is telephony. Speech is digitally encoded and transmitted as bit stream. It also offers a variety of data services. GSM users can send & receive data to & from various other systems like  POTS, ISDN, PSPDN, CSPDN at a rates up to 9600 bps. In contrast with its analog counterparts, GSM provides a unique feature  SMS. Two modes are available for SMS  point to point & cell broadcast. A lot of other services are currently available for the users of GSM. GSM Network Architecture:
Figure 1.2: GSM architecture Several building blocks composed the network architecture. The layout of a generic GSM network is shown in Figure1.2. From the figure we can see that the whole network is composed of three subsystems  Mobile Station, Base Station Subsystems & Network Subsystem. The first Part is carried by the user, second part controls the radio link and the third part involves with switching. Mobile Station: The mobile equipment (the terminal) & the Subscriber Identity Module (SIM) make the Mobile Station (MS). SIM provides operator mobility to the user. Identification of mobile equipment is done by a unique 16 digit number called IMEI. For SIM card identification another unique number is used called IMSI. IMEI & IMSI are independent from each other. Base Station Subsystem: In this subsystem, there are two parts. The Base Transceiver System (BTS) & the Base Station Controller (BSC). BTS is responsible for defining a call & handles the radio link protocols with Mobile Stations. Requirements for BTS deployments are ruggedness, reliability, portability and minimum cost. While radio resources for one or more BTS is managed by the BSC. It also deals with the process of radiochannel setup, frequency hopping and handovers. Network Subsystem: Mobile services Switching Center (MSC) is the main part of network subsystem. It works as a switching node and some extra functionality that are needed to handle a mobile subscriber, such as registration, authentication, location updating & call routing to roaming subscribers is also provided by MSC. For the extra functionality VLR, HLR, EIR & AuC are used together with MSC. Technical Aspects of GSM system: Different carrier frequency ranges are used by GSM. Mostly used are either 900 MHz or 1800 MHz Due to limitations of frequency spectrum, some other ranges are also used like 850 MHz, 1900 MHz, 400 MHz, 450 MHz etc. Regardless of carrier frequency, frequency is divided into timeslot for the use of individual phones. By doing this we get 8 fullrate or 16 halfrate voice channels per Hertz of frequency. Time slots are then grouped to form a Time Division Multiple Access (TDMA) frame. The data rate is 270.833 Kbit/sec. and frame duration is 4.615 ms. The modulation scheme that is selected for GSM is Gaussian Minimum ShiftKeying (GMSK) considering a lot of factors like spectral efficiency, complexity of the transmitter and limited spurious emission. The speech coding technique for GSM is a Regular Pulse Excited  Linear Predictive Coder (RPE  LPC) with a Long Term Predictor Loop. The length of each speech sample frame is 20 milli seconds. Each frame is encoded as 260 bits with a total bit rate of 13 Kbps. In case of Channel coding, GSM uses conventional coding and block interleaving. And finally come security. GSM is a very secured network. Here authentication of receiver is done in two ways. It uses a secret a key between SIM card and Authentication Center (AuC) which is ideally nonbreakable. In conclusion, it can be said that GSM is the most popular and widely accepted mobile communication standard. Though it is a complex standard but this complexity gives us a standard level of integrated service and quality along with high level of security. 1.2.2 CDMA In code division multiple access (CDMA) system, the narrowband massage signal is multiplied by a very large bandwidth signal called the spreading signal [46]. All CDMA users use the same carrier frequency and may transmit simultaneously which we see in Figure 1.3. Each user has its own pseudorandom codeword. The receiver performs a time correlation operation to detect only the
specific desired codeword. All other codeword appear as noise. Each user operates independently with no knowledge of the other users.
Figure 1.3: CDMA system There are three ways to spread the bandwidth of the signal: Frequency hopping: The signal is rapidly switched between different frequencies within the hopping bandwidth pseudorandomly, and the receiver knows before hand where to find the signal at any given time. Time hopping: The signal is transmitted in short bursts pseudorandomly, and the receiver knows beforehand when to expect the burst. Direct sequence: The digital data is directly coded at a much higher frequency. The code is generated pseudorandomly, the receiver knows how to generate the same code, and correlates the received signal with that code to extract the data. Key Features of CDMA System: The key features of a CDMA system (Particularly IS95) are given below: Diversity: To mitigate the effect of fading, some form of diversity is required in cellular systems. CDMA system provides following types of diversity: Time diversity, provided by symbol interleaving, error detection & correction coding. Frequency diversity provided by the 1.25 MHz wideband signal. Space (Path) diversity, provided by dual cellsite receive antennas, multipath rake receivers, and multiple cell sites (soft handoff) Power Control: CDMA is interference limited multiple access system. Because all users transmit on the same frequency, internal interference generated by the system is the most significant factor in determining system capacity and call quality. The transmit power for each user must be reduced to limit interference, however, the power should be enough to maintain the required E b/No (signal to noise ratio) for a satisfactory call quality. Maximum capacity is achieved when E b/No of every user is at the minimum level needed for the acceptable channel performance. As the MS moves around, the RF environment continuously changes due to fast and slow fading, external interference, shadowing, and other factors. The aim of the dynamic power control is to limit transmitted power on both the
links while maintaining link quality under all conditions. Additional advantages are longer mobile battery life and longer life span of BTS power amplifiers. Soft Handoff: Since all cells in CDMA use the same frequency, it is possible to make the connection to the new cell before leaving the current cell. This is known as a "makebeforebreak" or "soft" handover. Soft handovers require less power, which reduces interference and increases capacity. CDMA System Capacity: The theoretical capacity of a CDMA system (IS95) in terms of calls per 1.25 MHz channel per cell is provided by:
N p=
(W / R) υ s (Eb / N 0) F
(1.1)
Where Np = Capacity in terms of calls/1.25 MHz channel/cell W/R= Ratio of the spreading code to the maximum information rate. U= Voice activity gain S = Sectors per cell. F = Frequency reuse factor Eb/N0= Minimum ratio of bit energy to noise power Advantages of CDMA: • Increased cellular communications security. • Simultaneous conversations. •
Increased efficiency, meaning that the carrier can serve more subscribers.
•
Smaller phones.
•
Low power requirements and little celltocell coordination needed by operators.
•
Extended reach  beneficial to rural users situated far from cells.
Disadvantages of CDMA: • •
Due to its proprietary nature, all of CDMA's flaws are not known to the engineering community. CDMA is relatively new, and the network is not as mature as GSM.
•
CDMA cannot offer international roaming, a large GSM advantage.
1.2.3: Third Generation (3G) 3G stands for Third Generation. It is a telecommunication standard developed by the International Telecommunication Union – Radio Communication (ITU – R). Its specifications are set to facilitate a global wireless infrastructure. Its standard name is IMT – 2010. IMT – 2000 is a general name used
for all 3G systems. More advanced capabilities are included here and it provides a clear direction for smooth transformation from 2G to 3G [2]. The key features of the IMT – 2000 systems are [5]: • • • • • •
High degree of commonality of design worldwide. Compatibility of services within IMT – 2000 and fixed networks (e.g. PSTN) High quality of service for voice and data. Small terminal at subscriber end for worldwide use including Pico, Micro, Macro and satellite cells. Worldwide roaming capabilities. Capability for multimedia applications and a wide range of services and terminals.
Services provided by 3G cellular systems: • • •
High bearer rate capabilities, including 2Mbps for fixed environment 384 Kbps for indoor / outdoor and pedestrian environment. 144 Kbps for vehicular environment.
Standardization Work: The following table gives an idea about standardization works at different region Table 1.4: Regional Standardization of 3G Europe (ETSI: European Telecommunications Standardization Institute) = > UMTS (WCDMA)
Approved Radio Interfaces:
Japan (ARIB: Association of Radio Industries & Business) = > WCDMA
USA (TIA: Telecommunications Industry Association) = > CDMA 2000
The following figure gives an idea about the radio interfaces approved for to be used in 3G system. Different techniques that are used for multiplexing purposes are customized to be used in 3G system
Figure 1.4: Approved radio interface of 3G Comparison between different 3G systems: Table 1.5: A comparison of different standard of 3G systems in 3 different regions Parameter
W – CDMA (Europe)
W – CDMA (Japan)
CDMA 2000 (USA)
Multiple Access
WB DSCDMA
WB DSCDMA
WB DSCDMA
Duplex Method
FDD / TDD
FDD / TDD
FDD
Channel Bandwidth
1.2/5/10/20 MHz
1.25/5/10/20 MHz
1.25/5/10/20 MHz
Chip Rate (Mcps)
1.024*(1,4,8,16)
1.024*(1,4,8,16)
1.2288*(1,3,6,12)
Frame Length
10 ms
10ms
20.5ms
Inter – BS synch.
Asynch.
Asynch./Synch.
Synch.
Data Modulation
QPSK/BPSK (FDD)
QPSK/BPSK (FDD)
QPSK/BPSK
QPSK/QPSK (TDD)
QPSK/BPSK (TDD)
QPSK/QPSK
QPSK/QPSK
Spread Modulation
QPSK/QPSK
MultiRate Concept
VSF+ Multicode +
VSF+ Multicode +
Multislot (TDD)
Multislot (TDD)
CLPC, 1.6 Ks/s
CLPC, 1.6 Ks/s
CLPC, 0.8 Ks/s
OLPC, 1.6 Ks/s
OLPC, 1.6 Ks/s
OLPC, 0.8 Ks/s
Spreading Codes
Short/Long
Short/Long
Short/Long
Coherent Detection
With Pilot Symbol
With Pilot Symbol
With Pilot Symbol
Voice Codecs
Variable or fixed rate
Variable or Fixed rate
Variable (EVRC)
Tx. Power Control
VSF/Multicode
Rate
1.2.4 WiFi Introduction: WiFi is a shorted form of “Wireless Fidelity” [2]. Currently this is one of the most popular wireless communication standard. In its early stages, it was used solely to wirelessly connect laptop computers to the internet via Local Area Network (LAN). But due to further advances in technology, the scenario has changed totally. Nowadays it is used to connect not only computer but also almost all sort of noncomputer electronic devices such as – Home theater receivers, Portable gaming devices, DVD players, Digital camera and even GPS receiver. Wireless Standard: The official name for the specification is IEEE 802.11, and it is comprised of more than 20 different standards, each of which is denoted by a letter appended to the end of the name. The most familiar standards are 802.11b and 802.11g (Wireless B and G) which are used in the majority of commercial WiFi devices. Both of these standards operate in the 2.4 GHz band, and the only major difference between the two is the transfer rate. Some consumer electronics, however, use a different standard— Wireless A. These devices operate within the 5 GHz range and have transfer rates equivalent to 802.11g. However, since they operate on different frequencies, devices using the 802.11a standard cannot communicate with B and Genabled devices. Comparison of standards: Table 1.6: An overview of the three most popular current 802.11 standards Standard
Frequency
Data Transfer Rate Range (indoor) Typical (Max)
802.11a
5 GHz
25 (50) Mb/sec
about 10 m (30 ft)
802.11b
2.4GHz
6.5 (11) Mb/sec
30 m (90 ft)
802.11g
2.4 GHz
25 (54) Mb/sec
30+ m (90+ ft)
Advantages of WiFi: The major advantages of WIFi are given below •
• •
It provides unparalleled mobility and flexibility to the user. For example, if anyone had a WiFi enabled mp3 player, he can listen to the music from the local server of the LAN or any computer attached to the network. Even he can listen to the internet radio without facing the hassle of wire. Setting up a WiFi network is a very easy and quick process. Many modern routers are “PlugandPlay” devices. Just connect and start using services even without installing any software’s. Fast data transfer rate is the main advantage of WiFi. The standard 802.11g is currently the fastest commercially available WiFi protocol in the market with transfer speed up to 54Mbps.
Limitations of WiFi: WiFi has some limitations also. They are pointed out below • • •
Though it is easy to setup, securing the network requires some more cautious effort. Otherwise, it will be an easy target of the hacker. Encryption of data does not come automatically. It has to be done when the network is running. The frequency spectrum for WiFi lies primarily within the 2.4 GHz spectrum. Which make it susceptible to the interference that comes from neighboring equipments such as – Bluetooth devices, cordless telephones, Micro wave oven and other household devices. Though it supports high data rate, but this data rate is still beyond the limit of some of the today’s highend media. HighDefinition audio and video files are bandwidth and timelydeliveryintensive. But WiFi cannot do this consistently and flawlessly.
1.2.5 WiMAX WiMAX is an acronym for Worldwide Interoperability for Microwave Access. It is Based on Wireless Metropolitan Area Network (MAN) technology [46]. It is optimized for the delivery of IP centric services over a wide area. This is a scalable wireless platform for constructing alternative and complementary broadband networks. And also WiMAX is a certification that denotes interoperability of equipment built to the IEEE 802.16 or compatible standard. This technology can provide Broadband Wireless Access (BWA) up to 30 miles (50 kilometers) for fixed stations, and 310 miles (515 kilometers) for mobile stations. In a typical cell radius deployment of three to ten kilometers, WiMAX forum certified system can be expected to deliver up to 40 Mbps per channel, for fixed and portable access applications. Services: WiMAX can provide two form of wireless services: Nonlineofsight: service is a WiFi sort of service. Here a small antenna on your computer connects to the WiMAX tower. In this mode, WiMAX uses a lower frequency range  2 GHz to 11 GHz (similar to WiFi). Lineofsight: service, where a fixed dish antenna points straight at the WiMAX tower from a rooftop or pole. The lineofsight connection is stronger and more stable, so it's able to send a lot of data with fewer errors. Lineofsight transmissions use higher frequencies, with ranges reaching a possible 66 GHz.
Features of WiMAX: Some key features of WiMAx are given below: •
OFDMbased physical layer
•
Very high peak data rates
•
Scalable bandwidth and data rate support
•
Adaptive modulation and coding (AMC)
•
Linklayer retransmissions
•
Support for TDD and FDD
•
WiMAX uses OFDM
•
Flexible and dynamic per user resource allocation
•
Support for advanced antenna techniques
•
Qualityofservice support
•
Robust security
•
Support for mobility
•
IPbased architecture
WiMAX Standards: Following is the chart of comparison of various IEEE 802.16 Standard related to WiMAX Table 1.7: Different aspects of three different WiMAX standards Spectrum Configuration Bit Rate Modulation
802.16 1066 GHz Line of Sight 32 to 134 Mbps (28 MHz Channel) QPSK, 16QAM, 64QAM
Mobility Channel Bandwidth
Fixed 20, 25, 28 MHz
Typical Cell Radius Completed
13 miles Dec, 2001
802.16a 211 GHz Non Line of Sight ≤ 70 or 100 Mbps (20 MHz Channel) 256 Subcarrier OFDM using QPSK, 16QAM, 64QAM, 256QAM, Fixed Selectable 1.25 to 20 MHz 35 miles Jan, 2003
802.16e <6 GHz NonLine of Sight Upto 15 Mbps Same as 802.16a
≤ 75MPH 5 MHz (planned) 13 miles 2nd Half of 2005
WiMAX Architecture: A wireless MAN based on the WiMAX air interface standard is configured in much the same way as a traditional cellular network with strategically located base stations using a pointtomultipoint architecture to deliver services over a radius of up to several miles, depending on frequency, transmit power, and receiver sensitivity. In areas with high population densities, the range will generally be capacity limited rather than range limited, owing to limited bandwidth. The base stations are typically backhauled to the core network by means of fiber or pointtopoint microwave links to available fiber nodes or via leased lines from an existing wireline operator. The range and NLOS capability make the technology equally attractive and cost effective in a wide variety of environments. The technology
was envisioned from the beginning as a means of providing wireless last mile broadband access in the MAN with performance and services comparable to or better than traditional DSL, cable, or T1/E1 leased line services.
Figure 1.5: WiMAX Network Architecture The technology is expected to be adopted by different incumbent operator types, for example, wireless internet service providers (WISPs), cellular operators (CDMA and WCDMA), and wire line broadband providers. Each of these operators will approach the market with different business models based on their current markets and perceived opportunities for broadband wireless as well as different requirements for integration with existing (legacy) networks. As a result, 802.16 network deployments face the challenging task of needing to adapt to different network architectures while supporting standardized components and interfaces for multivendor interoperability. 1.2.6 Fourth Generation (4G) 4G is the short name for fourthgeneration wireless, the stage of broadband mobile communications that will supersede the third generation [46]. It is a fourth generation cellular communication system based on fourth generation mobile technology. In this system, networks operate on internet technology and combine all other applications & technologies such as WiFi with this. This is a fully IP – based wireless communication system with high level of network security. It can provide high data speed of up to 100 Mbps (Outdoor) & 1Gbps (indoor). One of the key features of this system is that it can provide any services, anytime, anywhere at an affordable cost. Objectives: • • • • • • • •
Efficient and High network capacity Nominal date rate: 100 Mbps1 Gbps Smooth handoff across heterogeneous network Seamless connectivity Global roaming across multiple networks High quality of service for multimedia support (real time audio, high speed data, HDTV video content, mobile TV, etc) Interoperation ability with the existing wireless standards All IP system, packet switched network
Table 1.8: Comparison between 3G & 4G
3G (including 2.5G, sub3G)
4G
Major Requirement Driving Architecture
Predominantly voice driven â€“ Converged data and voice over data was always add on IP
Network Architecture
Wide area cellbased
Hybrid  Integration of Wireless LAN (WiFi, Bluetooth) and wide area
Speeds
384 Kbps to 2 Mbps
20 to 100 Mbps in mobile mode
Frequency Band
Dependent on country or Higher frequency bands (2 8 continent (18002400 MHz) GHz)
Bandwidth
520 MHz
100 MHz (or more)
Switching Design Basis
Circuit and Packet
All digital with packet voice
Access Technologies
WCDMA, 1xRTT, Edge
OFDMA and MCCDMA (Multi Carrier CDMA)
Forward Error Correction
Convolutional rate 1/2, 1/3
Concatenated coding scheme
Component Design
Optimized antenna multiband adapters
IP
A number of air link protocols, All IP (IP6.0) Including IP 5.0
design, Smarter Antennas, software multiband and wideband radios, SoftwareDefined Radio
Figure 1.6: 4G Network Architecture 4G Key Components: Access Schemes To add advantages in scalability new access schemes like OFDMA, Single carrier FDMA, and MCCDMA has been proposed as part of the next generation UMTS, 802.16e and 802.20 standards. IPv6 Using Ipv6 Removes the need for Network Address Translation (NAT). It enables a number of applications with better multicast, security and route optimization capabilities. Provides support to a great number of wireless enabled devices. It also provides more available address space and number of addressing bits. This also enables 4G coding schemes innovation MultiAntenna Systems By using multi – antenna systems we can use MIMO (Multipleinput and multipleoutput) multiplexing Which is used to send data via various routes across a network in order to increase date capacity. MIMO increases the peak data rates and average throughput of data systems. SoftwareDefined Radio (SDR) 4G devices will constitute all collection of wireless standards. This can be realized by using SDR technology. SDR is one form of open wireless architecture (OWA). 1.3 Motivation and objective of the present work In wireless communication, the channel though which we transmit the information is very important. During Transmission through the channel the signal suffers some unavoidable phenomena like fading, path loss, noise and relative movement. To overcome those phenomena, adaptive modulation schemes
can be applied. Another phenomena is the time varying nature of the channel, which requires the adjustment of modulation schemes, coding techniques and transmit power levels according the channel instantaneous SNR. If the channel SNR can be estimated then the desired modulation scheme can be adjusted. So it very important to model and predict the future channels. In our thesis paper, first we investigate the combined adaptive transmission techniques with transmitter diversity. Then we study the capacity of Rayleigh fading channel under different adaptive transmission techniques. At last we study the long range channel prediction. 1.4 Organization of the paper This thesis consists of 3 chapters – chapter 1 gives an introduction of various types of communication systems. In chapter 2 we shall discuss the features of different communication channels and then importance of channel modeling is elaborated. Finally the adaptive transmission, combined adaptive modulation with transmitter diversity, long range prediction etc are explained. In chapter 3 we have given our simulated results for different combined adaptive modulation schemes. CHAPTER 2 COMMUNICATION CHANNEL MODELS 2.1 Physical Communication Channels Communication channels are the transmission medium through which the transmission of information across a communication network is accomplished [7]. It is the center to the operation of communication system. Its properties determine both the information carrying capacity of the system and the quality of service offered by the system. It is used to convey an information signal from one or several senders (transmitters) to one or several receivers. Depending on mode of transmission we can classify two basic groups of communication channels.
Communication channel
Channels based on guided propagation Examples: Telephone channels Coaxial cables Optical fibers
Channels based on free space propagation Examples: Broadcast channels Mobile radio channels Satellite channels
2.1.1 Channels Based on Guided Propagation Telephone channels A telephone network uses circuit switching to establish an end to end communication link on temporary basis [7]. Communication link is established between a speaker at one end of the link and a listener at the other end. The telephone channel supports only the transmission of electrical signals. Appropriate transducers are used at the transmitter and receiving ends of the system. A microphone is placed near the speaker’s mouth to convert sound waves into electrical signal and the electrical signal is converted back into acoustic form by using a moving–coil receiver placed near the listener’s ear. The telephone channel is a bandwidth limited channel as sharing of channel among a multitude of user at one time.
The telephone channel is built using twisted pairs for signal transmission. A twisted pair consists of two solid copper conductors, each of which is encased in a polyvinylchloride (PVC) sheath. Typically, each pair has a twist rate of 2 to 12 twists per foot and a characteristic impedance of 90 to 110 ohms. Twisted pairs are usually made up into cables, with each cable consisting of many pairs. Twisted pairs are naturally susceptible to electromagnetic interference (EMI), the effects of which are mitigated through twisting the wires. Coaxial cables A Coaxial cable consists of an inner conductor and an outer conductor, separated by a dielectric insulating material [7]. The inner conductor is made of a copper wire encased inside the dielectric material. As for the outer conductor, it is made of copper, tinned copper, or copper coated steel. A coaxial cable has a characteristic impedance of 50 to 75 ohms. Compared to twisted pair cable it is less affected by EMI and has higher bandwidth. It has a bit rate up to 20 Mb/s with 10 Mb/s being the standard. Applications: •
Coaxial operate as a multiple access medium by using high impedance tap.
•
Used as a transmission medium for local area network in an office environment.
•
Used in cable television system, also known as community antenna television (CATV) system.
Optical fiber An optical fiber is a dielectric wave guide that transports light signals from one place to another just as a twistedwire pair or a coaxial cable transports electrical signals [7]. It consists of a central core within which the propagating electromagnetic field is confined and which is surrounded by a cladding layer, which itself surrounded by a thin protective jacket. The core and cladding are both made of pure silica glass, whereas the jacket is made of plastic. Characteristics: •
Enormous potential bandwidth ranging from GHz to THz
•
Low transmission loss, as low as 0.1db/km.
•
Immunity to electromagnetic interference
•
Small size and weight
•
Ruggedness and flexibility
Applications: •
Used in long distance communication as low transmission loss.
•
To transmit telephone signals Internet communication, and cable television signals.
•
To supply a low level of power (around one watt) to electronics situated in a difficult electrical environment (high powered antenna elements).
Twisted pair cable
coaxial cable
Optical fiber cable Figure 2.1: Different Channels based on guided propagation
2.1.2 Wireless Communication Channels Wireless broadcast channels Wireless broadcast channel support the transmission of radio and television signals [7]. The information bearing signal, representing speech, music, or pictures, is modulated onto a carrier frequency that identifies the transmitting station. The transmission originates from an antenna that acts as the transition or matching unit between the source of the modulated signal and electromagnetic waves in free space. The antenna is designed to excite the waves in required directions. The transmitting antenna is mounted on a tower to provide an unobstructed view of the surrounding area. Radio waves are bent around the earth’s surface by the virtue of the phenomenon of diffraction. At the receiving end, an antenna is used to pick up the radiated waves, establishing a communication link to the transmitter. Most radio receivers are of superheterodyne type. This technique consists of down converting the received signal to some convenient intermediate frequency (IF) band, and then recovering the original information – bearing signal by means of appropriate decoder. Mobile radio channel Mobile radio channel extends the capacity of the public telecommunication network by introducing mobility into the network by the virtue of its ability to broadcast. The term mobile radio is usually meant to encompass terrestrial situations where a radio transmitter or receiver is capable of being moved, regardless of whether it actually moves or not. This channel is applied where there is no “lineofsight” path for communication; rather, radio propagation takes place mainly by the way of scattering from the surfaces of the surrounding buildings and by diffraction over and around them. The result is multipath phenomena in that the various incoming radio waves reach their destination from different direction with different time delays. The multitude propagation paths with different
electrical length are combined in different ways. The received signal strength may vary with the variation of the receiver. So the mobile radio channel can be viewed as a linear time varying channel that is statistical in nature. Satellite channel A satellite channel adds invaluable dimension to the public telecommunication network by providing broadarea coverage in both a continental and an intercontinental sense [7]. The satellites are placed in geostationary orbit. For the orbit to be geostationary it requires that the satellite orbits the earth in 24 hours and it is placed in orbit directly above the equator on an eastward heading. A satellite communication system, a message signal is transmitted from an earth station via an uplink to a satellite, amplified in a transponder on board the satellite, and then retransmitted from the satellite via a downlink to another earth station. The frequency band for satellite communication is 6 GHz for the uplink and 4 GHz for the downlink. Characteristics: •
Broad coverage area.
•
Reliable transmission links.
•
Wide transmission bandwidth.
•
Less inexpensive microwave equipments.
•
Low attenuation due to rainfall.
Application: •
For communication.
•
Forecast the weather and give alert for imminent disaster.
•
To provide GPS service.
•
For scientific research and in military.
Wireless broadcast channels
Mobile radio channel
Satellite channel
Figure 2.2: Channels based on free space propagation 2.2 Communication Channel Models A channel can be modeled physically by characterizing the physical processes which modify the transmitted signal. For example in wireless communications the channel can be modeled by calculating the reflection off every object in the environment [2]. A sequence of random numbers might also be added in to simulate external interference or electronic noise in the receiver. Statistically a communication channel is usually modeled as a triple consisting of an input alphabet, an output alphabet, and for each pair (i,o) of input and output elements a transition probability p(i,o). Semantically, the transition probability is the probability that the symbol o is received given that ‘i’ was transmitted over the channel. Statistical and physical modeling can be combined. For example in wireless communications the channel is often modeled by a random attenuation (known as fading) of the transmitted signal, followed by additive noise. The attenuation term is a simplification of the underlying physical processes and captures the change in signal power over the course of the transmission. The noise in the model captures external interference and/or electronic noise in the receiver. If the attenuation term is complex it also describes the relative time a signal takes to get through the channel. The statistics of the random attenuation are decided by previous measurements or physical simulations. Table 2.1: Examples of digital and analog channel models Digital Channel Analog Channel 1. Binary symmetric channel (BSC), a 1. Noise model, for example discrete memoryless channel with a certain Additive white Gaussian noise bit error probability (AWGN) channel, a linear continuous memoryless model Phase noise model
2. Binary bursty bit error channel model, a 2.Interference model, for example crosstalk channel "with memory" (cochannel interference) and intersymbol interference (ISI) 3. Binary erasure channel (BEC), a discrete channel with a certain bit error detection (erasure) probability
3.Distortion model, for example a nonlinear channel model causing intermodulation distortion (IMD)
4. Packet erasure channel, where packets are 4.Frequency response model, lost with a certain packet loss probability or attenuation and phaseshift packet error rate.
including
5. Arbitrarily varying channel (AVC), 5.Modeling of underlying physical layer where the behavior and state of the channel transmission techniques, for example a can change randomly complexvalued equivalent baseband model of modulation and frequency response 6.Radio frequency propagation model, for example Longdistance path loss model Fading model, for example Rayleigh fading, Rician fading, lognormal shadow fading and frequency selective (dispersive) fading Doppler shift model, which combined with fading results in a timevariant system Ray tracing models, which attempt to model the signal propagation and distortions for specified transmitterreceiver geometries, terrain types, and antennas. 2.2.1 Binary symmetric channel A binary symmetric channel (or BSC) is a common communications channel model used in coding theory and information theory [2]. In this model, a transmitter wishes to send a bit (a zero or a one), and the receiver receives a bit. It is assumed that the bit is usually transmitted correctly, but that it will be "flipped" with a small probability (the "crossover probability"). This channel is used frequently in information theory because it is one of the simplest channels to analyze.
Figure 2.3: Binary symmetric channel [2] The BSC is a binary channel; that is, it can transmit only one of two symbols (usually called 0 and 1). (A nonbinary channel would be capable of transmitting more than 2 symbols, possibly even an infinite number of choices.) The transmission is not perfect, and occasionally the receiver gets the wrong bit. This channel is often used by theorists because it is one of the simplest noisy channels to analyze. Many problems in communication theory can be reduced to a BSC. On the other hand, being able to transmit effectively over the BSC can give rise to solutions for more complicated channels. Definition A binary symmetric channel with crossover probability p denoted by BSCp, is a channel with binary input and binary output and probability of error p; that is, if X is the transmitted random variable and Y the received variable, then the channel is characterized by the conditional probabilities Pr( Y = 0  X = 0 ) = 1 − p Pr( Y = 0  X = 1) = p Pr( Y = 1  X = 0 ) = p Pr( Y = 1  X = 1 ) = 1 − p It is assumed that 0 ≤ p ≤ 1/2. If p > 1/2, then the receiver can swap the output (interpret 1 when it sees 0, and vice versa) and obtain an equivalent channel with crossover probability 1 − p ≤ 1/2. 2.2.2 Binary erasure channel
Figure 2.4: Binary erasure channel [2] The channel model for the binary erasure channel showing a mapping from channel input X to channel output Y (with known erasure symbol). The probability of erasure is pe A binary erasure channel (or BEC) is a common communications channel model used in coding theory and information theory. In this model, a transmitter sends a bit (a zero or a one), and the receiver either receives the bit or it receives a message that the bit was not received ("erased"). This channel is used frequently in information theory because it is one of the simplest channels to analyze. The BEC was introduced by Peter Elias of MIT in 1954 as a toy example.
Closely related to the binary erasure channel is the packet erasure channel which shares many similar theoretical results with the binary erasure channel. Definition A binary erasure channel with erasure probability p is a channel with binary input, ternary output, and probability of erasure p. That is, let X be the transmitted random variable with alphabet {0, 1}. Let Y be the received variable with alphabet {0, 1, e}, where e is the erasure symbol. Then, the channel is characterized by the conditional probabilities Pr( Y = 0  X = 0) = 1p Pr( Y = e  X = 0) = p Pr( Y = 1  X = 0) = 0 Pr( Y = 0  X = 1) = 0 Pr( Y = e  X = 1) = p Pr( Y = 1  X = 1) = 1p 2.2.3 Packet erasure channel The packet erasure channel is a communication channel model where sequential packets are either received or lost (at a known location). This channel model is closely related to the binary erasure channel. An erasure code can be used for forward error correction on such a channel. 2.2.4 Arbitrarily varying channel An arbitrarily varying channel (AVC) is a communication channel model used in coding theory, and was first introduced by Blackwell, Breiman, and Thomasian [2]. This particular channel has unknown parameters that can change over time and these changes may not have a uniform pattern during the transmission of a codeword. uses of this channel can be described using a stochastic matrix , where is the input alphabet, is the output alphabet, and is the probability over a given set of states
, that the transmitted input
is equal to the received output . The state in set can vary arbitrarily at each time unit . This channel was developed as an alternative to Shannon's Binary Symmetric Channel (BSC), where the entire nature of the channel is known, to be more realistic to actual network channel situations.
2.3 Channel Characterization 2.3.1 Fading In the case of receiving signal from base station (BS) to MS multipath will occur due to reflection from the ground and surrounding structures. The incoming radio waves arrive from different direction with different propagation delay. The signal received by mobile may have randomly distributed amplitudes, phases and angle of arrivals. Theses multipath components are combined vectorially at the receiver antenna and cause the received signal to distort or fade [46]. Factors influencing fading
•
Multipath propagation
•
Speed of mobile
•
Speed of surrounding objects
•
The transmission bandwidth
Table 2.2 (a): Comparison between large and small scale fading Large scale fading
•
Due to shadowing and variation in the distance between the mobile and base station.
•
Changes with time at relatively slow rate.
•
Power control can be use to compensate this effect.
Small scale fading
•
Due to multipath propagation.
•
Changes with time at relatively faster rate.
•
Diversity and errorcorrection coding are used to overcome this effect.
Table 2.2(b): Small scale fading based on delay spread Small scale fading (based on multipath time delay spread)
Flat fading
Frequency selective fading
•
BW of signal < BW of channel
•
BW of signal > BW of channel
•
Delay spread < Symbol period
•
Delay spread > Symbol period
Table 2.2(c): Small scale fading based on Doppler spread Small scale fading
(based on Doppler spread)
Fast fading
slow fading
•
high Doppler spread
•
low Doppler spread
•
coherence time < symbol period
•
coherence time > symbol period
•
channel variations faster baseband signal variation
•
channel variations slower baseband signal variation
than
than
Characterization of Fading Channels In wireless communication system, the received signal experiences significant power fluctuations due to fading. Signal fading is caused by multipath propagation and Doppler frequency shift. Multiple scatterers give rise to multipath that causes interference between reflected transmitter signal components [8]. The superposition component waves leads to either constructive (peaks) or destructive interference (deep fades). When all the delayed components arrive at the receiver within a small fraction of the symbol duration, the fading channel is frequencynonselective, or flat. This often occurs due to narrow band signaling. In wideband transmission, the multipath delay is nonnegligible relative to the symbol interval and frequency –selective fading results. When the receiver, transmitter, and/or the scatterers are moving, the nth scattered component undergoes a Doppler frequency shift given approximately by: (2.1) Where fc is the carrier frequency, v is the vehicle speed; c is the speed of light, Ɵn is the incident radio wave angle with respect to the motion of the mobile. F dm is the maximum Doppler frequency shift. The complex envelope of the flat fading signal at the receiver is (2.2) Where N is the number of scatters, and for the nth scatterer, A n is the amplitude, fn is the Doppler frequency shift and Øn is the phase. The parameter An, fn and Øn are slowly timevariant. We assume that without loss of generality that the average channel power E (c(t) 2) is normalized to one. This standard assumption simplifies performance analysis and is not used in channel estimation and prediction. A fading channel is often called rapidly timevarying when a mobile passes through several fades in a second. Faster vehicle speeds and larger carrier frequencies cause more rapid fluctuations in the fading signal. 2.3.2 Doppler shift calculation Due to relative motion between the mobile and base station, each multipath experience a shift in frequency. The shift in received signal frequency due to motion is called Doppler shift [6].
Figure 2.5: Doppler shift due to receiver movement
Fd = change in received frequency = fr â€“ fc
= = F r = fc + fd F r = fc +
Where,
= angle between transmitter and receiver fc = carrier frequency fr = received frequency
2.3.3 Rayleigh Fading Distribution A common phenomenon encountered in mobile communications is Rayleigh fading [45]. Signal reflections from buildings, hills, etc. cause interference at the receiver. As a result, the received signal power varies strongly within a few meters of distance. In deep fades (positions of very low signal power) communication is not possible at all. Rayleigh fading is a statistical model that is used to describe the statistical time varying nature of the received envelope of a flat fading signal in a mobile radio channel. It is a reasonable model when there are many objects in the environment that scatter the radio signal before it arrives at the receiver. Rayleigh fading is most applicable when there is no dominant propagation along a line of sight between the transmitter and the receiver.
The Rayleigh distribution has a probability density function (PDF) given by
(2.3) Where r is the envelope of fading signal, Ďƒ is the r.m.s value of the received voltage before envelope detection. And Ďƒ^2 is the time average power of the received signal before envelope detection. Following figure shows the pdf of Rayleigh distribution
Figure 2.6: The pdf of Rayleigh Fading Distribution The following figure shows a Rayleigh distributed signal envelope as a function of time.
Figure 2.7: Rayleigh distributed signal envelope as a function of time The mean value rmean of the Rayleigh distribution is given by
(2.4) And the variance of the Rayleigh distribution is given by Ďƒ, which represents the ac power in the signal envelope.
(2.5)
2.3.4 Rician Fading Distribution Signal degradation is a common phenomenon in wireless communication [45]. There are many reasons that degrade the signal quality. The reasons are mainly attenuation, reflection, refraction and diffraction. As a result of these factors, the received signal power varies with distance. In deep fades (positions of very low signal power) communication is not possible at all. : When there is a dominant stationary (non fading) signal component present, such as a lineofsight propagation path, the small scale fading distribution is Rician. In such a situation, random multipath components arriving at different angles are superimposed on a stationary dominant signal. At the output of an envelope detector, this has the effect of adding a dc component The pdf of Rician Distribution is given by
(2.6) Where, r is the envelope of fading signal, σ is the r.m.s value of the received voltage before envelope detection, σ^2 is the time average power of the received signal before envelope detection, A is the amplitude of the direct signal and I0(*) is the zeroorder modified Bessel function of first kind.
Following figure shows the pdf of Rician distribution
Figure 2.8.: The pdf of Rician Fading Distribution When A is very large – that is, the direct signal is very strong (r≈σ) – Equation 5.55 can be approximated by a Gaussian distribution. When A is very small  that is, there is no direct signal (the standard deviation σ≈0) – Equation 5.55 can be approximated by a Rayleigh distribution.
2.3.5 Channel Capacity Channel Capacity [2, 17] is concerned with the information handling capacity of a given channel. It is affected by: The attenuation of a channel which varies with frequency as well as channel length. The noise induced into the channel which increases with distance. Nonlinear effects such as clipping on the signal. Some of the effects may change with time, e.g. the frequency response of a copper cable changes with temperature and age. For this reason we need a way to model a channel in order to estimate how much information can be passed through it. Although we can compensate for non linear effects and attenuation it is extremely difficult to remove noise. The maximum rate of information that can be reliably (error free) transmitted through a channel is called the channel capacity, C. Shannon’s Channel Coding Theorem: Shannon’s Channel Coding Theorem [7] states that if the information rate, R (bits/s) is equal to or less than the channel capacity, C, (i.e. R < C) then there is, in principle, a coding technique which enables transmission over the noisy channel with no errors. The inverse of this is that if R > C, then the probability of error is close to 1 for every symbol. Shannon’s Channel Capacity Theorem: Shannon’s Channel Capacity Theorem (ShannonHartley Theorem) states that: Bits/s
(2.7)
Where, C=Channel Capacity. B=Channel bandwidth in hertz. S=Signal power in watt N=Noise power in watt The channel capacity, C, increases as the available bandwidth increases and as the signal to noise ratio increases. This expression applies to information in any format and to both analogue and data communications, but its application is most common in data communications. The channel capacity theorem is one of the most important results of information theory. In a single formula it highlights the interplay between 3 key system parameters: channel bandwidth, average transmitted or received signal power,
Noise power at the channel output.
For a given average transmitted power, S and channel bandwidth, B, we can transmit information at the rate C bits/s with no error, by employing sufficiently complex coding systems. It is not possible to transmit at a rate higher than C bits/s by any coding system without a definite probability of error. Hence the channel capacity theorem defines the fundamental limit on the rate of errorfree transmission for a powerlimited, bandlimited channel.
From the channel capacity equation, as bandwidth increase the capacity should increase proportionally. But this does not happen, because as bandwidth increase the noise power also increases. Noise power, So,
=
C=
(2.8)
As B→∞, S/
As,
the Channel Capacity goes to,
= 1.44
(2.9)
This gives the maximum information transmission rate possible for a system of given power but no bandwidth limitations. 2.3.6 Diversity combining Diversity combining techniques are used to mitigate channel impairments like fading and intersymbol interference (ISI) [6]. Diversity combining is the technique applied to combine the multiple received signals of a diversity reception device into a single improved signal. Space diversity: The message signal is transmitted by using multiple transmitting antennas and/or receiving antennas. The space separation between adjacent antennas should be large enough so that the signals from different antennas are independently faded. Examples are SISO, MISO, SIMO, MIMO.
Frequency diversity: The desired message is transmitted simultaneously over several frequency slots.
Time diversity: The desired message is transmitted repeatedly over several time periods.
ď ś Angle diversity: The desired message is received simultaneously by several directive antennas pointing in widely different direction. 2.4 Adaptive channel prediction 2.4.1 Channel prediction The idea behind the channel prediction is to use the past and present channel samples to predict the future samples. Channel prediction allows the system to adapt modulation methods to an estimated future channel state information (CSI) [1314]. Example: Pilot Symbol Assisted Modulation (PSAM) method [11]: The idea behind PSAM is to insert known symbols in our transmission at set intervals. These symbols are called pilot symbols. The purpose of the pilot symbol is to have a way at the receiver to know what the channel value is at the pilot. Using this system, we will have fairly accurate channel samples at a frequency equal to the pilot symbol rate. Using the pilots, we can interpolate the channel values inbetween using a proper interpolation method.
Figure 2.9: pilot symbol insertion Long range prediction: long range channel prediction algorithm [8,12] characterized the fading channel using an autoregressive (AR) model and computes the minimum mean square error (MMSE) estimate of a future fading coefficient sample based on a number past observations. This method gives long memory span that permits much further into the future. For a fixed model order the long memory span is achieved by using low sampling rate (on the order of twice the maximum Doppler shift and much slower than the data rate). Short range prediction: For very slow varying channel outdated CSI is sufficient for reliable adaptive system design. As the slow varying channel we need a small memory span.
2.4.2
The importance of long range channel prediction in adaptive transmission
Accurate knowledge of future CSI is very important for realizing the potential of adaptive transmission [8]. As an example, consider the application of STD [15] in the proposed 3 rd generation
WCDMA system. One of the key features that make WCDMA feasible globally is its high carrier frequency of 2 GHz. Moreover this high carrier frequency results in very large Doppler shifts at moderate vehicular speeds (e.g. 65 mi/h corresponds to f dm=200Hz) that cause significant variations of the fading channel coefficients over short time periods. Thus, outdate channel estimates fed back to the transmitter becomes less useful for adaptive signaling application and longrange fading prediction capacity becomes more important. Based on the received power, the strongest antenna that is selected at the receiver. The antenna selection bit is sent back to the transmitter and determines the antenna that is going to transmit during the next slot of during the next four slots. For STD without prediction, this bit is based on the power of the noiseless plot symbol received in the last slot. Thus the CSI is delayed by the slot duration relative to the beginning of the switching interval. When long range prediction is utilized, previous noiseless pilot symbols collected at the rate of 1.6 KHz are used to predict the average channel power during the next switching interval. The most recent observation show that significant performance gains are achieved for fast vehicle speeds when LRP is employed. 2.4.3
Adaptive transmission techniques
High speed wireless data transmission requires strong and spectrally efficient communication techniques for flat fading channels. Adaptive transmission is the way for high speed communication which includes adaptive modulation, adaptive channel coding, adaptive power control, and adaptive transmitter antenna diversity. For modulation to be adaptive the channel state information (CSI) must be available at the transmitter. CSI can be estimated at the receiver and sent to the transmitter via a feedback channel. So feedback delay, processing delay, antenna switching rate have to be taken into account in the performance analysis of adaptive transmission [15]. Now we need a way to change the modulation scheme depending on the present channel condition. This can be done by estimating the SNR of the link. Now considering the BER performance of the three modulation [10] schemes below.
PQPSK (Îł) = Q (
P16QAM (Îł) =
)
(2.10)
(2.11)
P64QAM (Îł) =
+
+
+
(2.12)
In above equations Îł is the SNR and Q (.) is the Qfunction.
Figure 2.10: BER performance of three modulation schemes From this BER plot we can decide the proper switching level of modulation. Now we chose an operation point or a desired BER of 103. With this operation point we have the following SNR range. Table 2.3: SNR level for different modulation schemes QPSK 16QAM 64QAM
SNR < 17 db 17 db <= SNR <= 23 db SNR > 23 db
For SNR less than 17dB, there is only one scheme that gives us performance below 103, and that is QPSK. Between 17 and 23dB, 16QAM gives us our desired BER at a better spectral efficiency than QPSK. And at SNR higher than 23dB, 64 QAM gives us the best performance. 2.5
Combined Adaptive Modulation for Flat Fading Mobile Radio Channel
Adaptive modulation is proposed recently to satisfy the tremendous growth in demand for wireless communications capacity. Adaptive modulation is a useful approach to achieve bandwidth efficient transmission by adapting the modulation parameters (e.g., constellation size, transmitted signal power, symbol rate, etc.) to current fading conditions. As, it is well known that diversity improves channel capacity. The combined adaptive modulation and transmitter diversity methods depend on accurate
channel state information, but the rapid variation of the fading channel makes feedback of the current channel estimate insufficient. 2.5.1 Combined Adaptive Modulation (AM) and Selective Transmitter Diversity (STD) Scheme [15].
Figure 2.11: Driving configuration of AM+STD scheme From figure we can see an AM+STD scheme for two antennas. Here the received signal r(t) is given by, r(t)= αsc(t)s(t)+n(t) (2.13) Here s(t) is the transmitted signal and n(t) is white Gaussian noise, and α sc(t) = max(α1(t), α2(t)). Then the instantaneous SNR can be calculated as: γ=γ αsc2(t) Then we can identify the AM+STD scheme with a single transmission antenna system with the channel: gAM+STD(α1, α2)=max(α1, α2) (2.14) Now we can select the constellation size of AM+STD scheme based on max(α 1, α2). Let us analyze the performance of AM+STD. The pdf of the channel gAM+STD(α1, α2)=max(α1, α2) can derived as: fAM+STD(x)=
(1
)
(2.15)
Here σ2 is the average power of the fading channels. Now the data rate performance of combined AM+STD scheme for ideal CSI is given by: RAM+STD =
2
Mi
AM+STD
(x)dx
(2.16)
We know according to modulation switching policy that the transmission will be interrupted when the fading gain α falls below the threshold α1. Thus AM+STD scheme suffers the outage probability, PoutAM+STD=
(x)dx= (1
)2
(2.17)
2.5.2 Combined Adaptive Modulation (AM) and Transmit Adaptive Array (TxAA) Scheme [15]:
Figure 2.12: Driving configuration of AM+TxAA From figure we can see the operation of the AM+TxAA for two transmitter antennas case. Here for each transmission antenna the signals are transmitted coherently with the same data and code for the TxAA scheme but with antennaspecific amplitude and phase weighting, say w 1 and w2 in the Figure2.12. These complex values w1 and w2 (array weights), are selected to maximize the received power at the mobile, and the same diversity gain as receiver diversity with MRC can be achieved. Now for the flat fading channel, the weights w1 and w2 are given as w1=c1*/
(2.18) w2=c2*/
(2.19)
Here normalization is necessary to maintain the total transmit power at a constant level. Given these weights, the received signal is: r(t) = s(t)
+ n(t)
(2.20)
Now the instantaneous SNR is γ=γ (α12(t)+ α12(t)). Then the AM+TxAA scheme is equivalent to a single transmission antenna system but with the channel: gAM+TxAA(α1, α2)= Now based on the
(2.21)
the constellation size can be selected. Now the equation (2.21) which is
the pdf of the channel can be derived as: fAM+TxAA(x)=(1/2 σ4)x3exp(x2/ 2σ2)
(2.22)
As in (2.16), the data rate performance of combined AM+TxAA scheme for ideal CSI is given by: RAM+TxAA=
2
Mi
AM+TxAA
(x)dx
Then the outage probability of AM+TxAA is
PoutAM+TxAA=
(x)=1

(2.24)
(2.23)
2.5.3 Adaptive SpaceTime Modulation (AM+STTD):
Figure 2.13: Driving configuration of AM+STTD The operation of the twobranch adaptive spacetime transmit diversity (AM+STTD) scheme [15] is shown in the Figure2.13. Here two signals are simultaneously transmitted from the two antennas, say antenna 1 and antenna 2 at a given signal period. The signal s1 is transmitted from antenna 1 and s2 is transmitted from antenna 2 during the first symbol interval. On the other hand, during the second symbol period, signal –s*2 is transmitted from antenna 1 and s *1 is transmitted antenna 2, where * represents the conjugate operation. Now the signal transmission matrix for STTD shown in Figure 2.13 is given by: s1 s2 –s*2 s*1 (2.25) Where in the equation (2.25) the encoding is done in both space and time, and it is an example of the spacetime coding method. Now we can express the received signal where we assume that fading is constant across two consecutive symbols. r1=r(t)=c1s1+c2s2+n1. r2= r(t+T)= c1s2*+ c2s1*+n2
(2.26) (2.27)
Here T is the symbol interval, r1 and r2 are the received signals at times t and t+T, and n1 and n2 are white Gaussian noise samples. The maximum likelihood detector is based on the variables ŝ1=c*1r1+c2r*2 (2.28) ŝ2=c*2r1c1r*2
(2.29)
Substituting (2.26) and (2.27) into (2.28) and (2.29) we get: ŝ1= (α12+ α22)s1+ c*1n1+ c2n2 ŝ2= (α12+ α22)s2c1n2*+ c2*n1
(2.30) (2.31)
Now we calculate the instantaneous SNR for the STTD scheme. If we denote the noise term n’= c*1n1+ c2n2. For symbol s1, and n”= c1n2* + c2*n1 for s2. Then variances of n’ and n” are given by: Var(n’) = Var(n”)= (α12+ α22)N0/2. (2.32)
Here we assume Var(n’) = Var(n”)= N0/2. In order to make a fair comparison of performance with AM+STD and AM+TxAA schemes, the total radiated power of STTD , sayE s, has to be same as for STD and TxAA. Thus, each antenna radiates half of the total power. E{s 12}=E{s22} =Es/2. Therefore, the instantaneous SNR is given by: γ(t)= Es/2(α12+ α22)2/N0(α12+ α22)= (Es/ N0) (α12+ α22)/2 =γ˜(α12+ α22)/2 (2.33) Thus, AM+STTD is equivalent to a single transmission antenna system with the channel: gAM+STTD(α1, α2) =[(α12+ α22)/2]0.5 (2.34) Therefore, the constellation size of AM+STTD scheme is selected based on [(α 12+ α22)/2]0.5. The pdf of the channel gAM+STTD(α1, α2) is fAM+STTD(x)=
x3exp( )
fTxAA(
(2.35)
The data rate performance of combined AM+STTD scheme for ideal CSI is given by: RAM+STTD=
2
Mi
AM+STTD
(x)dx
(2.36)
The probability of outage of AM+STTD PoutAM+STTD, is: PoutAM+STTD=
(x)=1

(2.37)
2.6 Calculation of Channel capacity Now we will discuss the capacity of Rayleigh fading channels under different adaptive transmission and diversity–combining techniques [9]. The different adaptive transmission policies are, Optimal simultaneous power and rate adaptation Constant power with optimal rate adaptation Channel inversion with fixed rate And different diversity–combining techniques are, No diversity Maximal ratio combining (MRC) diversity Selective combining (SC) diversity Some assumption are made to drive the channel capacity, •
We assume that the channel changes at a rate much slower than the data rate, so the channel remains constant over hundreds of symbol.
•
The variation in γ is sent back to the transmitter via an errorfree feedback path.
•
Time delay in feedback path is negligible.
The probability distribution function (PDF) of CNR (γ) of a Rayleigh fading channel is given by
In MRC diversity the individual signals from each branch be weighted by their signal voltage to noise power ratios then summed coherently. The PDF of the received CNR at the output of a perfect Mbranch MRC combiner is given by
SC diversity only processes one of the diversity branches. Specifically, the combiner chooses the branch with the highest CNR. The PDF of the received CNR at the output of an Mbranch SC combiner is given by
Using the binomial expansion it can be written as
Where 2.6.1 Optimal simultaneous power and rate adaptation The channel capacity of a fading channel with received CNR distribution and optimal power and rate adaptation
Where, of
is the optimal cutoff CNR level below which data transmission is suspended. The value
always lies in the interval [0,1].Now consider the following cases 1. No Diversity: Substituting (2.38) in (2.42) we have
As
, the channel capacity becomes,
And
so capacity
2. Maximal Ratio Combining (MRC): Substituting (2.39) in (2.42) we can have Channel capacity for MRC
3. Selective Combining(SC) : Substituting (2.41) in (2.42) we can have Channel capacity for MRC
2.6.2 Optimal rate adaptation with constant transmit power With optimal rate adaptation to channel fading with a constant transmit power, the channel capacity
1.
No Diversity: Substituting (2.38) in (2.47) we can have channel capacity
2.
Maximal Ratio Combining (MRC): Substituting (2.39) in (2.47), channel capacity
3. Selective Combining(SC) : Substituting (2.41) in (2.47), channel capacity
2.6.3 CHANNEL INVERSION WITH FIXED RATE The channel capacity with channel inversion technique is given by
1. No Diversity: Substituting (2.38) in (2.51) , channel capacity
2.
Maximal Ratio Combining (MRC): Substituting (2.39) in (2.51), channel capacity
3. Selective Combining(SC): Substituting (2.41) in (2.51), channel capacity
Comparison:
FIGURE 2.14: CHANNEL CAPACITY PER BANDWIDTH FOR A RALEIGH FADING CHANNEL VERSUS AVERAGE CARRIER TO NOISE RATIO FOR DIFFERENT POLICIES WITH MRC DIVERSITY [(A)M=1, ( B)M=2, ( C)M=4] •
For no diversity the optimal power and rate adaptation gives a small increase in capacity over just rate adaptation.
•
In case of MRC, as the number of combining branches increases, the capacity difference between optimal power and rate adaptation versus optimal rate adaptation alone becomes negligible for all values of CNR (γ).
•
SC provides less diversity gain then MRC for all policies.
2.7 Adaptive Prediction for Frequency Non –Selective Fast Fading Channel As we know that deep fades in signal power due to multipath radio propagation severely degrade the performance of mobile radio systems and impose high power requirements [18]. As the Channel changes rapidly, the transmitter and receiver are not generally optimized for current channel conditions, and thus fail to exploit the full potential of the wireless channel. Propagation studies in a variety of environments show that the multipath signal consists primarily of a small number of discrete sinusoidal components. Here we described the prediction algorithm which characterizes the channel as an autoregressive model (AR) with slow sampling rate. We provide the insight into the performance gains of this prediction technique relative to the traditional approach. We augment the algorithm with an adaptive method which reduces error propagation and tracks channel parameter
variations. Finally, performance gains made possible by channel prediction are illustrated by analyzing the channel inversion with threshold method. 2.7.1 Prediction of the flat fading channel Here, we concentrate on flat fading signals which result from interference between several coherent scattered components [1819]. The received signal is given by
(2.55) Where (for the nth scatter) An is the amplitude, fn is the Doppler frequency, and φn is the phase. Due to multiple scatterers, the fading signal varies rapidly for large vehicle speeds and undergoes "deep fades". Our approach to prediction of future fading conditions is based on the fact that the parameters An ,fn and φn vary much slower than the actual fading coefficient c(t). The discretetime system model at the output of the matched filter [19] and sampler is given by yk=Ckbk+Zk (2.56) Where ck is the fading signal c(t) sampled at the symbol rate, b k is the data sequence, and zk is the discrete AWGN process. Here even for a modest number of scatterers, c(t) and c k can be accurately modeled as correlated complex Gaussian random processes with Rayleigh distributed amplitudes and uniform phases , where the accuracy increases as N in (2.55) grows. Our objective is to predict the future behavior of the fading coefficient c k. By prediction we imply estimating an entire future block of coefficients c k based on the observation of the received signal during an earlier time interval.
Figure 2.15: The theoretical autocorrelation function for the Rayleigh fading channel (solid line) and the experimental autocorrelation function for N=16 oscillators (dotted line). Linear prediction (LP) method is based on the AR channel modeling. We form the linear MMSE prediction of the future channel sample Ĉn based on p previous channel samples cn1……..cnp. Ĉ n=
cnj
(2.57)
Note that the samples have to be taken at least the Nyquist rate, which is twice the maximum Doppler frequency fdm. . The sampling rate we choose is close to this Nyquist rate . To date, most investigations
of fading channel modeling and estimation assume sampling at the data rate. As a result, even with very accurate coefficient adjustment, it is impossible to specify future channel coefficients from past observations the filter length is not long enough. This can be illustrated by considering the parameters involved in the MMSE prediction. The channel is modeled as the complex stationary Gaussian process with the autocorrelation function, r(τ)=J0(2Πfdm.τ) where J0 is the zeroorder Bessel function of the first kind. We consider the LP of order p, where the objective is to find the model coefficients d j , which minimize the MSE, E[e 2]=E[ckĈk] ; where ck is an arbitrary future fading coefficient. So the observations are taken prior to τ=0.
Ĉk=
cj
(2.58)
The minimum MSE is given by E[e2]=1
rk+j
(2.59)
Where rm=E[cn *cαn+m].When the future sample to be predicted is located further than a few bits from the observations, these autocorrelations become small, and the MSE (2.59) increases. If we try to predict the future coefficient about half a unit ahead this corresponds to the first zerocrossing of the autocorrelation function and is often defined in terms of the coherence time τ0 as approximately 2Πτ0), all these autocorrelations become negligible, and prediction becomes impossible. When some autocorrelations are low, the others are large, since they result from sampling large side lobes of the autocorrelation function (not accessible when the data rate is used). As a result, the MSE is much smaller. Thus, when the sampling rate is reduced greatly relative to the data rate, but the filter length p remains the same, prediction much further ahead becomes feasible.
(a)
(b) Figure 2.16: Prediction error reduction using adaptive prediction and tracking. Prediction error for the nineoscillator model during the prediction interval is shown. (a) Prediction error for noisefree channel. Dotted: predicted using past actual values; dashdotted: using previously predicted values. (b) Prediction error for the channel inversion method (threshold=0.1, snr=15dB). Dashdotted: predicted using noisy low rate samples; dotted: predicted with adaptation of a k only. The transmitter interrupts the transmission for the kth symbol if the power level  Ĉ k 2, is below previously chosen threshold value. Furthermore, if  Ĉ k 2 is above the threshold, the transmitter sends the data bits bk, by multiplying them with the inverse of the predicted Ĉk values (2.58). This power adjustment is not proposed as a practical solution, since it will result in large transmitter power fluctuations. It is considered here to access performance advantages of the proposed prediction technique. We are currently investigating efficient adaptive coding and modulation methods for transmitter optimization. 2.7.2 Adaptive prediction and tracking For adaptive prediction and tracking we make a table which gives the main factors that affect the prediction accuracy of the algorithm and its affects. Table 2.4: Factors affecting the prediction accuracy Main factor (a) Previously predicted values used to predict the future fading coefficients. (b) Limited number of observations used in initial acquisition of the LP coefficients. (c) Limited order p of the AR model. (d) Fixed LP coefficients d j used throughout the entire future prediction block. (e) Additive noise and decisiondirected tracking.
Affects of main factor Factor (a) Causes error propagation later in the prediction and often makes prediction accuracy unacceptable. Factors (bd) result in inaccurate channel modeling. Factor (d) causes parameter mismatch. Factor (e) result in poor prediction accuracy.
From the above observation, the new modified discretetime received signal [18] is given by: yk=akbk+zk (2.60) Where the prediction accuracy factor ak=ck/ Ĉk. When the prediction gets better, the value of a k approaches 1. Now the LMS adaptive algorithm to track the variation of the factor a k at the data rate at the receiver as: ãk+1=ãk+µekb^k (2.61) Here µ is the stepsize controlling the convergence rate, b^k is the decision of bk and error signal ek is defined as: ek=yk ỳk= yk ãkbk (2.62) Adaptive tracking of ak is beneficial when noise is nonnegligible and/or decisiondirected operation is desired. Since variation of a k is not significant, the convergence is better than for channels without inversion. The estimate ãk is used for coherent detection. In addition, the updated factor â n is sent back to transmitter at the low sampling rate and used to update previously predicted fading channel coefficient Ĉ n as, Č n=ãn Ĉn (2.63) When the estimates Čnj are used in (2.58) to predict future samples, the prediction accuracy is maintained even in the presence of additive noise as illustrated in Figure 2.16(b). The performance of the adaptive approach is almost the same as using actual noisefree values in the prediction. In practice, a greater prediction range might be desired, and previously predicted Ĉ nj might have to be used in (2.58) for a few recent samples, but this does not significantly increase the propagation error. In addition to the error propagation problem, short observation interval and the timevariant channel model also significantly affect the prediction accuracy. These factors are mainly reflected in the LP coefficients dj in (2.58). The LMS algorithm for updating model parameters is: d(n+1)=d(n)+ η.en.Čn (2.64) Where η is the stepsize d(n)=(d1(n),……..dp(n)) is the time dependent vector of channel model parameters. Čn=( Čn1………. Čnp) is the vector of updated channel estimates, and the error signal, en= Čn Ĉn (2.65) The improvement in prediction accuracy using joint adaptive tracking of a k;s and dj;s is illustrated in Figure 2.16 for the channel with parameter variation and high SNR.
(a)
(b) Figure 2.16: Comparison of prediction accuracy for the nine oscillator model with the incidence angle variation of 4.2째/s. (a) Solid: actual channel samples; dashdotted: predicted with adaptive tracking; dashed: predicted using actual past samples with fixed parameters d j; dotted: no adaptation. (b) Prediction error comparison. Solid: predicted using actual past samples with fixed parameters dj; dashdotted: predicted with adaptive tracking; dotted: no adaptation.
2.7.3 The MMSE prediction of the flat fading channel suing the AR model The objective of the longrange prediction is to forecast future values of the fading coefficient far ahead [8]. Consider the equivalent lowpass discretetime system model at the output of the matched filter and sampler given by:
Yk=ck bk + zk
(2.66)
Where ck is the flat fading signal sampled at the symbol rate, b k is the binary phase shift keying (BPSK) data sequence and zk is the complex discrete AWGN process with the variance N 0/2. Suppose a sequence of p previous samples of the fading signal is observed. The MMSE prediction of the future channel sample
based on p previous samples cn1 , … , cnp is given by (2.67)
Where p is the AR model order and the optimal coefficient d j are determined by the orthogonality principle as: d= R1 r
(2.68)
Where d = (d1, . . . dP )T, R is the autocorrelation matrix (p*p) with coefficients Rij =E cni cnj*  and r is the autocorrelation vector (px1) with the coefficients r j = E cn cnj* . The correlation coefficients Rij and rj can be estimated from the observation samples without the prior knowledge of the Maximum Doppler shift or the number of scatterers. The samples in equation (2.67) have to be taken at least at the Nyquuist rate given by twice the maximum Doppler frequency f dm . The predicted samples can be interpolated to forecast the fading signal at the data rate. To show that the lower rate sampling can result in more accurate long range prediction when the filter length p in (2.67) is fixed, we extended onestep prediction in (2.67) to general channel prediction problem as follows. The objective is to find the MMSE estimate of a future sample c ( τ ) ( τ > 0 ) by the observing p previous samples collected at and prior to time zero at the sampling rate fs = 1/Ts. the predicted value: (2.69) The interval �= v Ts , is called the prediction range where ν can be any positive real number. The LP filter coefficients dj can be determined as in (2.68) by minimizing the MSE, E[ e(�)c^(�)2 ]. The resulting MMSE is given by: (2.70) Where the autocorrelation function r(t) =E c(s)c*(s+t) . For the Rayleigh fading channel r(t) = J0(2πfdmt) Where, J0 (.) is the zeroorder Bessel function of the first kind.
2.7.4 Utilization of long range prediction in adaptive modulation The BER gains can be achieved using adaptive modulation when LRP is employed. If we consider a fixed power modulation levelcontrolled scheme based on square MQAM signal constellations. The target BERtg=103. We will restrict the MQAM constellation to sizes M=0, 2, 4, 16, 64. In the design of an adaptive modulation system, one needs to take into account the accuracy of available CSI. If the modulation rule is designed for perfect CSI and there are CSI errors, the algorithm will not meet its target BER specifications. Now we need a statistical model for the CSI error of the MMSE channel
prediction that can aid the appropriate modulation level selection. This model produces the probability density function (p.d.f.) pβ(X) of the ratio β(t)=α(t)/ά(t), where α(t)=c(t) is the actual fading coefficient and ά(t) is its estimation. The design rule for the modulation level selection is as follows:
•
Given fixed transmitted power Es or the average received SNR per symbol is (We assume that E(α2(t))=1) This is required to maintain a target BER.
•
We need to adjust the modulation size M according to the instantaneous channel gain α(t).
•
In other words the adaptive modulation scheme can be specified by the threshold values α i , i=1, . . ., 4 defined as : When α(t) ≥ αi ,MiQAM is employed , where M1=2, Mi=22(i1), i>1. When perfect CSI α(t) is available these thresholds can be directly calculated from the BER bound of MQAM for an AWGN channel:
For M>2 and BER2= Q ((2γ)1/2)
where
is the instantaneous
received SNR. •
When the predicted CSI ά(t) is used the appropriate bound BER *M can be obtained by evaluating the expectation of BERM over β(t) using pβ(X).
•
The bound BER*M should be used to calculate thresholds instead of BER M when only the predicted CSI is available.
When this selection rule is applied to CSI obtained without the aid of long range prediction, the bit rate gains associated with adaptive modulation are significantly reduced for realistic mobile radio condition.
2.7.5 Performance analysis of the channel inversion with threshold algorithm In the bit error rate (BER) simulations, we assumed coherent detection and used Binary Phase Shift Keying (BPSK) modulation scheme [12].
Given binary signal bk and E(ck2) = 1, the signaltonoise (SNR) is γb=E(bk)2/N0 (2.71) Without transmitter precompensation, the channel is closely approximated by the Rayleigh fading channel with the BER, Pa=1/2(1( γb/1+ γb)0.5) (2.72) When channel inversion is applied, the power of the transmitted signal is multiplied by 1/ĉ k2. On the other hand, given the threshold ρ>0, the average transmitted power is, E(1/ĉ k21 /ĉk2 <1/ ρ =(1/ eρ )Γinc(0,ρ), where Γinc is the incomplete gamma function defined as Γinc(0,ρ) = ∫e1/x /xdx. By increasing the threshold from 0.1 to 0.6, we observe performance improvement. However, the throughput reduces with the increasing thresholds. The throughputs are calculated for a given ρ as Pr(ĉk2 >ρ)=∫ ey dy = e ρ and confirmed by the simulations. 1. The power of the transmitted signal b k/Ĉ is greater than E(b k2) for thresholds <0.4, the BERs for these threshold values are above the AWGN channel BER. 2. For the threshold=0.4, the transmitted power is equal to E(b k2), and the analytical curve in this case is also the BER of the AWGN channel Pa= Q( 2γb)0.5 , where the Q(x) = (1/2 ∏) ∫ exp(t2/2)dt.
(2.73)
3. Moreover, for thresholds greater than 0.4, the BER is lower than for the AWGN channel. This is due to the fact that for these thresholds the most favorable channel conditions are chosen for transmission, i.e., the data is sent only when the channel is strong.
Figure 2.17: Probability of bit error vs SNR for Rayleigh fading channel with no threshold and no compensation at the transmitter (o_o); channel inversion with prediction for thresholds 0.1 (**), 0.2 (++), 0.4 (oo) and 0.6 (xx). Channel inversion (thr. 0.1) for feedback without prediction (◊◊). CHAPTER 3
Comparative Study on Transmit Diversity Schemes 3.1 Theoretical Study on Transmit diversity schemes 3.1.1 TwoBranch Transmit Diversity with One Receiver (Previous study [20]): The Figure 3.1 shows the baseband representation of two branch transmit diversity scheme [20].
Figure 3.1: Twobranch transmit diversity scheme with one receiver.
Table 3.1: the encoding and transmission sequence for the twobranch transmit diversity scheme Antenna 0
Antenna 1
Time t
s0
s1
Time t+T
s1*
s0*
The channel at time t may be modeled by a complex multiplicative distortion h 0(t) for transmit antenna zero and h1(t) for transmit antenna one. Assuming that fading is constant across two consecutive symbols, we can write h0(t)= h0(t+T)= h0=α0ejθ0 h1(t)= h1(t+T)= h1=α1ejθ1 (3.1) Where T is the symbol duration. The received signals can then be expressed as r0=r(t)=h0s0+ h1s1+n0 r1`=r(t+T)= h0s1*+ h1s0*+n1 (3.2) Where r0 and r1 are the received signals at time t and t+T and n 0 and n1 are complex random variables representing receiver noise and interference. The Combining Scheme: The combiner shown in Figure3.1 builds the following two combined signals that are sent to the maximum likelihood detector: Ŝ0= h0*r0+ h1r1* Ŝ1= h1*r0 h0r1* (3.3) Substituting (3.1) and (3.2) into (3.1.3) we get,
Ŝ0= (α02+α12)s0+ h0*n0+ h1n1* Ŝ1= (α02+α12)s1 h0n1*+ h1*n0
(3.4)
``
3.1.2 TwoBranch Transmit Diversity with M Receivers (Previous study [20]): The Figure 3.2 shows the baseband representation of two branch transmit diversity with two Receivers scheme.
Figure 3.2: Twobranch transmit diversity scheme with two receivers.
Table 3.2: the definition of channels between the transmit and receive antennas. rx antenna 0
rx antenna 1
tx antenna 0
h0
h2
tx antenna 1
h1
h3
Table 3.3: the notation for the received signals at the two receive antennas rx antenna 0
rx antenna 1
time t
r0
r2
time t+T
r1
r3
Figure.3.2 shows the baseband representation of the new scheme with two transmits and two receive antennas. The encoding and transmission sequence of the information symbols for this configuration is identical to the case of a single receiver, shown in Table 1. Table 2 defines the channels between the transmit
and receive antennas, and Table 3 defines the notation for the received signal at the two receive antennas. Where, r0=h0s0+ h1s1+n0 r1`= h0s1*+ h1s0*+n1 r2=h2s0+ h3s1+n2 r3`= h2s1*+ h3s0*+n3 (3.5) n0, n1, n2 and n3 are complex random variables representing receiver thermal noise and interference. The combiner in Figure.3.2 builds the following two signals that are sent to the maximum likelihood detector: Ŝ0= h0*r0+ h1r1*+h2*r2+h3r3* Ŝ1= h1*r0 h0r1*+h3*r2h2r3* (3.6) Substituting the appropriate equations we have Ŝ0= (α02+α12+α22+α32)s0+ h0*n0+ h1n1*+h2*n2+h3n3* Ŝ1= (α02+α12+α22+α32)s1 h0n1*+ h1*n0h2n3*+h3*n2 (3.7)
Figure 3.3: The BER performance comparison of coherent BPSK with MRRC and twobranch transmit diversity in Rayleigh fading. 3.1.3 TwoBranch Transmit Diversity with Three Receivers (Present work): Here for twoBranch Transmit Diversity with three Receivers, we can write r0=h0s0+ h1s1+n0 r1`= h0s1*+ h1s0*+n1 r2=h2s0+ h3s1+n2 r3`= h2s1*+ h3s0*+n3 r4=h4s0+ h5s1+n4 r5`= h4s1*+ h5s0*+n5 (3.8) The combiner builds the following signals that are sent to the maximum likelihood detector: Ŝ0= h0*r0+ h1r1*+h2*r2+h3r3*+ h4*r4+h5r5* Ŝ1= h1*r0 h0r1*+h3*r2h2r3*+ h5*r4h4r5* (3.9)
Substituting the appropriate equations we have Ŝ0= h0*(h0s0+ h1s1+n0)+h1(h0s1*+ h1s0*+n1)*+h2*( h2s0+ h3s1+n2)+h3( h2s1*+ h5s1+n4)+h5(h4s1*+ h5s0*+n5)*
h3s0*+n3)*+ h4*(h4s0+
Ŝ0= (α02+α12+α22+α32+α42+α52)s0+ h0*n0+ h1n1*+h2*n2+h3n3*+ h4*n4+h5n5* Ŝ1= h1*(h0s0+ h1s1+n0) h0(h0s1*+ h1s0*+n1)*+h3*( h2s0+ h3s1+n2)h2(h2s1*+ h3s0*+n3)*+ h5*( h4s0+ h5s1+n4)h4(h4s1*+ h5s0*+n5)* Ŝ1= (α02+α12+α22+α32+α42+α52)s1 h0n1*+ h1*n0h2n3*+h3*n2h4n5*+h5*n4 Finally we have, Ŝ0= *
(α02+α12+α22+α32+α42+α52)s0+
h0*n0+
h1n1*+h2*n2+h3n3*+
*
h4 n4+h5n5
Ŝ1= (α02+α12+α22+α32+α42+α52)s1 h0n1*+ h1*n0h2n3*+h3*n2h4n5*+h5*n4 (3.10)
3.2 Study I (Effect of fading gains & average SNR on system performance) The following figures are Matlab simulated on the basis of three combined schemes with constellation size M=2.In Figure3.4 we set the value of α 1 and α2 at 10 db and 5 db respectively and vary the average SNR ( ) from 5 to 20 db. In Figure3.5 set the value of α 1 and α2 at 10 db and 1 db respectively and vary the average SNR ( ) from 5 to 20 db. In Figure3.6 set the value of α 1 and α2 at 10 db and 2 db respectively and vary the average SNR ( ) from 5 to 20 db. In Figure3.7 set the value of α1 and α2 at 10 db and 10 db respectively and vary the average SNR ( ) from 5 to 20 db. In Figure3.8 set the value of α1 and α2 at 10 db and 15 db respectively and vary the average SNR ( ) from 5 to 20 db. In Figure3.9 set the value of α 1 and α2 at 10 db and 20 db respectively and vary the average SNR ( ) from 5 to 20 db. In Figure3.10 set the value of α 1 and α2 at 10 db and 5 db respectively and vary the average SNR ( ) from 1 to 5 db. In Figure3.11 set the value of α 1 and α2 at
10 db and 5 db respectively and vary the average SNR ( ) from 20 to 40 db. In Figure3.12 set the value of α1 and α2 at 10 db and 1 db respectively and vary the average SNR ( ) from 1 to 5 db. In Figure3.13 set the value of α1 and α2 at 10 db and 1 db respectively and vary the average SNR ( ) from 20 to 40 db. In Figure3.14 set the value of α 1 and α2 at 10 db and 2 db respectively and vary the average SNR ( ) from 1 to 5 db. In Figure3.15 set the value of α 1 and α2 at 10 db and 2 db respectively and vary the average SNR ( ) from 20 to 40 db. In Figure3.16 set the value of α 1 and α2 at 10 db and 10 db respectively and vary the average SNR ( ) from 1 to 5 db. In Figure3.17 set the value of α1 and α2 at 10 db and 10 db respectively and vary the average SNR ( ) from 20 to 40 db. In Figure3.18 set the value of α1 and α2 at 10 db and 15 db respectively and vary the average SNR ( ) from 1 to 5 db. In Figure3.19 set the value of α 1 and α2 at 10 db and 15 db respectively and vary the average SNR ( ) from 20 to 40 db. In Figure3.20 set the value of α 1 and α2 at 10 db and 20 db respectively and vary the average SNR ( ) from 1 to 5 db. In Figure3.21 set the value of α 1 and α2 at 10 db and 20 db respectively and vary the average SNR ( ) from 20 to 40 db.
Figure 3.4: BER performance when α1 and α2 are fixed at 10 dB and 5 dB
Figure 3.5: BER performance when α1=10 dB and α2=1 dB
Figure 3.6: BER performance when α1=10 dB and α2=2 dB
Figure 3.7: BER performance when α1=10 dB and α2=10 dB
Figure 3.8: BER performance when α1=10 dB and α2=15 dB
Figure 3.9: BER performance when α1=10 dB and α2=20 dB
Figure 3.10: BER performance when α1=10 dB ,α2=5 dB and
=15 dB
Figure 3.11: BER performance when α1=10 dB ,α2=5 dB and
=2040 dB
Figure 3.12: BER performance when α1=10 dB ,α2=1 dB and
=15 dB
Figure 3.13: BER performance when α1=10 dB , α2=1 dB and
=2040 dB
Figure 3.14: BER performance when α1=10 dB , α2=2 dB and
=15 dB
Figure 3.15: BER performance when α1=10 dB ,α2=2 dB and
Figure 3.16: BER performance when α1=10 dB , α2=10 dB and
=2040 dB
=15 dB
Figure 3.17: BER performance when α1=10 dB , α2=10 dB and
=2040 dB
Figure 3.18: BER performance when α1=10 dB, α2=15 dB and
=15 db
Figure 3.19: BER performance when α1=10 dB , α2=15dB and
=2040 db
Figure 3.20: BER performance when α1=10 dB , α2=20 dB and
=15 db
Figure 3.21: BER performance when α1=10 dB , α2=20 dB and
=2040 db
Comments: Over here we vary the value of fading gain α 1 and α2 and average SNR power per channel. In Figure3.4 when we set the value of α1=10 and α2= 5 and
= 520, the BER of AM+TxAA is much better
than the AM+STD and AM+STTD. It is very important to observe that when we change the value of average SNR power but fixed the value of α1 and α2 the BER is better at the increment of the average SNR power. If we see the Figure3.10, Figure3.11 and Figure3.12, it’s clear that the BER is improved as the average SNR is increasing. At the same time if we fixed the average SNR but change fading gain, the BER performance is decreasing. If we see the Figure3.4, Figure3.5, Figure3.6 and Figure3.7, the performance the BER per channel is very poor for Figure3.4 for all three systems. In all cases the 2nd system is better than 1 st and 3rd one. In Figure3.20 and Figure3.21 we can see that the AM+TxAA and AM+STTD are aliened when α1=10 and α2= 20 and
= 2040. So it’s clear that
if the value of fading gain are much high then the change of AM+TxAA and AM+STTD is not considerable. 3.3 Study II (Effect of constellation size on system performance) The following figures are Matlab simulated on the basis of three combined scheme with constellation size M, varying from 4 to 64.In Figure3.22 set the value of α 1 and α2 at 10 db and 1 db respectively with constellation size M=4 and vary the average SNR ( ) from 5 to 20 db. In Figure3.23 set the value of α1 and α2 at 10 db and 2 db respectively with constellation size M=4 and vary the average SNR ( ) from 5 to 20 db. In Figure3.24 set the value of α 1 and α2 at 10 db and 5 db respectively with constellation size M=4 and vary the average SNR ( ) from 20 to 40 db. In Figure3.25 set the value of α1 and α2 at 10 db and 1 db respectively with constellation size M=16 and vary the average SNR ( ) from 5 to 20 db. In Figure3.26 set the value of α 1 and α2 at 10 db and 2 db respectively with constellation size M=16 and vary the average SNR ( ) from 5 to 20 db. In Figure3.27 set the
value of α1 and α2 at 10 db and 1 db respectively with constellation size M=16 and vary the average SNR ( ) from 20 to 40 db. In Figure3.28 set the value of α 1 and α2 at 10 db and 2 db respectively with constellation size M=16 and vary the average SNR ( ) from 20 to 40 db. In Figure3.29 set the value of α1 and α2 at 10 db and 1 db respectively with constellation size M=64 and vary the average SNR ( ) from 5 to 20 db. In Figure3.30 set the value of α 1 and α2 at 10 db and 2 db respectively with constellation size M=64 and vary the average SNR ( ) from 5 to 20 db.
Figure 3.22: Performance of BER when α1=10 dB, α2=1 dB, M=4 and
=520dB
Figure 3.23: Performance of BER when α1 = 10 dB, α2 = 2 dB, M = 4 and
= 5 – 20 dB
Figure 3.24: Performance of BER when α1 = 10 dB, α2 = 5 dB, M = 4 and
= 20 – 40 dB
Figure 3.25: Performance of BER when α1 = 10 dB, α2 = 1 dB, M = 16 and
= 5 – 20 dB
Figure 3.26: Performance of BER when α1 = 10 dB, α2 = 2 dB, M = 16 and
= 5 – 20 dB
Figure 3.27: Performance of BER when α1 = 10 dB α2 = 1 dB M = 16 and
= 20 – 40 dB
Figure 3.28: Performance of BER when α1 = 10 dB, α2 = 2 dB, M = 16 and
= 20 – 40 dB
Figure 3.29: Performance of BER when α1 = 10 dB, α2 = 1 dB, M = 64 and
= 5 20 dB
Figure 3.30: Performance of BER when α1 = 10 dB, α2 = 2 dB, M = 64 and
= 5 – 20 dB
Comments: In this section we use another technique. Here we change the constellation size and observe the effect of three system. If we set the value of M=4, and
= 2040 and increase fading gain then the
performance is becoming low. If see the Figure3.22, Figure 3.23 and Figure3.24, the BER is becoming very poor at the change of fading gain. But if we change the value of M=16 rather than 4, but keep the value of other parameter unchanged, the performance is increasing. But at the increment of fading gain, the performance is decreasing also. But it should be noted that if the constellation size is increased the performance also increased. Now see the Figure3.25 and Figure3.26, where we can see the performance by changing the constellation size M=16 rather than 4. In Figure3.27, the average SNR power is increased from 520 to 2040. In this case the performance is much better than any other changes before. So it’s clear that, if we change the constellation size or average SNR or decrease the fading gain, the performance of BER will be much better. 3.4 Study III (Effect of Rayleigh fading on system performance) The following figures are Matlab simulated on the basis of three combined schemes on account the Rayleigh fading. In Figure3.31 we set the value of α 1 and α2 at 10 db and 5 db respectively and vary the average SNR ( ) from 20 to 40 db. In Figure3.32 we set the value of α 1 and α2 at 10 db and 1 db respectively and vary the average SNR ( ) from 20 to 40 db. In Figure3.33 we set the value of α1 and α2 at 10 db and 2 db respectively and vary the average SNR ( ) from 20 to 40 db. In Figure3.31 we set the value of α1 and α2 at 10 db and 2 db respectively and vary the average SNR ( ) from 5 to 20 db.
Figure 3.31: BER performance When α1 =  10 dB, α2 = 5 dB and
= 2040 dB
Figure 3.32: BER performance When α1 =  10 dB, α2 = 1 dB and
= 2040 dB
Figure 3.33: BER performance When α1 =  10 dB, α2 = 2 dB and
= 2040 dB
Figure 3.34: BER performance When α1 =  10 dB, α2 = 2 dB and
= 520 dB
Comments: In this section we will observe the performance of relay fading. In Figure3.31, Figure3.32 and Figure3.33, the value of average SNR is set at 2040. Now at the change of the fading gain the performance of the BER is also changing. When fading gain is lower, then the performance of BER is better. But the increment of the fading gain the performance of BER is slowing down. But if we change the value of average SNR power and fixed all other parameter, the performance of BER also increased. APPENDIX Appendix A Explanation of Some Important Terms A.1 Channel Capacity The AWGN channel is represented by a series of outputs Yi at discrete time event index i. Yi is the sum of the input Xi and noise, Zi, where Zi is independent and identicallydistributed and drawn from a zeromean normal distribution with variance n (the noise). The Zi are further assumed to not be correlated with the Xi.
The capacity of the channel is infinite unless the noise n is nonzero, and the Xi are sufficiently constrained. The most common constraint on the input is the socalled "power" constraint, requiring that for a codeword (x1,x2,...,xn) transmitted through the channel, we have:
, Where P represents the maximum channel power. Therefore, the channel capacity for the powerconstrained channel is given by:
Where f(x) is the distribution of X. Expand I(X;Y), writing it in terms of the differential entropy:
But X and Z are independent, therefore:
Evaluating the differential entropy of a Gaussian gives:
Because X and Z are independent and their sum gives Y:
From this bound, we infer from a property of the differential entropy that
Therefore the channel capacity is given by the highest achievable bound on the mutual information:
Where I(X;Y) is maximized when:
Thus the channel capacity C for the AWGN channel is given by:
A.2 Phase noise Phase noise is the frequency domain representation of rapid, shortterm, random fluctuations in the phase of a waveform, caused by time domain instabilities ("jitter"). Generally speaking, radio frequency engineers speak of the phase noise of an oscillator, whereas digital system engineers work with the jitter of a clock. Historically there have been two conflicting yet widely used definitions for phase noise. The definition used by some authors defines phase noise to be the Power Spectral Density (PSD) of a signal's phase, the other one is based on the PSD of the signal itself [3]. Both definitions yield the same result at offset frequencies well removed from the carrier. At closein offsets however, characterization results strongly depends on the chosen definition. [4] Recently, the IEEE changed its official definition to fluctuations.
where Sφ is the (onesided) spectral density of a signal's phase
Consider the following noise free signal: v(t) = Acos(2πf0t). Phase noise is added to this signal by adding a stochastic process represented by φ to the signal as follows: v(t) = Acos(2πf0t + φ(t)). Phase noise is a type of cyclostationary noise and is closely related to jitter. A particularly important type of phase noise is that produced by oscillators. Phase noise (L(f)) is typically expressed in units of dBc/Hz. A.3 Intersymbol interference In telecommunication, intersymbol interference (ISI) [5] is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have similar effect as noise, thus making the communication less reliable. ISI is usually caused by multipath propagation or the inherent nonlinear frequency response of a channel causing
successive symbols to "blur" together. The presence of ISI in the system introduces errors in the decision device at the receiver output. Therefore, in the design of the transmitting and receiving filters, the objective is to minimize the effects of ISI, and thereby deliver the digital data to its destination with the smallest error rate possible. Ways to fight intersymbol interference include adaptive equalization and error correcting codes. A.4 Attenuation In physics, attenuation (in some contexts also called extinction) is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, Xrays are attenuated by lead, and light and sound are attenuated while passing through seawater. In electrical engineering and telecommunications, attenuation affects the propagation of waves and signals in electrical circuits, in optical fibers, as well as in air (radio waves). Attenuation coefficient Attenuation coefficients are used to quantify different media according to how strongly the transmitted ultrasound amplitude decreases as a function of frequency. The attenuation coefficient (Îą) can be used to determine total attenuation in dB in the medium using the following formula: Attenuation [dB] =Îą [dB/(Mz*cm)]* l[cm]* f[MHz] As this equation shows, besides the medium length and attenuation coefficient, attenuation is also linearly dependent on the frequency of the incident ultrasound beam. Attenuation in fiber optics, also known as transmission loss, is the reduction in intensity of the light beam (or signal) with respect to distance travelled through a transmission medium. Attenuation coefficients in fiber optics usually use units of dB/km through the medium due to the relatively high quality of transparency of modern optical transmission media. The medium is typically a fiber of silica glass that confines the incident light beam to the inside. Attenuation is an important factor limiting the transmission of a digital signal across large distances. Thus, much research has gone into both limiting the attenuation and maximizing the amplification of the optical signal. Empirical research has shown that attenuation in optical fiber is caused primarily by both scattering and absorption. Attenuation in fiber optics can be quantified using the following equation:
A.5 Group delay and phase delay All signal components are delayed when passing through a device such as an amplifier or a loudspeaker. The signal delay can be (and often is) different for different frequencies. The delay variation means that signals consisting of different frequency components suffer delay (or time) distortion. A small delay variation is usually not a problem, but larger delays can cause trouble such as poor fidelity and intersymbol interference. High speed modems use adaptive equalizers to compensate for group delay.
Group delay is a useful measure of time distortion, and is calculated by differentiating the insertion phase response of the DUT versus frequency. Another way to say this is that group delay is a measure of the slope of the transmission phase response. The linear portion of the phase response is converted to a constant value (representing the average signaltransit time) and deviations from linear phase are transformed into deviations from constant group delay. The variations in group delay cause signal distortion, just as deviations from linear phase cause distortion. Group delay is just another way to look at linear phase distortion. In LTI system theory, control theory, and in digital or analog signal processing, the relationship between the input signal,
, to output signal,
, of an LTI system is governed by:
Or, in the frequency domain,
Where
and
. Here
is the time domain impulse response of the LTI system and
Laplace transforms of
,
, and
, respectively.
LTI system and, as does the impulse response, the LTI system.
,
,
, are the
is called the transfer function of the
, fully defines the inputoutput characteristics of
When such a system is driven by a quasisinusoidal signal, (a sinusoid with a slowly changing amplitude envelope
, relative to the change of phase,
, of the sinusoid),
the output of such an LTI system is very well approximated as
if
and and , the group delay and phase delay respectively, are as shown below and potentially functions of Ď‰. In a linear phase system (with noninverting gain), both and are equal to the same constant delay of the system and the phase shift of the system increases linearly with frequency Ď‰. It can be shown that for an LTI system with transfer function H(s) that if such is driven by a complex sinusoid of unit amplitude,
the output is
where the phase shift
is
Additionally, it can be shown that the group delay, shift as
, and phase delay,
, are related to the phase
. In physics, and in particular in optics, the term group delay has the following meanings: 1. The rate of change of the total phase shift with respect to angular frequency,
through a device or transmission medium, where
is the total phase shift in radians, and
the angular frequency in radians per unit time, equal to if group delay is measured in seconds).
is
, where is the frequency (hertz
2. In an optical fiber, the transit time required for optical power, traveling at a given mode's group velocity, to travel a given distance. Note: For optical fiber dispersion measurement purposes, the quantity of interest is group delay per unit length, which is the reciprocal of the group velocity of a particular mode. The
measured group delay of a signal through an optical fiber exhibits a wavelength dependence due to the various dispersion mechanisms present in the fiber. It is often desirable for the group delay to be constant across all frequencies; otherwise there is temporal smearing of the signal. Because group delay is , as defined in (1), it therefore follows that a constant group delay can be achieved if the transfer function of the device or medium has a linear phase response (i.e., where the group delay is a constant). The degree of nonlinearity of the phase indicates the deviation of the group delay from a constant. Appendix B Matlab Codes
B.1 Matlab code for QPSK, 16QAM and 64QAM modulation schemes clc; clear all; close all; % QPSK: x_db=0:30; x=10.^(x_db/10); p=0.50.5*erf((x/2).^(0.5)); %16QAM: k=(x/10).^(0.5); q1=0.50.5*erf(k); q3=0.50.5*erf(3*k); p1=(1/4)*(q1+q3)+(1/2)*q1; %64QAM: k1=(x/42).^(0.5); e1=0.50.5*erf(k1); e3=0.50.5*erf(3*k1); e5=0.50.5*erf(5*k1); e7=0.50.5*erf(7*k1); e9=0.50.5*erf(9*k1); e11=0.50.5*erf(11*k1); e13=0.50.5*erf(13*k1); p2=(1/12)*(e1+e3+e5+e7)+(1/6)*e1+(1/6)*e3+(1/12)*e5+(1/12)*e7+(1/3)*e1+(1/4)*e3(1/4)*e5(1/6)*e7+(1/6)*e9+(1/12)*e11(1/12)*e13; semilogy(x_db,p,x_db,p1,x_db,p2); axis([0 30 10^6 10^0]) xlabel('SNR(db)'),ylabel('Probability of Bit Error') grid;
B.2 Matlab code for Effect of α1, α2 and
on BER
close all; clear all; clc; %a1_db=10 and a2_db=5 where gmb_db=520; a1_db=10; a2_db=5; A1=10^(a1_db/10); A2=10^(a2_db/10); alp1=A1^2; % for first technique. gmb_db=linspace(5,20,50); gmb=10.^(gmb_db/10); gm1=gmb*alp1; z1=sqrt(gm1.*2); BER1=qfunc(z1); semilogy(gmb_db,BER1,'ro') hold on alp2=(A1^2+A2^2); % for 2nd technique. gm2=gmb*alp2; z2=sqrt(gm2.*2); BER2=qfunc(z2); semilogy(gmb_db,BER2,'.b') hold on alp3=(A1^2+A2^2)/2; % for 3rd technique. gm3=gmb*alp3; z3=sqrt(gm3.*2); BER3=qfunc(z3); xlabel('average SNR per channel') ylabel('BER') title('when a1db and a2db both are fixed') semilogy(gmb_db,BER3,'ms') grid on legend('AM+STD','AM+TxAA','AM+STTD',3); hold on B.3 Matlab code for Effect of Constellation size on BER close all; clear all; clc; %a1_db=10 and a2_db=5 where gmb_db=520; M=16; a1_db=10; a2_db=2; A1=10^(a1_db/10); A2=10^(a2_db/10);
alp1=A1^2; % for first technique. gmb_db=linspace(5,20,50); gmb=10.^(gmb_db/10); gm1=gmb*alp1; %z1=sqrt(gm1.*2); BER1=0.2*exp(1.5*gm1/(M1)); semilogy(gmb_db,BER1,'ro') hold on alp2=(A1^2+A2^2); % for 2nd technique. gm2=gmb*alp2; %z2=sqrt(gm2.*2); BER2=0.2*exp(1.5*gm2/(M1)); semilogy(gmb_db,BER2,'.b') hold on alp3=(A1^2+A2^2)/2; % for 3rd technique. gm3=gmb*alp3; %z3=sqrt(gm3.*2); BER3=0.2*exp(1.5*gm3/(M1)); xlabel('average SNR per channel') ylabel('BER') title('when a1db and a2db both are fixed and M=64 ') semilogy(gmb_db,BER3,'ms') %axis([5 20 10^20 10^0]) grid on legend('AM+STD','AM+TxAA','AM+STTD',3); hold on B.4 Matlab code for Effect of Rayleigh fading on BER close all; clear all; clc; %a1_db=10 and a2_db=5 where gmb_db=520; a1_db=10; a2_db=20; A1=10^(a1_db/10); A2=10^(a2_db/10); alp1=A1^2; % for first technique. gmb_db=linspace(20,40,50); gmb=10.^(gmb_db/10); gm1=gmb*alp1; %z1=sqrt(gm1.*2); BER1=0.5.*(1sqrt(gm1./(1+gm1))); semilogy(gmb_db,BER1,'ro') hold on alp2=(A1^2+A2^2); % for 2nd technique. gm2=gmb*alp2; %z2=sqrt(gm2.*2); BER2=0.5.*(1sqrt(gm2./(1+gm2))); semilogy(gmb_db,BER2,'.b')
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