Like this document? Why not share!

- Modulation QAM sous MATLAB by omaymabelkadi 2362 views
- EEP306: Quadrature amplitude modula... by Umang Gupta 4460 views
- QAM Presentation by mogs22 1799 views
- ASK,FSK and M-PSK using Matlab by Amyra Ghazali ,Da... 22979 views
- What is 16 qam modulation by Fiber Optics For ... 4731 views
- Qam by karthiksunkesula 3121 views

4,654

Published on

Published in:
Education

No Downloads

Total Views

4,654

On Slideshare

0

From Embeds

0

Number of Embeds

0

Shares

0

Downloads

330

Comments

0

Likes

1

No embeds

No notes for slide

- 1. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK CHAPTER 1 INTRODUCTION With the fast development of modern communication techniques, the demand for reliable high date rate transmission is increased significantly, which stimulate much interest in modulation techniques. Different modulation techniques allow you to send different bits per symbol and thus achieve different throughputs or efficiencies. QAM is one of widely used modulation techniques because of its efficiency in power and bandwidth. In QAM system, two amplitude-modulated (AM) signals are combined into a single channel, thereby doubling the effective bandwidth. The QAM is one of the adaptive modulation techniques that are commonly used for wireless communications. Different order modulations allow sending more bits per symbol and thus achieving higher throughputs or better spectral efficiencies. When using a modulation technique such as 64-QAM, better signal-to-noise ratios (SNRs) are needed to overcome any interference and maintain a certain bit error ratio (BER) [1]. Generally, as the transmission range increases, a step down to lower modulations would be required (e.g. Binary Phase Shift Keying "BPSK"). But, for closer distances higher order modulations like the QAM could be utilized for higher throughput. Additionally, the adaptive modulation techniques allow the communication systems to overcome fading and other interferences. Digital formats of QAM are often referred to as "Quantized QAM" and they are being increasingly used for data communications often within radio communications systems. This project aims at developing a Simulink model to simulate different types of QAM modulation/demodulation techniques at different bit rates of (8, 16, 32, 64, 128, and 256 bits) using Matlab/Simulink Communication System Toolbox. Also, the BERTool under Matlab is used to evaluate the performance of each QAM technique through plotting the Bit Error Rate (BER) vs. the ratio of bit energy to noise power spectral density (Eb/No). Dept. of E&C, BIT Page 1
- 2. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK CHAPTER 2 QUADRATURE AMPLITUDE MODULATION Quadrature amplitude modulation, QAM may exist in what may be termed either analog or digital format. The analog versions of QAM are typically used to allow multiple analog signals to be carried on a single carrier. For example it is used in PAL and NTSC television systems, where the different channels provided by QAM enable it to carry the components of chroma or colour information. In radio applications a system known as CQUAM is used for AM stereo radio. Here the different channels enable the two channels required for stereo to be carried on the single carrier. Digital formats of QAM are often referred to as "Quantized QAM" and they are being increasingly used for data communications often within radio communications systems. Radio communications systems ranging from cellular technology through wireless systems including WiMAX, and Wi-Fi 802.11 use a variety of forms of QAM, and the use of QAM will only increase within the field of radio communications. The QAM modulation scheme encodes data by varying both amplitude and phase of the carrier signal. Thus, it is sometimes viewed as a combination of ASK and PSK modulation. A more fundamental way of viewing QAM thought is that it encodes data by varying the amplitude of two carrier signals that are In-Quadrature (phase difference of 90). Therefore it is named as “Quadrature - amplitude modulation”. 2.1 Design Equations and Calculations: Mathematically, M-ary QAM is described by, 𝑠 𝑚𝑛 𝑡 = 𝐴 𝑚 cos 2𝜋𝑓𝑐 𝑡 + 𝜃 𝑛 𝑚 = 1,2, … , 𝑀1 𝑛 = 1,2, … , 𝑀2 ..................................................Eq.2.1 The combined amplitude and phase modulation results in the simultaneous transmission of log M M bits/symbol. 2 1 2 Quadrature amplitude modulation is a modulation scheme that creates a modulation signal from a binary bit stream. The binary data is broken up into bit sets. Each bit set is represented on a constellation. The position of the point on the constellation representing the bit set is mapped to In-phase and Quadrature components using the complex envelope. The complex envelope can be expressed as: Dept. of E&C, BIT Page 2
- 3. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK ………………………………………………………………. Eq. 2.2 In Equation 2.2, x (t) represents the in-phase and y (t) represents the Quadrature component. Since the QAM in the software was at baseband frequencies, mixing of the in-phase and Quadrature parts of the QAM symbol were not needed. However, for transmission of a QAM symbol it must be mixed to higher frequencies for transmission, and can be represented as: ………………………………………… Eq. 2.3 Using the complex envelope notation in Equation 2.2, a four level QAM constellation was used (Figure 2.1) to represent the combinational pairs of binary values. Figure 2.1: 4 Level QAM Constellations For example, the QAM Constellation in Figure 2.1 would map the bits “10” to the symbol “1-j”. The constellation diagrams show the different positions for the states within different forms of QAM, Quadrature amplitude modulation. As the order of the modulation increases, the number of points on the QAM constellation diagram. Let‟s look at the time‐domain representation of QAM signals. Taking 4‐QAM as an example, suppose we wish to transmit the bit stream 100111, we map these to 4 QAM symbols representing 10, 01 and 11. Dept. of E&C, BIT Page 3
- 4. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK Figure 2.2: 4 and 8 Level QAM Constellations Figure 2.3: Phase and amplitude csccccccccccccccccccccccccccccccccccccccccccccccc transitions of the carrier signal Figure 2.4: 8-QAM signal (2 amplitudes and 4 phases) The constellation plot in this Figure 2.3 shows the phase and amplitude transitions of the carrier signal. The raw IQ data is represented by the red trance with the white dots representing those samples of IQ data that occur on symbol clock periods and that are mapped back to digital bit patterns based on the 4‐QAM symbol map. We note that the transitions go through the origin. This causes abrupt amplitude variations between consecutive symbols and causes noise to be injected in the transmitted symbol due to the amplifier turning off and back on abruptly. Dept. of E&C, BIT Page 4
- 5. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK 2.2 Signal Constellations for QAM: For a I*J rectangular QAM constellation, ............................................................................................................Eq. 2.4 Where ……………………………………………….Eq. 2.5 …………………………………………….…Eq. 2.6 If 2d is the Euclidean distance between two adjacent signal points. Denoting Eb as the bit energy, d can be written in terms of Eb, I and J as, ………………………………………………………Eq. 2.7 For the case of M-ary square QAM (2.7) becomes, ……………………………………………………………...Eq. 2.8 Figure 2.5: Square 16-QAM constellation with Gray encoding Dept. of E&C, BIT Page 5
- 6. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK Signal constellations of QAM at different bitrates using equations (2.7) and (2.8) with Eb=1watt is as following: 8-QAM: (I=4*J=2) [-2.13-.71i -2.13+.71i -.71-.71i -.71+.71i 2.13-.71i 2.13+.71i .71-.71i .71+.71i] Figure 2.6: 8-QAM constellation 16-QAM: (M=4) [-1.89-1.89i -1.89-.63i -1.89+.63i -1.89+1.89i -.63-1.89i -.63-.63i -.63+.63i -.63+1.89i 1.89-1.89i 1.89-.63i 1.89+.63i 1.89+1.89i .63-1.89i .63-.63i .63+.63i .63+1.89i] Figure 2.7: 16-QAM constellation Dept. of E&C, BIT Page 6
- 7. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK 32-QAM: (I=8*J=4) [-3.08-1.32i -3.08-.44i -3.08+.44i -3.08+1.32i -2.2-1.32i -2.2-.44i -2.2+.44i -2.2+1.32i -1.32-1.32i -1.32-.44i -1.32+.44i -1.32+1.32i -.44-1.32i -.44-.44i -.44+.44i -.44+1.32i 3.08-1.32i 3.08-.44i 3.08+.44i 3.08+1.32i 2.2-1.32i 2.2-.44i 2.2+.44i 2.2+1.32i 1.321.32i 1.32-.44i 1.32+.44i 1.32+1.32i .44-1.32i .44-.44i .44+.44i .44+1.32i ] Figure 2.8: 32-QAM constellation Similarly for 64, 128, 256 QAM we get signal constellations as, Figure 2.9: Dept. of E&C, BIT (a) 64-QAM (left) (b) 128-QAM (right) Page 7
- 8. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK Figure 2.10: 256-QAM Dept. of E&C, BIT Page 8
- 9. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK CHAPTER 3 METHODOLOGY AND IMPLIMENTATION Figure 3.1: General QAM modulation/demodulation Simulink model The model is built using a random signal generator that feeds into the QAM modulation module for transmission. In addition, an Additive White Gaussian Noise (AWGN) channel is introduced into the transmitted signal. The added noise is calculated based on the input ratio of bit energy to noise power spectral density (Eb/N0) in decibel to this AWGN module. The relation between the signal energy and bit energy is given by the equation: …………………………….……….Eq. 3.1 Where, Es = Signal energy (Joules). Eb = Bit energy (Joules). No = Noise power spectral density (Watts/Hz). “k” is the number of information bits per input symbol. Then, the signal is getting demodulated by the corresponding demodulation QAM module and the recovered signal is used as an input to calculate the Error Rate for the transmission process. Dept. of E&C, BIT Page 9
- 10. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK 3.1 Random Integer Generator: The Random Integer Generator block generates uniformly distributed random integers in the range [0, M-1], where M is the M-ary number defined in the dialog box. The M-ary number can be either a scalar or a vector. If it is a scalar, then all output random variables are independent and identically distributed. If the M-ary number is a vector, then its length must equal the length of the Initial seed; in this case each output has its own output range. M-ary number is the positive integer, or vector of positive integers, that indicates the range of output values. Figure 3.2: Parameter Setting for Random Integer 3.2 General QAM: The General QAM Modulator Baseband block modulates using Quadrature amplitude modulation. The output is a baseband representation of the modulated signal. The Signal constellation parameter defines the constellation by listing its points in a length-M vector of complex numbers. The input signal values must be integers between 0 and M-1. The block maps an input integer m to the (m+1)th value in the Signal constellation vector. This block accepts a scalar or column vector input signal. The General QAM Modulator Baseband block provides the capability to visualize a signal constellation from the block mask. This Constellation Visualization feature allows you to visualize a signal constellation for specific block parameters. Dept. of E&C, BIT Page 10
- 11. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK Figure 3.3: Parameter Setting for General QAM Modulator/Demodulator 3.3 AWGN: The term noise refers to unwanted electrical signals that are always present in electrical systems and the term additive means the noise is superimposed or added to the signal that tends to obscure or mask the signal where it will limit the receiver ability to make correct symbol decisions and limit the rate of information transmission. The transmitted waveform gets corrupted by noise „n‟, typically referred to an Additive White Gaussian Noise (AWGN), illustrated as Additive: As the noise gets „added‟ (and not multiplied) to the received signal, Probability distribution function p (z), where is the variance ………………………………………..Eq. 3.2 Thus, AWGN is the effect of thermal noise generated by thermal motion of electron in all dissipative electrical components i.e. resistors, wires and so on. 3.3.1 AWGN channel: The AWGN block adds white Gaussian noise to the input signal. The variance of the noise added per sample affecting the final error rate is given by equation: ………… Eq. 3.3 Dept. of E&C, BIT Page 11
- 12. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK Where, Signal Power is the actual power of the symbols. Symbol Period is the duration of a channel symbol, in seconds. Sample Time is the sampling time, in seconds. Es/No is the ratio of signal energy per symbol to noise power spectral density, in decibels. The relation between Es/No and Eb/No is given in equation (3.1). Figure 3.4: Parameter Setting for AWGN Channel 3.4 Error rate calculation: The Error Rate Calculation block compares the input data before the signal modulator as it is generated from the signal generator to the output of the demodulator on the receiving end. It calculates the error rate as a running statistic, by dividing the total number of unequal pairs of data elements by the total number of input data elements from one source. Then, the output error vector of this block is being used as the output to the Matlab workspace under the QAMBER as a variable name. Dept. of E&C, BIT Page 12
- 13. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK Figure 3.5: Parameter Setting for Error Rate Calculation 3.5 “To Workspace” block: The “To Workspace” block inputs a signal and writes the signal data to the MATLAB workspace. The block writes the data to an array or structure that has the name specified by the block's Variable name parameter. The Save format parameter determines the output format. Figure 3.6: (a) Parameter setting for “To Workspace” block (b) Matlab Workspace Dept. of E&C, BIT Page 13
- 14. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK 3.6 BER-Bit Error Rate: Bit error rate, BER is a key parameter that is used in assessing systems that transmit digital data from one location to another. Systems, for which bit error rate-BER is applicable, include radio data links as well as fibre optic data systems, Ethernet, or any system that transmits data over a network of some form where noise, interference, and phase jitter may cause degradation of the digital signal. Although there are some differences in the way these systems work and the way in which bit error rate is affected, the basics of bit error rate itself are still the same. When data is transmitted over a data link, there is a possibility of errors being introduced into the system. If errors are introduced into the data, then the integrity of the system may be compromised. As a result, it is necessary to assess the performance of the system, and bit error rate, BER, provides an ideal way in which this can be achieved. Unlike many other forms of assessment, bit error rate, BER assesses the full end to end performance of a system including the transmitter, receiver and the medium between the two. In this way, bit error rate, BER enables the actual performance of a system in operation to be tested, rather than testing the component parts and hoping that they will operate satisfactorily when in place. As the name implies, a bit error rate is defined as the rate at which errors occur in a transmission system. This can be directly translated into the number of errors that occur in a string of a stated number of bits. The definition of bit error rate can be translated into a simple formula: …………………Eq. 3.4 3.6.1 BER and Eb/No: Signal to noise ratios and Eb/No figures are parameters that are more associated with radio links and radio communications systems. In terms of this, the bit error rate, BER, can also be defined in terms of the probability of error or POE. The determine this, three other variables are used. They are the error function, erf, the energy in one bit, Eb, and the noise power spectral density (which is the noise power in a 1 Hz bandwidth), No. It should be noted that each different type of modulation has its own value for the error function. This is because each type of modulation performs differently in the presence of noise. In particular, higher order modulation schemes (e.g. 64-QAM, etc) that are able to Dept. of E&C, BIT Page 14
- 15. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK carry higher data rates are not as robust in the presence of noise. Lower order modulation formats (e.g. BPSK, QPSK, etc.) offer lower data rates but are more robust. The energy per bit, Eb, can be determined by dividing the carrier power by the bit rate and is a measure of energy with the dimensions of Joules. No is a power per Hertz and therefore this has the dimensions of power (joules per second) divided by seconds. Looking at the dimensions of the ratio Eb/No all the dimensions cancel out to give a dimensionless ratio. It is important to note that POE is proportional to Eb/No and is a form of signal to noise ratio. Bit error rate BER is a parameter which gives an excellent indication of the performance of a data link such as radio or fibre optic system. As one of the main parameters of interest in any data link is the number of errors that occur, the bit error rate is a key parameter. Knowledge of the BER also enables other features of the link such as the power and bandwidth, etc to be tailored to enable the required performance to be obtained. 3.6.2 BERTool: The BERTool invokes the simulation for Eb/No specified range (in this example it is 0 to 12 dB with a step change of 3), collects the BER data from the simulation, and creates a plot. Figure 5 shows the resulting plot of the error rates for the different QAM techniques used in this model using the Monte Carlo simulation of the BERTool. Also, the BERTool enables easily change of the Eb/No range and stopping criteria for the simulation. To invoke the BERTool, the command “BERTool” needs to be entered in main command window of Matlab. The main interface of the BERTool is shown in Figure 3.7. Figure 3.7: The main interface of the BERTool Dept. of E&C, BIT Page 15
- 16. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK CHAPTER 4 RESULTS AND DISCUSSIONS 4.1 BER of QAM at Different bitrates: The resulting bit error rate from the Monte Carlo simulation for the different QAM bit rates (8 to 256) have been exported to the Matlab workspace as a vector of error values for each bit rate versus the noise power spectral density (Eb/No) variations and then plotted as shown at Figure 4.1 in absolute values. The figure illustrates the fact that at higher transmission bit rates, the error in the received signal increases. Therefore, it becomes a tradeoff between the transmission speed and the accuracy of the transmitted data. The increase in the error or distortion in the received signal may add to the complexity of the receiver design in order to recover the original signal or information. Figure 4.1: Plots of the BER of the Simulated QAM techniques Dept. of E&C, BIT Page 16
- 17. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK 4.2 BER of 8-QAM at different levels of (Eb/No): Figure 4.2 shows a comparison between the transmission errors in the received signal at different noise levels. Since Eb/No is defined as the ratio of bit energy per symbol to the noise power spectral density, in decibels, then increasing this ratio should result in less overall transmission error and decreasing this ratio should result in higher transmission error as shown in the figure. This illustrates how the model captures the variation of the signal power to the power of the applied noise during the transmission process. The results in Figure 4.2 illustrate that the more energy utilized for the transmitted bits and symbols compared to the superimposed noise component the less the transmission error. Theoretically, this could be considered as an option to improve the transmission quality but it also would contribute to higher cost on the transmitter end associated with the required higher energy levels. Figure 4.2: Plots of the BER of the Simulated 8-QAM at different levels of the noise power spectral density (Eb/No) Dept. of E&C, BIT Page 17
- 18. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK 4.3 BER of 8-QAM at different levels of the input signal power (SNR): Figure 4.3 shows the impact of changing the power of the transmitted signal on the generated Noise Variance by the AWGN block. Equation (3.2) shows the proportional relation between the signal power and the noise variance. The power of the input signal is referenced to 1 ohm and is given in Watts in this model. The simulation illustrates that as the power of the transmitted signal increases, the error rate increases too according to the relation in Equation (3.2) which is implemented in the AWGN block. Figure 4.3: Plots of the BER of the Simulated 8-QAM at different levels of the input signal power Dept. of E&C, BIT Page 18
- 19. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK CHAPTER 5 CONCLUSION Many research papers have studied the different modulation techniques. The theory of M-ary QAM and the details of a simulation model have been provided in [1] and [3]. This model was used to evaluate the QAM system for adaptive modulation. In [4], a Simulink based simulation system was implemented using Additive White Gaussian Noise channel (AWGN) to study the performance analysis of Bit Error rate (BER) vs. Signal to Noise ratio (SNR). An Orthogonal Frequency Division Multiplexing (OFDM) system design was proposed in [5] simulated using the Simulink. The digital modulation schemes such as MPSK (M-ary Phase Shift Keying) and M-QAM (M-ary Quadrature Amplitude Modulation), which provide way of parallel transmission, were also compared to analyze the BER performance of designed OFDM system [5]. Different modulation techniques allow transmitting different bits per symbol and thus achieving different throughputs or efficiencies. QAM is a widely used modulation technique as it provides high efficiency in power and bandwidth. In QAM technique, two amplitude-modulated signals are combined into a single channel and then transmitted at different bit rates which are multiples of 8 bits [1]. The project discusses a Matlab/Simulink model to simulate different QAM modulation techniques (8, 16, 32, 64 and 256). It demonstrates the utilization of the BERTool provided under the Matlab software package to implement a Monte-Carlo simulation approach in evaluating and comparing the performance of the different QAM techniques. A detailed step-by-step modeling approach is presented to develop the Simulink model. Analysis and simulation are conducted to evaluate the transmission performance from a transmission error perspective at different noise and input signal power levels. The results show that the higher the QAM bit rate, the higher the error could be which implies less transmission range/distance for higher bit rates techniques. Also, the simulation results illustrate the correlation between noise power spectral density and the BER of the transmitted data. Finally, the paper discusses the proportional relation between the power of the input signal and the noise variance implemented by the added white Gaussian noise component. It provides a way to simulate the performance of these communication techniques along with using the BERTool in performing the evaluation phase in this model. Dept. of E&C, BIT Page 19
- 20. PERFORMANCE EVALUATION OF DIFFERENT QAM TECHNIQUES USING MATLAB/SIMULINK REFERENCES [1] Sam, W. Ho, "Adaptive modulation (QPSK, QAM),” www.intel.com/netcomms/technologies/wimax/303788.pdf, December 30, 2007. [2] Xiaolong Li, “Simulink-based Simulation of Quadrature Amplitude Modulation (QAM) System”, Proceedings of the 2008 IAJC-IJME International Conference. [3] Md. Abdul Kader, Farid Ghani and R. Badlishah, “Development and Performance Evaluation of Hierarchical Quadrature Amplitude Modulation (HQAM) for Image Transmission over Wireless Channels”, Third International Conference on Communication, Networking & Broadcasting, 2011. [4] T.P. Surekha, T. Ananthapadmanabha, C. Puttamadappa, "Modeling and Performance Analysis of QAM-OFDM System with AWGN Channel", Circuits, Communications and System (PACCS), 2011 Third Pacific-Asia Conference. [5] Jigisha N. Patel, Upena D.Dalal, “A Comparative Performance Analysis of OFDM using MATLAB Simulation with M-PSK and M-QAM Mapping”, International Conference on Computational Intelligence and Multimedia Applications 2007. [6] “Exact BER Analysis of an Arbitrary Square/ Rectangular QAM for MRC Diversity with ICE in Non-identical Rayleigh Fading Channels” (2005 IEEE) by Laleh Najafizadeh, Chintha Tellambura. [7] Mathworks, Matlab and Simulink software package documentation. Dept. of E&C, BIT Page 20

Be the first to comment