Performance Evaluation of Different QAM Techniques Using Matlab/Simulink full report

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).

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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:
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………………………………………………………………. 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.

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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.

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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

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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]

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 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 ]


Similarly for 64, 128, 256 QAM we get signal constellations as,

Figure 2.9:

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(a) 64-QAM (left)

(b) 128-QAM (right)

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Figure 2.10: 256-QAM

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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.

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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.

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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

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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.

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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

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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
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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
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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

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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)

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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

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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.

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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.

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