Performance Evaluation of Different QAM
Techniques Using Matlab/Simulink
Tamer Youssef
Eman Abdelfattah
Department of Computer Science and Engineering
University of Bridgeport
Bridgeport, CT, USA
tyoussef@bridgeport.edu
Department of Computer Science and Engineering
University of Bridgeport
Bridgeport, CT, USA
eman@bridgeport.edu
Abstract— This paper presents a performance evaluation
approach using the BERTool module provided under
Matlab/Simulink software package. It compares different
Quadrature Amplitude Modulation (QAM) techniques at
different bit rates (8, 16, 32, 64, 128, and 256) based on the Bit
Error Rate (BER) versus the Ratio of Bit Energy to Noise
Power Spectral Density (Eb/No). The paper provides a detailed
model built in Simulink to simulate the QAM techniques along
with the results of the performance analysis. Analysis of the
impact of variations in the different model parameters on the
resulting error rate in the transmitted data has been conducted
as well. The motivation for this paper is to review, model, and
simulate the QAM technique at its various bit rates using the
Matlab/Simulink. Also, this paper serves an educational
purpose for researchers in the wireless communication field or
related topics by illustrating a step-by-step approach to build
the model and simulate the system using the Matlab/Simulink in
conjunction with the BERTool used for performance analysis to
evaluate different QAM wireless communication techniques.
The Monte Carlo simulation is utilized by the BERTool to
conduct the performance analysis. The resulting bit error rate
from the simulation at the different QAM transmission rates (8
to 256) showed the variation of the error values for each bit rate
versus different noise power spectral densities (Eb/No). Also, the
results show a comparison between the resulting transmission
errors in the received signal at different noise or Eb/No levels.
Since Eb/No is defined as the ratio of bit energy per symbol to
noise power spectral density, in decibels, then increasing this
ratio should result in less overall transmission errors and
decreasing this ratio should result in higher transmission error.
This illustrates how the model captures the variation of the
signal power to the power of the applied noise during the
transmission process. Also, the model simulates the impact of
changing the power of the transmitted signal on the generated
Noise Variance by the Additive White Gaussian Noise (AWGN)
generator. The simulation illustrates that as the power of the
transmitted signal increases, the error rate increases too as a
result of the logic implemented in the AWGN generator which
in turn increases the noise component imposed to the
transmitted signal.
Keywords— Modulation, QAM, Matlab, Simulink,
Performance, Evaluation
1
I. INTRODUCTION
Many digital modulation techniques are being used in the
communication systems today. These modulation techniques
are the basis of communications for systems like cable
modems, DSL modems, CDMA, 3G, Wi-Fi (IEEE 802.11)
and WiMAX (IEEE 802.16) [1]. One of these techniques is
the quadrature amplitude modulation (QAM) which is used to
increase the capacity and speed of a wireless network.
Generally, the modulation is the process by which a
carrier wave is able to carry the message or digital signal
(series of ones and zeroes). The three basic methods to
perform the modulation are amplitude, frequency and phase
shift keying [1]. Quadrature amplitude modulation (QAM)
has been widely used in adaptive modulation because of its
efficiency in power and bandwidth [2]. In the QAM scheme,
the two carrier waves, usually sinusoids, are 90° phase
shifted and are thus called quadrature carriers. The modulated
waves are summed, and the resulting waveform is a
combination of both phase-shift keying (PSK) and amplitudeshift keying (ASK).
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 M-PSK
(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 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. However, it must also be noted that 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.
Table 2: Parameter Setting for Random Integer
Parameter
M-ary number
Initial seed
Sample time
Frame-based output
Interpret Vector parameters as 1-
Table 3: Parameter Setting for AWGN Channel
Parameter
Initial see
Mode
BER
Eb·/No(dB)
Constant or variable
Input signal power
(watts)
Symbol period
1
Parameter
Receive delay
Computation delay
Computation mode
Output data
Variable name
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 (EblN0) in decibel to this
AWGN module. The relation between the signal energy and
bit energy is given by the equation (1):
EblNo + 10*loglO(k) in dB
Value
Any positive
integer
I/symbol rate
'Table 4: Parameter Setting for Error Rate Calculation
II. THE MODEL
=
M = 2J'l, n is an
integer
Anv positive integer
1/symbol rate
Unchecked
Unchecked
D
In this paper, a Simulink model has been developed 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 (EbINo).
EslNo
Value
Value
0
0
Entire frame
Workspace
Nameofa
variable
(1)
Where
Es
=
Signal energy (Joules)
Eb
=
Bit energy (Joules)
No
=
Noise power spectral density (Watts/Hz)
Simulink model [1]
k is the number of information bits per input symbol
Figure 2 shows the location of the used system blocks in
the model shown in Figure 1 as they appear under the
Simulink/Communication System Toolbox library.
Figure 1: General QAM modulation/demodulation
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.
Figure 1 shows the Simulink model described above. The
system parameters used as an input to this model's blocks are
given in Tables 1, 2, 3, and 4. These parameters and model
structure are designed based on the model developed by
Xiaolong Li [2].
Table 1: Parameter Setting for General QAM Modulator/Demodulator
Parameter
Signal constellation
Samples per symbol
'Value
Coordinates of signal points in constellation
diagram (row by row)
Figure 2-a: Random-Integer Generator
1
2
output is a baseband representation of the modulated signal.
The Signal constellation parameter in Table 1 defines the
constellation by listing its points in a length-M vector of
complex numbers. Then, the input signal values (integers
between 0 and M-1) are mapped to the (M+1) values in the
Signal constellation vector [6].
The AWGN Channel block adds white Gaussian noise to
the input signal.The General QAM Demodulator Baseband
block demodulates a signal that was modulated using
quadrature amplitude modulation. The Signal constellation
parameter in Table 1 defines the constellation by listing its
points in a length-M vector of complex numbers. The block
maps the M point in the Signal constellation vector to the
integer M-1 [6].
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 [1,
6]. Then, the output error vector of this block is being used as
an output to the Matlab workspace under the QAMBER as a
variable name. This variable is then used by the BERTool
which implements the Monte Carlo simulation technique to
generate and analyze the BER data. The tool simulates the
communication system to study its performance.
Figure 2-b: General QAM Modulator/Demodulator
Baseband
Figure 2-c: AWGN Channel
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 [4, 5]. 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 4.
Figure 2-d: Error Rate Calculation
In Figure 3, a representation of a 16-QAM constellation is
presented. Similar constellation diagrams are also developed
for the rest of modulation techniques used in this paper.
However, the 16-QAM was used for the illustration purpose.
Figure 3: 16-QAM constellation diagram
The Random Integer Generator block generates a
uniformly distributed random integers in the range [0, M-1],
where M is the M-array number defined in Table 2. In this
model, M is selected equal to the bit rate of the used QAM
technique (8, 16, or 32….etc.) [6].
Figure 4: The main interface of the BERTool
The General QAM Modulator Baseband block modulates
the input signal using quadrature amplitude modulation. The
3
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.
0
The results in Figure 7 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.
-2
10
QAM8
QAM16
QAM32
QAM64
QAM128
QAM256
-4
10
0
10
6
Eb/N0 (dB)
4
2
0
8
12
10
-1
10
Figure 5: Plots of the BER of the Simulated QAM
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 6 in
absolute values. Also, the Matlab/BERTool generates its own
plotting of the resulting error after the simulation is complete,
as shown in logarithmic scale plot of Figure 5. Both figures
illustrate 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.
BER
techniques
-3
0.8
Base Eb/No
(Eb/No)*2
(Eb/No)/2
-4
10
0
2
4
6
Eb/N0 (dB)
8
10
12
Figure 7: Plots of the BER of the Simulated QAM8 at
different levels of the noise power spectral density (Eb/No)
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 (2):
8-QAM
16-QAM
32-QAM
64-QAM
128-QAM
256-QAM
0.9
-2
10
10
1
0.7
𝑁𝑜𝑖𝑠𝑒 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =
0.6
ERROR
BER
10
0.5
Where
0.4
𝑆𝑖𝑔𝑛𝑎𝑙 𝑃𝑜𝑤𝑒𝑟 ∗ 𝑆𝑦𝑚𝑏𝑜𝑙 𝑃𝑒𝑟𝑖𝑜𝑑
𝑆𝑎𝑚𝑝𝑙𝑒 𝑇𝑖𝑚𝑒 ∗ 10
(𝐸𝑠/𝑁𝑜)
10
(2)
0.3
Signal Power is the actual power of the symbols.
0.2
Symbol Period is the duration of a channel symbol, in
0.1
seconds.
0
0
2
4
6
Eb/No
8
10
Sample Time is the sampling time, in seconds.
12
Es/No is the ratio of signal energy per symbol to noise
Figure 6: Error vs. the noise power spectral density
power spectral density, in decibels. The relation between
(Eb/No)
Es/No and Eb/No is given in equation (1).
Figure 7 shows a comparison between the transmission
error 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
Figure 8 shows the impact of changing the power of the
transmitted signal on the generated Noise Variance by the
AWGN block. Equation (2) shows the proportional relation
between the signal power and the noise variance. The power
4
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 (2) which
is implemented in the AWGN block.
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 PacificAsia 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] Mathworks, Matlab and Simulink software pakage documentation.
0
10
-2
10
BER
V. BIOGRAPHIES
-4
10
Tamer Youssef has received his BSEE and MSEE from
Ain Shams University at Cairo-Egypt in 2001 and 2007,
respectively. Currently, he is an IEEE
student member and a Ph.D. student at
the department of Computer Science
and Engineering at the University of
Bridgeport. He works as a lead
planning engineer at the United
Illuminating Company in Connecticut,
USA. He also works as an adjunct
instructor at the department of
Electrical and Computer Engineering at
the University of New Haven.
Input Signal Power, Referenced to 1 ohm = 1 Watt
Input Signal Power, Referenced to 1 ohm = 2 Watt
Input Signal Power, Referenced to 1 ohm = 0.5 Watt
-6
10
0
2
4
6
Eb/N0 (dB)
8
10
12
Figure 8: Plots of the BER of the Simulated QAM8 at
different levels of the input signal power
III. CONCLUSION
Eman Abdelfattah has received her
Ph.D. Degree in Computer Science and
Engineering, University of Bridgeport,
Fall 2011. Also, she has received her
M.Sc. Degree in Computer Science,
University of Bridgeport, May 2003.
She was awarded the “Academic Achievement Award” in
Computer Science, University of Bridgeport, School of
Engineering, May 2003. Currently, she is working as an
adjunct instructor in the department of Computer Science and
Engineering and the department of Mathematics at the
University of Bridgeport. Eman has research interests in
security, networking and communications.
This paper discusses a Matlab/Simulink model to simulate
different QAM modulation techniques (8, 16, 32, 64, 128,
256). It demonstrates the utilization of the BERTool provided
under the Matlab software package to implement a MonteCarlo simulation approach in evaluating and comparing the
performance of the different QAM techniques. A detailed
step-by-step modelling 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.
IV. 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
5