QAM and PSK Modulation Schemes under Impulsive Noise530269/FULLTEXT01.pdf · Ezequiel Pérez Rodenas QAM and PSK Modulation Schemes under Impulsive Noise iii Acknowledgements I am

FACULTY OF ENGINEERING AND SUSTAINABLE DEVELOPMENT .

QAM and PSK Modulation Schemes under Impulsive

Noise

Ezequiel Pérez Rodenas

April 2012

Master’s Thesis in Electronics

Master’s Program in Electronics/Telecommunications

Examiner: José Chilo

Supervisor: Javier Ferrer Coll

Ezequiel Pérez Rodenas QAM and PSK Modulation Schemes under Impulsive Noise

i

Abstract

Nowadays most of the communications systems are designed considering only to work under

AWGN (Additive White Gaussian Noise). But the implementation of wireless systems in industrial

facilities brings different kind of interference from machines or any other kind of electronic devices.

Some of them are sources of randomly and high power noise, which commonly is known as impulsive

noise. The objective in this thesis is to study the impact of the impulsive noise on a communication

using QAM (Quadrature Amplitude Modulation) and PSK (Phase-Shift Keying) schemes, by

observing the BER (Bit Error Rate) and the APD (Amplitude Probability Distribution). For that, it is

developed a measurement method that will be used in a real industrial environment in future work.

The content of this thesis is divided in two parts. In the first part is made a program in MATLAB to

simulate the communication through a noisy channel. Then is developed a measurement method which

is tested in three different ways corresponding to 3 different outputs of an spectrum analyzer, namely,

20,4 MHz IF output, video output and IQ data output.

The relation of impulsive noise is presented in the second part with different statistical properties in

the BER and the APD, in the setup with the best performance. At the end of the thesis a concluding

section summarizes the results obtained during the work and some lines of future work in a real

industrial environment with the developed method.


ii


iii

Acknowledgements

I am very grateful to my supervisor Javier Ferrer Coll for guiding and the knowledge he gave to me

to carry out this thesis, and the help I had in every problem or trouble it was presented both in the

thesis and during my stance here in Gävle. I would also give thanks to Efrain Zenteno, Per Landin and

Per Ängskog, for the help that they gave me during the development of the thesis.

Additionally, I also would like to express my thanks to Dr. Jose Chilo that gave me the opportunity

to come here to Sweden as Erasmus student to get this project.

Finally, gave thanks to my girlfriend and my family, including my mother, father and brother for all

the support they gave me during my period here.


iv


v

Table of contents

Abstract .................................................................................................................................................... i

Acknowledgements ................................................................................................................................ iii

Table of contents ..................................................................................................................................... v

1 Introduction ..................................................................................................................................... 1

1.1 Background ............................................................................................................................. 1

1.2 Thesis Objective ...................................................................................................................... 2

1.3 Thesis outline .......................................................................................................................... 2

2 Theory ............................................................................................................................................. 5

2.1 Introducction ........................................................................................................................... 5

2.2 Gaussian Noise ........................................................................................................................ 5

2.3 Impulsive Noise ....................................................................................................................... 5

2.3.1 Models ............................................................................................................................. 6

2.4 Amplitude probability distribution .......................................................................................... 8

2.5 Digital modulations ............................................................................................................... 10

2.5.1 Relation between APD and BER ................................................................................... 12

2.6 Minimum mean square error ................................................................................................. 12

3 Measurement Setups and Simulations ........................................................................................... 14

3.1 Introduction ........................................................................................................................... 14

3.2 Simulated communication system ......................................................................................... 15

3.3 Setups .................................................................................................................................... 15

3.3.1 Setup 1: 20.4 MHz IF Output ........................................................................................ 18

3.3.2 Setup 2: Video Output ................................................................................................... 20

3.3.3 Setup 3: IQ Data Output ................................................................................................ 21

3.3.4 Measurement setups comparison ................................................................................... 22

3.4 Effect of impulsive interference in M-QAM and M-PSK modulation schemes ................... 23

3.5 Interaction of multiple impulsive interference in 4-QAM and 64-QAM .............................. 24

3.6 Interaction of multiple impulsive interference in 16-PSK ..................................................... 25


vi

4 Discussion and Conclusions .......................................................................................................... 28

4.1 Future work ........................................................................................................................... 29

References ............................................................................................................................................... 1

Appendix A ............................................................................................................................................. 3


1

1 Introduction

1.1 Background

Man-made interference has become a real problem, particularly because of the limited available

bandwidth resources. As telecommunication systems rapidly grown, the interference among such

systems is becoming increasingly serious, especially on industrial environments. Measurement of

interfering signals is the initial and main step for realizing coexistence of these systems. Numerous

works have studied the impact of impulsive interference into multiple modulation schemes but they

have not performed real measurements [1]. The main objective in this thesis is to develop three

different measurement setups to test the performance of multiple modulation schemes under certain

interference. Two types of noise models are generally used to describe noise interference. These

models include the Gaussian noise and the non-Gaussian noise (impulsive noise).

Actual wireless systems are designed to work under certain signal to noise ratio, considering this

noise as Additive White Gaussian Noise (AWGN). However impulsive interferences have different

statistical properties than AWGN and consequently their impact into the communication system is

different too.The man-made environment, and much more of the natural one as well, is basically

impulsive, that can drastically degrade the performance of the systems that are usually assumed to

operate effectively against background noise.

The requirement to combat the interfering noise to improve the quality of any communication

system, requires to parameterize the interference noises in a statically way. For high quality

communications, is required a low BER that it is not always obtained, in some cases due to impulsive

noise. But we cannot fight only the impulsive noise, in order to get a realistic noise model it should be

a combination of the both noises, Gaussian and Non-Gaussian, where Middleton’s class A model is

the one that fits better with most of Non-Gaussian noises [2].

The main parameter of the Gaussian model is the average noise power across the channel. The

Gaussian probability density function and a constant power spectral density characterize this model. In

the other hand, impulsive noise is completely random and has an unpredictable power and cannot

know when it is going to occur. The only way to get statistical information about it is doing

measurements in a specific place and characterizing it [3].


2

1.2 Thesis Objective

The principal parts of the thesis will contain theory study of previous work, developing the

measurement system and test the impact of impulsive interferences into different modulations

schemes, specifically QAM and PSK modulations.

To implement those systems we will use MATLAB, and develop a program where it can be

simulated with diverse modulations and discuss about the different configurations and the impact on

the communications of that kind of noise.

First it will be studied the previous work, to get the knowledge enough to simulate a communication

system with AWGN and impulsive interference. Then, develop the different measurement setups

consisting in a Transmitter (with multiple modulations), a channel with both noises, AWGN and

impulsive, and a receiver. Finally we will measure and compute the BER and APD.

The acquisition of the data in the receiver will be perform in two different ways; acquiring the

captured data displayed in the spectrum analyser, or using an ADC module at a sampling rate of 400

Megasamples/s. These methods will be compared between them.

The project is centered on measuring the BER and ADP of a received signal, in a channel with

Gaussian and non-Gaussian noises. It started with a study of the impulsive noise, how it is made and

which parameters characterize it. For the measurement, and in order to see the difference between

capturing the data with the spectrum analyzer or with the ADC, we use a signal generator and, of

course, a spectrum analyzer and ADC, which are controlled by a computer.

It is implemented on MATLAB a program to create a random signal to modulate it, add the two

kinds of noises, simulating the impulsive channel, and demodulating it to compute BER and APD

results. It is made two programs, for each kind of modulations that are going to be tested, in this case

M-QAM and M-PSK. On each program, it will be simulated 3 different modulations; 4, 16 and 64 for

QAM and 2, 8 and 16 for PSK.

1.3 Thesis outline

The chapter 2 provides a theoretical background of Impulsive noise and its main parameters as well

as its differences with Gaussian noise. It contains to how to quantify and the different models of this


3

noise, and explains the three models of impulse noise. Moreover, it describes what APD is, how to get

it and how to use it. A brief description of used modulations, how they are obtained and how they

work.

Chapter 3 is about three measurement setups used, which are the main differences between them,

explains the devices that are used to carry out each configuration, how they are connected. Simulations

made with the three configurations are discussed together. The figures of the most interesting

simulations are shown in this chapter also.

Finally, on chapter 4 it is shown the conclusions of the results obtained on the previous chapter, and it

provides information about some futures researches.


4


5

2 Theory

2.1 Introducction

This chapter is going to provide the theoretical information needed to understand the thesis. First of

all is explained the 2 different noises used to simulate the channel we are testing out, gaussian and non

gaussian. As we are focusing on impusive noise (non gaussian), is explained the main parameters of

this noise, and the differences between the 3 kind of impulsive noise models, according to its

parameters. After that, is explained the APD, which is the way to quantify the impulsive noise, to

study it in a statistical way. Following a brief description of modulations schemes used, to explain the

relation of APD and BER for each modulation. The chapter ends with the explanation of the minimum

mean square error method, that will be used on next chapters to compare the different measurement

setups between them.

2.2 Gaussian Noise

Gaussian noise is defined as noise with some particular statistical properties. This noise has a

probability density function as a normal distribution, also known as Gaussian distribution. That means

that the power of the noise is Gaussian distributed. An specific case of this noise, and the noise we are

going to work with, is Additive White Gaussian noise, which besides of that, the values of the noise in

two different times are statistically independent and uncorrelated, what makes it appear broadband [4].

This kind of Gaussian noise does not represent a problem, while the power of the wanted signal is

higher than this noise.

2.3 Impulsive Noise

Impulsive noise, is non-stationary and is compounded by irregular pulses of short duration and

signifier energy spikes with random amplitude and spectral content, this is why impulsive noise is

considered the main cause of burst error occurrence in data transmission causing a temporary loss of

signal.

Therefore is essential to know the statistical nature of impulse noise in order to be able to evaluate

its impact on a communication system. These pulses are made by 2 main causes, ambient

electromagnetic interferences (storms), natural electromagnetic interference, or errors on

telecommunications systems, man-made.


6

The model of impulsive noise is a sequence of pulses characterized by three of those parameters: the

pulse amplitude, the time-duration of the pulse, and the time between consecutive pulses.

Figure 1. Impulsive noise and Gaussian noise power levels

An impulse noise filter can be used to enhance the quality of noisy signals, in order to achieve

robustness in pattern recognition and adaptive control systems. A classic filter used to remove impulse

noise is the median filter, at the expense of signal degradation. Thus it is quite common, in order to get

better performing impulse noise filters, to use model-based systems that know the properties of the

noise and source signal (in time or frequency), in order to remove only impulse obliterated samples.

That is why is needed to characterize the impulsive noise, and depending on some parameters it will

be classified in three different models [5].

2.3.1 Models

Different authors have proposed various statistical distributions, as Spaulding and Middleton that

have studied optimum reception of signals for the different models [2]. Gilbert characterized “shot

noise” as an amplitude distribution of pulses with the same shape occurring at random Poisson

distributed times. Middleton and Spaulding proposed a more complex model that also characterizes

the pulse duration and time between pulses. Middleton’s three models (class A, B and C) are statistical

physical models which include the non-Gaussian components of natural and man-made noise. These

models are canonical in nature i.e. their mathematical form is independent of the physical

environment. The distinction between the three models is based on the relative bandwidth of noise and

receiver.

Middleton Class A Model: Refers to impulsive noise with a spectrum that is narrow compared to the

receiver bandwidth and includes all pulses which do not produce transients in the receiver front end.

Its probability density function is [6, 7]:

0 1 2 3 4 5 6 7 8 9 10

x 104

-30

-29

-28

-27

-26

-25

-24

-23

Samples

Pow

er le

vel (

dBm

)

Impulsive noiseAWGN noise


7

�� = �� !�2��

��

Where m is the different impulsive sources, and �� is written as:

�� = � + Γ1 + Γ,

and is the noise variance, where A = vtTs is impulse index, vt is mean impulse rate and Ts is mean

impulse duration. Equation is a weighted sum of Gaussian distributions. By increasing impulse index,

A, the noise can be made arbitrarily close to Gaussian and by decreasing A it can be made arbitrarily

close to a conventional Poisson process. The model assumes that the individual impulses are Poisson

distributed in time [8].

Small values of A mean that the probability of pulses overlapping in time is small. Large values of A

mean that this probability is large. In the latter case the central limit theorem can be invoked resulting

in a distribution that tends to Gaussian. The scale factor Γ is the ratio of powers between the Gaussian

and Impulsive (non-Gaussian) components.

Γ = �� !��

Middleton Class B Model: Refers to impulsive noise with a spectrum that is greater than the

bandwidth of the receiving system. Class B noise impulses produce transients in the receiver.

Although it can accurately model a broadband impulsive noise environment its practical applications

are limited because of the complicated form of its APD which has five parameters and an empirically

determined inflection point [9].

Middleton Class C Model: Class C noise is a linear sum of class A and class B noise. In practice

class C noise can often be approximated by Class B [8, 9].


8

2.4 Amplitude probability distribution

Usually, all the communications are made to work under AWGN noise with good results, with

constant power spectral density. But, in many cases, as at industrials environments, there is no only

that kind of noise. It can be seen impulsive noise, and as it has statistical properties completely

different as AWGN, those systems get affected by the impulsive noise, because they are not adapted

for it.

APD was originally used to categorize electromagnetic interference (EMI), but recently it has

attracted attention as an EMI test method since it was found to have strong correlation with the bit

error probability (BEP) of a digital communication system subjected to the interference. Due to

atmospheric factors, each APD is specific for each geographic place, each year season, and even each

day. A change on frequency or bandwidth also means different APDs. It shows information about the

noise, where you can characterize the behavioral of a communications system. Every APD group

obtained under the same conditions got combined to get an average of the APD.

First of all, we will define the cumulative distribution function (CDF). This shows the probability for

random amplitude X does not exceed certain amplitude X0. The CDF is denoted as Fx(X0)

"#�� = $%&� < ��(

and its probability density function (PDF) is written as

�#�� = **�� "#��

However, the preferred model to describe noise is the envelopes around accumulative distribution of

noise in a limited band, known as Amplitude Probability of Distribution (APD). Is the complementary

cumulative distribution function, is a probabilistic function of field intensity, and portion of

measurement time on which the envelope noise gets higher than any other value of field intensity.

�$+�� = $%&� > ��( = 1 −"#��

The amplitude probability distribution is a very useful function when it comes to characterizing

signals and evaluating interference effects on transmissions, and there are many studies of the

advantages of the APD, especially for Impulsive noise [10, 1].


9

Similarly, the mathematics and terminology of the APD are based on the concept of random

variables, X, which assigns a real number, X (v), to every element, v, of a sample space. The random

variable assigns a real number representing the amplitude of a baseband signal drawn from a sample

space via signal simulation or measurement. The APD is expressed as:

"�.� = $��/� > .�

or more commonly:

"�.� = $�� > .�,

where a is an amplitude value and P ( ) means probability.

A discrete estimate of the APD can be obtained from a finite set of samples. This is accomplished by

sampling the complex-baseband signal N times, converting these samples to the amplitudes:

.�0�, 0 = 1,…2,

ordering the amplitudes from smallest to largest:

.&0(, 0 = 1,…2,

where the brackets distinguish the ordered amplitudes from the unordered amplitudes. For a X value

given, it counts how many amplitudes are above that level. A way to differentiate between Gaussian

noise and impulsive noise is by setting a threshold amplitude witch above it will be considered as

impulsive noise [11].

Figure 2. Impulse noise and its parameters

0 1 2 3 4 5 6 7 8 9 10

x 104

-30

-29

-28

-27

-26

-25

-24

-23

Samples

Pow

er le

vel (

dBm

)

Impulsive noiseAWGN noiseThreshold


10

Measuring the noise in a certain free bandwidth, and drawing a graphic about quantity of amplitudes

above this level and the amplitude of noise measured (in dB), you get an amplitude probability of

distribution:

Figure 3. APD

It can be used to know an optimal communication system and how it will be affected by the

surrounding noises.

2.5 Digital modulations

Two modulations schemes are used to test our system. For QAM (Quadrature Amplitude

Modulation) with 3 different constellations of 4, 16, and 64 symbols are studied. This modulation

consists on a change of amplitude or phase of the carrier to create the modulated message. And for

PSK (Phase-shift keying), conveys data by changing the phase of the carrier. Using another 3 different

constellations for this scheme of 2, 8 and 16 symbols, where each symbol contains log2 M bits, being

M the number of symbols.

All these modulations have been used with a Gray code. This code is used to refer to a binary

number where two successive values only differ in one bit. This code facilitates the error correction at

the receptor in digital communications.

-32 -30 -28 -26 -24 -22 -2010

-5

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

Impulsive NoiseGaussian Noise


11

Figure 4. Constellations for 2, 8 and 16 PSK with AWGN and impulsive noises

Figure 5. Constellations for 4, 16 and 64 QAM with AWGN and impulsive noises

Previous figures (figures 4 and 5) show constellations of the 2 different modulations, where it can be

appreciate the received symbols with AWGN noise (clusters) and impulsive noise (all over the

graphic). The probability of bit error for M-PSK modulation used is defined as:

$3 = 2log�789:2;32� log�7sin?�7@A and for M-QAM

$3 = 4log�78C:3EFGH log�77 − 1 I

being Q written as:

8�� = 1√2�K �� L��

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

Qu

ad

ratu

re

In-Phase-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

Qu

ad

ratu

re

In-Phase-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

Qu

ad

ratu

re

In-Phase

-4 -3 -2 -1 0 1 2 3 4-4

-3

-2

-1

0

1

2

3

4

Qu

ad

ratu

re

In-Phase-5 -4 -3 -2 -1 0 1 2 3 4 5

-5

-4

-3

-2

-1

0

1

2

3

4

5

Qu

ad

ratu

re

In-Phase-5 -4 -3 -2 -1 0 1 2 3 4 5

-5

-4

-3

-2

-1

0

1

2

3

4

5

Qu

ad

ratu

reIn-Phase


12

2.5.1 Relation between APD and BER

The information it is gotten from the APD of the received signal, it can be used to estimate the BER,

as it shows the degradation at the receiver. There are many studies [1] that show the strong correlation

between them, with various modulations. It is defined as:

$3,�M� ≈ O�$+9P:;3 Q�R3A

where α is the relation between Pr[bit error] and Pr[symbol error],β takes different values for each

modulation scheme, Eb is the average energy per bit, Z0 the impedance of the receiver and Tb is the bit

interval time [1]. Table 1 shows the relation between them for some modulations schemes.

Modulation β α Relation

2-PSK 1 1 $3,�M� = APDV�;3W 8-PSK 0.66 1/3 $3,�M� = 13APDV0.66�;3W

16-QAM 0.63 1/4 $3,�M� = 14APDV0.63�;3W 64-QAM 0.38 1/6 $3,�M� = 16APDV0.38�;3W

Table 1. Different modulation schemes and its relations

2.6 Minimum mean square error

To compare the measurement systems we are going to perform and explain on the next chapters, it is

going to be used the minimum mean square error, to get an idea of how different are between them.

Being X and unknown random variable and Y the known variable, a measurement, the estimator �\�]�of the measurement Y is given by 7^; = ; _V�\ − �W�`

where the expectation is taken over both X and Y. The MMSE estimator is defined just as the

estimator of the minimal MSE [12].


13


14

3 Measurement Setups and Simulations

3.1 Introduction

On this chapter we are going to give a detailed explanation of the different measurement setups we

are going to test, together with the results of the simulations for the setup that presents the best

performance. First, is going to be explained the program we use to test the measurement

configurations. Then, how is connected each setup and the differences between them. To continue

with the results of comparing the three setups, and end up with the simulations made with the setup

that presents the best performance.

We connect the devices with a MATLAB tool called Test & Measurement Tool (TMTool). At that

point, the program is set to send the signals through the signal generator and receive it from the

spectrum analyzer. Once we get that part working, we tried with the different measurement setups,

connecting the ADC on the computer and then feeding it with the video output from the spectrum

analyzer. Getting the signal measurement and then computing ADP. Same as for the IF output from

the SA, it is connected to the ADC input, to get measured signal with the ADC and then to the

computer to get BER and APD results. For the setup number 3, taken from the regular SA output (IQ

Data) BER and APD will be directly computed from its output, without the ADC.

For the last setup, we will use antennas to transmit and receive the signal instead of cables to see the

impact of different impulsive noises in our communication. The environment is shown at figure 6.BER

and APD are computed directly from the regular spectrum analyzer output, without the ADC.

Figure 6. Real setup measurement with antennas


15

3.2 Simulated communication system

In order to use the measurement system we proposed, it got developed a program in MATLAB. This

program, consist on create a random message, to modulate it and resample it 10 times for the better

sampling at the reception (spectrum analyzer) and send it through the noisy channel. In this channel, it

will be added AWGN and impulsive noise. After this, it will be received and downsampled to

demodulate it. Finally, BER and APD are computed with the received signal. A simple schematic of

the process is shown on figure 7. Hilbert block is only used on the IF output setup, to change the signal

to an equivalent lowpass signal.

3.3 Setups

It were developed 3 different systems using a signal generator and a spectrum analyzer connected to

a computer. The signal generator will be used from the computer with MATLAB, and it will make a

modulated signal with AWGN noise and impulsive noise, in order to test our measurement systems.

The created signal will be sent through our simulated channel with both noises, and received at our

receptor (Spectrum Analyzer). The spectrum as well as the signal generator (figure 8), are managed

from the computer, and it will receive the data to be analyzed with MATLAB, to compute BER and

APD measurement.

Rand msg Gray Mod Resample + Hilbert Downsample

Demod

BER

AWGN

Impulsive

noise

APD

Figure 7. Simulated communication in MATLAB


16

Figure 8. VSG SMU 200Ain the upside, and below the SA FSQ 26

To begin with the setups we will describe the devices used on each one. The signal generator used

on all of them, is a VSG (Vector Signal Generator) SMU 200A form Rohde &Schwarz will be the

transmitter which will be generating the modulated signal simulating an AWGN channel and an

impulsive channel with MATLAB.

Frequency

Frequency range 100 kHz to 2.2 GHz/3 GHz/4 GHz/6 GHz

Setting time 850 kHz


17

Wideband noise

(carrier offset > 5 MHz, 1 Hz measurement

bandwidth)

typ. -153 dBc (CW)

typ. -149 dBc (I/Q modulation)

Table 2. Vector signal generator specifications

This generator will be connected with an Ethernet cable to the computer and controlled from

MATLAB, through TCP/IP, sending a modulated signal at 2 GHz with 2 MHz of bandwidth. It will be

connected to the receiver, a SA (Spectrum Analyzer) FSQ 26, from Rohde & Schwarz also. In all the

measurement setups, this device will be the reference master; will send the reference clock to the

others.

Figure 9. Spectrum Analyzer before the digital treatment [14]

In figure 9 it is shown the signal processing before the digital treatment. There is a first mixer to

convert to an IF (intermediate frequency) of 3475.4 MHz. After that, 2 more mixer will change the

signal frequency, first to 404.4 MHz, and finally to 20.4 MHz. The SA has 2 signal outputs at those

two last Ifs (404.4 and 20.4).

This final IF signal, will feed the digital block. In this section, the signal passes the resolution

bandwidth filter (RBW). RBW filter determines how close two sinusoids can be resolved. The smaller

RBW has higher resolution, but higher acquisition time too. After it, there is an ADC (Analog to

Digital Converter) of 81.6 MHz of sampling rate with 14 bits resolution. It gets the baseband signal

getting the IQ data, and after a digital treatment it is sent through the LAN output to the computer.


18

Figure 10.Digital processing of the Spectrum Analyzer [14]

At the end of the digital processing (figure 10), there is a video output which contains the

information to display the received signal at the screen. This output will be used in one of the

measurement configurations.

Figure 11. Measurement system

All the devices will be connected to a HP Procurve 2626 Switch by TCP/IP through cables of

Ethernet. They were installed on the computer by using the Test & Measurement Tool (TMTool) of

MATLAB.

3.3.1 Setup 1: 20.4 MHz IF Output

With this setup, we get the signal from the IF output of 20.4 MHz, before all the digital treatment. In

order to get the data to the computer to get the BER and APD, we have to convert it into a digital data,


19

so it is used an ADC from Agilent, U1066A Acquiris, with 420 Megasamples/s and 12 bit resolution

with 2 channels. Table 3 shows its specifications.

Signal input - 50Ω BNC

Channels

U1066A-001: Dual at 420 MS/s

U1066A-002: Dual at 200 MS/s

Maximum input voltage

±15 V DC + 2 V RMS (AC component) at

50Ω

(diode clamping at 6 V AC pk-pk)

Bandwidth (-3dB)

DC to 100 MHz

Coupling

AC

Bandwdth limit filter

35 MHz 2-pole Bessel filter

Impedance

50 Ω ± 5%, AC coupled

Full sacle (FS)

250 mV, 500 mV, 1 V, 2 V, 5 V, 10 V

Connectors

SMA, gold plated

Offset range

±1 V for 250, 500 mV, 1 V FS

± 2 V for 2 V FS

± 5 V for 5 V FS

± 10 V for 10 V FS

Digital conversion

Sample rate

-001: 100 S/s to 420 MS/s

-002: 100 S/s to 200 MS/s

Maximum input voltage

± 10 V DC (2 W) or 10 V RMS at 50Ω

(Diode clamping at ± 11 V DC)

Sample rate adjustment granularity

-001: < 0.25% of SR; 500 kS/s in 200·420

MS/s range

-002: < 10% of SR

Coupling

DC into 50 Ω

Resolution

-001: 12 bits at SR > 200 MS/s.

13 bits at SR ≤ 200 MS/s

-002: 12 bits at SR > 110 MS/s.

13 bits at SR ≤ 110 MS/s

Impedance

50 Ω ± 1% at DC

Connectors

BNC, gold plated

DNL

In the range [-0.9, 0.5] LSB

Table 3. ADC specifications

This setup gives a bandpass signal at 20.4 MHz, so it will be needed to get the equivalent lowpass

signal before computing the BER and APD. An important thing is to remember to not to feed the ADC

with an input higher of 15V. Figure 11 shows how this setup is connected.


20

Figure 12. Capturing data with the ADC from IF output

3.3.2 Setup 2: Video Output

In this configuration it is used the Video output that the SA has at the end of the digital block, so it is

gotten the data that is going to be represented at the SA screen. This representation is only a level of

voltage, so the phase information is lost, what makes impossible to compute the BER.

This output, is connected to the ADC, as the previous configuration, controlling it with MATLAB,

computing the received signal at 400 Megasamples/s.

As it is show on the block diagram (figure 13), the signal from the analog block (figure 9) is affected

by the entire digital treatment (figure 10) and then pass through a lowpass filter called Video Filter,

placed after the detector. It is reducing the amount of fast variations of the signal reaching the display,

used in this way as an averaging facility or smoothing of the presented signal.

Figure 13. Block diagram of the Video Output


21

3.3.3 Setup 3: IQ Data Output

On this setup, it will be measured the BER and APD from the IQ data given by the SA, through its

regular output. To make it more realistic, it is used antennas to transmit the signal and for receive it.

The antennas used are Sencity Optima from Huber+Suhner. Those are omnidirectional with vertical

polarization and works on the range between 1.7 GHz and 3 GHz. On our setup, we use them at 2 GHz

and feeding them with powers between -30 and 15 dBm. On table 4 is shown the antennas

specifications, while figure 14 is the measurement setup scheme.

Table 4. Antennas specifications[15]

Figure 14. Measuring system with antennas

In this chapter is presented the graphics from the different simulations that were made. With the

systems explained before, and in order to get the BER and APD measurement, is simulated the noisy

channel and compared the received signal with the original one, checking the errors for different


22

energy bit to noise (Eb/N0) rate, and taking the ADP from the last Eb/N0 simulated (20 dB). The

MATLAB code uses a for bucle to generate the BER for different values of Eb/N0 and for diverse

QAM and PSK modulations schemes or parameters of impulsive noise, as we will see on this chapter.

The APD is computed as explained on previous chapter from the last value of Eb/N0 of the BER

simulated.

3.3.4 Measurement setups comparison

On the figure 15, it is made a comparison between 4-QAM (as well as for 64-QAM in figure 16)

with fixed Γ = 0.01 and A = 0.01 but with the 3 different configuration setups.

Figure 15. APD for 4-QAM with 3 different measurement systems

Figure 16. APD for 64-QAM with 3 different measurement systems

-50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

4-QAM IF4-QAM Video4-QAM SA

-60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

64-QAM IF64-QAM Video64-QAM SA


23

As we can see, IF output and SA output (referred to the IQ Data output as regular SA output) are

very close for both modulation schemes, it even fits for the slopes it does for the different power levels

of the 64-QAM. On the other hand, video output, does not show a good measurement, is suffering like

some filtering or average process. This process should be some extra treatment that the signal gets in

order to be presented to the spectrum analyzer display.

For the IF output, we used sequences of 104 bits, instead of 105 as for the other two setups, due to the

Hilbert transformation. The computer used to do this transformation, could not handle the computation

with bigger sequences, so that is because the graphic for IF is shorter than the other ones.

3.4 Effect of impulsive interference in M-QAM and M-PSK

modulation schemes

On figure 17, it can be seen the effect of the impulsive noise on BER curves. We can appreciate a

minimum BER level, because the impulsive noise is strong enough to still interfering even with high

values of Eb/N0.

Figure 17. Theoretical and simulated BER and APD for M-QAM

As for the APD on figure 17, can be seen the effect of impulsive noise also, and in the same way as

BER, so we can see the strong correlation that APD has with BER. On the same figure, another

important point to be observed is the differences between the QAM modulations. As APD shows

power level, for 4-QAM there is one power for its symbols, while for 16-QAM has 3 different, which

is why it has 3 little slopes around the received power of the signal. Same for 64-QAM, that has 7

levels of power for its symbols.

0 2 4 6 8 10 12 14 16 18 2010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

0 dB

BE

R

4-QAM Theory4-QAM16-QAM64-QAM

-40 -35 -30 -25 -20 -15 -1010

-5

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

4-QAM16-QAM64-QAM


24

Figure 22 on Appendix A show the same results for PSK modulations. Notice that now, the curves

on APD for different PSK modulations, are the same, which is because its symbols in the constellation

are disposed in the same way, they all have the same power level, as the only thing that changes is the

phase.

Varying A and Γ parameters of the impulsive noise, it can be seen how they affect to the BER and

APD results. As saw before, A is the quantity of samples affected by impulsive noise, while Γ is the

relation of AWGN power and impulsive noise power.

3.5 Interaction of multiple impulsive interference in 4-QAM and

64-QAM

Simulating for the third measurement system with antennas, and fixing Γ, and changing A, and vice

versa, it gets next results for BER and APD for different modulations.

Figure 18.BER and APD for 4-QAM with Γ = 0.1

At figure 18 can be seen how at high values of Eb/N0, the power of the signal gets greater than the

impulsive noise, so BER start to decrease. For both figures, we can see the difference between diverse

values of A

On figure 19, for the same QAM modulation, it is shown BER and APD for multiples Γ. For Γ = 10,

means that AWGN noise is 10 times bigger than Impulsive noise, so it is gotten the same result as the

4-QAM Theory, that is without Impulsive noise. For the APD, we can see how the received power

level gets increased as Γ is decreased due to received impulses.

0 5 10 15 20 2510

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

0 dB

BE

R

4-QAM TheoryA = 0.001A = 0.01A = 0.1

-50 -48 -46 -44 -42 -40 -38 -36 -35

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

A = 0.001A = 0.1A = 1


25

Figure 19. BER and APD for 4-QAM with A = 0.01

Same for the 64-QAM case, on figure 23 on Appendix A, changing A and fixing Γ. For this case, it

is important to notice the different power levels of the received symbols. As A gets increased, BER

gets increased too due to more samples are interfered with impulsive noise, and in the APD figure, the

power level of the received signal is near the same, but there are more amount of impulsive samples.

On figure 24, on Appendix A also, at BER curves, it can be seen that there is a maximum level of Γ

that does not increment the bit error rate. In the other hand, as we saw on figure 23, changing A, the

bigger A results in more erroneous bits. That does not happens on Γ, since A is not changed, and there

is always the same amount of impulsive samples that are received as errors, as soon as they are

received with more power than AWGN does not matter how much more.

3.6 Interaction of multiple impulsive interference in 16-PSK

The last simulation was made for the 16-PSK modulation. Both figures, 20 and 21 got the expected

results, while increasing A, more BER we get, but it will be the same if only Γ is varying.

Figure 20. BER and APD for 16-PSK with Γ= 0.1

0 5 10 15 20 25 30 35 40 45 5010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N0 dB

BE

R

4-QAM TheoryΓ = 10Γ = 0.1Γ = 0.01

-70 -65 -60 -55 -50 -45 -40 -35 -30

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

Γ = 10Γ = 0.1Γ = 0.01

0 2 4 6 8 10 12 14 16 18 2010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N0 dB

BE

R

16-PSK TheoryA = 0.001A = 0.01A = 0.1

-40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

A = 0.001A = 0.01A = 0.1


26

Is easy to know which parameter of the impulsive noise is changing by analysing APD figures. On

20, it can be seen how curves end up on the same power level, around 32 dBm (Impulsive noise),

which means that Γ is fixed, furthermore the only thing that changes is the quantity of samples with

high power, which means that A is varying. The other case at figure 21, on APD graphic, the quantity

of samples with high power are always the same (around 10-2), because A is fixed, and only Γ has

different values, what is translated into different power of those samples that are affected by the

impulsive noise.

Figure 21. BER and APD for 16-PSK with A = 0.01

0 2 4 6 8 10 12 14 16 18 2010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

0 dB

BE

R

16-PSK TheoryΓ = 10Γ = 0.1Γ = 0.01

-45 -40 -35 -30 -25 -20 -15

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

Γ = 10Γ = 0.1Γ = 0.01


27


28

4 Discussion and Conclusions

It is usual to see impulsive interference at industrial scenes. This electromagnetic interference on

most of cases is caused by surroundings electronic machines and cannot be eliminated. On those

scenarios, wireless communications are very important, and usually, high quality communications are

needed, what means low bit error rates. On this thesis, we have developed a measurement method to

obtain BER and APD values which was tested under an impulsive noise channel with different

modulation schemes. Simulating a communication system, we have studied how this noise can affect a

real communication.

Chapter 3 contains BER and APD simulations. Three different setups of the measurement method

are compared, with IF output, Video output (both with the external ADC) and directly from the regular

output of the SA, with its own ADC. First of all, from the simulations of the Video output, is clearly

that the results are not quite good. It can be seen that IF output curve (for 4 and 64 QAM) fits very

well with the curve taken from the regular SA output, not like the Video output curve, that is a bit

different.

As explained on same chapter, Video output is used to represent the values at the screen. This signal

could be modified for some treatment that we are missing, and that may be the reason that make us to

not to get the correct output. It is not known, even the exact blocks that this signal is going through.

Since we could not get the complete block composition of the SA from R&S, it was not possible to

detect which block is affecting the signal from the Video output. Comparing the other 2 methods left,

with the MMSE method explained on chapter 2, it is gotten an error of MMSE = 0.0092 (for the worst

case, shown in figure 18 for 64-QAM with fixed A and Γ to 0.01 both). That express the difference

between the 2 curves of APD, as the results shows, they are pretty close.

We assume that the APD curve gotten from the regular SA output, is closer to the real measurement

due to several reasons. One of them is because the SA has an internal treatment to equalize the path

that the signal follows inside of it, to cancel the variations that it suffers. Besides of that, the internal

ADC from the SA, has a bigger dynamic range thanks to having 14 bits resolution, instead of 12 bits

of the external ADC we are using for the IF output, even though this is not a main characteristic (the

ADC quality is given by some other factors too), it will help to improve its results.

Using the best measurement setup for our method, the IQ data output one, and varying the most

important parameters of the impulsive noise, A and Γ, is shown how it affects this kind of noise to the

BER and the power level at the receiver. As it was commented, as Γ increments, the communication is


29

not going worse while it has enough power to interference the desired signal. Samples with impulsive

noise will make an error in reception whenever its power is bigger than AWGN. From the simulations,

we can observe that with a Γ=10, which means AWGN 10 times higher than impulsive noise, the

result can be approximated to a regular AWGN as impulsive noise is not affecting the signal. With the

parameter A, we can see that as the bigger is it, the more errors we get. Having its maximum around

10, where it can be approximated as AWGN with higher power level.

4.1 Future work

The work can be continued improving the synchronization method. For make the measurements and

in order to compare the received signal with the sent one, it is added a pilot in a known position to the

transmitted signal. With this method, and due to we are working with Impulsive noise, we got errors at

synchronization part when this impulsive noise was bigger than the pilot. This could be easily solved

using a known sequence to synchronize with, so it can be used Impulsive noise with power higher than

the pilot without problems.

Another improvement it can do, is working on the Video output of the SA FSQ 26 from Rohde &

Schwarz, research to know exactly the processing that the signal suffers and compute the corrected

APD measurement.

This thesis can be extended measuring real impulsive noise at some industrial environment to

recognize patterns and to characterize specifics impulsive noises of a concrete place. Doing this

characterization of the impulsive noise, it can be used to improve the BER at the reception and combat

the interference.


30


C1

References

[1] K. Wiklundh, “Relation Between the Amplitude Probability Distribution of an Interfering

Signal and its Impact on Digital Radio Receivers”, IEEE Transactions on Electromagnetic

Compatibility, vol. 48, no. 3, pp. 537-544, August 2006.

[2] J. Seo and S. Cho, “Impact of Non-Gaussian Impulsive Noise on the Performance of High-

Level QAM”, IEEE Electromagnetic Compatibility, vol. 31, no. 2, pp. 177-180, May 1989.

[3] A. D. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference

Environment. Part 1: Coherent Detection”, IEEE Transactions on Communications, vol. 25, no.

9, pp. 910-923, September 1977.

[4] K. McClaning and T. Vito, “Radio Receiver Design”, Noble Publishing Corporation, Atlanta,

GA, February 2001.

[5] S. V. Vaseghi, “Advanced Digital Signal Processing and Noise Reduction”, J. Wiley & Sons

Ltd, Second Ed, September 2000.

[6] S. Miyamoto, M. Katayama, N. Morinaga, “Performance analysis of QAM systems under class

A noise environment”, IEEE Transactions on EMC, vol. 37, no. 2, pp. 260-267, May 1995.

[7] D. Middleton, “Canonical non-Gaussian noise models: Their implications for measurement and

for prediction of receiver performance”, IEEE Transactions on Electromagnetic Compatibility,

vol. EMC-21, no. 3, pp. 209-220, August 1979.

[8] A B. Shahzad, “Impulsive Noise Modeling and Prediction of its Impact on the performance of

WLAN Receiver”, Glasgow, Scotland, August 2009.

[9] L. A. Berry, “Understanding Middleton’s Canonical Formula for Class A Noise”, IEEE

Transactions on Electromagnetic Compatibility, vol. EMC-23, no. 4, pp. 337-344, November

1981.

[10] J. Ferrer, “RF Channel Characterization in Industrial, Hospital and Home Environments”,

Stockholm, Sweden, February 2012.

[11] R. J. Achatz, M. G. Cotton, and R. A. Dalke, “Estimating and Graphing the Amplitude

Probability Distribution Function of Complex-Baseband Signals”, Colorado, USA, August

2004.

[12] D. Johnson, “Minimum Mean Squared Error Estimators”, Texas, USA, November 2004.

[13] K. Wiklundh, “An Approach to Using Amplitude Probability Distribution for Emission Limits

to Protect Digital Radio Receivers Using Error-Correction Codes”, IEEE Transactions on

Electromagnetic Compatibility, vol. 52, no. 1, pp. 223-229,February 2010.

[14] R&S®FSQ Signal Analyzer - Data sheet, from http://www2.rohde-schwarz.com, April 2012.

[15] Sencity Optima antenna – Technical Data, from http://www.hubersuhner.com, April 2012.


C2


C3

Appendix A

Figure 22. Theoretical and simulated BER and APD for M-PSK

Figure 23. BER and APD for 64-QAM with Γ= 0.1

Figure 24. BER and APD for 64-QAM with A = 0.01

0 2 4 6 8 10 12 14 16 18 2010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

0 dB

BE

R

BPSK TheoryBPSK8-PSK16-PSK

-35 -30 -25 -20 -1510

-5

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

2-PSK8-PSK16-PSK

0 2 4 6 8 10 12 14 16 18 2010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

0 dB

BE

R

64-QAM TheoryA = 0.001A = 0.01A = 0.1

-45 -43 -41 -39 -37 -35 -33 -31 -29 -27 -25

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

A = 0.001A = 0.01A = 0.1

0 2 4 6 8 10 12 14 16 18 2010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N

0 dB

BE

R

64-QAM TheoryΓ = 10Γ = 0.1Γ = 0.01

-45 -40 -35 -30 -25 -20 -15

10-4

10-3

10-2

10-1

100

Power Level (dBm)

AP

D

Γ = 10Γ = 0.1Γ = 0.01

Documents

QAM and PSK Modulation Schemes under Impulsive Noise530269/FULLTEXT01.pdf · Ezequiel Pérez Rodenas QAM and PSK Modulation Schemes under Impulsive Noise iii Acknowledgements I am