Practical approach: the example analysis of OFDM

The example analysis of OFDM

OFDM – is one of the most difficult sorts of modulation for the analysis. The difficulties are about the fact that, the channels, at OFDM usage, as a rule, do not have clear boundaries, and thereupon it is hard to select any channel or for the detailed analysis. Sometimes, in special cases, it is possible, but not always. OFDM the technology allows to create very not trivial signals, and the classical analysis of such signals is extremely difficult and polysemantic.

The example of such difficult signal(signal1) is here Japaneese Military 8 freq , compare to it this signal(signal2) Mixed mode, PSK-2 and OFDM, system unknown is even more difficult, because it is impossible to select the channel in this signal(signal2).
We will try to analyze the signal2.
But before it we will consider some common principle of analysis on classical signals, as on real ones and on synthesized ones.
The Possibility to synthesise OFDM signal with the specified parameters is very effective, at least it allows to accept some hypothesis or to reject that, it is very useful.

Let’s start.

The link above consist full version of this article, where the principles of OFDM analysis are descrbed step by step on the real example.

The author of this article is SergUA6.

The classical analysis of OFDM signals. Possibilities and limitations.

The classical analysis of OFDM signals

The arctile is written by SergUA6.

Thist article is big enough to put it whole in the blog. Below there will be little bit information from the article, and whole text with pictures and examples you can read here.

The Classical OFDM analysis surely represents difficulty. Before analyze the real signals we will consider the main methods and principles on the synthesized signals. It is typical enough and very productive method.

For synthesis of OFDM signals the OCG program is used. As usually, I underline, you can use any other program both for the analysis and for synthesis, it is important that results would not call doubts, could be verified and have been repeated.

It is supposed that some bases of OFDM creation are known, it does not demand special substantiations as the analysis it is not simple and not only usage of this or that analyzer.

Extensively, it is experience and knowledge of an analyst, it is an ability to generalise, to draw the conclusions etc. Before appearance of OCG, the analysis of OFDM of signals, at least, for me, carried chaotic, unsystematic and extremely not productive character, but the possibility of synthesis of the various by parameters signals has allowed to develop certain techniques and the common approaches. In practice all it does work and does work good enough.

Standardly the task of OFDM analysis is to define:

• the clock frequency of manipulation,
• the value of frequency spacing of channels
• quantities of the channels,
• modulation in the channels
• definition of the presence and length of the cyclic prefix (CP),
• features of the signal if the such are exist.

Advantages of the classical analysis:

• it doesn’t matter how many frequencies in the analyzed OFDM signal, 3-30-300 or 3000
• it is also, generally, doesn’t matter if the signal is generated on even or odd harmonics it does not influence results
• for the score of the very strong averaging-out, the classical analysis is insensitive to separate/single/some anomalies in the signal

Disadvantages of the classical analysis are:

• impossibility to work correctly with short signals
• impossibility of reception of a bit stream (while the universal demodulator can provide it)
• impossibility to allocate the necessary channel in the pure state
• the extremely big problem is to work with the signals having very short CP.

Despite minuses, the classical analysis, in most cases, allows to receive quite good results at the analysis of overwhelming majority of OFDM signals. I hope this article in some measure will help with it.

Auhtor SergUA6 from MSM team.

Signal MSK, Submarine broadcast or the practical application of previous article (FSK, GFSK, MSK, GMSk and other modes).

VLF, MSK, Submarine broadcast, Anthorn station(?) GBK(?)
Br - 200, Shift - 100

The example of the signal is here

Author: SergUA6
Band Width: 300 Hz
Low Range: floating
Baud Rate: 200 Hz
n-Ary (PSK/MPSK): conditionally 4
Count of Carriers: 2 indistinguishable frequency of manipulaion
Step between carriers: 100 Hz
The modulation, in which the signal was recieved )RX mode): Source I/Q record

Sonograms:

pic.1 The group of signals. General view.

pic.2 the graphical spectrum

pic.3 speed of manipulation signal 4

Diagrams

pic.4 MSK in 2 and 4 degree

pic.5 the frequency manipulation spacing

pic.6 MSK on the Phase Plane

pic.7 MSK after frequency detector

VLF, MSK, Submarine broadcast, Anthorn station(?) GBK(?) The VLF range is very rich with curious enough signals. It seems like the group of signals is managed to be identified. There are lot of information in we-bsearchers by the word "Anthorn", and also the infromation about frequency 19.6khz is mentioned. In this record this is the signal number one. All five signals have the classical set of parametres for MSK: the spectrum is equal to 1.5*Br,characteristic bell-looking-like shape, and others. Pay attention that the carrier in the fourth degree it is expressed very poorly, sometimes it is almost not visible at all.

There shouldn't be problems with an identification of modulation, but there are some problems with determination of belongings, because the signals are faceless enough (encryption) and without features, that does not eliminate a possible error.

MSM team

FSK, GFSK, MSK, GMSK and some other modes.

Author: SergUA6

The reason of creation of this article is the interesting discussion on our forum, the second reason is that I’v got e-mail with same subject to discuss, after all I saw same problem discussed on the one of Internet’s forums.To ignore these coincidences would be a bad form, that’s why we will try to look into the existing problem of modulations.

This article is only own attempt of researchment and analysis of the modulation’s problem. I will stick to bases and general principles from the theory, I won’t go deep into details, but the common approaches and principles will be considered.

FSK

Let's consider FSK modulation. Standardly, in a general view, the modulator circuit looks like this (pic.1):

pic.1

The rectangular bit stream as 01001..11010, which is transformed to levels + / - 1 goes on the modulator (the Voltage Control Oscillator), where one frequency corresponds to level +1, and another one to level -1.In this case we have the classical FSK modulation on output. As we can see the frequency spacing (shift) is specified in the modulator and it can has any value, but no less than Br (BaudRate – manipulation speed). We won’t consider the reasons why it shouldn’t be less then BR, because it is well-described in theory, but I will note that it is impossible to demodulate the signal, where the frequency spacing is lesser then BR.

It is important to mark now, that the generator in the modulator and the bit stream, as a whole, are not directly linked and are not synchronized. The spectrum of such signal contains many harmonics, due to squareness of the impulses of modulation and due to sharp switching of the generator in the modulator in unsuitable moments of the time. The main energy is concentrated around the frequencies of manipulation in area, which is equal to Br. That gives minimum possible spectrum of such signal = 2*Br, with the spacing = Br, or Shift (spacing of frequencies of manipulation) + Br in the more common case. Harmonics, which are outside of this spectrum can be effectively suppressed without damage to successful demodulation, as becomes on practice.

pic.2

Please pay attention, that the spectrum around the frequency manipulation, with spacing equal to Br, is exactly fit into the space between frequencies without overlapping. If to put the frequencies together further, then there will be an overlap of spectra of "anothers" impulses and mutual strong interferences. This is evident graphics image of limitation of the minimum spacing at classical FSK (pic.2). The mathematical substantiation is well described in the theory. The main idea of reduction of the frequency spacing at the same speed of manipulation, (and as consequence rising of FSK efficiency ) is well-visible from the graphical representation(pic.2).

It is enough to reduce/restrict an area of primary energy of laterals around the frequencies of manipulation, this way allows to decrease/reduce the spacing. This idea is realized through the pre-filtering of bit stream, before it’s feeding on the modulator.

Guassa filters are widespread in FSK, they provide:

• effective enough narrowing of the band/strip by smoothing abrupt/sharp transitions of the voltage manipulation
• good controllability of parameters.

In principle, any filter, which is smoothing abrupt/sharp transitions is good for this purpose, but the Gaussian filters have better performance and characteristics.

GFSK

The Classical FSK with preliminary filtering by Gaussian filter has received the name GFSK. The common circuit of the modulator is the same, but the bit stream passes through Gaussian filter(pic.3).

pic.3

This allows to evade from restriction of the minimum shift of the classical FSK, Shift> = Br towards reduction. The parameters of the Gaussian filter have an influence on how much the basic spectrum of laterals will be narrowed, and how much it is possible to shift the frequencies of manipulation. Let’s name this “how much” value as X. In practice (actually in the theory too) the size of X value is always more than Br/2, because the reduction of the laterals is reached by the strong declivity/sloping of fronts of manipulation voltage/power, that leads to incursion of one impulse on another impulse, and as consequence to impossibility of demodulation.

Typical reduction of the spacing for GFSK is about 30-40 % from the classical Shift = Br, that is Shift = (0.7-0.6) *Br. It is very difficult, in the general case, to say that it is GFSK is used at analysis, because the same or similar effect can be achieved with other filters.

pic.4

MSK

Further development of FSK manipulation technique led to the appearance of MSK manipulation, the manipulation with the minimal frequency shift.It has been theoretically well-founded under what conditions manipulation with the frequency spacing=Br/2 is possible. I will notice, that in this case there was a refusal from the Voltage Controlled Oscilator, and for creation of MSK manipulation quadrature modulators are used.

The Circuit of MSK modulator is essentially more difficult and looks approximately like this(pic.5).I will notice that there are a lot of circuits, but for us the general principle is important.

pic.5

It can seem that the modulator in MSK is also independent and not synchronized with a bit stream, however it not so, conditions of MSK manipulation demand, so as the change of bits would occur at extremums of oscillations of the generator in the manipulator, or is easier in absolute peaks of a sinusoid and-or in zeros. At performance of all conditions the frequency spacing of manipulation= Br/2 is automatically installed, and the common width of the spectrum is becoming approximately 1.5*Br.

It is not difficult to understand, that the manipulation is represented as one frequency, which is having different phase on the different impulses, and the phase is never stops, thus it gives two frequencies with the minimal spacing. All that is well represented in the theory.

pic.6

GMSK

Insertion(adding) Gaussian filter in MSK modulator’s circuit allows more reduce the common spectrum of the signal, but the payment for that will be reducing of the protectability from interferences(noise immunity further). Such manipulation has received GMSK name. Standardly, GMSK manipulation can has spectrum, which is bigger than BR only on 12-15 %, smaller values are perilous with strong losses of the noise immunity.

pic.7

pic.8

Certainly MSK manipulation has the most noise immunity at the coherent demodulator. However as it is not difficult to notice, that the essence of all tricks is the narrowing of a bar/stripe at FSK manipulation, that allows to demodulate MSK, GMSK modes by usual frequency detectors, but, ofcourse it is more likely forced way, and basically it is not so correct way. It is also not difficult to notice that MSK and GMSK, in the first, manipulate the phase of carrier oscillation, and in the second, demand the coherent demodulators for complete realization of their potential possibilities.


Thus we have following characteristics of these modulations:

• FSK – the simplicity of implementation and relatively wide spectrum;
• GFSK – the simplicity of implementation, and smaller spectrum, but also slightly worse noise immunity in relation to FSK
• MSK – the very high noise immunity at relatively small spectrum, but the difficult circuit of the modulator-demodulator.
• GMSK - the spectrum width is almost close to theoretical limit of Br, slightly worse noise immunity in comparison with MSK, and the complexity of the modulator-demodulator same as for MSK.

HALF-MODES

The "two-faced" signals, such as MSK and GMSK I name half-modes, ofcourse, it is not the standard name. It simply was required to allocate somehow this class of signals from the general PSK family, because such signals possessing both PSK signs and FSK signs.

The second harmonic of these half-modes, has two bright spectral lines, the spacing between these lines is equal to Br, that is one of the signs of these modes.This is the necessary condition of their
definition at the analysis, but not the sufficient. Two lines in the second degree/power can be also given by both SDPSK and OQPSK modes.

SDPSK, generally, does not demand synchronism of transitions in extremums of the carrier, and because of this, it has the bigger width of the spectrum than MSK. This width of the spectrum can be reduced by filtering of the bit-stream before feeding on the modulator, this procedure is usually realizing through RRC filters.

SDPSK (PSK-2 with phase rotation) in essence, has same resulting signal as MSK, only with wider spectrum. It can also be demodulated by FSK demodulator, becos of getting under definition of half-modes.

Modern methods of creation of the various signals do often erase the distinction between various modes, for the reason, that developers are almost always (it strongly simplifies development) aspire to select a multiple relation between the clock frequency of manipulation and the frequency of the carrier.

In this case developer declares and forms, for example,that the modulation is SDPSK, but the resulting signal, in essence, is MSK. Thus, casually or deliberately some confusion is brought into diversity of the various modes and their definitions.

Very often GFSK modulation is specified,in descriptions of the signals, while in actual fact it is typical SDPSK according to all signs. The example is the signal of the Finnish radiosonde.

When we are looking at the circuit of formation of GFSK modulation, it is easy to understand that if the clock frequency and the generator will be synchronized, and the frequency spacing will be choosen as BR/2, then such “GFSK” will easily turn into one of our half-modes, at defined parameters of Gaussian filter and high stability of generator’s parameters. Seems like developers just don’t think about it or just do not know.

By the way, in one’s time, by this reason, GFSK was mistakenly classified to these half-modes on one of sites the modulation ACARS VHF has been declared as GFSK.

In analysis it is very desirable to define what type of modulation is used, at least approximately. It is also necessary to be oriented on the width of the spectrum, which is occupied by the signal and on
its form.

At pure MSK modulation, width of the spectrum is about 1.5*Br, at GMSK spectrum is lesser than this value, and in it’s limit is very close to theoretical Br, at the same time the spectrum of MSK, GMSK is obviously expressed as bell-looking-like shape/form, at SDPSK the spectrum is more then 1.5*Br. The basic sign of half-modes is two lines in the second degree/power, the basic but not sufficient, it demands certain accuracy and attention. The spectrums form does also require certain accuracy, because often receivers distort it to unrecognizability, especially if the signal is taking off from AF’s output or from discriminator, in this sense it is much more preferable the I/Q record or IF.

MSM team

Offline analyzers and real-time analyzers.

In the almost four years of the development of the Signals Analyzer, practically constantly we are taking part in the discussions, where most popular questions are:

- Why SA is offline signals analyzer and not the real-time?
- Why is this necessary to use Signals Analyzer while some people can define signals by ear?
- What will I have by using SA?
- There are lots of professional real-time analyzers and everything works okey in real timeanalyzators aswel?
- Why SA do not include real time analyzer and decoder? And etc etc

We have decided to reply on most popular questions, and the answers, which will be represented - are the result of long-standing practice, not just our opinion. I think you will agree that the best
answer on the question, is the fact which was admitted on practice many times.

First of all, I have to disappoint people who analyze signals by ear. I do not deny, that some people have abilities for that, but it is the absolute impasse, even when you have abilities for that.There are tens of hundreds of signals, where these people frankly give up, but they greatly are proud of the fact that they can distinguish CW of RTTY, but nevertheless they ask “why can’t I decode anything in MiX or SkySweeper?”

Our team is also still getting surprised, when people send us sonograms and ask to analyze them, or they try to analyze the sonogram by their own. The real analysis must have the object of analysis, and the object of the signals analysis – it is record of the signals first of all. In 90% of cases, we can see one stuff on the sonogram and hear completely other stuff on the record. Analyst has no interest to shadow of the signal, the record of the signal is the first thing, which is necessary.

These two aspects explain paradox: on hundreds of forums we see lots of same questions like: what is rustled yesterday? I heard grunted signal, something is hisses in my dynamics what was that?? And only small amount of people can intelligible answer what was it, who was it and etc.
The paradox is: everyone want to know details about the signal they cached, but only small number of people able to know it for real. Besides, signals analysis isn’t that terrible hard as many people think about it.

Now couple of words about real-time analysis. Don’t want to disappoint most of people, but…….today, the real-time analysis it is fiction, it does not exist in that kind of way, which most of people imagine. Of course, many developers are occupied by the real-time analysis, and our MSM team is also engaged into it. But we can’t create real-time tools, until all problems of the offline analysis will be fully solved.Surely, analysts who need fast and unclear analysis with an absolutely not accurate, not precise, not exact and not clear results, can please themselves with the illusion of the real-time analysis.

I underline, we are speaking about real true analysis, when the signal is unknown, and even, when it is not even known if it is signal or just noise. Sorting from the known signals as many programs do - this is not analysis. Especially, we can’t deny that we all need secure exact results, and get such results we can only through offline analysis.

The next question is : why SA does not include decoder, this is sooooo bad!

Well, let me explain. First of all, please, pay attention on the fact, that decoders work ONLY with
absolutely known signals. If the signal is unknown or it is shifted or it has parameters, which are
different from the expected parameters, then the decoder sharply moving in the category of the
beautiful expensive knickknack. Any of bit streams, in this case, can’t be considered seriously.
Thus, we see that the signals analysis and decoding of the signals are two completely different
categories. Analysis identifies the signal, gets parameters of it, studies it, and only after the
signal is analyzed, it can be placed into decoder. The better signal is analyzed, the better results
you will get after decoding.

Professional expensive software, mostly consist of real-time decoders, where functions of the signals analysis are declared. But in reality these functions of analysis just do not work. It is impossible to do reliable trustworthy analysis by such functions.
The overwhelming majority of people don’t want to admit it, but it does not change anything actually.


Thus, you understand, that analysis of the signals and decoding of the signals, are completely
different spheres of activities, which are going together and analyzers prepare material for decoders. And there is no other way.

So why SA? No problem, you can choose any other product, if it will give secure and reliable results as SA gives, will be more comfortable and better then SA and will be cheaper then SA.
Our MSM team has been developing and creating methods and principles of the signals analysis within 4 years, we still develop our own unique tools, which are designed specially for the practical applying, and seems like we have some success here:) SA is in constant development and evolution.

Recently there was the very interesting hypothesis that SA it is the plagiarism of Centurion. To visitors Resource (www.radioscanner.ru) it is not necessary to explain anything because the evolution of SV program (the first versions 2004-2005) into SV + (2006-2007), and after into SA (2009) occurred on eyes of many people. Monteria company really had the licence for usage of the program SV + under The COA brand, in their products. Approximately one year ago,probably a bit more, the licence was expired, the project SV + had been recognised by us as outdated and succssesfully abandoned.We decided to realise all our operating time and new ideas in the commercial project SA , and this decision was accepted. Whole mathematic had undergoned the careful analysis and full re-processing, it had allowed to increase speed of processing on the average by 30 %. Most of algorithms were realized on qualitatively another level, and today SA has not anything common with SV + and-or COA in the plan of mathematics and realisation of algorithms. The general concept is saved, becasue to us it does seem convenient enough, and the bases of this concept had been put into SV (2004-2005).


Many people write that SA free is too functional for demo version. I have to dissapoint you , it is only seems so. SA free is practically version SV + from March-April, 2007, with certainly out-of-date
solutions and the mathematics, it is having problems and inaccuracies in the analysis, and it is accessible only with the purpose of familiarization with the main ideas and principles. Eventually in the process of SA development the distance between commercial version of SA and SA free will only increase.

And in conclusion...What will You get from all that analysis stuff? All same what you have from book that you had read, from the QSO that you done, from the contact with your friends and etc.
Can You have more?Of course you can. Good analysts are on demand nowadays, this is profession. After all this is sphere, where amount of skilled, competent specialists is less then no matter where.