This page is a collection of  thoughts born from some readings or discussions.

Contact : f4dan at yahoo dot fr

Last Update january 13, 2008



Digital Signal Processing

Digital Communications

Information Theory and Coding

Radio History


Antenna shapes (10/06/2007) 

In french only ...

10,7 MHz IF, FM broadcast band, and image frequency

The 10,7 MHz Intermediate Frequency (IF) is commonly used in FM broadcast receivers. Why this particular value has been choosen ? Here is maybe an explanation...

To downconvert the FM broadcast band (88-108 MHz) around a 10,7 MHz IF, one must use an L0 with frequency between 98,7 and 118,7 MHz (superhétérodyne mixing).
our ramener la bande FM (88 - 108 MHz) autour d'une FI à 10,7 MHz,  on utilise un OL de fréquence comprise entre 98,7 et 118,7 MHz (mélange superhétérodyne). .

With this LO value, image frequencies (i.e. unwanted frequencies downconverted around our 10,7 MHz IF) are between 109,4 and 129,4 MHz.

Hence, bottom of image band (109,4 MHz) lies just bellow the top of the FM broadcast band (108 MHz). Simple permanent high-cut filtering is then enough to reject image frequencies. That's where the 10,7 MHz value comes from !

More generally, one shows that to downconvert (
superhétérodyne mixing) a frequency band of size B around an IF, one has to choose an IF greater than B/2 in order to filter easily images frequencies..

Attenuator pads and impedance matching

André Jamet (F9HX) published a very instructive article in Radio Ref (october 2005), about attenuators.

A key sentence in this article :
"Input restistance of an attenuator is equal to its characteristic impedance only if it is loaded by a resistance with equal value ; if it is different, the error is all the more important as the attenuation value is small". 

Example :
A 3 dB attenuator (50 Ohms) loaded by a variable resistance between 0 and 150 Ohms shows an input impedance between 18 and 802 Ohms.
A 20 dB attenuator (50 Ohms) loaded by a variable resistance between 0 and 150 Ohms shows an input impedance close to 50 Ohms all the time.

Conclusion : a high value attenuator can be used, in a transceiver design, to easely achieve an impedance matching with an other stage showing a different input impedance from the characteristic impedance of the chain (usually 50 Ohms).

Why 50 Ohms ?

We usually use transmission lines and deviced with 50 Ohms characteristic impedance. Why this value ?

Yves Oesh HB9DTX has the following explanation :

- one can show that attenuation of a coaxial transmission line is minimal for an external conductor / internal conductor diameter ratio equal to 3,59. This ratio gives a characteristic impedance of about 77 Ohms

- one can show that the diameter ratio that allows to transmit maximal power through a coaxial line without cracking is : 1.65. This ratio gives 
a characteristic impedance of about 30 Ohms 

That's why industry choosed an middle value of 50 Ohms, which is a compromise between minimal loss and maximal transmitted power.

We also understand why TV installation use 75 Ohms impedance : this is impedance that allows minimal loss. And because TV doesn't use (on the receiver side) high amount of power, impedance has been choosen to minimize loss.

P.A Rizzi, Microwave Engineering- Passive Circuits, Prentice Hall, New Jersey 1988.
P-G. Fontolliet, Traité d'électricité volXVIII, Presses Polytechniques et universitaires romandes 1996

New Radio transmission modes (13/01/2008) update

New radio transmission modes appear each year.
In order to follow this evolution, here is a list of dates when I started to be interested by each of them.
This list will be updated when necessary.
1998 : GSM
1999 : APRS
2000 : DECT
2001 : PSK31
2002 : Wifi
2002 : WorldSpace
2003 : Bluetooth
2003 : Thuraya
2004 : DVB-RCS
2005 : JT65
2005 : DVB-S2
2005 : UMTS
2006 : DRM
2006 : Wimax
2006 : Téléphone mobile WIFI
2007 : Olivia
2007 : FDMDV (Digital HF voice, in 1,1 kHz bandwidth)

Is free space attenuation frequency dependant ?
In french only. English coming soon.

SDR advantages

One often gives as main advantage of SDR that it allows quick re-programming to handle new modulations for example.
An other advantage, at least as important, and sometimes forgotten, is the ability to demodulate
several channels simultanously .  


The Argand Diagram (14/01/2007) 

We know throughout the world the way of representing complex numbers in a diagram where complex number a+ib corresponds to the point with coordinates (a, b).

This diagram is today broadly teached in french universities and schools. 

This diagram has a name : the Argand Diagram.

What surprises me, and this is the reason of this note, is that I spent 30 years of my life using this representation through articles, books and exercices, before learning it had a name ! I learned this name for the first time in an article published in the QEX paper : 
"An Alternative Transmission Line Equation", Ron Barker G4JNH VK3INH, QEX Jan/Feb 2007.

Jean-Robert Argand was an amateur swiss mathematician
(1768 - 1822) who introduced its diagram in the paper :"Essai sur une manière de représenter les quantités imaginaires dans les constructions géométriques".

I/Q receiver and QAM modulation (2006/06/30) 

I thought for a while that an I/Q receiver could be used only to demodulate digital QAM modulation, and that a digital QAM modulation could only be demodulated by an I/Q receiver.

In fact, the "I/Q property" of QAM modulation is quite independant of the "I/Q property" of a receiver.

For example :
- an I/Q receiver can demodulate any non-QAM modulation (FM, CW, SSB, ...)
- a QPSK (4-QAM) modulation can be demodulated by a non-I/Q receiver

QEX Nov/Dec 2005

In my opinion, the conclusions made in the article "Quadrature Phase Concept" (QEX Nov/Dec 2005) are wrong. Here is why :

1/ In figure 2, p. 21, if the author had made a "difference" instead of a "sum" at the end of the treatments, he would have obtained ZERO : this shows that there is a mean to eliminate part of the frequency spectrum, contrary to what he assumes !!!

2/ The main error of the article comes from the fact that [Eq 5] and [Eq 6] are actually only correct if F-O > 0, and the author use them also when F-O is negative. If F-O < 0, the equations take an other form. So when the author says p.21 "Assuming F-O is positive or F-O is negative, it doesn't matter", it actually matters, because the equations are not the same.

The fact that the equations are not the same for positive and negative frequencies comes from the Hilbert Transform [HT] properties. For example :

HT[cos(2.pi.F.T)] = sin(2.pi.F.T)  if F > 0, and -sin(2.pi.F.T) if F < 0
HT[sin(2.pi.F.T)] = -cos(2.pi.F.T) if F>0, and cos(2.pi.F.T) if F < 0

Sampling frequency of a band limited signal

In french only. English coming soon.

Modulation and demodulation

Designing a digital modulator is much easier than designing its associated demodulator.

For instance, generation of a digital QAM signal is very easy. On the contrary, the demodulator must implement smart methods to :
  • estimate channel response (egalization)
  • estimate carrier frequency (carrier tracking)
  • estimate carrier phase (carrier phase recovery)
  • estimate symbol rate  (symbol timing recovery)
  • estimate optimal sampling decision instant (moment of maximal opened eye diagram) 
The same idea has been noticed by other. For example in an article from EDN ([EDN] march 2005) : "designers generally accept that receiving is an order of magnitude more difficult than transmitting; without the necessity of extracting rapidly changing information from signals buried within a sea of noise, transmitter algorithms are relatively simple. Equally, many receiver techniques similarly apply in the reverse direction, so most discussion centers on receiver architectures and how best to adapt schemes to fit within the SDR context". 


Difference between "Software Defined Radio" and "Software Radio" (18/08/2007) 

Joseph Mitola, one of the founder of the concept of software (defined) radio, makes a difference between "software defined radio" and "software radio".

"software defined radio" will handle digitally only a limited portion of spectrum at one time. For example, an instantaneous bandwidth of 3 MHz among a 200 MHz large spectrum band. The choice of the instantaneous 3 MHz sub-band is done in analog, for instance by using a mixer exitated by a programmable local oscillator.

A "software radio", on the other hand, handles the whole 200 MHz numerically. Eventually, only a sub-band is afterward handled, but it is selected digitally (typically with a DDC).

These two types of architectures can be found in amateur projects. The 3rd "key paramter" of the classifcation found here distinguish the 2 types of designs.

Examples of software radio : USRP, PERSEUS, MERCURY/OZY HPSDR, SDR-IQ, SDR-14, ... (other projects here)
Examples of software defined radio : µwSDR, SDR-1000, Ciao radio, ... (other projects here)

Source : "Cognitive Radio : an integrated agent architecture for software defined radio". Joseph Mitola, May 2000

Practical implementation of theoritical digital modes

Digital modes are often characterized by their performances in term of bit error rate related to signal to noise ratio.

For instance, this system will have a
10-3 bit error rate for a signal to noise ratio of  -5 dB in 3 kHz.

Yet, these values are theoretical values. Practical implementations of these modes (softwares) deteriorate the performances, and two different implementations may have signicative different performances !

A study is currently carried out by
VE3NEA [VE3NEA]. Its goals is to compare 3 RTTY decoders : TrueTTY, MixW and MMTTY. First results show that :

- in additive white gaussian noise conditions, performances disparity of almost 3 dB exist between softwares 
- softwares that are the best under
additive white gaussian noise conditions are not automatically the best under other conditions (selective fading, echo, ...) 

Références :
[VE3NEA] : "RTTY Software Comparison"

Source Coding and Channel Coding : removing redundancy, and then adding some more again

A digital transmission chain comprises often (in the transmitting way) a source coding block, followed by a channel coding block.

This is funny to see that source coding tries to remove redundancy from the source, while channel coding immediately adds some redundancy again, but in a controled manner.

The choice of baud rate

The baud rate (or symbol rate) of a digital transmission must be carrefully choosen, and must be the result of a compromise.

If it is too small, then the channel characteristics can't be considered any longer as constant during a symbol period . This causes troubles for the receiver.

If it is too large, then multi-path phenomenon creates inter-symbol interference. In HF for example, temporal difference between two paths can be as large as 30 ms. That's what explains why sometimes some RTTY transmissions (symbol period = 22 ms), even with excellent signal to noise ratio, are difficult to decode.

Examples of baud rates (and associated symbol period) of some HF modes : 

Frequency modulation systems :
JT65 : 2,7 bauds / 370 ms
MFSK16 : 15,625 bauds / 64 ms

RTTY : 45 bauds / 22 ms
PACTOR : 100 bauds (10 ms) ou 200 bauds (5 ms)
G-TOR : 100 bauds (10 ms) à 300 bauds (3 ms)

Phase modulation systems : 
PSK31 : 31 bauds / 32 ms
CLOVER : 31,25 bauds / 32 ms
CLOVER 2000 : 62,5 bauds / 16 ms
Q15X25 : 83,33 bauds / 12 ms

The GSM burst length

The duration of a GSM burst is 0.577 ms. Here is one of the reason that can explain this value.

Wave length at 900 MHz (low GSM band) is 33 cm.

A this frequency, and if situated inside a train travelling at 200 km/h, one shift from half a wave length in about 3 ms.

This period represents the coherence period of the channel : this is the period during which channel properties don't change in a significant manner.

On can see that GSM burst length is more than 5 times smaller than the
coherence period of the channel. Channel characteristics can then be considered as constant by the receiver during the whole burst duration : this highly simplifies the demodulation task (particularly egalization).

That's why a longer burst duration would have been less convenient.

Note : For a 1800 MHz wave (second GSM band), coherence period drops down to 1.5 ms. It still remains 3 times greater than the burst duration.

Source :
"Rayleigh Fading Channels in Mobile Digital Communications Systems. Part II : Mitigation". Bernard Sklar, IEEE Communications Magazine, Juillet 97

The GSM redundancy

The GSM vocoder rate is 13,0 kbits/s.

After adding erroc detector and corrector codes, rate increases up to 22,8 kbits/s (+75% compared to previous rate).

Then, after adding the burts midamble, (used for a "data aided" egalization), rate increases again up to 30,3 kbits/s (
+33% compared to previous rate).

All in all, redundancy represents more than half of the used rate !

Putting it differently, GSM convey far more redundancy than useful information.

This is the price to pay to figtht against numerous perturbations that signal encounters in a radiomobil network.

GSM Audio perturbations and 217 Hz frequency

GSM protocol uses a time division multiple access (TDMA) to convey 8 different channels on the same frequency.

Each channel uses a temporal window of length
0,577 ms. A given mobile station transmits a 0,577 ms burst each 0,577*8 = 4,616 ms.

Consequently bursts have a transmit frequency of  
1/4,616 = 217 Hz.

This discontinuous transmission phenomenon then generates a spectrum with a fundamental frequency of 217 Hz, and harmonics situated at
434 Hz (2x217), 631 Hz (3x217), etc. ...

Unfortunately this frequencies are precisely situated in an audible band for humans : they are the typical perturbation we can hear when a mobile phone is placed close to a loud-speaker.

In order to validate the previsous explanation, here is a simulated audio signal, composed of 3 sinus with same intensity and frequency
217, 434 and 631 Hz. We can confirm that this sound is indeed the one of a GSM perturbation.

Were these perturbations were discovered after GSM normalization, or were ingineers aware of them from the beginning ? Anyway, 3G telephony (UMTS) has not the same problem, because transmission is continuous and not discontinuous.

Are Eb/N0 and S/N equivalent ?

Coming soon


Compressing French and English languages (14/08/2006) 

French language is composed of 300 000 different words (including all conjuged forms of the words).

Existing compression algorithms allow to code these words in less than 200 Kbytes (
DAWG algorithm : Directed Acyclic World Graph).

This represents less than 0.68 byte par word ! Much better than a Baudot code (0.63 byte par letter) !

English language is composed of only 110 000 different words (less than french language). Amazingly, the same DAWG algorithm only allows a compression in 240 Kbytes (more than french language).

This comes from the fact that french grammar is much more richer/complicated than English grammar, e.g. one verb will have dozens of forms, each consuming very little space in a DAWG

Source : [Braun]

Improving JT65 source coding

JT65 protocol encodes information, in order to make it as compact as possible (source coding).

To do that, JT65 makes strong assumptions about emitted messages, by limiting them to a minimal format : source call-sign, destination call-sign, locator square. With these hypothesis, a message is encoded within 72 bits, and each call-sign within 28 bits.

The 28 bits coding  comes from the fact that a call-sign is composed of one prefix with 1 or 2 symbol, one of it at least being a digit, followed by a digit and a suffix with 1 to 3 letters.

We could improve this coding.

Indeed, if we consider that the number of OMs in the world is about 2 to 4 millions, 22 bits should be enough to encode all call-signs (with a centralized mapping list for example).

If we consider that number of OM active in EME is less than 50 000, then we could further reduce the list, and a 16 bits coding should be enough.

We could then shorten the message size from 72 bits to 48 bits, and a
RS(63, 8) correcting code could be used instead of a RS(63,12).

Coding theory : the needs evolutions

In french only. English coming soon.

"All codes are good, except those we can think of" 

Shannon introduced in 1948 the concept of "channel capacity", representing the maximal quantity of information it is possible to convey with an arbitrary low error rate, through a given noisy channel.

Shannon's work showed the existence of codes allowing to reach this limit,  but didn't show how to construct them.

To reach this theoretical limit, researchers and engineers invented new coding techniques. Each new technique allowed to approach a bit closer the 
theoretical limit. 

However for a long time, invented codes didn't allow to reach the theoretical limit very closely. Scientific community became pessimist and skeptic, illustrated by these two beautiful sentences :

"All codes are good, except those we can think of"
"Any code of which we cannot think is good" (1961 : Wozencraft and Reiffen)

Note 1 : Pessimism and sceptisism about the possibility to find codes allowing to reach the Shannon limit vanished with the french discovery of turbo-codes in 1993

Note 2 : The seconde sentence even received a formal demonstration in 1990 (Coffey and Goodman, IEEE Trans. on Inf. Theory, nov. 1990)

Source :
"Théorie de l'information. Application aux techniques de communication", Gérard Battail, Ed. Masson.

Error free transmission through a noisy channel : the unbelievable proven. 

Shannon works (1948) showed that it was possible to realize an error-free transmission (or at least with an arbitrarly small error probability), even through an noisy channel. Here is a comment from Gérard Battail about this subject :

"This is probably the most unexpected result given by the information theory. By proving the possibility of an arbitrary reliable transmission through a noisy channel, it was going against the immediate intuition and even experience aquired at the time it was stated. Engineers did'nt even think an error-free transmission was possible, persuaded that channel noise prohibited from doing it".

Source :
"Théorie de l'information. Application aux techniques de communication", Gérard Battail, Ed. Masson.

Information throughput through a noisy channel

In french only. English coming soon.

Random sequence generated by a human

In french only. English coming soon.

Channel capaity : theorical and practical performance comparison (27/05/2006) 
In french only. English coming soon.

An economical view of the information theory
In french only. English coming soon.

GOLAY codes and football

In french only. English coming soon.


J. Mitola, year 1992 and software radio (2007/01/07) 

The article entitled "Software radios survey, critical evaluation and future direction", published in 1992 during the National Telesystems conference, is in a way historic.

This text is indeed considered as beeing the funder of the software radio concept. 

Cell Phones

It took only 21 years for cell phone (radio-mobile phones) to reach 1 billion users ower the world.

It took 125 years for fixed telephony....

Baudot / Murray code

Baudot code is well known in France, invented in 1870 and patented in 1874. This code was internationnaly adopted by CCITT union, and named CCITT-1.

American people prefer to speak of Murray code, or Baudot-Murray code.

Indeed, in 1901 Murray rearranged Baudot code, in order that most frequent characters were coded by symbols with minimum 1/0 transitions. This allowed to reduce load of eletromechanical equipments used at this time. This code was named CCITT-2.

This is this code, and not the original one, that is in fact commonly used today, and called "Baudot code".


In french only. English coming soon.

First uses of radio (11/03/2006)

In french only. English coming soon.

The frequency of the first trans-atlantic radio wave

The first transatlantic radio transmission took place at the 12nd hour of the 12nd day of the 12nd month of year 1901 : december 12th 1901 at 12h30. It was carried out by Marconi.

Yet some scientists remain sceptical about the reality of this exploit, and think about the fact that Marconi only received impulsional noise this day, and not the emitted signal. All the more so as the test signal was the letter "S" sent in Morse code, and that it often happens that impulsionnal noise gives the same sound as this letter [DUCR].

The frequency of the wave sent from Poldhu is not precisely known :
100 kHz, 166 kHz, 328 kHz, 500 kHz, 800 kHz, 820 kHz, ... depending on the references and sources. This comes from the fact that measurement systems were not very precise at this time, and that exact nature of transmit devices was not known.

What is sure is that at this day time, F layer reflects short waves, and D layer attenuates long waves. It is then not very likely that a long wave would have travel across Antlantic Ocean, and even less likely that Marconi's receiver could collect it.  All the more so as 1901 was a minimum in solar cycle.

If a signal was received at Poldhu, it probably was a short wave : between 5 and 15 MHz.

But even if a doubt remains about the experience of december 12 1901, one year later, in december 15 1902, Marconi tried again its experiment at Glace Bay, without any possible contestation this time.

[DUCR] : "Eugène Ducretet, Pionnier français de la Radio", J-C Montagné, Autoédition J.C. Montagné.

Radio and life expectancy

Heinrich Hertz, radio pionner, died particularly young : 37 years old (1857 - 1894).

Edouard Branly, 
radio pionner, died particularly old : 96 years old (1844 - 1940).

Inventeurs et prix Nobel

In french only. English coming soon.

TELSTAR and polarization

The american satellite TELSTAR was launched on July 10, 1962 from Cap Canaveral, Florida. It allowed  to carry out the first TV transmission by satellite.

3 terrestrial stations were able to transmit and receive satellite signals :
- Pleumeur-Bodou (France)
- Andover (USA, Maine)
- Goonhilly Downs (Angleterre)

The day after launching, first transmission test was a success : at least between USA and France, English station being not functionnal.

The problem became quickly identified : english engineers had an inverse definition compared to American and French engineers for right/left polarization of a radio wave !!!!

The error was solved on July, 23 and english people were able their turn to receive transmissions coming from USA.

Le baccalauréat de Jeanne BRANLY

In french only. English coming soon.

Marconi's spelling mistake

March 28, 1899 : Marconi transmitted the first radio telegram between Great Britain (South-Foreland) and France (Wimereux) - 46 km.

The transmitted message is exacly this one, including the spelling mistake :