An Introduction to
Multi-Frequency Shift Keying
(MFSK)

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Introduction

The Professionals
Professional communications engineers are always interested in sending information faster and more reliably than was previously possible, if necessary by using complex technology, greater bandwidth or higher power to achieve this. In addition, commercial and military users for whom this equipment is designed, are generally interested in short distance communications with high reliability and relatively high signal strengths. Usually cost is a secondary consideration to performance.

These types of communications are also often full duplex or unidirectional rather than one way at a time (half duplex).

Amateurs
Although some Amateur Radio applications have similar goals, especially on VHF, most Amateur Radio HF, MF and LF data communication has limited bandwidth available, and usually involves half duplex operation, while the available transmitter power is definitely limited, both by legislation and by cost. Fortunately, Amateurs have reduced expectations of reliability, and can always postpone operation until conditions improve, or simply talk to someone else instead! Amateur Radio operators also have an almost unique interest in real-time communications, now abandoned by almost all other HF services in favour of automated message techniques.

Radio Amateurs wishing to transmit data or text rather than voice (digital modes) are often interested in very robust transmissions over very long distances, such as from one side of the world to the other. Bandwidth needs to be kept to a minimum, since all the Amateurs in the world share the same limited space, and power requirements should be modest. Fortunately transmission speeds can often also be modest, which is helpful since speed can be traded off for improved reliability, lower power, or narrower bandwidth. This concept is the logical concept of early work in communications theory by Claude Shannon (1947).

DX Conversation Modes
Thus there is always an interest in improving the communication performance of low power long distance links, typically casual person to person conversations where each person takes a turn to type on the keyboard and transmit what he types, while the others receive and print what is sent. Radio Teletype (RTTY) was used in this way for many years. Hellschreiber has recently been revived for the same purpose, and has proved to be very effective. Newer techniques such as PSK31 by Peter G3PLX and PSK63F (included in STREAM by Nino IZ8BLY, have extended the performance of narrow-band links considerably.

The recent trend in these new modes, as illustrated in the last two examples, has been to use differential binary PSK (DBPSK) transmissions, since DBPSK offers very high sensitivity and rejection of noise. Such modes are therefore ideal for low power. However, the biggest problems facing very long distance (DX) communication on HF are generally selective fading and ionospheric modulation of the signal, rather than sensitivity, and in general PSK modes do not handle these problems very well.

The MFSK Option
Few Amateurs had until recently even heard of MFSK, while some that had may have dismissed MFSK as being "old fashioned". As has been clearly demonstrated by the recent successful revival and acceptance of Hellschreiber, old ideas combined with modern techniques such as DSP can prove to be very effective. MFSK was used successfully by the British Foreign Office, the Belgian and French military and others, using such systems as Piccolo and Coquelet.

Such systems were designed for high communications reliability in the days of electromechanical equipment, at a time when advanced signal processing and forward error correction were not practical. These old MFSK systems provided very good performance for the time - robust, sensitive and reliable, with good results in fading and poor ionospheric conditions without requiring error correction. There are some military systems of a broadly similar nature still used for similar reasons (ALE for example).

The opportunity has now arrived to modernise the MFSK technique, creating a new high performance yet inexpensive mode that will benefit from the advantages of MFSK, plus the simplicity of the PC and sound card, and the advantages of many associated DSP techniques, since PCs are now fast enough to perform this type of processing.

MFSK Overview for Beginners

MFSK is a technique for transmitting digital data using multiple tones, extending the RTTY two-tone technique to many tones, usually, but not always, one tone at a time.

MFSK means Multi - Frequency Shift Keying, and should not be confused with MSK (Minimum Shift Keying). There are a number of different techniques, using concurrent (or parallel) tones, sequential (one after another) tones, and combinations of tones. MT-Hell can be either concurrent or sequential, DTMF tones used for telephone signalling are concurrent tone pairs, while Piccolo and Coquelet, although they use tone pairs, are decidedly sequential.

MFSK transmissions have a unique sound, almost musical, which is why Piccolo and Coquelet received their names (Coquelet means rooster).

277kB WAV file Piccolo Mk 6 sample (277kB)

MFSK uses relatively narrow tone spacings, so remarkable data rates are achieved for a given bandwidth - 64 bps in a signal bandwidth of 316 Hz is typical. The following picture is a spectrogram of an MFSK16 signal (16 carriers) with a spacing of 15.625 Hz and operating at 15.625 baud. The transmission operates at 62.5 bps (raw data rate of about 80 words per minute!) and occupies about 316 Hz bandwidth. The two black horizontal lines in the picture are at 1000 Hz and 1300 Hz, and the horizontal scale is about 20 seconds. This short transmission contains about 120 letters. MFSK16 is always operated with FEC, so the text throughput is actually only about 42 WPM (31.25 bps).

Spectrogram of MFSK16 signal
Fig. 1. Spectrogram of an MFSK16 Signal

Advantages
MFSK has several performance advantages:

Most important of all, with an MFSK system, the error rate improves as the number of tones is increased, so with as many as 32 tones the performance is unrivalled. With PSK systems the opposite is true.

Disadvantages
Let's be fair - there are disadvantages to MFSK! The main disadvantages are related to the narrow spacing and narrow bandwidth of the individual tone detectors - drift can be a problem and accurate tuning is essential. Good tuning indicators and AFC are necessary at the slower speeds. It is important that the radio transceiver be very stable, and also that it has very small frequency offset between transmit and receive (preferably less than 5 Hz).

MFSK also uses more bandwidth for a given text speed than a 2FSK or PSK system, but by the same token it is therefore more robust.

How MFSK Works

MFSK is a system where individual pulses of different radio frequencies carry information, and the data carried depends on the frequency of the pulse. This is the same as FSK, for example radio teletype (RTTY), but rather than two different frequencies, many more are used - from six to 64, for example. MFSK16 uses 16 tones. Each tone transmitted is just like a Morse code dot, but they follow each other without pause, on slightly different frequencies.

MFSK systems generally use non-coherent detection, and space the many tones as closely as possible, to restrict the transmitted bandwidth. The transmitted tones must be spaced at a separation equivalent to the baud rate, or a multiple of the baud rate - the rate at which the "dots" are sent, otherwise it is difficult to separate one tone from another. This allows the signalling to be orthogonal,(each tone can be separately detected without being influenced by another tone, or affecting the result of any other detector) as will be explained over the next few paragraphs. For example, the tone carriers can be spaced by 20 Hz when keyed at 20 baud.

MFSK signals are traditionally "hard keyed", i.e. each tone starts and stops suddenly, as in the following example.

A single tone pulse

On the air you don't actually see a single tone element like this, because a train of data elements are transmitted, and since the tones switch from one to another phase synchronously (no abrupt change of phase) the keying bandwidth is minimized. However this hard keyed tone burst gives the signal its characteristic frequency domain sin(x)/x shape, just the same as a Morse Code (CW) dot:

Characteristic Sin(x)/x curve
Fig. 2. The frequency domain response of a
hard keyed single tone.

The shape of the transmitted signal has a main peak, with nulls spaced either side of the carrier frequency. The first nulls occur at the carrier frequency ± the baud rate. The humps and nulls are clearly visible on either side in Fig. 2. If you look carefully at the spectrogram in Fig. 1, you will see these sidelobes as grey streaks above and below the individual dots. The big hump in the centre of Fig. 2 is the wanted signal, and it is these that cause the black dots in Fig. 1.

Of course the dots or tone bursts are not isolated, but preceded and followed immediately by other dots at the same or different close frequencies. We can superimpose the sin(x)/x shape of each one to see what happens, and then arrange the spacing of the tones to achieve the best results.

Fig. 3 shows seven of these hard keyed tones superimposed, so that the nulls of each carrier coincide with the peak of the next, to minimise cross-talk (energy intended for one receiver channel appearing in the next channel) in the receiver and therefore allow orthogonal signalling. This occurs when the baud rate and tone spacing are numerically the same, i.e. the spacing is the same as the baud rate or at multiples of the baud rate. Fig. 3 is a spreadsheet simulation, where the spacing is X=pi radians, and would be identical to the result of seven tones transmitted in turn at the baud rate spacing.

Spectrum of multiple hard keyed carriers
Fig. 3. Frequency domain response of seven different Sin(x)/x tones

The vertical scale in this graph is linear, 0 - 1, and the horizontal scale is in radians, from -20 to +20, or about ±12 Hz. The baud rate is assumed to be 1 Hz.

When the transmission consists of multiple tones spaced as described, the signal broadens out across the peak, but retains the characteristic shape, as illustrated above. When random data is transmitted, the broad peak "fills out", but the side lobes remain obvious. The following image shows the spectrum of a real 8FSK signal transmitting random data at 31.25 baud with a tone spacing of 31.25 Hz. The vertical axis in this image is logarithmic, so the side lobes are more obvious than in the simulations above. Note that the sidelobes are spaced 31.25 Hz because of the 31.25 Hz baud rate. The broad centre peak and the side lobe peaks are a little ragged because the data is random and does not average out in the time of the spectrogram recording.

Spectrum of a real MFSK transmission (Courtesy Peter G3PLX)
Fig. 4. The spectrum of an MFSK transmitter (Courtesy Peter Martinez G3PLX)

The spectrogram was taken with 0dB set at the level of a single constant tone. A standard method of calculating the necessary bandwidth of radio transmissions is laid out by the CCIR, and for the above transmission is 331.25 Hz (±166 Hz). Looking at the spectrum, the signal is well below -30dB from the single tone carrier at this bandwidth (indicated by the vertical red lines), easily exceeding the CCIR definition of 0.5% of the total transmitter power (about -20dB). The performance (indicated by the horizontal blue line) is this good because with modern DSP technology the signal is transmitted using phase-synchronous tones (CPFSK). It so happens that this occurs naturally and easily using DSP when the duration of each tone (the symbol period) is the reciprocal of the tone spacing.

Here's another spectrogram, this time of an eight tone MFSK transmission, received over 18,000 km on 18 MHz. Note the characteristic appearance!

Spectrogram of DX 8-MFSK transmission
An 8-tone MFSK signal at 18,000 km range

Convolutional Coding

One important improvement that can now be made to an MFSK system is to add Forward Error Correct (FEC), in order to dramatically reduce the number of received errors. Since MFSK is inherently robust, the addition of FEC makes the system virtually "bullet proof". It also transpires that there are very elegant FEC solutions ideally suited to the features of MFSK.

Forward Error Correction is achieved by sending extra redundant but relevant data (typically twice as much data as without coding), but it is done in such a way that more than twice the advantage is achieved. In addition, with a properly designed FEC system, the improvement in copy achieved is greater than the loss in performance which results from having to use twice the bandwidth to send the data! This is called the coding gain.

The coding of the data for FEC is in principle quite simple, the best method being to multiply the data in a binary bit-stream with a special polynomial algorithm (a process called convolutional coding), but the decoding process is much more than a beginner can be expected to understand. Chip Fleming has an interesting Tutorial on Convolutional Coding if you would like to learn more.

Interleaving

One of the problems with FEC coding is that it works best if all the errors are spread out evenly. Unfortunately interference (especially static and splatter) is burst-type noise, and tends to take out data several bits at a time, which makes life very difficult for the decoder. To avoid this problem, we muddle up the order of the transmitted bits using an Interleaver. Then, when bursts destroy adjacent bits, the process of de-interleaving spreads the errors out, easing the job of the decoder.

One really cool thing about MFSK (unique to this mode) is that the order of the FEC data bits and the placement of bits in the Interleaved data are always known, since the bits are received in groups of 3, 4, 5 etc, always with the same position in the group. This means that (if properly designed) the FEC decoder bit assignment and Interleaver un-muddling become virtually automatic. The transmitter does not need to waste bandwidth transmitting synchronizing information, and in addition the receiver does not have to work out how to arrange the incoming bits as the bit group positions infer the positions.

Bits and Bauds

One of the most confusing things about MFSK is that the signalling rate is not the same as the data rate, because each tone carries more than one data bit. To explain this, we'll define all the terms used and show how they inter-relate.
Symbol Rate
The basic element of transmission in any data mode is the Symbol. In most modes, each symbol implies a "0" or "1", but in MFSK systems, each symbol carries information according to how many tones there are - three bits of information for 8 tones, four bits for 16 tones, and so on. Each MFSK tone burst is one symbol. The symbol rate is always measured in baud (symbols/second), the reciprocal of the duration of the symbol.

Channel Data Rate
The data carried by the MFSK tones is inevitably coded in some way so that the "raw data" rate may not be the same as the user input or output data rate. However, the Channel Data Rate is always the number of bits per symbol x the Symbol Rate. The channel data rate is measured in bits/second (bps). For example, for a 10 baud 8FSK mode (8 tone FSK) there are three data bits per symbol, so the raw Channel Data Rate is 3 bits x 10 baud = 30 bps.

User Data Rate
Very often data is coded using an FEC system Forward Error Correction designed to reduce errors that occur due to the transmission path. For MFSK systems the most appropriate type of FEC is the sequential type, where every user data bit is represented in the transmission by two or more coded data bits. This ratio is the Coding Rate of the coder. For example, if there are two coded bits for every one data bit, the Coding Rate = 1/2. Thus the User Data Rate is the Channel Data Rate x Coding Rate.

Alphabet Coding
There are many ways to encode the alphabet from the keyboard for transmission. Perhaps the most common now is ASCII (ITA-5), but ITA-2 (as used by teleprinters) is also widely used. MFSK16, like Morse and PSK31, is based on a Varicode, which, unlike most alphabets, assigns a different number of bits to different characters, so that more frequently used characters have fewer bits and are therefore sent faster.

The number of bits per alphabet character therefore depends on the character frequency, just like Morse. For example: 

Character   Varicode
  space      100
  a          101100
  e          1100
  E          111011100
  Z          101010110100
Thus, the alphabet coding performance depends on the chosen code, and with a Varicode, even on the text sent:

Alphabet Bits/Char
ITA-5 ASCII 10
ITA-2 7.5
Varicode ~ 7-8

The strength of the varicode is that the alphabet is essentially infinitely expandable. For example, all the European accented characters are defined, and others have been added for control purposes, that are outside the character set. The MFSK16 varicode is not the same as the PSK31 varicode, although the technique is similar.

Another important advantage of using a varicode is that the stream of data can be much more quickly resynchronised in case of errors, than is possible with other systems, and so a minimum of data is lost.

Text Throughput
The user is most interested in the actual usable text throughput, which is specified in characters per second (CPS) or words per minute (WPM). Both depend on the alphabet used, and the number of words per minute depends on the average word size. In English this is taken for convenience to be five letters plus a letter space. So we can say that:

Text Throughput (CPS) = User Data Rate / Alphabet Bits per Character

Text Throughput (WPM) = CPS x 60 / letters per word

Worked Example
Say we are using an MFSK system with 16 tones (16FSK), operating at 15.625 baud with FEC Rate = 1/2, and an ASCII alphabet using 10 bits/character. Then: 

Symbol Rate           = 15.625 baud
Channel Data Rate     = 15.625 x log216 = 15.625 x 4        = 62.5   bps
User Data Rate        = 62.5 x 1/2 (FEC RATE)               = 31.25  bps
Text Throughput (CPS) = 31.25 / 10 CPS                      =  3.125 CPS
Text Throughput (WPM) = 31.25 x 60 / (10 x 6)               = 31.25  WPM
This will take place in a bandwidth little more than 16 x 15.625 = 250 Hz.

Comparisons
Amateur Radio RTTY operating at 45.45 baud achieves 60 WPM with no error correction, and requires about 300 Hz bandwidth. 300 baud packet is error corrected, but is unsuited by its design to HF conditions, and rarely delivers better than 30 WPM, and often much less. Packet requires 1 kHz bandwidth. PSK31 operates at 31.25 baud, and in QPSK mode gives error corrected text at 31.25 WPM approximately. It has the narrowest bandwidth, less than 100 Hz.

Graph of digital modes showing raw data rate vs. bandwidth
Fig. 5. Graph showing raw data rate of various digital modes
versus approximate bandwidth.

In terms of performance, of the examples given, only MFSK16 and PSK31 are considered practical for DX QSOs. PSK31 often performs poorly on long path, and provides no improvement when the FEC is used, so is usually used without it. MFSK is at least as sensitive as PSK31, and is unaffected by doppler. It is also less affected by interference, and offers effective FEC. These results are supported by ionospheric simulation tests.

MFSK16

The first serious Amateur Radio MFSK modes were developed in 2000 - MFSK16 (and slower but more robust MFSK8). Using test software by Nino IZ8BLY, initial QSOs were held 18 June 2000. The first QSO was from ZL1BPU - IZ8BLY on 18.105 MHz, and the second ZL1AN - ZL1BPU on 3.560 MHz. During the initial tests, rates from 7.8 to 31.25 baud were tested, with from 8 to 32 tones!

The parameters which now form the MFSK16 specification proved to be the best performing compromise. MFSK8 and MFSK16 are now freely available in the STREAM software by Nino IZ8BLY, and several other free and commercial programs. Several other modes have been developed since:

MFSK16 is the most sophisticated of these, and is (arguably) the best mode for long distance DX, and is by far the most widely used MFSK mode. Here's what you can expect using MFSK16:

The software is being continually upgraded as a result of feedback from expert testers. These tests build up operating experience and provide feedback to software designers on how best to control and operate the MFSK16 mode.

Ionospheric simulation tests by Johan KC7WW on his sophisticated equipment have shown excellent results. MFSK16 compares well with PSK31 and MT63.

The MFSK16 mode includes continuous phase tones and many other improvements, especially to the receiver. The mode is loosely based on Piccolo, but differs in a few important ways:

  1. The system can therefore potentially transmit text and binary files, any alphabet including varicodes, and can use error coding.
  2. The tones and baud rates (15.625 Hz, 31.25 Hz etc) are chosen to allow straightforward PC sound card sampling at 8 kHz sample rate.
  3. This means the transmitter need not be linear. Using the receiver FFT, the transmitted carrier phase can be extracted, and from it the symbol phase is deduced. This technique is very fast and reliable.

Of course MFSK16 is computer oriented, rather than an electromechanical system, so will be easy and inexpensive to install, and easy to operate, with no performance compromises. The same setup is used as for PSK31 or IZ8BLY Hellschreiber. All you need is a Pentium™ class computer, a Soundblaster™ type 16-bit sound card and Windows™ 95/98/NT/2000/XP or newer operating system. Several Windows versions are available, as well as one for LINUX. The first release software to meet the MFSK16 specification was STREAM by IZ8BLY. The MFSK16 software specification includes:

See the Technical Specifications to see what the software must meet.

The MFSK Varicode is slightly more efficient than others, since more smaller codes are available. This in turn is because the combinations "000", "0000" etc do not need to be reserved for idle and can be used inside character bit streams. Only the combination "001" is forbidden, as this signals the end of one character and the start of the next. The speed on plain language text is almost 20% faster than using the G3PLX varicode. The average number of bits per character for plain text has been measured at 7.44, giving MFSK16 a text throughput of 42 WPM at 31.25 baud user data rate.

Copyright © M. Greenman 1997-2005. All rights reserved. Contact the author before using any of this material.
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