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The Communications Edge ™

Tech-note

Author: Bob Watson

FSK: Signals and Demodulation

The most commonly used signal parameters
for describing an FSK signal are shown in
Figure 2
...
Typical values for element length are
between 5 and 22 milliseconds, but element
lengths of less than 1 microsecond and greater
than 1 second have been used
...
5 millisecond
...
The keying speed in “bauds” is
equal to the inverse of the element length in
seconds
...
02 seconds) is equivalent to
a 50-baud keying speed
...
The data are transmitted by shifting the
frequency of a continuous carrier in a binary
manner to one or the other of two discrete
frequencies
...
The mark and space correspond to binary one and zero, respectively
...
Figure 1 shows the relationship between the data and the transmitted
signal
...

The deviation is also equal, numerically, to
one-half of the shift
...
Coherency implies that the phase of
each mark or space tone has a fixed phase
relationship with respect to a reference
...
The shift is the frequency difference between the mark and space frequencies
...
The nominal center frequency is
halfway between the mark and space frequencies
...
The deviation is equal to the absolute
value of the difference between the center fre-

t

(b)

t

MARK

(c)

SPACE

FREQUENCY

Frequency shift keying (FSK) is the most
common form of digital modulation in the
high-frequency radio spectrum, and has
important applications in telephone circuits
...
Both modulation and
demodulation schemes will be discussed

Figure 1
...
Binary data (a) frequency modulates the carrier to produce the FSK signal (b)
which has the frequency characteristic (c)
...
FSK parameters
...
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While this method is sometimes used, the
constraint that transitions from mark to space
and vice versa must be phase continuous
(“glitch” free) requires that the shift and keying rate be interrelated
...
) of the
keying rate in bauds, is the most common
form of coherent FSK
...

Noncoherent FSK has no special phase relationship between consecutive elements, and,
in general, the phase varies randomly
...
They can be classified into two major groups: synchronous and
asynchronous
...

Asynchronous signals do not require a reference clock but instead rely on special bit patterns to control timing during decoding
...

A very common asynchronous coding system
is the 5-bit Baudot code with leading start
(release) and trailing stop (latch) elements
...
The binary values of the 5
bits correspond to a particular character
...
The 5 “information” bits are immediately followed by a stop or “latch” bit lasting a
minimum of 1
...
The latch
bit stops the printing decoder until the
decoder is again started by the next “release”

SIGNAL
(a)
CLOCK

t

(b)
t

Figure 3
...


C

W

0

L

R

1

1

0

0

1

2

3

4

5

1

L

R

0

0

1

1

1

2

3

4

5

L
t

1 ELEMENT
LATCH
RELEASE

1
...
Baudot coded start-stop system (typical)
...
The length of the latch bit may be
very long between characters, especially in the
case of manually generated characters where
the operator types more slowly than the system can transmit characters
...

A common synchronous system uses Moore
ARQ coding
...

Bit synchronization is maintained by using a
reference clock which tracks the keying speed
of the received signal
...


FREQUENCY DIVISION
MULTIPLEX (FDM)
Several FSK signals can be transmitted simultaneously in a given frequency band by
assigning different center frequencies to each
of the FSK signals
...
In the radio
spectrum several audio FSK signals are often
combined for transmission by a single-sideband transmitter
...
To
minimize bandwidth, the individual FSK
channels usually have “narrow” shifts of
between 50 and 200 Hertz
...
HF radio systems usually transmit 16 tone channels, but
24 or more tone channels per 3-kHz sideband are possible
...

HF radio is subject to random multi-path signal fading
...
As a defense against fading, it is
common practice to run duplicate data in
tone channels in the same FDM group
...
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...
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...
An alternate approach to the
diversity problem is to use “interleaved”
FDM
...
5

170 Hz
425 Hz

1
382
...
Typical 16-channel FDM (VFT) FSK signal
...
This suggests that
reception of the mark or space alone is sufficient to determine the transmitted data
...
To combine widely separated mark and space tone pairs into a single
FDM sideband, each pair must be interleaved with the other pairs
...
By interleaving the
FSK tone pairs it is possible to achieve good
performance against multipath fading without sacrificing bandwidth efficiency
...


DOUBLE FREQUENCY SHIFT
KEYING (DFSK)

FREQENCY

DFSK, sometimes called DFS or twinplex, is
a scheme to transmit two independent binary
data streams by shifting the frequency of a
single carrier among four discrete frequencies
...
For
example, if bit X and bit Y are 1 and 0,
respectively, the output state is C
...
Figure 8 illustrates a typical
DFSK signal
...
Interleaved FDM FSK signal
...

For this reason it is possible to take advantage of in-band frequency diversity to greatly improve
system performance against multipath fading
...
The disadvantage of this scheme is that only

INPUT BITS
X
Y
0
0
1
1

0
1
0
1

OUTPUT STATE
A
B
C
D

Figure 7
...


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The Communications Edge ™

Tech-note

Author: Bob Watson

combination of synchronous and asynchronous signals
...
Bit synchronization
between channels is not required
...
Early designs for FSK demodulation
tended to be FM detector types so they will
be discussed first
...
There are 24 different ways (4 factorial permutations) that the
four states can be assigned to four frequencies
...


FM DETECTOR DEMODULATORS

FSK DEMODULATION
The demodulation methods for FSK can be

The FM detector demodulator treats the FSK
signal as a simple FM signal with binary
modulation
...
The limited signal is FM-detected to produce a positive output for a mark condition and a negative output for a space condition
...
DFSK signal
...


DATA
OUT

FSK
SIGNAL
BAND
PASS
FILTER

LIMITER

Figure 9
...


LOW PASS
FM
FILTER
DISCRIMINATOR

DECISION
(SLICER)

makes all positive voltages into binary 1’s and
all negative voltages into binary 0’s
...
Phase-locked-loop (PLL) demodulators are a more recent technique, but they
have very similar performances to that of FM
detector demodulators
...

FM detector-type demodulators are somewhat complex for FDM work and cannot
generally be used with interleaved FDM signals
...

FM-type detectors are non-optimal in the
sense that they perform more poorly than signal detection theory would predict is possible
...
As
shown in Figure 10, it can be seen that virtually all the energy in the mark and space tones
is within a bandwidth equal to twice the baud
rate, centered about the mark and space frequencies, respectively
...

The interfering signal at fA is rejected because
it is out of the passband of the FM detector
input filter
...
Unfortunately, the
interfering signal at fC is the strongest in-band
signal and, as a result, completely prevents
demodulation of the desired FSK signal
...
Therefore, during mark transmissions,
demodulation is severely affected
...
If the envelope of the noise exceeds that of the FSK signal, demodulation is prevented
...
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...


FILTER-TYPE FSK
DEMODULATORS
FREQUENCY
fSPACE

fMARK
∆f = KEYING SPEED
IN BAUDS

Figure 10
...


IN-BAND
INTERFERENCE

OUT-OF-BAND
INTERFERENCE

AMPLITUDE

FM DETECTOR
INPUT BAND PASS FILTER

FREQUENCY
fA

fSPACE

fB

fC

fMARK

Figure 11
...


AMPLITUDE

IN-BAND INTERFERENCE

FREQUENCY
fSPACE

fB

fMARK

Figure 12
...


A comparison of the FSK spectrum with the spectrum over which an FM-type FSK detector is
sensitive to interference leads to the conclusion that the performance of an FM-type FSK detector is severely limited by its relatively wide input bandwidth
...

At this point it is appropriate to ask, “What is the optimum demodulation method?” Using sig-

Filter-type demodulators attempt to optimally
match the FSK signal parameters to the
demodulator configuration to optimize
demodulator error performance
...
The proper filter design
depends not only on the signal parameters,
but also on the nature of the signal interference
...
Other filter-type
demodulators are used for noncoherent FSK
and/or non-stochastic noise environments
...
In the demodulator, the output of
the matched filters is compared, and if the
output from the mark filter is larger than that
from the space filter, a decision is made that a
mark signal was transmitted
...
A matched filter
demodulator is optimum because its filters are
matched” to the transmitted signal so that
their response to the desired signal is maximized with respect to their noise response
...
Because noncoherent
FSK is so much more common than coherent
FSK, it is necessary to have a type of demodulator that does not depend on phase information
...
A demodulator of this type is
shown in Figure 15
...
Note that phase information is not required
...
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The “right” filter shape for
a white noise interference environment is one
that has the same spectral shape as the transmitted signal
...
Optimum normalized bandwidth for each filter is at the SNR
minimum
...
To the
right, excess white noise energy is the dominant interferer
...
If we consider filters with a bandwidth normalized by
multiplying the 3-dB bandwidth (B) by the
element length (T), we can plot a single performance curve for each filter shape, independent of system keying speed
...
The spectral shape of
optimum mark and space filters would be the
same as that of the mark and space spectrum
of Figure 10
...

For the general case of noncoherent FSK with
non-white noise interference, the problem of
optimum filter design is more complex
...
Because of the unpredictable nature of this kind of interference, it
is desirable to create a filter type which performs well with both white and non-white
interference
...
It is
also desirable that the filter perform well in
white noise
...
In general, if the filter bandwidth
is too wide, excess noise energy will be included
...
This is called intersymbol interference
...

To specify filter characteristics, it is convenient to talk in terms of the filter’s 3 dB
bandwidth
...
Simplified demodulation spectrum for filter type FSK demodulators
...
Matched filter FSK demodulator
...
Non-coherent FSK demodulation with spectrally matched filters and envelope detection
...
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The filter bandwidths and center frequencies must be independently variable over a wide range to optimally match the signal parameters of keying
speed and shift
...
Figure 18(a) shows the
combined output for alternating mark and
space transmissions
...

In the summing configuration, the decision
circuit compares the differential sum with a
voltage reference, which determines the decision “threshold
...
When the signal has
equal mark and space amplitudes, the optimum threshold is a fixed zero-voltage reference
...
2 0
...
6 0
...
0

1
...
0

1
...
0 BT

Figure 16
...


LOWER ERROR BOUND FOR VARIABLE THRESHOLD FSK
IN INDEPENDENT RAYLEIGH FADING

0
...
1
FPROBABILITY OF ERROR

The decision element of Figure 15 can be
realized by several different circuit configurations
...
With equal amplitude transmitted signals and no selective fading, this is the theoretically optimum decision
circuit
...
If the FSK signal
is subject to selective fading (Rayleigh amplitude statistics), the performance of the
demodulator is severely degraded
...
01
10-3
10-4
10-5
10-6
NON-FADING FSK
5 dB

10 dB

15 dB

20 dB

25 dB

30 dB

SNR as
Eb
Nb

=

Eb
Nb

SIGNAL ENERGY PER BIT
NOISE POWER PER H2

Figure 17
...


decision threshold to achieve optimum
demodulation
...

Performance of a variable-threshold detector
can be compared to diversity demodulation
of two independently fading, amplitudeshift-keyed (ASK) signals
...
The error
performance of diversity ASK and a lower
error bound limit of performance for variable
threshold FSK are shown in Figure 17
...


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...
com • Web site: www
...
com

The Communications Edge ™

Tech-note

Author: Bob Watson

CONCLUSION
MARK
TONE
AMPLITUDE
+

FADING MARK
ENVELOPE
VARIABLE DECISION
THRESHOLD

(a)
–
MARK
TONE
AMPLITUDE

(b)

FADING SPACE
ENVELOPE

1
0

(c)

FIXED DECISION
THRESHOLD

FSK signals take many different forms
depending on their intended application
...


t FIXED
DECISION DATA

1
0

t VARIABLE
DECISION DATA

Figure 18
...
The differential sum (a) of the mark
and space detectors produces distorted data (b) with a fied decision threshold and undistroted data (c) with a
variable decision threshold
...
7 No
...

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...
com • Web site: www
...
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