fsk signals demod

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The Communications Edge™

Tech-note Author: Bob Watson

FSK: Signals and DemodulationFrequency shift keying (FSK) is the mostcommon form of digital modulation in thehigh-frequency radio spectrum, and hasimportant applications in telephone circuits.This article provides a general tutorial on FSKin its many forms. Both modulation anddemodulation schemes will be discussed

BINARY FSK

Binary FSK (usually referred to simply asFSK) is a modulation scheme typically usedto send digital information between digitalequipment such as teleprinters and comput-ers. The data are transmitted by shifting thefrequency of a continuous carrier in a binarymanner to one or the other of two discretefrequencies. One frequency is designated asthe “mark” frequency and the other as the“space” frequency. The mark and space corre-spond to binary one and zero, respectively. Byconvention, mark corresponds to the higherradio frequency. Figure 1 shows the relation-ship between the data and the transmittedsignal.

The most commonly used signal parametersfor describing an FSK signal are shown inFigure 2. The minimum duration of a markor space condition is called the elementlength. Typical values for element length arebetween 5 and 22 milliseconds, but elementlengths of less than 1 microsecond and greaterthan 1 second have been used. Bandwidthconstraints in telephone channels and signalpropagation considerations in HF channelsgenerally require the element length to begreater than 0.5 millisecond. An alternate wayof specifying element length is in terms of thekeying speed. The keying speed in “bauds” isequal to the inverse of the element length inseconds. For example, an element length of20 milliseconds (.02 seconds) is equivalent toa 50-baud keying speed.

Frequency measurements of the FSK signalare usually stated in terms of “shift” and cen-

ter frequency. The shift is the frequency dif-

ference between the mark and space frequen-

cies. Shifts are usually in the range of 50 to

1000 Hertz. The nominal center frequency is

halfway between the mark and space frequen-

cies. Occasionally the FM term “deviation” is

used. The deviation is equal to the absolute

value of the difference between the center fre-

MARK SPACE

time (a)

t (b)

t (c)

DAT

AF

RE

QU

EN

CY

SIG

NA

LA

MP

LIT

UD

E

1

0

Figure 1. FSK modulation. Binary data (a) frequency modulates the carrier to produce the FSK signal (b)which has the frequency characteristic (c).

FREQUENCY

F2

F1

NOMINALCENTERFREQUENCY SHIFT

DEVIATION

DEVIATION

ELEMENTLENGTH

ELEMENT LENGTH(IN SECONDS)

t

SHIFT = | F2 - F1 |

CTR FREQ =

DEVIATION = =

F2 + F1

2

F2 + F1

2SHIFT

2

KEYING SPEED IN BAUDS =1

Figure 2. FSK parameters.

quency and the mark or space frequencies.The deviation is also equal, numerically, toone-half of the shift.

FSK can be transmitted coherently or nonco-herently. Coherency implies that the phase ofeach mark or space tone has a fixed phaserelationship with respect to a reference. This issimilar to generating an FSK signal by switch-




ing between two fixed-frequency oscillators toproduce the mark and space frequencies.While this method is sometimes used, theconstraint that transitions from mark to spaceand vice versa must be phase continuous(“glitch” free) requires that the shift and key-ing rate be interrelated. A synchronous FSKsignal which has a shift in Hertz equal to anexact integral multiple (n = 1, 2,...) of thekeying rate in bauds, is the most commonform of coherent FSK. Coherent FSK is capa-ble of superior error performance but nonco-herent FSK is simpler to generate and is usedfor the majority of FSK transmissions.Noncoherent FSK has no special phase rela-tionship between consecutive elements, and,in general, the phase varies randomly.

Many different coding schemes are used totransmit data with FSK. They can be classi-fied into two major groups: synchronous andasynchronous. Synchronous transmissionshave mark-to-space and space-to-mark transi-

element. The length of the latch bit may bevery long between characters, especially in thecase of manually generated characters wherethe operator types more slowly than the sys-tem can transmit characters. The nonintegerminimum latch element length of 142 ele-ments and the random nature of manualcharacter generation emphasizes the asynchro-nous nature of this scheme.

A common synchronous system uses MooreARQ coding. The Moore code is a 7-bit-per-character code with no start or stop elements.Bit synchronization is maintained by using areference clock which tracks the keying speedof the received signal. Character synchroniza-tion is maintained by sending periodic “idle”or “dummy” characters between valid datacharacters.

FREQUENCY DIVISIONMULTIPLEX (FDM)

Several FSK signals can be transmitted simul-taneously in a given frequency band byassigning different center frequencies to eachof the FSK signals. This method of simultane-ous transmission is called FDM. In the radiospectrum several audio FSK signals are oftencombined for transmission by a single-side-band transmitter. This form of FDM is oftencalled Voice Frequency Telegraph (VFT). Tominimize bandwidth, the individual FSKchannels usually have “narrow” shifts ofbetween 50 and 200 Hertz. A typical FDMsystem is shown in Figure 5. HF radio sys-tems usually transmit 16 tone channels, but24 or more tone channels per 3-kHz side-band are possible. Telephone standard is typi-cally 12 or 24 tone channels per 3-kHz side-band (voice band).

HF radio is subject to random multi-path sig-nal fading. The relatively narrow-band natureof this fading phenomenon causes only oneor two tone channels to be severely affected atany moment. As a defense against fading, it iscommon practice to run duplicate data intone channels in the same FDM group. If theduplicate channels are separated by 1 kHz or

tions in synchronism with a reference clock.Asynchronous signals do not require a refer-ence clock but instead rely on special bit pat-terns to control timing during decoding.Figure 3 compares synchronous and asyn-chronous keying.

A very common asynchronous coding systemis the 5-bit Baudot code with leading start(release) and trailing stop (latch) elements.Originally designed for use with mechanicalteleprinters, the system is “latched” until a“release” element is received, causing theprinter to interpret the next 5 element inter-vals as code bits. The binary values of the 5bits correspond to a particular character. InFigure 4, the two character patterns corre-spond to the characters “C” and “W” respec-tively. The 5 “information” bits are immedi-ately followed by a stop or “latch” bit lasting aminimum of 1.42 element lengths. The latchbit stops the printing decoder until thedecoder is again started by the next “release”

SIGNAL

CLOCK

(a)

(b)

t

t

t

0 1 1 0 0 1 0 0 1 1

C

L R 1 2 3 4 5 21 3 4 5 LL R

W

LATCH

RELEASE 1.42ELEMENTS(MINIMUM)

1 ELEMENT

Figure 3. Synchronous (a) and asynchronous (b) signals.

Figure 4. Baudot coded start-stop system (typical).




half as many channels can be transmitted dueto duplication. An alternate approach to thediversity problem is to use “interleaved”FDM.

Interleaved FDM takes advantage of the factthat a mark tone’s activity is the complementof the space tone activity. This suggests thatreception of the mark or space alone is suffi-cient to determine the transmitted data. If themark and space tones are separated by 1 kHzor so, they can be separately detected for fre-quency diversity. To combine widely separat-ed mark and space tone pairs into a singleFDM sideband, each pair must be inter-leaved with the other pairs. This scheme isdemonstrated in Figure 6. By interleaving theFSK tone pairs it is possible to achieve goodperformance against multipath fading with-out sacrificing bandwidth efficiency. In spiteof the advantages of interleaving, it is a lesspopular scheme than simple tone duplicationbecause the required demodulator is morecomplex.

DOUBLE FREQUENCY SHIFTKEYING (DFSK)

DFSK, sometimes called DFS or twinplex, isa scheme to transmit two independent binarydata streams by shifting the frequency of asingle carrier among four discrete frequencies.Figure 7 shows a code table to convert twobinary bits to one of four output states. Forexample, if bit X and bit Y are 1 and 0,respectively, the output state is C. If each ofthe four output states (A through D) isassigned to a corresponding FSK frequency,then it is possible to transmit any two bits asa single element. Figure 8 illustrates a typicalDFSK signal. Because the two binary chan-nels are independent, they may contain any

AUDIOFREQUENCY

18

15

14

4

3

2

1

2975 Hz

2805 Hz

765 Hz

595 Hz170 Hz

85 Hz

425 Hz467.5

382.5

SHIFT = 85 HzKEYING SPEED = 50 BAUDS = CENTER FREQUENCY

t

Figure 5. Typical 16-channel FDM (VFT) FSK signal.

FREQENCY

MARK 3

MARK 2

MARK 1

SPACE 3

SPACE 2

SPACE 1

t

Figure 6. Interleaved FDM FSK signal.

INPUT BITS OUTPUT STATEX Y

0 0 A0 1 B1 0 C1 1 D

Figure 7. One-of-four code table for two binary bits.

so, the fades in one tone channel are relatively uncorrelated with fades in the duplicate channel.For this reason it is possible to take advantage of in-band frequency diversity to greatly improvesystem performance against multipath fading. In a 16-channel HF scheme, channel 1 is pairedwith channel 9, channel 2 with channel 10, etc. The disadvantage of this scheme is that only




combination of synchronous and asynchro-nous signals. It is not uncommon to have ateleprinter in one channel and a Morse codesignal in the other. Bit synchronizationbetween channels is not required.

In the example of Figures 7 and 8, outputstates A through D are assigned to frequenciesf1 through f4, respectively. There are 24 differ-ent ways (4 factorial permutations) that thefour states can be assigned to four frequencies.Because the DFSK signal transmits only onefrequency at a time, transmitter power effi-ciency can be much higher than an FDMtransmitter, which has a linearity requirementto prevent intermodulation of tones.

FSK DEMODULATION

The demodulation methods for FSK can be

makes all positive voltages into binary 1’s andall negative voltages into binary 0’s.

This type of demodulator was very populardue to its relative simplicity and its noncriticaltuning. Phase-locked-loop (PLL) demodula-tors are a more recent technique, but theyhave very similar performances to that of FMdetector demodulators. However, for a smallclass of signals specifically designed for PLLdemodulation, PLL demodulators may per-form better than FM detector demodulators.FM detector-type demodulators are some-what complex for FDM work and cannotgenerally be used with interleaved FDM sig-nals. They are also not commonly used withDFSK signals.

FM-type detectors are non-optimal in thesense that they perform more poorly than sig-nal detection theory would predict is possible.To see why this is true, it is necessary to exam-ine the spectrum of a typical FSK signal. Asshown in Figure 10, it can be seen that virtu-ally all the energy in the mark and space tonesis within a bandwidth equal to twice the baudrate, centered about the mark and space fre-quencies, respectively. Figure 11 shows theFSK signal spectrum with interfering signals.The interfering signal at fA is rejected becauseit is out of the passband of the FM detectorinput filter. The interfering signal at fB isrejected by the action of the FM limiter,which forces the strongest signal to dominate(FM “capture” effect). Unfortunately, theinterfering signal at fC is the strongest in-bandsignal and, as a result, completely preventsdemodulation of the desired FSK signal. Inthe case of selective fading, as shown in Figure12, even though the space signal is strongerthan the in-band interference, the amplitudeof the mark signal, reduced by multipath fad-ing, is less than that of the in-band interfer-ence. Therefore, during mark transmissions,demodulation is severely affected. More diffi-cult to show graphically is the effect of broad-band “white” noise interference. If the enve-lope of the noise exceeds that of the FSK sig-nal, demodulation is prevented.

divided into two major categories: FM detec-tor demodulators and filter-type demodula-tors. Early designs for FSK demodulationtended to be FM detector types so they willbe discussed first.

FM DETECTOR DEMODULATORS

The FM detector demodulator treats the FSKsignal as a simple FM signal with binarymodulation. Figure 9 shows a functionalblock diagram for an FM detector-typeremove out-of-band interference and thenlimited to remove AM interference. The lim-ited signal is FM-detected to produce a posi-tive output for a mark condition and a nega-tive output for a space condition. The raw,detected signal is lowpass-filtered to removenoise components at frequencies above thebaud rate, and, finally, the decision circuit

FSKSIGNAL

BANDPASS

FILTER

LIMITER FMDISCRIMINATOR

LOW PASSFILTER

DECISION(SLICER)

DATAOUT

Figure 9. FM detector-type FSK demodulator.

1

0

X

1

0

Y

FREQUENCY

f4

f3

f2

f1

(a)

(b)

(c)

t

t

Figure 8. DFSK signal. Digital channels X (a) and Y (b) are combined into a single DFSK.




nal-detection theory, it can be shown that a“matched-filter” detector will give the theoret-ically best demodulation performance.

FILTER-TYPE FSKDEMODULATORS

Filter-type demodulators attempt to optimallymatch the FSK signal parameters to thedemodulator configuration to optimizedemodulator error performance. A simplifiedspectrum for filter-type demodulators isshown in Figure 13. The proper filter designdepends not only on the signal parameters,but also on the nature of the signal interfer-ence. The classic “matched” filter demodula-tor is optimal for coherent FSK in whitegaussian noise interference. Other filter-typedemodulators are used for noncoherent FSKand/or non-stochastic noise environments.

A block diagram of a simple, matched-filterdemodulator for coherent FSK is shown inFigure 14. In the demodulator, the output ofthe matched filters is compared, and if theoutput from the mark filter is larger than thatfrom the space filter, a decision is made that amark signal was transmitted. Space detectionis similarly performed. A matched filterdemodulator is optimum because its filters arematched” to the transmitted signal so thattheir response to the desired signal is maxi-mized with respect to their noise response.For white noise, the optimum filter has animpulse response equal to the time-reversed,input signaling element. Because noncoherentFSK is so much more common than coherentFSK, it is necessary to have a type of demod-ulator that does not depend on phase infor-mation.

Optimum demodulation of non-coherentFSK can be achieved by envelope detection ofthe signal filter outputs in a filter-typedemodulator. A demodulator of this type isshown in Figure 15. The outputs of the markand space filters are envelope-detected andthen compared to determine which hasgreater magnitude. Note that phase informa-tion is not required. With the “right” filter

AM

PLI

TU

DE

FREQUENCYfSPACE fMARK

∆f = KEYING SPEEDIN BAUDS

Figure 10. Simplified frequency spectrum of a typical binary FSK signal.

AM

PLI

TU

DE

FREQUENCYfSPACEfA fB fC fMARK

OUT-OF-BANDINTERFERENCE

IN-BANDINTERFERENCE

FM DETECTORINPUT BAND PASS FILTER

Figure 11. FSk signal spectrum with in-bnd and out-of-band interference.

AM

PLI

TU

DE

FREQUENCYfSPACE fB fMARK

IN-BAND INTERFERENCE

Figure 12. FSK signal spectrum with in-band interference and selective fading.

A comparison of the FSK spectrum with the spectrum over which an FM-type FSK detector issensitive to interference leads to the conclusion that the performance of an FM-type FSK detec-tor is severely limited by its relatively wide input bandwidth. The inclusion of large portions offrequency spectrum that do not contain significant signal energy is clearly a non-optimalapproach to FSK demodulation.

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




shape, performance of this type of demodula-tor approaches the theoretical optimum fornoncoherent FSK. The “right” filter shape fora white noise interference environment is onethat has the same spectral shape as the trans-mitted signal. For the “rectangular” modula-tion of FSK, the right shape is a sinc function

sin xx

bandpass filter centered about the desiredmark or space tone. The spectral shape ofoptimum mark and space filters would be thesame as that of the mark and space spectrumof Figure 10. Unfortunately, the assumptionof white noise interference is not justified inmost real signal environments.

For the general case of noncoherent FSK withnon-white noise interference, the problem ofoptimum filter design is more complex. Twocommon types of non-white noise interfer-ence are adjacent channel interference andCW interference. Because of the unpre-dictable nature of this kind of interference, itis desirable to create a filter type which per-forms well with both white and non-whiteinterference. To minimize the effect of non-white interference, it is desirable to use abandpass filter with relatively steep attenua-tion skirts and without the side lobes that arecharacteristic of the sinc-function filter. It isalso desirable that the filter perform well inwhite noise.

For each filter shape, there is an optimumbandwidth. In general, if the filter bandwidthis too wide, excess noise energy will be includ-ed. If the filter bandwidth is too narrow, con-secutive signal elements will interfere witheach other. This is called intersymbol interfer-ence. In narrow filters, this is caused by “ring-ing” or by the filters inability to “dump” theenergy of the previous element before thenext element is received.

To specify filter characteristics, it is conve-nient to talk in terms of the filter’s 3 dBbandwidth. The optimum 3 dB bandwidthvaries directly with the signal keying speed

to-noise ratio (SNR) for constant error per-formance in white noise. Optimum normal-ized bandwidth for each filter is at the SNRminimum. To the left of the SNR minimum,intersymbol interference dominates. To theright, excess white noise energy is the domi-nant interferer.

and inversely with element length. If we con-sider filters with a bandwidth normalized bymultiplying the 3-dB bandwidth (B) by theelement length (T), we can plot a single per-formance curve for each filter shape, indepen-dent of system keying speed. Figure 16 plotsnormalized filter bandwidth versus the signal-

AM

PLI

TU

DE

FREQUENCYfSPACE fMARK

SPACEFILTER

MARKFILTER

Figure 13. Simplified demodulation spectrum for filter type FSK demodulators.

FSK SIGNAL DATA OUT

MATCHEDMARKFILTER

MATCHEDSPACEFILTER

DECISION(COMPARE)

Figure 14. Matched filter FSK demodulator.

FSKSIGNAL

DATAOUT

MARKBAND PASS

FILTER

SPACEBAND PASS

FILTER

DECISION(COMPARE)

ENVELOPEDETECTOR

ENVELOPEDETECTOR

Figure 15. Non-coherent FSK demodulation with spectrally matched filters and envelope detection.

( )




2ND-ORDER FILTER

"IDEAL" (SQUARE) FILTER

FR

EQ

UIR

ED

SN

R F

OR

CO

NS

TAN

T P

ER

FO

RM

AN

CE SNR

NORMALIZEDBANDWIDT

0.2 0.4 0.6 0.8 1.0 1.5 2.0 1.5 3.0 BT

1 dB

Figure 16. Constant error performnce curves for two FSK filter types.

FP

RO

BA

BIL

ITY

OF

ER

RO

R

30 dB25 dB20 dB15 dB10 dB5 dB

0.5

0.1

0.01

10-3

10-4

10-5

10-6

SNR asEb

Nb

Eb

Nb

SIGNAL ENERGY PER BITNOISE POWER PER H2

=

NON-FADING FSK

LOWER ERROR BOUND FOR VARIABLE THRESHOLD FSKIN INDEPENDENT RAYLEIGH FADING

RAYLEIGH FADING DUAL DIVERSITY ASK

RAYLEIGH FADING FSK

Figure 17. Constant error performnce curves for two FSK filter types.

By selecting a filter type which has both goodwhite-noise performance and steep attenua-tion skirts, excellent noncoherent FSKdemodulation is possible in either white ornonwhite noise interference. The filter band-widths and center frequencies must be inde-pendently variable over a wide range to opti-mally match the signal parameters of keyingspeed and shift.

DECISION THRESHOLDSELECTION

The decision element of Figure 15 can berealized by several different circuit configura-tions. The simplest decision circuit is a voltagecomparator which decides that a mark signalwas received if the output from the markdetector is greater than the “noise” outputfrom the space detector. With equal ampli-tude transmitted signals and no selective fad-ing, this is the theoretically optimum decisioncircuit. The error performance of this type ofdecision for binary noncoherent FSK in whitenoise is shown in Figure 17. If the FSK signalis subject to selective fading (Rayleigh ampli-tude statistics), the performance of thedemodulator is severely degraded.

If the mark and space tones are separated infrequency so that they fade independently, itis possible to differentially sum the outputs ofthe mark and space detectors to diversity-combine the signals. Figure 18(a) shows thecombined output for alternating mark andspace transmissions. The envelopes of themark and space detector voltages vary withthe fading mark and space signal amplitudes.In the summing configuration, the decisioncircuit compares the differential sum with avoltage reference, which determines the deci-sion “threshold.” When the sum is greaterthan the threshold, a mark decision is madeand when the sum is less than the threshold, aspace decision is made. When the signal hasequal mark and space amplitudes, the opti-mum threshold is a fixed zero-voltage refer-ence. However, during selective fading condi-tions, it is necessary to dynamically vary the

that predicted for diversity ASK. The errorperformance of diversity ASK and a lowererror bound limit of performance for variablethreshold FSK are shown in Figure 17. Forbest performance, the parameters of the vari-able threshold detection circuitry must beoptimized with respect to the signal charac-teristics.

decision threshold to achieve optimumdemodulation. The effect of selective fadingon signal data with fixed and variable thresh-olds is demonstrated in Figure 18(b) and (c).

Performance of a variable-threshold detectorcan be compared to diversity demodulationof two independently fading, amplitude-shift-keyed (ASK) signals. In fact, because ofthe differential nature of the mark and spacesignals, error performance can be better than




t

1

0

(c)

VARIABLEDECISION DATA

t

1

0

(b)

(a)

FIXEDDECISION DATA

MARKTONE

AMPLITUDE

MARKTONE

AMPLITUDE

FADING MARKENVELOPE

VARIABLE DECISIONTHRESHOLD

FIXED DECISIONTHRESHOLD

FADING SPACEENVELOPE

+

–

Figure 18. Independent fading FSK with fixed and variable decision thresholds. The differential sum (a) of the markand space detectors produces distorted data (b) with a fied decision threshold and undistroted data (c) with avariable decision threshold.

CONCLUSION

FSK signals take many different formsdepending on their intended application.With the increasing sophistication of elec-tronics and signal detection theory, it is clearthat FSK demodulators, are required to opti-mally demodulate the many different signalformats.

Copyright © 1980 Watkins-Johnson CompanyVol. 7 No. 5 September/October 1980

Revised and reprinted © 2001 WJ Communications, Inc.

fsk signals demod

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