System for demodulation and synchronizing multiple tone waveforms

A multiple tone signal is demodulated and synchronization is obtained by precisely locating frame boundaries in order to ensure reliable communication in the presence of anomalies such as Doppler shift, multipath propagation, and additive electronic noise. One such signal, TADIL-A or Link-11, employs multiple tone audio waveforms that are used to modulate RF carriers for the transmission of digital data. Initially, the signal is frequency divided and classified to determine if the incoming frame is a preamble, data or noise. For preamble frames, a digital filter is used to extract the 605 Hz tone in the time domain, and the resulting real-valued signal is passed through a first Hilbert transform to generate the corresponding imaginary complex-valued signal. Unfiltered data frames are passed through a second Hilbert transform and the output is multiplied by the complex conjugate of the stored Doppler reference signal to produce a Link-11 Signal stripped of Doppler. As a result of the demodulation process, the entire waveform now includes frequencies separated by an integer multiple of 110 Hz. Therefore, the composite waveform has a period of 9.09 milliseconds. The composite waveform partially repeats itself at least once in each 13.33 msec frame interval. Using this property, it is possible to determine the location at which the composite signal becomes discontinuous and thereby locate the synchronization frame boundaries.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The invention relates to a system for demodulating a multiple tone Link-11 
Signal, stripping off the Doppler component and locating the 
synchronization frame boundaries. 
2. Background of the Invention 
It is important to maintain continuous secure communication over a 
computer-to-computer radio link during military operations. Typically, a 
base Net Control Station (NCS), located on an aircraft carrier, keeps in 
constant contact with moving aircraft or surface vessels referred to as 
pickets or Participating Units (PU's). As the PU move towards and away 
from the aircraft carrier, Doppler shifts and other aberrations may be 
introduced. Various prior art devices and methods have been proposed to 
overcome these problems. 
The standards for communications in the United States Navy over a 
computer-to-computer radio data link are set forth in military standard 
MIL-STD-188-203-1A dated Jan. 8, 1988 and entitled "INTEROPERABILITY AND 
PERFORMANCE STANDARDS FOR TACTICAL DIGITAL INFORMATION LINK (TADIL)A" 
otherwise known as Link-11. A useful discussion of prior art technology 
and difficulties is also set forth in U.S. Pat. No. 4,199,809. 
A Link-11 data message consists of 48 binary digits. The bits are assembled 
in two frames, each of 24 bits. Six Hamming code parity check bits are 
added in each frame to make 30 bits for transmission. Each of the 15 pairs 
of bits in the frame are converted into a phase shift, with shifts of 
-45.degree., -135.degree., -225.degree. and -315 representing 4 bit pairs, 
namely (1,1), (0,1), (0,0) and (1,0). Differential Quadrature Phase Shift 
Keying (DQPSK) is applied to each of 15 audio tones. 14 of the tones are 
at frequencies of 935 Hz through 2,365 Hz at 110 Hz intervals, with a 15th 
tone at 2,915 Hz. The transmitted audio signal is the sum of the 15 
modulated signals plus a Doppler reference tone of 605 Hz. Therefore, the 
signal consists of 16 superimposed sine waves, with nominal frequencies 
given by the tone library of 605, 935, 1045, 1155, 1265, 1375, 1485, 1595, 
1705, 1815, 1925, 2035, 2145, 2255, 2365, and 2915 Hz. It is important to 
note that all of the 16 frequencies are separated from each other by 110 
Hz or an integer multiple thereof. The Doppler reference tone of 605 Hz is 
used for Doppler shift corrections. 
The transmitter at the NCS uses the audio signal to amplitude modulate an 
HF radio frequency carrier and transmit a double sideband suppressed 
carrier HF signal. Each of the two sidebands, the upper and the lower, 
contain the same audio signal upon transmission, but anomalies in the 
propagation path, noise, and interference may cause the received sidebands 
to differ. 
Each Link-11 message is made up of a preamble consisting of five frames 
which contain only 605 Hz and 2915 Hz tones, followed by an arbitrary 
number of data frames containing all 16 tones. During the five frame 
preamble, the 2915 Hz tone is given twice its normal amplitude and is 
phase shifted 180.degree. at each frame boundary to provide for frame 
synchronization. The 605 Hz tone is given twice the amplitude of the 2915 
Hz tone during the preamble frames and twice the amplitude of the 
information carrying tones for all other transmitted frames. The 6th frame 
is a reference frame during which all data tones are transmitted to 
establish a reference phase for each. Frame positions 7 and 8 provide a 
start code control signal indicating that data will follow. After the data 
is transmitted, a picket stop code control signal is transmitted to 
complete the message. 
Link-11 signals are divided into fixed-length frames having a duration of 
13.33 msec (fast) or 22 msec (slow), at the operator's option. Within 
individual frames, each tone has a fixed phase. With the exception of the 
605 Hz tone, which is unmodulated and used for Doppler correction, the 
phase of each tone changes at each frame boundary. At the fast speed of 
13.33 msec, the throughput is 2250 bits per second or 47 bits per frame. 
Differential Quadrature Phase Shift Keying (DQPSK) is used to encode data, 
so that the phase change of each tone at the frame boundary encodes a 
2-bit value depending upon the quadrant in which the differential phase 
value occurs. 
The protocol of Link-11 includes 5 modes of operation namely, Roll Call, 
Net Sync, Net Test, Broadcast and Short Broadcast. Further discussion of 
the protocol may be found in military standard. MIL-STD-188-203-1A 
referred to previously. 
As described in military standard MIL-STD-188-203-1A, the multi-tone 
Link-11 waveform is usually transmitted over the HF band (2-30 MHz) or the 
UHF band (200-400 MHz). In the case of UHF, the waveform frequency 
modulates the carrier (FM) while at HF the modulation is single side band 
AM (SSB). In the latter case, a frequency shift of the carrier due either 
to relative motion induced Doppler shift or relative miss-tuning of the 
transmitter with respect to the receiver, results in a uniform translation 
of all frequency components of the audio waveform. See, in particular, 
Sections 5.1.1 and 5.1.2 of military standard MIL-STD-188-203-1A. 
Regardless of its physical causes, this uniform frequency shift is 
generally referred to as "Doppler shift." Therefore, with respect to a 
conventional multiple tone Link-11 waveform, this means that all 16 tones, 
including the unmodulated 605 Hz Doppler reference tone and the 15 phase 
modulated data tone (935 to 2915 Hz) will all undergo an identical uniform 
frequency shift, f.sub. DP. For further discussion, see sections 5.1.10 
and 5.2.7 of military standard MIL-STD-188-203-1A. The aforementioned 
shift f.sub.DP, which can be as great as + or -75 Hz, affects the entire 
signal and must be removed or large data errors will occur. 
The patent literature describes the difficulties with earlier approaches. 
In particular, U.S. Pat. No. 4,199,809 describes clearly how the prior art 
hardware equipment is highly customized and difficult to maintain. The 
size of prior art Link-11 systems is relatively large and generally 
requires chilled water cooling. Changes to equipment are difficult to 
implement and costly to obtain. 
The use of Hilbert transforms in the context of a Link-11 system is 
discussed in U.S. Pat. No. 4,076,956. Other U.S. Patents relating to the 
correction of Doppler shift in the context of Picket systems include U.S. 
Pat. Nos. 4,719,468; 4,875,050 and 4,876,546. 
Phase correction is also a problem in Link-11 systems and is discussed 
along with Fast Fourier Transforms (FFT), and frame boundary sync 
detection in U.S. Pat. No. 4,199,809. Phase correction in a 
quadrature-like phase shift signal is discussed in U.S. Pat. No. 
4,707,839. 
The invention arose in the context of the above-described prior art. 
SUMMARY OF THE INVENTION 
Briefly described, the invention comprises a system including a method and 
apparatus for detecting synchronization frame boundaries in a Link-11 
signal that has been demodulated and Doppler stripped. The incoming 
Link-11 composite signal at 14,080 Hz is initially frequency divided to 
7,040 Hz and classified to determine if it is a preamble or data segment 
or noise. For preamble frames, a digital filter extracts the 605 Hz 
Doppler tone in the time domain plus the Doppler shift, and the resulting 
real-valued signal is passed through a first Hilbert transform to generate 
a complex-valued signal. The output of the first Hilbert transform 
contains a measure of the Doppler shift and is stored for later use in 
processing data frames. The date frames are also passed through a second 
Hilbert transform and the output is multiplied by the complex conjugate of 
the stored Doppler reference signal to produce a Link-11 signal stripped 
of Doppler. The signal is then passed through a 32-point FFT to transform 
it into frequency space. The phase values outputted from the FFT are then 
corrected to account for frame-to-frame delay. Phase differences between 
the current and previous frames determine the dibit values for the encoded 
digital data. 
At the fast rate of 2250 bits per second, each data frame interval is 13.33 
msec. Since the difference between each of the 16 tones in the tone 
library is 110 Hz, or an integer multiple thereof, the composite complex 
waveform begins to repeat itself in a periodic manner 9.09 msec into the 
13.3 msec frame (9.09 msec equals 1/110 Hz). Therefore, for the remaining 
approximately 4.24 msec of the frame, the composite signal is identical to 
the first 4.24 msec of the same frame. If the first 4.24 msec of the frame 
are subtracted from the last 4.24 msec of the frame, the outcome is 
substantially zero and can be represented by the following difference 
function 
EQU D=S(m+32)-S(m) 
where m equals the number of samples. According to the preferred 
embodiment, there are 47 samples in the entire frame and in the first 9.09 
seconds 32 samples are taken. Since the composite signal repeats during 
the last 15 bits (i.e. 4.24 msec) of the frame, the function 
D=S(m+32)-S(m) will be substantially zero until the beginning of the next 
frame boundary at which point all the tones in the tone library change 
phase with the exception of the continuous 605 Hz Doppler reference 
signal. This produces a very strong discontinuity in the function 
D=S(m+32)-S(m), thereby indicating the beginning of a new frame. 
The foregoing technique for demodulation and synchronization is faster and 
less expensive than other techniques known to date.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
During the course of this description, like numbers will be used to 
identify like elements according to the different figures that illustrate 
the invention. 
A Navy battle group 10 employing a Link-11 system is illustrated in FIG. 1. 
An aircraft carrier 12 typically acts as the Net Control Station (NCS) and 
is in continuous contact with aircraft 14 or surface vessels 16 (referred 
to collectively as Participating Units (PU's)). Because of the high 
relative speeds of the Picket aircraft 14 with respect to the Net Control 
Station 12, undesirable phase and Doppler shifts are often introduced into 
the computer-to-computer radio Link-11 signals. 
A typical prior art Link-11 signal S 18 is generated according to the 
procedure shown in the modulation vector diagram of FIG. 2A. As described 
in the Background of the Invention, each of the 15 pairs of bits in each 
data frame are converted into a phase shift, with shifts of -45.degree., 
-135.degree., -225.degree. and -315.degree. representing bits pairs (1,1), 
(0,1), (0,0), and (1,0). Differential Quadrature Phase Shift Keying 
(DQPSK) is applied to each of the 15 tones. The 15 tones f.sub.n plus the 
605 Hz Doppler reference signal (f) comprise a 16 tone library consisting 
of the frequencies of f.sub.n =605, 935, 1045, 1155, 1265, 1375, 1485, 
1595, 1705, 1815, 1925, 2035, 2145, 2255, 2365 and 2915 Hz. Each of the 
nominal frequency tones f.sub.n is separated from the other by 110 Hz or 
an integer multiple thereof. 
Each data frame is encoded with a 30 bit digital data value at an aggregate 
data rate of 2250 bits per second at a frame interval of 13.33 msec (fast 
speed). 
The format of a typical prior art Link-11 Signal S is illustrated in FIG. 
2B. The first five frames of a Link-11 message S consist of only the 605 
Hz Doppler correction tone f.sub.DR and the 2915 Hz framing tone. The 2915 
Hz framing tone is given twice its normal amplitude and is phase shifted 
180.degree. at each frame boundary F.sub.Bl to provide for frame 
synchronization. The 605 Hz tone is given twice the amplitude of the 2915 
Hz tone during the preamble frames and twice the amplitude of the 
information carrying tones f.sub.n on all other transmitted frequencies. 
The information may be transmitted at a slow 22 msec speed or a fast 13.33 
msec speed. The fast 13.33 msec speed is used for purposes of illustration 
in this disclosure. 
The five frame preamble is followed by a 6th reference frame during which 
all the 16 tones are transmitted to establish a reference phase for each 
tone. 
The information segment starts with frame 7 and ends with as many frames as 
is necessary to complete the message (n+2). Frames 7 and 8 each comprise a 
start code and the actual data begins with frame 9. The transmission is 
completed with a picket stop code in the n, n+1 and n+2 frames. During the 
information segment all 16 tones are present producing 30 bits of 
information per frame. 
The foregoing describes a basic, prior art Link-11 system which is 
described in further detail in Military Standard MIL-STD-188-203-1A. 
The demodulation system according to the preferred embodiment is 
illustrated in FIG. 3. The demodulation system 22 begins with the 14,080 
Hz Link-11 composite signal and divides it by frequency divider 24 to 
reduce it to a 7040 Hz signal S. 
The next step is to classify the signal to determine if a valid signal is 
present. If 64 samples are examined, do the previous 64 samples consist of 
pure noise, mixed noise and signal, or all signal?. The first step in the 
classification process is to determine if there is any Link-11 component 
present at all in the signal. To make this determination a 64 point 
windowed Fast Fourier Transform (FFT) is performed on the data and the 
ratios of the 605 Hz power to total power is determined as a function of 
the number of noise samples in the set. The results are shown in the graph 
of FIG. 5 for Doppler shifts f.sub.DP of zero and plus or minus 75 Hz. 
Note, for a Doppler frequency of 0 (f=0) and no noise samples, the ratio 
is 0.8, the nominal value for a Link-11 preamble. There is an ambiguity, 
however, in this ratio since a signal with a large Doppler shift (f.sub.DP 
=large) can produce the same ratio as signals with no Doppler shift 
(f.sub.DP =0) and a large number of noise samples. This conflict is 
resolved by taking the following steps: 
1. Introduce a 75 Hz interrupt. 
2. Provide a windowed FFT and form the Doppler ratio of R.sub.D. 
3. If R.sub.D is less than 0.4 (R.sub.D &lt;0.4), reject the data, and go back 
to step 1 for the next interrupt. 
4. If R is greater than 0.4 (R.sub.D &gt;0.4), set the valid signal flag VS=1. 
5. Introduce 75 Hz interrupt if VS=1 and accept the previous 64 samples. 
The valid signal VS=1 indicates that there is at least a partial signal in 
the current frame. The next 75 Hz interrupt that occurs 94 samples later 
is then guaranteed to contain completely valid data regardless of noise or 
Doppler shift. Signal Classification takes place in Classify unit 26 and 
is based upon a power spectrum analysis on a 64 point windowed FFT 
(disguised as 32 point complex FFT) over a -75 Hz to +75 Hz Doppler shift. 
Once it has been determined that a Link-11 signal is present, the second 
step in the classification process is to determine if the Link-11 signal 
is preamble, data or both. That determination is made as follows: 
##EQU1## 
If we call the sample no. S.phi., 64 points back from the pointer value at 
the time of the last interrupt, then, in the through S.phi. through 
S.phi.+50, there must be at least one frame boundary at a sampling rate of 
7040 Hz. 
Once the signal is classified in Classify unit 26, it is then passed to the 
low pass digital filter 28, where the Doppler reference frequency f.sub.DR 
of a Link-11 system is always 605 Hz. The characteristics of digital 
filter 28 are illustrated in FIG. 6. The preferred embodiment is an eight 
tap FIR (Finite Impulse Response) digital filter which passes the 605 Hz 
signal plus or minus the 75 Hz Doppler shift f.sub.DP but which provides 
approximately 70 dB attenuation for the 2915 Hz signal. Therefore, the 605 
Hz plus or minus 75 Hz (i.e. 530 Hz to 680 Hz range) signal is easily 
passed but all other signals are generally rejected. This produces a real 
signal having the form of 
EQU R=cos (2.pi. [605+f.sub.DP ] t). 
The resulting output from digital low pass filter 28 provides an input to a 
first Hilbert transform 30 which produces the imaginary portion of the 
signal in the form 
EQU I=sin (2.pi. [605+f.sub.DP ] t). 
The ideal characteristics of a Hilbert transform are illustrated in FIG. 
7A. The purpose of a Hilbert transform is to provide an all pass 
90.degree. phase shift so as to produce the imaginary portion of the 
complex signal. Since the signals only range in frequency from 530 Hz (605 
Hz-75 Hz=530 Hz) to 2915 Hz, any signal above approximately 3500 Hz is 
irrelevant. Therefore, even though the ideal Hilbert transform acts like 
an all pass 90.degree. phase shift filter, for all intents and purposes, 
it is only important that the Hilbert transform exhibit that 
characteristic from between approximately 600 Hz and 3000 Hz. 
The accuracy of the Hilbert transformation 30 depends upon the number of 
samples in the window chosen. If the window sample rate is fairly high, 
then the accuracy is also high. FIG. 7B illustrates the condition where 
the window has 43 samples (W=43). Unfortunately, the larger the number of 
samples the longer the process takes. Accordingly, it has been found that 
a sample rate of 9 (W=9) is generally satisfactory to produce the 
approximate 90.degree. phase shift over the frequency range of 600 Hz to 
3000 Hz. FIG. 7C illustrates the Hilbert transform characteristic 
according to the preferred embodiment of Hilbert transforms 30 and 32 
where the sample rate for the window is W=9. 
The digital technique for forming a Hilbert transform is known and is 
determined by the following discrete approximation: 
##EQU2## 
Y(T)=a complex signal having the form Y(T)=X+jY; and, 
nMAX=W=window size which determines the accuracy of the transform. 
The real portion of the signal R from digital filter 28 and the imaginary 
portion of the signal I from first Hilbert transform 30 are combined and 
fed into complex multiply 34. The complex signal has the following form: 
EQU S(W.sub.o)=R+j I=cos (2.pi. [605+f.sub.DP ] t)+j sin (2.pi. [605+f.sub.DP ] 
t) 
which can also be expressed in the following way: 
EQU S(w.sub.o)=.SIGMA.e.sup.jwot where w.sub.o =2.pi. (605+f.sub.DP). 
The above expression consists of the passed 605 Hz complex signal with a 
Doppler frequency component f.sub.DP. 
The other input to the complex multiply 34 comes from a second Hilbert 
transform 32. The characteristics of the second Hilbert transform 32 are 
the same as the characteristics of the first Hilbert transform 30 and are 
shown generally in FIGS. 7C. Since the input to second Hilbert transform 
32 is not filtered by the low pass digital filter 28, the output will 
comprise a complex signal including all of the 16 tones in the Link-11 
library plus the Doppler signal (f) and will have the general form of 
EQU S(w.sub.nd)=cos (2.pi.[f.sub.n +f.sub.DP ]t)+j sin (2.pi. [f.sub.n 
+f.sub.DP ]t) 
EQU or 
EQU S(w.sub.nd)=.SIGMA. e.sup.jwndt 
The foregoing expression can be further simplified to the following 
EQU S(w.sub.nd)=.SIGMA. e.sup.jwndt 
where 
w.sub.nd =2.pi. (f.sub.n +f.sub.DP), and 
f=605+f.sub.DP, 935+f.sub.DP, . . . , 2915+f.sub.DP 
The output from digital filter 28 and first Hilbert transform 30 has 
previously been stored in memory in the form of 
EQU S(w.sub.o)=.SIGMA.e.sup.jwot 
wherein 
w.sub.o =2.pi. (605+f.sub.DP). 
The complex multiply 34 multiplies the complex conjugate of the output from 
filter 28 and first Hilbert transform 30 (S(w.sub.o)) by the output from 
second Hilbert transform 32 (S(w.sub.nd)). The multiplying by a complex 
conjugate implies the changing of the expression j to -j Therefore, the 
new Link-11 signal S (Link-11) 
##EQU3## 
The foregoing has the effect of subtracting from every tone the Doppler 
frequency shift f wherein f is also expressed as follows: 
##EQU4## 
where f.sub.c =carrier frequency 
V.sub.r =platform speed 
C=speed of light 
There is often an additional Doppler component due to the mistuning of 
transmitter and receiver. 
The affect of the foregoing is that the Doppler shift f.sub.DP can be 
stripped from the Link-11 signal S(n) without even knowing what the 
Doppler shift is. This is a distinct advantage over prior art techniques 
which require the identification of the exact Doppler shift and the 
subsequent subtraction thereof. The real time Doppler stripping technique 
described herein is a much faster and more efficient way of stripping 
Doppler signals than was available by prior art techniques. 
The sampling rate of the signal is important. General sampling theory 
suggests that for a given maximum frequency B, the sampling frequency 
F.sub.S should be greater than 2B which is expressed by the equation: 
EQU F.sub.S &lt;2B 
According to the present invention, however, it is only necessary to sample 
a complex signal S at a rate wherein F.sub.S is greater than B, or 
EQU F.sub.S &lt;B 
This sampling rate for a Link-11 Signal S considerably reduces the signal 
processing time by operating on just half the number of samples throughout 
(i.e. F.sub.S =3520 Hz). Accordingly, the execution time, per sideband, is 
significantly faster than the prior art. 
The Link-11 signal S stripped of its Doppler component is fed from the 
complex conjugate multiplier 34 into a 32 point Fast Fourier Transform 
(FFT) analyzer which reconstructs the original 16 tone library from the 
data signals and produces 16 outputs all corrected for Doppler shift and 
in the form of 
EQU f.sub.n =f.sub.nDP -605 Hz 
where 
f.sub.nDP =Doppler shifted f.sub.n 
The output from the FFT unit 36 is fed as an input to the correction unit 
38. At this location, phase correction is applied to the 15 data tones 
along with the appropriate Doppler update. Prior to this time, the 
waveform stored during the preamble phase is updated and outputted to a 
variety of locations indicated by element 40 for further analysis and 
utilization. For example, conventional Error Data and Correction codes 
(EDAC) may be appropriate at this point. 
The Doppler shift f.sub.DP can be updated in the following manner. The 
Doppler shift may slew at rates of up to 3.5 Hz/second. The variation may 
be slow but can build up large phase errors over a long message. 
Therefore, it is useful to measure the Doppler error by observing 
differential phase shift in the DC BIN (605 Hz 1.65.degree. per Hz shift). 
Periodically (e.g., every 15 frames), it is useful to premultiply the 
complex time domain signal by the conjugate of the observed error. 
The operation of the demodulation and Doppler stripping system of FIG. 3 
can be summarized as follows. The incoming signal S is frequency divided 
from 14,080 to 7,040 Hz. The preamble frames of a message are processed 
separately from the data frames, so that the