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Description  |
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BACKGROUND OF THE INVENTION
This invention relates to a spread spectrum communications system, more
particularly to a system comprising a transmitter and a receiver linked by
a communication channel.
Applications of communications systems employing the spread spectrum (SS)
technique are growing in a wide range of fields, including mobile
communications and satellite communications, because of the security of SS
systems, their resistance to jamming, their compatibility with other
existing communications systems, and other features.
FIG. 2 shows an example of a conventional baseband SS communications
system. The communications system in this figure comprises a transmitter
12 and a receiver 13 linked by a communication channel 6. The transmitter
12 comprises a data modulator 2 for modulating transmit data received from
an input terminal 1, an SS code modulator 4 for modulating a spread
spectrum (SS) code received from an input terminal 3, and a multiplier 5
for multiplying the output from the data modulator 2 and the output from
the SS code modulator 4 together. The receiver 13 comprises an SS code
modulator 8 for modulating an SS code received from an input terminal 7, a
multiplier 9 for multiplying the signal received from the communication
channel 6 and the output from the SS code modulator 8 together, an
integrate-and-discharge filter 10, and an output terminal 11.
The operation of this SS communications system will be described next. The
explanation begins with the operation of the transmitter 12.
A series of transmit data {b.sub.m } (where m=-.infin., . . . , -1, 0, 1, .
. . , +.infin.) is input in sequence from the input terminal 1 and
converted by the data modulator 2 to the transmit data signal:
##EQU1##
wherein b.sub.m satisfies the relation b.sub.m .epsilon.{-A, A}, A being a
positive real number, and g(t) is the data pulse waveform:
##EQU2##
where T is the data pulse duration. At the same time, a spread spectrum
code (SS code) {a.sub.l } with period N.sub.c is input from the input
terminal 3 and converted by the SS code modulator 4 to the SS signal a(t):
##EQU3##
where a.sub.l .epsilon. {-1, 1} and g.sub.c (t) is the SS code pulse
waveform:
##EQU4##
T.sub.c is the duration of the SS code pulse and satisfies the relation
N.sub.c =T/T.sub.c. The transmit data signal b(t) and the SS signal a(t)
are multiplied together in the multiplier 5 and the resulting output d(t)
is sent on the communication channel 6:
##EQU5##
Next, the receiver 13 performs the following process. First it receives the
transmitted signal r(t) via the communication channel 6. It also inputs an
SS code {a.sub.l } (the same code as used in the transmitter) with period
N.sub.c from the input terminal 7. This SS code is converted by the SS
code modulator 8 to exactly the same SS signal a(t) as used in the
transmitter, described by Eq. (3). The multiplier 9 multiplies the signals
r(t) and a(t) together, and the resulting output r(t)a(t) is input to the
integrate-and-discharge filter 10, the output Z from which is used to
restore the original transmit data series {b.sub.m }.
The spread spectrum communications system described above suffers from the
following problems.
The power spectrum density of the signal d(t) transmitted to the
communication channel 6, given by Eq. (5), has comparatively large peak
values, as shown in the Denshi Tsushin Gakkai Rombunshi (B), Vol. J66-B,
11 (November 1983), pp. 1362-1369. It therefore interferes strongly with
other existing communications systems. The above system also provides
inadequate security, despite the listing of security as a feature of SS
communications systems. Using pulse detector receiving equipment, for
example, it is comparatively easy to intercept the transmission even
without knowing the SS code {a.sub.l }.
SUMMARY OF THE INVENTION
An object of the present invention is to eliminate these problems in the
prior art and provide an SS communications system that is highly secure
and highly compatible with existing communications systems.
To solve the above problems in a spread spectrum communications system
comprising a transmitter that transmits a signal resulting from
multiplication of a modulated transmit data signal and a modulated spread
spectrum code, and a receiver, linked to the transmitter by a
communication channel, that receives the signal transmitted from the
transmitter and multiplies it by a modulated spread spectrum signal to
restore the original transmit data, in the present invention an FIR filter
is inserted in the output section of the transmitter and a filter having a
characteristic inverse to that of the FIR filter is inserted in the input
section of the receiver.
In a spread spectrum communications system structured according to this
invention as above, the means employed by this invention function as
follows. The FIR filter functions to reduce the peaks of the power
spectrum density of the transmitted signal, and to conceal the transmitted
signal in the noise on the communication channel. The filter in the
receiver functions to restore the signal received from the transmitter via
the communication channel, which has been distorted by the characteristic
of the FIR filter, to the original signal by application of the inverse
characteristic. In this manner the problems cited above in the prior art
can be solved.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1A is a block diagram of an embodiment of the present invention.
FIG. 1B is a block diagram of the FIR filter in FIG. 1A
FIG. 1C is a block diagram of the IIR filter in FIG. 1A.
FIG. 2 is a block diagram of a spread spectrum communications system of the
prior art.
FIG. 3A through 3E and FIG. 4A through 4D show signal waveforms at various
points in the embodiment in FIG. 1.
FIG. 5A through 5C describe the power spectrum density of the transmitted
signal in the embodiment in FIG. 1.
FIG. 6 describes the effect of the FIR filter in suppressing peak values in
the power spectrum of the transmitted signal.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 1A shows a block diagram of an embodiment of this invention. Component
elements labeled with the same reference numbers as in FIG. 2 are
identical to the corresponding elements in FIG. 2. The SS communications
system of this invention comprises a transmitter 16 and a receiver 17
linked by a communication channel 6. The transmitter 16 comprises, in
addition to the component elements of the transmitter 12 in FIG. 2, an FIR
(Finite Impulse Response) filter 14 connected to the output of the
multiplier 5. The receiver 17 comprises, in addition to the component
elements of the receiver 13 in FIG. 2, an IIR (Infinite Impulse Response)
filter 15 connected to the input of the multiplier 9.
FIG. 1B shows the internal structure of the FIR filter 14. As seen in FIG.
1B, the FIR filter 14 comprises delay elements 18-1, 18-2, . . . , 18-N,
mulltipliers 19-1, 19-2, . . . , 19-N, an adder 20, an input terminal 21,
and an output terminal 22.
FIG. 1C shows the internal structure of the IIR filter 15. As seen in FIG.
1C, the IIR filter 15 comprises an input terminal 23, an adder 24, an
output terminal 25, delay elements 26-1, 26-2, . . . , 26-N, and
multipliers 27-1, 27-2, . . . , 27-N.
The operation of an SS communications system with the above configuration
will be described next.
First the operation of the transmitter 16 will be explained. A series of
transmit data {b.sub.m } (where m=-.infin., . . . , -1, 0, 1, . . . ,
+.infin.) is input in sequence from the input terminal 1 to the
transmitter 16 and converted by the data modulator 2 to the transmit data
signal b(t) described earlier:
##EQU6##
where b.sub.m and g(t) are the same as in the earlier description. In
addition, a spread spectrum signal (SS code) {a.sub.l } with a period of
N.sub.c is input at the input terminal 3 and converted by the SS code
modulator 4 to an SS signal a(t):
##EQU7##
where a.sub.l and g.sub.c (t) are the same as described earlier. The
transmit data signal b(t) and the SS signal a(t) are multiplied together
in the multiplier 5, and the resulting output d(t)
##EQU8##
is input to the FIR filter 14. The output signal e(t) from this FIR filter
14 is sent on the communication channel 6.
The process performed by the FIR filter 14 will be explained with reference
to FIG. 1B. At time t the transmit data signal d(t) is input at the input
terminal 21. This transmit data signal d(t) is applied to the delay
element 18-1, which delays it by a time T.sub.d. At successive times t the
transmit data signal d(t) is shifted successively by the delay elements
18-1, 18-2, . . . , 18-N, each of which delays it by a time T.sub.d. At
time t the outputs d(t-T.sub.d), d(t-2T.sub.d), . . . , d(t-NT.sub.d) from
the delay elements 18-1, 18-2, . . . , 18-N are multiplied by A.sub.1,
A.sub.2, . . . , A.sub.N in the multipliers 19-1, 19-2, . . . , 19-N, and
the outputs A.sub.1 d(t-T.sub.d), A.sub.2 d(t-2T.sub.d), . . . , A.sub.N
d(t-NT.sub.d) from these multipliers are added to the transmit data d(t)
in the adder 20. The resulting signal e(t) is sent through the output
terminal 22 to the communication channel 6.
Next the operation of the receiver 17 will be described. The signal r(t)
received from the transmitter via the communication channel 6 is input to
the IIR filter 15. At this point the signal r(t) consists of the signal
e(t) sent by the transmitter 16 plus noise n(t) occurring on the
communication channel 6:
r(t)=e(t)+n(t) (6)
Next the output signal r(t) from the IIR filter 15 is multiplied in the
multiplier 9 by the SS signal a(t), which is identical to the signal used
in the transmitter and is described by Eq. (3). The signal a(t) is output
from the SS code modulator 8, which inputs from the input terminal 7 an SS
code {a.sub.l } (identical to the code used in the transmitter) having
period N.sub.c. The output r(t)a(t) from the multiplier 9 is fed to the
integrate-and-discharge filter 10, the output z from which is used to
restore the original data series {b.sub.m }.
The process performed by the IIR filter 15 will be explained with reference
to FIG. 1C. At time t the signal r(t) is input at the input terminal 23.
The outputs r(t-T.sub.d), r(t-2T.sub.d), . . . , r(t-NT.sub.d) from the
delay elements 26-1, 26-2, . . . , 26-N at time t multiplied by A.sub.1,
A.sub.2, . . . , A.sub.N in the multipliers 27-1, 27-2, . . . , 27-N, and
the outputs A.sub.1 r(t-T.sub.d), A.sub.2 r(t-2T.sub.d), . . . , A.sub.N
r(t-NT.sub.d) from these multipliers are added to the signal r(t) in the
adder 24. The output signal r(t) from the adder 24 is sent to the output
terminal 25 and is also input to the delay element 26-1, so that as time t
progresses the signal is shifted successively by the delay elements 26-1,
26-1, . . . , 26-N.
The operation of an embodiment of the present invention has been described.
Next the operation of this embodiment will be analyzed. As already
explained, the FIR filter 14 and the IIR filter 15 have the same order N.
The delay time T.sub.d of the delay elements 18-1, 18-2, . . . , 18-N in
the FIR filter 14 is also equal to the delaytime T.sub.d of the delay
elements 26-1, 26-2, . . . , 26-N of the IIR filter 15. The coefficients
A.sub.1, A.sub.2, . . . , A.sub.N of the multipliers 19-1, 19-2, . . . ,
19-N of the FIR filter 14 are also designed to be identical to the
coefficients A.sub.1, A.sub.2, . . . , A.sub.N of the multipliers 27-1,
27-2, . . . , 27-N of the IIR filter 15. The FIR filter 14 and IIR filter
15 are accordingly inverse filters. This means that if H.sub.F (f) is the
transfer function of the FIR filter 14 and H.sub.I (f) is the transfer
function of the IIR filter 15, then the following relation holds:
H.sub.F (f) H.sub.I (f)=1 (7)
If h.sub.I (t) is the impulse response of the IIR filter 15, then the
output signal r(t) of the IIR filter 15 is:
##EQU9##
Hence only the noise n(t) occurring on the communication channel 6 is
affected by the IIR filter 15. If the receiver 17 is synchronized, the
output signal Z.sub.m from the multiplier 9 corresponding to the
transmitted data b.sub.m can be expressed as:
##EQU10##
where Z.sub.s,m and Z.sub.N,m are:
##EQU11##
Let .sigma..sub.S,m.sup.2 =E[Z.sub.s,m.sup.2 ] and .sigma..sub.N,m.sup.2
=E[Z.sub.N,m.sup.2 ] (where E[.] denotes the set average), and assume that
the noise n(t) on the communication channel is a white Gaussian noise with
power spectrum density No/2. It follows that:
##EQU12##
where Sa(x) and S.sup.(1) (f) are given as below:
##EQU13##
the coefficients C.sub.1,1 (k) are as follows:
##EQU14##
From the above, the signal-to-noise ratio (SNR) of the receiver 17 is:
##EQU15##
A design procedure for the FIR filter 14 and the IIR filter 15 will be
described next. The order N, the delay time T.sub.d or the delay elements
18-1, 18-2, . . . , 18-N and the delay elements 27-1, 27-2, . . . , 27-N,
and the multiplier coefficients A.sub.1, A.sub.2, . . . , A.sub.N of the
FIR filter 14 and IIR filter 15 used in this invention correspond to the
order N, the sampling interval T.sub.d, and the coefficients A.sub.n
derived from the Yule-Walker equation for tha AR model of the time series
generated by the SS signal, and the FIR filter 14 and the IIR filter 15
are inversely related as seen above. Setting:
##EQU16##
let us define the following function M(f) for the transmit data signal:
##EQU17##
The continuous spectrum component Sc(f) of the transmit data signal d(t)
is determined by this function M(f) and the functions S.sup.(1) (f)
defined in Eq. (12):
S.sub.c (f)=T.sub.c [S.sub.a (.pi.fT.sub.c)].sup.2 M(f)S.sup.(1) (f) (17)
The auto-correlation of the transmit data d(t) can be found from the
inverse Fourier transform of Sc(f). Suppose the transmit data series
{b.sub.m } is statistically independent
(meaning that R(p)=0 for p=1, 2, . . . ). Then if
.vertline..tau..vertline.=(k+.xi.)T.sub.c (where 0.ltoreq..xi.<1), the
auto-correlation function R.sup.(1) (.tau.) of d(t) is:
##EQU18##
The normalized auto-correlation function r.sup.(1) (.tau.)=R.sup.(1)
(.tau.)/R.sup.(1) (0) can be used to find the multiplier coefficients
A.sub.1, A.sub.2, . . . , A.sub.N of the FIR filter 14 and the IIR filter
15 by solving the Yule-Walker equation:
##EQU19##
The solution can be obtained by the well-known Levinson-Durbin algorithm.
If the delay time of the delay elements 18-1, 18-2, . . . , 18-N and 26-1,
26-2, . . . , 26-N of the FIR filter 14 and the IIR filter 15 is written
as T.sub.d =.xi.T.sub.c (where .xi.=1/q, q=1, 2, . . . ), then r.sup.(1)
(k) is a discrete value that can be expressed as r.sup.(1) (k)=r.sup.(1)
(.tau.) 1.tau.=kT.sub.d.
The solution of the equation (19) gives coefficients An (n=1 to N) that
minimizes the average of the power of the output of the transmitter 16
which is proportional to e.sup.2 (t). Minimizing the average power of the
output of the transmitter 16 is considered to have the effect of
minimizing the peaks in the spectrum of the output of the transmitter,
i.e., suppressing, to the greatest degree, the peaks of the spectrum,
thereby making it difficult to analyze the features of the signal being
transmitted and to intercept it without the SS code. Use of the FIR filter
in the transmitter is advantageous in that the values of the coefficients
An can be determined unequivocally and relatively easily.
Use of the IIR filter 15 in the receiver 17 in combination with the use of
the FIR filter 14 in the transmitter 16 is advantageous in that the IIR
filter 15 has the transfer function inverse to that of the FIR filter 14
if the coefficients A.sub.1 to A.sub.N of the multipliers 27-1 to 27-N are
given the same values as those to the multipliers 19-1 to 19-N.
The IIR filter in the receiver can be replaced by an FIR filter. In this
case the coefficients of the multipliers of the FIR filter should be
determined such that the transfer function of the FIR filter in the
receiver is approximately, if not exactly, inverse to that of the FIR
filter in the transmitter. To obtain the exactly inverse relationship
between the transfer functions is difficult because the order N. (number
of steps) in the FIR filter is finite.
The above has been a description of the design of the FIR filter 14 and the
IIR filter 15. The effects of this embodiment of the invention will now be
described by presenting examples of specific numerical computations.
We shall use the well-known Gold code as the SS code {a.sub.l}, and assume
that the noise n(t) on the communication channel is white Gaussian noise
with mean value 0 and power spectrum density No/2. If .xi.=1 we select a
transmission bandwidth Be of Be=3f.sub.c (where f.sub.c =1/T.sub.c), and
if .xi.=1/3 we select Be=9f.sub.c. We also assume that there is no
distortion of the transmitted and received signals. Let the amplitude A of
the transmit data signal b(t) be 1 (A=1), the filter order be N=50, and
the period of the SS code be N.sub.c =127. FIG. 3A through 3E show the
signal waveform at various points under these conditions when .xi.=1. FIG.
4A through 4D show the signal waveform at various points under these
conditions when .xi.=1/3. We are assuming that the communication channel
noise (Gaussian noise) n(t) in FIG. 3 and FIG. 4 has a flat power spectrum
density within the postulated transmission bandwidth and is expressed by
the constant-amplitude Fourier series:
##EQU20##
where .sigma..sub.n.sup.2 is the noise power, N.sub.N is the number of
cosine waves, and .phi..sub.j is a uniform random variable on the interval
[0, 2.pi.], f.sub.0 is the fundamental frequency of the Fourier series,
determined by the formula Be=N.sub.N f.sub.0. The noise power
.sigma..sub.n.sup.2 is determined by the product of the power of the
transmit data signal d(t) with respect to the Gaussian noise power
spectrum density and the persistence time (duration) of the SS code pulse,
and is given by A.sup.2 T.sub.c /No. In the computation the following
values were used: A.sup.2 T.sub.c /No=10dB, Be=3/(.xi.Tc),
.sigma..sub.n.sup.2 =NoBe, and N.sub.N =100. As can be seen from FIG. 3
and FIG. 4, the signal e(t) output to the communication channel 6 by the
SS communications system of this invention is more easily concealed by the
noise n(t) on the communication channel than the signal d(t) output to the
communication channal 6 by the SS communications system of the prior art.
FIG. 5A through 5C show the power spectrum densities of the signals d(t)
and e(t). FIG. 5A shows the power spectrum density in the SS
communications system of the prior art. FIG. 5B and 5C show the power
spectrum density in the SS communications system of the present invention.
In FIG. 5B .xi.=1 and N=30. In FIG. 5C .xi.=1/3 and N=30. The power
spectrum density S.sub.cF (f) of the signal e(t) is S.sub.cF
(f)=G.sub.F,1.sup.2 S.sub.c (f).vertline.H.sub.F (f).vertline..sup.2 for a
transmitter gain of G.sub.F,1 with the transmitted power being
##EQU21##
As FIG. 5B and 5C indicate, the bandwidth of each lobe in the power
spectrum density of e(t) for a given .xi. is 1/.xi. times the
corresponding value for S.sub.c (f), indicating a lower density. As the
order N of the filter increases, spike-like variations decrease and peak
values are reduced. The effects of the FIR filter 14 in suppressing the
peak value of the power spectrum density of the transmitted signal is
expressed by the index below, which depends on the order N as shown in
FIG. 6.
.LAMBDA.=1-max[S.sub.c (f).vertline.H.sub.F (f).vertline..sup.2
]/max[S.sub.c (f)] (21)
Plot A in FIG. 6 is for .xi.=1, plot B is for .xi.=1/2, and plot C is for
.xi.=1/3. FIG. 6 indicates that the peak suppression effect increases with
increasingly small values of .xi. and increasingly large values of N.
As explained above, this invention, by providing an FIR filter in the
output section of the transmitter and an IIR filter in the input section
of the receiver, attains greater security than in spread spectrum
communications systems of the prior art, and promises to be compatible
with other existing communications systems.
* * * * *
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