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BACKGROUND OF THE INVENTION
1. Field of Invention
This invention relates to pulsed radar systems. Specifically, the present
invention relates to systems and methods for reducing the range sidelobes
of compressed pulse radar systems thereby facilitating the detection of
small targets in the presence of large targets.
2. Description of the Related Art
Radar systems are used in a variety of applications ranging from missile
guidance systems to air traffic control systems. Such applications require
radar systems to accurately detect and discriminate targets. A typical
radar system has a transmitter and a receiver. The transmitter transmits a
signal and the receiver detects signals that are reflected back to the
receiver. Signals that are reflected back are known in the art as radar
returns.
In pulsed radar systems, the transmitter transmits a pulsed signal at a
specified frequency. If a target is present, the received signal is a
delayed version of the transmitted signal. Pulsed systems facilitate the
calculation of the delay which is used to calculate the distance to the
target. If no target or object is present, the received signal is noise
only.
The transmitted signal is compared with the received signal to determine if
a target is present. Often, the received signal is heavily corrupted by
noise and visual inspection of the received signal does not reveal the
presence or absence of the target. Radar systems typically use correlation
to overcome this difficulty. The correlation involves a summation of
products of the received signal with the transmitted signal. The
correlation is a measure of the similarity of the transmitted signal to
the received signal. A large similarity between the transmitted and
received signals corresponds to a large probability that a target has been
detected which in turn corresponds to a large correlation between the
signals.
Typically a correlator correlates the transmitted signal with the received
signal. A correlator that is often used to perform this function is a
matched filter. The signal used by the correlator for correlation is
matched to the transmitted signal. The impulse response function of the
correlator is a shifted folded version of the transmitted signal and hence
also matches.
Output from the correlator is shown in a magnitude versus time graph for
analog signals and a magnitude versus sequence number graph for digital
signals. The output of the correlator has a main peak where the
correlation between signals is the strongest. Several smaller peaks next
to the main peak are range sidelobes.
Radar systems using matched filters often have large range sidelobes at the
output of the correlators. This reduces their ability to detect small
target returns close in range to stronger target returns. This is because
the main peak of a small target return may be comparable in magnitude to
the range sidelobes of a larger target return. The range sidelobes of the
larger target return may obscure the small target return.
To improve detection of small target returns near large target returns,
more complicated coding schemes were developed. Such coding schemes
typically add much complexity to the transmitted wave form to reduce the
range sidelobes. Several such coding schemes involve using poly-phase
codes. Poly-phase coding schemes are often very difficult to implement,
involve multiple phase shifts beyond 0/180 degree shifts, and involve
using a large signal set. As a result, such systems are expensive and time
consuming to build.
Complicated filters were also developed to reduce the range sidelobes of
radar systems. One such filter is described in "Optimum Mismatched Filters
for Sidelobe Suppression," by M. H. Achroyd and F. Ghani IEEE Trans AES-9
No. 2, March 1973, pp. 214-218. The filter is a specialized filter
inserted into the receiver. The filter is expensive and time consuming to
build and implement.
Hence, a need exists in the art for a radar system that cost effectively
reduces range sidelobes for improving detection of radar targets.
SUMMARY OF THE INVENTION
The need in the art is addressed by the system for reducing range sidelobes
of the present invention. In the illustrative embodiment the inventive
system is adapted for use with pulsed radar systems and includes a
mismatched filter for correlating a received signal with a correlator
signal having a different length than the transmit signal and for
providing a predetermined number of reduced range sidelobes at the output
of the mismatched filter.
In a specific embodiment, the inventive system includes a computer for
determining the transmit signal and the correlator signal for providing
the reduced range sidelobes at the output of the mismatched filter.
In the preferred embodiment, the mismatched filter includes a correlator
having a first locally optimum sequence that is the correlator signal. The
mismatched filter has an input for receiving an extended locally optimum
sequence that is the received signal. The first locally optimum sequence
is a sub-sequence of the extended locally optimum sequence.
In an alternative embodiment the mismatched filter has a Barker-based code
that is the correlator signal. The mismatched filter has an input for
receiving an extended Barker-based code that is the received signal. The
extended Barker-based code includes the Barker-based code as a
sub-sequence.
In a specific embodiment, the mismatched filter is implemented with an
adjustable length correlator and a programmable signal transmitter which
may be implemented in computer software.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1A is a diagram illustrating periodic autocorrelation.
FIG. 1B is a diagram illustrating aperiodic autocorrelation.
FIG. 2 is an example result from the periodic autocorrelation of a locally
optimum sequence of Type A.
FIG. 3 is a diagram illustrating the range sidelobe cancellations of the
autocorrelation of the locally optimum sequence of FIG. 2.
FIG. 4 is a graph of the aperiodic correlation of the sequence of FIG. 2
illustrating the lack of range sidelobe cancellation.
FIG. 5 is a graph of the result of the output of a mismatched filter
utilizing complementary codes, and constructed in accordance with the
teachings of the present invention.
FIG. 6A is a graph showing the output of a mismatched filter using a
correlator of length 64 and a transmit wave form of length 80 and
constructed in accordance with the teachings of the present invention.
FIG. 6B is a graph showing the output of a mismatched filter using a
correlator of length 64 and a transmit wave form of length 72 and
constructed in accordance with the teachings of the present invention.
FIG. 7 is a graph showing the output of a mismatched filter using a
correlator signal of length 22 and transmit signal of length 31
constructed in accordance with the teachings of the present invention.
FIG. 8 is a graph showing the result of the periodic autocorrelation of a
13 bit Barker code sequence.
FIGS. 9a, 9b and 9c illustrate a technique of the present invention for
constructing a mismatched code sequence for a mismatched filter for
achieving range sidelobe cancellation.
FIG. 10 is a graph showing the output of the mismatched filter constructed
using the technique of FIG. 9.
FIG. 11 is a graph comparing the result of the aperiodic autocorrelation of
a 13 bit Barker code sequence and the result of the output of the
mismatched filter of FIG. 9 under uncompensated Doppler conditions.
FIG. 12 is a block diagram of a radar system constructed in accordance with
the teachings of the present invention.
FIG. 13 is diagram of a mismatched filter constructed in accordance with
the teachings of the present invention.
DESCRIPTION OF THE INVENTION
The invention is described below in reference to the accompany drawings in
which like reference numerals denote like parts. While the present
invention is described herein with reference to illustrative embodiments
for particular applications, it should be understood that the invention is
not limited thereto. Those having ordinary skill in the art and access to
the teachings provided herein will recognize additional modifications,
applications, and embodiments within the scope thereof and additional
fields in which the present invention would be of significant utility.
FIG. 1A is a diagram illustrating periodic autocorrelation. A transmit
signal 20, a correlator signal 22, and a resulting output 24 of a
correlator (not shown) is shown. The transmit signal 20 is representative
of a reflected transmit signal received at the radar system receiver (not
shown). Periodic autocorrelation is used in systems employing continuous
wave (CW) radar receivers. Due to the nature of the transmit wave form 20
such systems are limited in their ability to establish accurate distances
to targets.
The transmit signal 20 is typically a periodic sequence with a period of
length N which is also the length of the correlator signal 22. One period
of the transmit signal 20 is the correlator signal 22. Both the transmit
signal 20 and the correlator signal 22 are represented by binary
sequences. Each element of the binary sequences may be a "one" or a
"negative one".
If the length N of the correlator signal 22 is even, then it is possible to
have sidelobe cancellation at the output of a radar system correlator
(matched filter) (not shown). This is because when performing correlation,
a particular filter output value is calculated by multiplying each bit
(not shown) of the correlator signal 22 with a corresponding bit in the
transmit signal, and then summing up the N products. An adjacent filter
output value (not shown) is calculated by shifting the transmit signal 20
so that a new bit 28 from the transmit signal 20 is included in the
correlation calculation and a previous bit 30 is excluded. When the
correlator length N is even, it is possible to have an equal number of
positive and negative "ones" after the multiplication of the transmit
signal bits with the correlator signal bits resulting in a sum of zero.
When performing aperiodic correlation, this is not possible.
The filter output 24 has a mainlobe or correlation peak 32 when the
correlator signal 22 overlaps a portion of the transmit signal 20 that is
identical to the correlator signal 22. Otherwise, sidelobes 34 result.
Fig. 1B is a diagram illustrating aperiodic autocorrelation. A transmit
signal 20', the correlator signal 22, and an output 24' of the correlator
(matched filter) is shown. The transmit signal 20' is equivalent to the
correlator signal 22. When the matched filter correlates the transmit
signal 20' with the correlator signal 22, the number of terms being
multiplied alternates from odd to even. Therefore, it is impossible to
obtain a plurality of continuous zero magnitude sidelobes.
FIG. 2 is an example result from the periodic autocorrelation of a locally
optimum sequence of Type A. A locally optimum sequence (of period N) has a
periodic autocorrelation response 36 with N/4 zeros 38 on each side of a
mainlobe 40. Type A sequences have an autocorrelation response where the
zero sidelobes 38 are adjacent to the mainlobe 40.
For the present specific example, the Type A sequence is constructed from
complementary codes of length N/4. Complementary codes are pairs of binary
sequences whose autocorrelation responses have sidelobes of equal
magnitude but opposite sign. For example, the code A=›1, 1, 1, -1! and the
code B=›1, 1, -1, 1! are complementary codes because their autocorrelation
responses are ›-1, 0, 1, 4, 1, 0, -1! and ›1, 0, -1, 4, -1, 0, 1!
respectively. When the autocorrelation responses of the sequences A and B
are added together, sidelobe cancellation results.
The periodic sequence with period P=›A, B, -A, B! of length N is the
locally optimum sequence of type A with the autocorrelation response 36.
The correlator signal is ›A, B, -A, B!.
A locally optimum sequence of type B is a sequence whose autocorrelation
has zero sidelobes in the region ›N/4, N/2! on either side of the
correlation peak. Those skilled in the art will appreciate that Type B
sequences may be used without departing from the scope of the present
invention.
FIG. 3 is a diagram illustrating the range sidelobe cancellations of the
autocorrelation of the locally optimum sequence 22' of FIG. 2. A
correlator signal 22' is represented by the sequence ›A, B, -A, B! and is
correlated with a transmit signal sequence 20" with a period corresponding
to the correlator signal 22'. The correlator signal 22' is shown shifted
two spaces to the right of where a correlation peak would be generated. A
correlation peak is generated when the correlator signal 22' overlaps an
identical portion of the transmit signal 20". For illustrative purposes,
the position of the correlator signal 22' with respect to the transmit
signal 20" is shown generating a second zero side lobe (not shown)
adjacent to the main peak (not shown). The following discussion applies to
the generation of the first, second, third, and fourth sidelobes all of
which have zero magnitude.
Let x and y represent any two sequences. The correlation of x and y is
denoted as x*y. The following properties hold for correlation:
(-x)*(-y)=x*y
x*(-y)=(-x)*y=-(x*y)
Partial correlations 42 are numbered 1 through 8. When partial cross
correlations 2 and 6 are added they cancel: B*A+B*(-A)=0. The partial
cross correlations 4 and 8 also cancel: (-A)*B+A*B=0. In addition the
partial correlation 1 (A*A) is a sidelobe from the autocorrelation of code
A. The partial correlation 3 (B*B) is a sidelobe from the autocorrelation
of code B. Since A and B are complementary codes, partial correlations 1
and 3 cancel each other. Similarly, partial correlations 5 and 7 cancel
each other.
Thus, when the partial correlations 42 are added to compute the second zero
sidelobe (not shown) the resulting value is zero. The above argument
applies to the calculation of the first zero sidelobe where the correlator
signal 22' is shifted to the left one (N/16), and the third zero sidelobe
where the correlator signal 22' is shifted to the right one (N/16) from
its current position. When calculating the fourth zero sidelobe, the
correlator signal 22' is shifted to the right two spaces (N/8) from its
current position. The correlation is: A*B+B*(-A)+(-A)*B+B*A=0, resulting
in the fourth zero sidelobe.
FIG. 4 is a graph of the aperiodic correlation of the sequence of FIG. 2
illustrating the lack of range sidelobe cancellation. When the correlator
signal (shown in FIG. 3 as 22') is correlated with an identical signal
having length N, no sidelobe cancellation results.
FIG. 5 is a graph of the result of the output of a mismatched filter
utilizing complementary codes, and constructed in accordance with the
teachings of the present invention. The mismatched filter (not shown) of
the present invention performs aperiodic correlation yet achieves sidelobe
cancellation similar to the sidelobe cancellation resulting from periodic
autocorrelation such as discussed in FIGS. 2 and 3.
In the present specific embodiment, sidelobe cancellation is achieved by
extending a period of the transmit signal (not shown) by a number of bits
k from the beginning of the next period. The period of the transmit signal
is equivalent to the correlator signal (not shown). As an example, assume
the correlator signal is ›A, B, -A, B!. The transmit signal is extended to
›A, B, -A, B, A!. The resulting correlation shown in FIG. 5 has a peak at
N=20, and four zero sidelobes 44.
Those skilled in the art will appreciate that the output of a mismatched
filter constructed in accordance with the teachings of the present
invention may be made arbitrarily long with variable length regions of
zero range sidelobes by selecting the appropriate code length N and the
number of bits k.
The result of FIG. 5 was obtained by using the mismatched filter whose
sequences were obtained by following a method of the present invention
that includes the steps of:
1. obtaining a first and second complementary code;
2. forming a locally optimum sequence of complementary codes having the
first complementary code and the second complementary code as
sub-sequences and using the locally optimum sequence to represent the
correlator signal;
3. designing a transmit signal by extending the locally optimum sequence by
a first subset of the locally optimum sequence. The subset depends on the
desired number of reduced range sidelobes.
Those skilled in the art will appreciate that the transmit signal and the
correlator signal may be switched without departing from the scope of the
present invention.
FIG. 6A is a graph showing the output of a mismatched filter using a
correlator of length 64 and a transmit wave form of length 80 and
constructed in accordance with the teachings of the present invention. The
resulting correlation has a peak at N=80 and has sixteen zero sidelobes 46
(k=16). The number of zero sidelobes corresponds to the amount k by which
the correlator signal (not shown) is extended to obtain the transmit
signal.
FIG. 6B is a graph showing the output of a mismatched filter using a
correlator of length 64 and a transmit wave form of length 72 and
constructed in accordance with the teachings of the present invention. The
resulting correlation has a peak at N=72 and has k=8 zero sidelobes.
FIG. 7 is a graph showing the output of a mismatched filter using a
correlator signal of length 22 and a transmit signal of length 31
constructed in accordance with the teachings of the present invention. The
resulting correlation has k=9 zero sidelobes.
The result of FIG. 7 was obtained by using a mismatched filter (not shown)
whose sequences (not shown) were obtained by the following method of the
present invention: performing a computer search to obtain a transmit
sequence and a correlator sequence such that the correlation between said
transmit sequence and the correlator sequence has a plurality of zero
magnitude sidelobes.
FIG. 8 is a graph showing the result of the periodic autocorrelation of a
13 bit Barker code sequence. Barker codes have autocorrelation sidelobes
52 whose magnitudes are at most one.
A number k of additional bits may be appended to the transmit signal (not
shown) or the correlator signal (not shown) to obtain zero sidelobes at
the output of the mismatched filter of the present invention (not shown).
The k bits may be determined through computer search, or by using an
alternative method of the present invention discussed in FIG. 9.
FIG. 9a is a diagram illustrating a technique of the present invention for
constructing a mismatched code sequence for a mismatched filter for
achieving range sidelobe cancellation. A correlator signal 56 is
represented by the Barker-based code C=›-1, 1, -1, 1, -1, -1, 1, 1, -1,
-1, -1, -1!. In a first test correlation 54 a test transmit signal 58 is
formed by appending a 0 bit to the Barker-based code C. The last twelve
bits of the test signal 58 are multiplied with corresponding twelve bits
in the correlator signal 56 and then added in a correlation process. The
result is a preliminary sidelobe value of -1. Only the first eleven bits
of the correlator signal 56 contribute to the value of the preliminary
sidelobe since the last bit of the test signal 58 is a zero. To obtain a
zero sidelobe value 61 in the correlation process the appended 0 bit must
be changed to -1. The resulting test signal 60 is shown producing a zero
magnitude sidelobe as output. When the twelfth bit (-1) of the code C is
multiplied by the appended bit (-1) the result is 1. When 1 is added to
the preliminary sidelobe value (-1), the result is a first zero which
represents the first zero sidelobe 61. The first appended bit 13 is -1.
To determine the value of the second appended bit 14, a zero is appended to
the resulting test signal 60, which results in a second test signal 62
(see FIG. 9b). A second test correlation 57 is similar to the first test
correlation 54 with the exception that the second test signal 62 is used
in place of the test signal 58 in the first test correlation 54. The
output of the test correlation 57 is 1. This implies that the appended 0
bit 14 must be changed to a 1 as shown in a second resulting signal 64.
When the bit 14 (1) of the second resulting signal 64 is multiplied by the
twelfth bit (-1) of the code C and added to the output of the test
correlation 57 (1), the result is a second zero sidelobe 63.
The above process is repeated (see FIG. 9c) to obtain the third appended
bit 15 to produce a third zero sidelobe 65. The output of a third test
correlation 59 is the appended bit 15.
Let n represent the number of bits in a test signal. C(n-1) represents a
test correlation output with bits (n-11) to (n-1). As long as C(n-1) has
unity magnitude, a zero sidelobe may be obtained. Using the above method
with the correlator signal 56, five zero sidelobes are obtained because
C(17)=3 which does not have a unity amplitude. The resulting test signal
is ›-1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1! and is
used as the final transmit signal and has length N=17. The resulting
mismatched code set is a (12/17) set, meaning that the correlator signal
is 12 bits long, and the transmit signal is 17 bits long.
The fourth appended bit (not shown) and the fifth appended bit (not shown)
are determined by following the above pattern for determining appended
bits. In general, the output of the test correlations 54, 57, 59
corresponds to the appended bits 13, 14, 15.
In the event that the twelfth bit of the correlator signal 56 was 1, then
the appended bits would correspond to negative of the output of the
corresponding test correlations. As a general rule an appended bit n of a
test signal may be found using the following equation: C(n-1)+(last bit of
correlator signal 56)*(bit n of the test signal)=0.
Those skilled in the art will appreciate that the final transmit signal and
the correlator signal may be switched without departing from the scope of
the present invention.
The above technique for determining a transmit signal and a correlator
signal for providing number of reduced range sidelobes at the output of a
radar system correlator has the following steps:
1. obtaining a Barker code and dropping one bit if the Barker code has an
odd length;
2. correlating the Barker code with a shifted version of the Barker code
for obtaining a correlation output value;
3. forming an extended sequence by appending a sequence value to the
shifted Barker code so that the resulting correlation between the shifted
Barker code and the Barker code cancels said correlation output value
resulting in a zero; and
4. repeating the above steps as necessary to form extended sequence that
will result in a pre-determined number of zero range sidelobes when
correlated with the Barker code in a radar system correlator (not shown).
FIG. 10 is a graph showing the output of the mismatched filter constructed
using the technique of FIGS. 9a-9c. Five zero sidelobes 66 are shown
adjacent to a main peak 68.
Correlation data presented up to this point is based on sequences with a
constant amplitude throughout the entire sequence. This corresponds to
target returns with zero frequency (DC pulses). In most radar receivers
target returns have a small remaining frequency component related to a
Doppler shift induced by the target velocity. The received pulse has a
small sinusoidal amplitude modulation referred to as uncompensated
Doppler. In addition, the target return has a noise component. Thus, the
radar system correlator (not shown) correlates a correlator signal with a
received signal that is not the exact transmit signal. This has the effect
of degrading the range sidelobe response of the biphase (0 degrees and 180
degrees corresponding to 1 and -1 respectively) code contained in the
pulse. The mismatched codes developed in accordance with the teachings of
the present invention are no more vulnerable to uncompensated Doppler than
their matched counterparts.
FIG. 11 is a graph comparing a result of the aperiodic autocorrelation 74
of a 13 bit Barker code sequence and a result 72 of the output of the
mismatched filter of FIG. 10 under uncompensated Doppler conditions. For
FIG. 11, the extended transmit signal ›-1, 1, -1, 1, -1, -1, 1, 1, -1, -1,
-1, -1, -1, 1, -1, 1, -1! of the mismatched filter of FIG. 10 is used as
the correlator signal (not shown) and the correlator signal ›-1, 1, -1, 1,
-1, -1, 1, 1, -1, -1, -1, -1! of FIG. 10 is used as the transmit signal
(not shown).
The graph of FIG. 11 is based on a sampling frequency of 10 Mhz which
corresponds to a range separation or range gate size of 15 meters between
samples. The transmit signals are amplitude modulated by a cosine (not
shown) of unit amplitude and an uncompensated Doppler frequency of 10 Khz.
In the present example, the initial phase of the cosine is 30 degrees.
The vertical axis represents decibels (dB) relative to the corresponding
correlation peaks 76 at 0 dB. The result 72 of the 12/17 code set of FIG.
10 has significantly reduced range sidelobes 78 in comparison to range
sidelobes 82 of the autocorrelation response 74.
Generally, the applicability of mismatched codes of the present invention
to reducing range sidelobes is not affected by uncompensated Doppler.
FIG. 12 is a block diagram of a radar system 10 constructed in accordance
with the teachings of the present invention. The radar system 10 includes
a signal generator 8 that is used to generate pulsed radar signals that
are transmitted via an antenna 12. Transmitted signals reflect off targets
(not shown) and are received at the antenna 12. Received analog signals
are processed by a set 14 of filters, amplifiers, mixers, and oscillators
before being converted to a digital format by an analog to digital
converter 16. The resulting digital signal is input to a mismatched filter
90 that correlates the digital signal with a correlator signal of a
different length. The output of the mismatched filter 90 having reduced
range sidelobes is then input to a processor 18 for further analysis. The
processor 18 may be implemented as a computer running target detection
software.
The signal generator 8 may also be implemented as a computer that may be
used to determine the transmit signal (not shown) and the correlator
signal (not shown) for providing the reduced range sidelobes at the output
of the mismatched filter 90.
Those skilled in the art will appreciate that if the mismatched filter 90
is an analog correlator, the positions of the analog to digital converter
16 and the filter 90 may be switched without departing from the scope of
the present invention.
FIG. 13 is diagram of a mismatched filter 90 constructed in accordance with
the teachings of the present invention. The mismatched filter 90 includes
an extend transmit sequence 84 that represents a received signal, a delay
line 86, a set of multipliers 88, a correlator sequence 92, an adder 94,
and an output shift register 96.
A programmable signal generator (not shown) generates the transmit sequence
84 which is extended by k extra bits beyond that of a correlator sequence
92. The transmit sequence 84 is shifted into the delay line 86 one bit at
a time. As the sequence 84 is shifted into the delay line 86, the
multipliers 88 multiply each bit of the sequence 84 with a corresponding
bit in the correlator sequence 92. The multiplied bits are then summed in
the adder 94 to produce a value for the correlation response which is
shifted into the shift register 96. When the correlation of the signal 84
with the correlator signal 92 is finished, the shift register 96 has k
zero sidelobes 97 included among the values 95 available from the shift
register 96.
In the present specific embodiment, the length of the shift register 96 is
the same as the length of the input shift register 84. Those skilled in
the art will appreciate that the correlator output sequence contained in
the shift register 96 does not need to have the same length as the
sequence values stored in the shift register 84. The shift register 96 may
have different lengths depending on the application.
Those skilled in the art will also appreciate that the delay line 86 may be
a shift register, that the sequences 84 and 92 may be switched without
departing from the scope of the present invention, and that an adjustable
length correlator of conventional design may be used without departing
from the scope of the present invention. In addition, the mismatched
filter 90 may be implemented in computer software.
Thus, the present invention has been described herein with reference to a
particular embodiment for a particular application. Those having ordinary
skill in the art and access to the present teachings will recognize
additional modifications applications and embodiments within the scope
thereof.
It is therefore intended by the appended claims to cover any and all such
applications, modifications and embodiments within the scope of the
present invention.
Accordingly,
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