Adaptive window CFAR apparatus

A constant false alarm rate (CFAR) apparatus is responsive to detected transitions in the clutter signal level to remove certain range cells from the alarm threshold calculation process, whereby the CFAR detector retains maximum sensitivity in the vicinity of clutter transitions while avoiding increased false alarm rates. A transition detection apparatus searches for transitions in range cells preceding the threshold calculation window and controls switches which remove range cells from the threshold calculation as the transition is shifted into and through the threshold calculation window.

FIELD OF THE INVENTION 
The present invention relates, in general, to constant false alarm rate 
(CFAR) detectors for use in conjunction with radar systems. More 
particularly, the invention relates to an adaptive window CFAR apparatus 
for increasing the sensitivity of the detector near transitions between 
two levels of clutter in the radar signal. 
BACKGROUND OF THE INVENTION 
Constant false alarm rate (CFAR) radar detectors are well known in the art 
for maintaining a consistent probability of false target detection in 
various environments. The basic approach is to set an alarm threshold for 
a range cell under test by averaging the signal levels in adjacent range 
cells within a predetermined window centered on the cell under test. 
Abrupt transitions between one level of clutter and another, for instance a 
transition from a grassy field to a grove of trees, are a particular 
problem for CFAR detectors. Pure range averaging detectors tend to alter 
the alarm threshold too slowly in response to abrupt clutter transitions 
and so to produce false detections. A "greatest-of" averaging technique 
obtains range averages from two windows, one on either side of the cell 
under test, and uses the greater of the two averages to set the threshold. 
This technique avoids false detections at abrupt transitions, but 
desensitizes the detector by excessively adjusting the threshold near such 
transitions. In addition, various adaptive CFAR detectors are available, 
but they are not directed at, nor do they solve the problem of clutter 
transitions. 
SUMMARY OF THE INVENTION 
Accordingly, it is an object of the present invention to provide an 
improved CFAR apparatus with increased sensitivity without increased false 
detections in the vicinity of clutter transitions. 
It is a further object of the invention to provide an improved CFAR 
apparatus which detects clutter transitions and alters the window 
surrounding the cell under test in response thereto. 
A particular embodiment of the present invention comprises a first range 
window preceding the cell under test and a second range window following 
the cell under test. In the absence of a detected transition, the range 
data units contained in each of the cells of the first and second windows 
are summed and multiplied by a threshold constant to yield the alarm 
threshold. A clutter transition detection apparatus comprises the first 
range window, a transition test cell preceding it, a third range window 
preceding that, a transition detection function generator and a transition 
detector. Clutter transitions are located by the apparatus and a series of 
switches are opened and closed according to a predetermined pattern to 
remove certain range cells in the first and second range windows from the 
threshold calculation. Simultaneously, the threshold constant is altered 
to reflect the number of range cells currently used in the calculation. 
Altering the window from which the alarm threshold is calculated in 
response to a detected transition allows maximum sensitivity near the 
transition while avoiding delayed response and false alarms. 
These and other objects and advantages of the present invention will be 
apparent to one skilled in the art from the detailed description below 
taken together with the drawings.

DETAILED DESCRIPTION OF THE INVENTION 
Referring now to FIGS. 1A through 1D, a clutter transition as seen by a 
CFAR apparatus is depicted in graphic form. The signal received by a CFAR 
apparatus comprises a plurality of range data units. Each range data unit 
has a signal power level attributable to objects reflecting the radar beam 
at that particular range and to electronic noise in the radar. For 
instance, referring to FIG. 1A, a first range data unit 10, which 
corresponds to a range R, has a signal power S.sub.1 and a second range 
data unit 12, corresponding to a range R', has a signal power S.sub.2. The 
range data units are shifted serially into and through the CFAR apparatus 
so that range data unit 12 will progress toward the origin along the range 
axis as range data units from greater ranges are shifted into the 
apparatus. The range data units are derived from the signal received by 
the radar antenna and may or may not be subjected to preliminary clutter 
rejection filtering prior to entering a CFAR apparatus. 
The purpose of a CFAR apparatus is to provide a predictable rate of false 
target detections by rejecting so-called clutter. In its broadest sense, 
clutter may be thought of as any return signal which does not represent a 
true target. To perform this function, CFAR systems calculate an alarm 
threshold based on the average signal power in the range data units 
surrounding the cell under test and indicate a detection only if the 
signal level in the cell under test exceeds the alarm threshold. The term 
cell or range cell is used herein to refer to a physical element of the 
CFAR apparatus, such as a digital data register or a tap on a delay line, 
through which range data units are shifted. In FIGS. 1A through 1D, cell 
under test T is surrounded by a first range window I comprising the 
sixteen range cells immediately preceding cell T and a second range window 
II comprising the sixteen range cells immediately following cell T. Range 
window I is said to precede cell T because range data units pass through 
it prior to entering cell T or window II, since it is at greater range. In 
FIG. 1A, a clutter transition 14, at which the clutter signal level 
changes from S.sub.1 to S.sub.2, has entered window I and is approaching 
cell under test T. The problem at this stage is to prevent premature 
upward bias of the alarm threshold resulting in decreased detector 
sensitivity. A pure average CFAR apparatus would average the range data 
units in all of the cells in windows I and II, which average would be 
weighted toward level S.sub.1, thus setting the alarm threshold only 
slightly above S.sub.1. A "greatest-of" CFAR apparatus would obtain the 
averages for windows I and II separately and use only that for window I, 
since it is the greater of the two, resulting in an alarm threshold 
significantly above level S.sub.1 and decreased sensitivity. 
Referring now to FIG. 1B, transition 14 has been shifted through range 
window I and cell under test T and into range window II. At this point, a 
pure average CFAR apparatus would still be significantly effected by the 
range data units in window II having a signal level S.sub.1, resulting in 
a low threshold level and the possibility of false alarms. A "greatest-of" 
apparatus would have a sufficiently high threshold level to avoid such 
false alarms. In FIG. 1C, transition 14 has been shifted out of the 
apparatus and a transition 16 at which the clutter level returns from 
level S.sub.2 to S.sub.1 has been shifted into window I. Again, the 
problem is premature bias. A pure average CFAR apparatus tends to lower 
the alarm threshold in response to the range data units in window I at a 
signal level S.sub.1 before transition 16 reaches cell under test T, 
resulting in false alarms. A "greatest-of" CFAR apparatus avoids this 
problem by calculating the alarm threshold purely from the range data 
units in window II. However, once transition 16 has passed cell under test 
T, as shown in FIG. 1D, a "greatest-of" CFAR apparatus tends to set the 
alarm threshold too high in response to the average of the range data 
units in window II whereas a pure average CFAR apparatus allows greater 
sensitivity by also responding to the range data units in window I. The 
problem then, is in detecting approaching transitions and preventing both 
premature bias and delayed response. 
Referring to FIG. 2A, an idealized clutter block 20 is shown in graphic 
form. At range R.sub.1, a transition 22 raises the clutter signal level 
from zero to ten in some arbitrary units. At range R.sub.2 a second 
transition 24 lowers the clutter level back to zero. It is desired that an 
easily implementable function be found that will detect transitions 22 and 
24. Consider equation (1) as follows: 
##EQU1## 
Equation (1) defines a difference window function of length 2l centered 
about cell X.sub.i. That is, the range data units on both sides of X.sub.i 
are included in the difference window out to a distance l. The average 
level of the range data units following X.sub.i is subtracted from the 
average of the units preceding X.sub.i, thus the term difference window. 
The responses of several difference window functions of various lengths 
are shown in FIG. 2B, which plots f.sub.l versus the distance in range 
units of a transition such as transition 22 of FIG. 2A from the transition 
test cell X.sub.i. As would be expected, each of the difference window 
functions has a maximum value equal to the amplitude of the transition (10 
in this case) and the maximum value occurs when the transition occurs in 
the transition test cell X.sub.i. The value of each of the functions falls 
off linearly until the transition is outside the window, thus making the 
functions fairly inaccurate as locators of a transition. However, consider 
a function E which is the product of the difference window functions shown 
in FIG. 2B. The response of this function to the passage of the clutter 
block of FIG. 2A through the transition test cell X.sub.i is shown in FIG. 
2C. 
A spike of amplitude 10.sup.4 is generated at range R.sub.1 and at range 
R.sub.2 corresponding to transition 22 and transition 24, respectively. 
The spike at R.sub.2 is negative since transition 24 is a negative one. 
The width of the spike is determined by the length of the smallest 
difference window (f.sub.2 in this case) since the product cannot rise 
above zero until all of the factors are non-zero. Since a narrow spike is 
desirable to precisely locate the transition, E should always include one 
small window. The contribution of the longer windows (besides building the 
amplitude of the spike) is best understood with reference to Table I: 
TABLE I 
______________________________________ 
CLUTTER 
BLOCK F.sub.2 F.sub.4 F.sub.8 
LENGTH (MAX) (MAX) (MAX) F.sub.16 (MAX) 
E (MAX) 
______________________________________ 
16 10 10 10 10 10.sup.4 
8 10 10 10 5 5 .times. 10.sup.3 
4 10 10 5 2.5 1.25 .times. 10.sup.3 
2 10 5 2.5 1.25 1.56 .times. 10.sup.2 
______________________________________ 
If the length of the clutter block, that is the difference between R.sub.1 
and R.sub.2, is less than the length of a particular difference window 
function, then the maximum value of that function will be less than the 
amplitude of the transition. This in turn, will result in a lower maximum 
amplitude of the function E. Therefore, longer difference window functions 
may be added to the function E to reduce the response of E to very short 
clutter blocks. Short clutter blocks are more easily averaged out by 
standard CFAR techniques and very short clutter blocks may be targets 
which should be detected. The precise choice of the factors of E will be 
made with consideration of the types of clutter anticipated. As will be 
described below, an apparatus will be utilized which detects spikes in the 
function E. This apparatus will also be designed according to the 
anticipated clutter and with consideration of the particular factors of E 
used so as to optimally detect transitions. For instance, if it desired 
that clutter blocks of length less than 8 not be detected, the transition 
detection apparatus can be designed to ignore values of E less than 
5.times.10.sup.3. Since CFAR systems are customarily designed by 
considering the anticipated clutter statistics, the choice of the 
particular difference window functions and a threshold for E must be made 
by each system designer. 
Referring now to FIG. 3, an apparatus for generating the difference window 
functions of FIG. 2B is shown in schematic form. Range data units are 
input serially into a range window 30 comprising 15 range cells. Each 
range cell is adapted to receive a single range data unit, store it and 
advance it to the next range cell when a new range data unit is shifted 
in. If the system is digital, range window 30 is a digital data register. 
Tapped delay lines are commonly used in nondigital systems. Range cell 1 
of range window 30 is coupled to a transition test cell 32, which is 
designated X.sub.i in accordance with the above difference window function 
definition. Transition test cell 32 is coupled to range window 34 
comprising 16 range cells. The range cells of windows 30 and 34 are 
numbered 1 through 16 to indicate the distance of the cell from transition 
test cell 32, again in accordance with equation (1). A range data unit 
entering range cell 15 of window 30 passes through the successively lower 
numbered cells of window 30, then into transition test cell 32, then into 
cell 1 of window 34 and through the successively higher numbered cells 
thereof and finally is output from cell 16 of window 34. 
A first summing circuit 36 has inputs coupled to range cells 1 and 2 of 
range window 34 and is adapted to sum the range data units stored therein. 
A second summing circuit 38 has an input coupled to range cell 1 of range 
window 30 and an input coupled to transition test cell 32 and is adapted 
to sum the range data units stored therein. A third summing circuit 40 has 
an input coupled to an output of summing circuit 38 and an inverted input 
coupled to an output of summing circuit 36 and is adapted to subtract the 
output of summing circuit 36 from the output of summing circuit 38. A 
divide-by-two circuit 42 has an input coupled to an output of summing 
circuit 40. The output of divide-by-two circuit 42 is, therefore, equal to 
the difference window function f.sub.2 as defined by equation (1). A 
summing circuit 44 has inputs coupled to an output of summing circuit 36, 
range cell 3 of range window 34, and range cell 4 of range window 34 and 
is adapted to sum the output of summing circuit 36 with the range data 
units stored in cells 3 and 4 of range window 34. A summing circuit 46 has 
inputs coupled to an output of summing circuit 38 and cells 2 and 3 of 
range window 30 and is adapted to sum the output of summing circuit 38 
with the range data units stored in cells 2 and 3 of range window 30. A 
summing circuit 48 has an input coupled to an output of summing circuit 46 
and an inverted input coupled to an output of summing circuit 44 and is 
adapted to subtract an output of summing circuit 44 from an output of 
summing circuit 46. A divide-by-four circuit 50 has an input coupled to an 
output of summing circuit 48, whereby the output of divide-by-four circuit 
50 is the difference window function f.sub.4. A summing circuit 52 has 
inputs coupled to an output of summing circuit 44 and range cells 5 
through 8 of range window 34 and is adapted to sum an output of summing 
circuit 44 with the range data units stored in cells 5 through 8 of range 
window 34. A summing circuit 54 has inputs coupled to an output of summing 
circuit 46 and cells 4 through 7 of range window 30 and is adapted to sum 
an output of summing circuit 46 with the range data units stored in cells 
4 through 7 of range window 30. A summing circuit 56 has an input coupled 
to an output of summing circuit 54 and an inverted input coupled to an 
output of summing circuit 52 and is adapted to subtract an output of 
summing circuit 52 from an output of summing circuit 54. A divide-by-eight 
circuit 58 has an input coupled to an output of summing circuit 56, 
whereby the output of divide-by-eight circuit 58 is equal to the 
difference window function f.sub.8. A summing circuit 60 has inputs 
coupled to an output of summing circuit 52 and range cells 9 through 16 of 
range window 34 and is adapted to sum an output of summing circuit 52 with 
the range data units stored in range cells 9 through 16 of range window 
34. A summing circuit 62 has inputs coupled to an output of summing 
circuit 54 and range cells 8 through 15 of range window 30 and is adapted 
to sum an output of summing circuit 54 with the range data units stored in 
range cells 8 through 15 of window 30. A summing circuit 64 has an input 
coupled to an output of summing circuit 62 and an inverted input coupled 
to an output of summing circuit 60 and is adapted to subtract an output of 
summing circuit 60 from an output of summing circuit 62. A 
divide-by-sixteen circuit 66 has an input coupled to an output of summing 
circuit 64, whereby the output of divide-by-sixteen circuit 66 is equal to 
the difference window function f.sub.16. A multiplying circuit 68 has 
inputs coupled to the outputs of divide-by-two circuit 42 and 
divide-by-four circuit 50 and a multiplier circuit 70 has inputs coupled 
to the outputs of divide-by-eight circuit 58 and divide-by-sixteen circuit 
66. A multiplier circuit 72 has inputs coupled to the outputs of 
multiplier circuit 68 and multiplier circuit 70 whereby the output of 
multiplier circuit 72 is equal to the transition detection function E 
which is equal to the product of the difference window functions f.sub.2, 
f.sub.4, f.sub.8 and f.sub.16. 
The choice of hardware to implement the above described apparatus, as well 
as various modifications thereto, will be apparent to one skilled in the 
art. 
Referring now to FIG. 4 an adaptive window CFAR apparatus according to the 
principles of the present invention is shown in block diagram form. A 
conventional CFAR window comprises a first range window 80 having N cells 
for receiving, storing and advancing range data units, a cell under test 
82 and a second range window 84 having N cells for receiving, storing and 
advancing range data units. Range data entering window 80 passes through 
each of the cells thereof, then through cell under test 82, then through 
each of the cells of window 84. Each of the range cells of window 80 is 
coupled to one of a first group of switches 86 and each of the range cells 
of window 84 is coupled to one of a second group of switches 88. All of 
the switches in first group 86 and second group 88 are initially closed. 
Each of the switches in first group 86 is coupled to an input of a summing 
circuit 90, whereby the output of summing circuit 90 is the sum of the 
range data units in the cells of first window 80. Each of the switches in 
second group 88 is coupled to an input of summing circuit 92 whereby the 
output of summing circuit 92 is the sum of the range data units in the 
cells of second window 84. A summing circuit 94 has inputs coupled to the 
outputs of summing circuits 90 and 92 whereby the output of summing 
circuit 94 is the sum of the range data units in first window 80 and 
second window 84. A multiplier circuit 96 has an input coupled to the 
output of summing circuit 94 and an input coupled to an output of 
threshold constant table 98. Threshold constant table 98 provides a 
threshold constant which, when multiplied with the sum provided by summing 
circuit 94, produces the desired alarm threshold. The particular threshold 
constant supplied by table 98 depends on the number of range data units 
represented by the sum from circuit 94, the type of clutter statistics 
anticipated and the desired false alarm rate. Many techniques for choosing 
threshold constants are familiar in the art. A comparator circuit 100 has 
an input coupled to the output of multiplier circuit 96 and an input 
coupled to cell under test 82. Comparator 100 compares the alarm threshold 
provided by multiplier circuit 96 to the range data unit stored in cell 
under test 82 and indicates a target detection if the range data unit is 
greater. 
To this point what has been described is a fairly conventional pure average 
CFAR apparatus. Range data units from a first window 80 and a second 
window 84 are input to an alarm threshold calculation apparatus indicated 
by dotted line 102. The threshold calculation apparatus sums all of the 
range data units from the windows, applies a threshold constant and 
produces an alarm threshold to be compared to the range data unit from 
cell under test 82. 
In addition to what has been described so far the adaptive window CFAR 
apparatus of FIG. 4 comprises a transition detection apparatus indicated 
by dotted line 104 which includes first range window 80, a transition test 
cell 106, a third range window 108 having N-1 range cells, a transition 
detection function generator 110 and a transition detector circuit 112. 
Transition test cell 106, each of the range cells of first range window 80 
and each of the range cells of third range window 108 are coupled to 
transition detection function generator 110. Function generator 110 is of 
the type described above with reference to FIG. 3 and it generates one or 
more difference window functions and a transition detection function E 
which is the product of the difference window functions generated. Range 
data is input initially to cell N-1 of third range window 108 and is then 
shifted through the apparatus as previously described. When a clutter 
transition approaches transition test cell 106 transition detection 
function generator 110 will produce a spike in the transition detection 
function E. The output of transition detection function generator 110 is 
coupled to a transition detection circuit 112 which is triggered by a 
spike in the function E. 
As the detected clutter transition leaves transition test cell 106 and 
enters first range window 80 it would normally begin to bias the alarm 
threshold. However, transition detection circuit 112 prevents this by 
opening the first switch in the first group of switches 86, thus 
preventing the range data unit containing the transition from entering the 
sum used to calculate the alarm threshold. Furthermore, as the range data 
unit containing the transition is shifted through first range window 80 
and new range data units at the new clutter signal level are shifted in 
behind it, transition detection circuit 112 opens more of the switches in 
first group 86 to prevent the premature bias of the alarm threshold 
towards the new clutter signal level. When the clutter transition is 
within a few range cells of cell under test 82 the alarm threshold is 
being calculated almost exclusively using range data units from second 
window 84 thus allowing greatly increased sensitivity. However, as the 
clutter transition approaches even closer it is necessary to quickly alter 
the alarm threshold to reflect the new clutter signal level. To accomplish 
this transition detection circuit 112 closes all of the switches in first 
group of switches 86 and opens the switches in second group 88 immediately 
prior to the entry of the clutter transition into cell under test 82. 
Consequently the new alarm threshold is set exclusively in response to 
range data units following the clutter transition. As the clutter 
transition is shifted through second range window 84 transition detection 
circuit 112 closes switches in the second group 88, beginning with the 
first switch in group 88, so as to allow more and more of the range data 
units following the clutter transition to effect the alarm threshold 
calculation. As is apparent, the number of range cells coupled to the 
threshold calculation apparatus varies from 2N to N and back to 2N as the 
clutter transition passes through the apparatus. This requires variation 
of the threshold constant used in the threshold calculation to reflect the 
number of range data units present in the sum at any one time. To 
accomplish this transition detection circuit 112 is coupled to threshold 
constant table 98 so that the correct threshold constant is supplied to 
multiplier circuit 96 at all times. Transition detection circuit 112 
passes to table 98 a number representing the number of switches currently 
closed and table 98 simply looks-up the proper constant which has been 
previously calculated and stored. The detailed operation of transition 
detection circuit is best understood by reference of FIG. 5. 
Referring to FIG. 5 a transition detection circuit is shown in block 
diagram form. A comparator 120 has an input coupled to transition function 
generator 110 (FIG. 4) and an input coupled to a transition threshold. An 
output of comparator 120 is coupled to a SET input of a flip-flop circuit 
122. An output of flip-flop circuit 122 is coupled to an ENABLE input of a 
modulo N counter 124. A CLOCK input of modulo N counter 124 is coupled to 
the same clock signal which shifts range data units through the apparatus 
of FIG. 4. A carryover (CO) output of modulo N counter 124 is coupled to a 
clock input of a modulo 2 counter 126. A carryover (CO) output of modulo 2 
counter 126 is coupled to RESET inputs of modulo N counter 124 and 
flip-flop circuit 122. A toggle circuit 128 has an input coupled to the 
carryover output of modulo N counter 124. A RESET input of toggle circuit 
128 is coupled to the output of comparator 120, which is also coupled to a 
RESET input of modulo 2 counter 126. An output of toggle circuit 128, 
which comprises either a logical "1 " or a logical "0", is coupled to 
first and second switch groups 86 and 88 (FIG. 4) and operates to select 
which of the switch groups will respond to the count from modulo N counter 
124. The count from modulo N counter 124 is also coupled to switch groups 
86 and 88. When the output of toggle circuit 128 is 0 first switch group 
86 responds by opening a number of switches, counting from right to left, 
equal to the count from modulo N counter 124. The remaining switches in 
first group 86 and all of the switches in second group 88 are closed. When 
the output of toggle circuit 128 is 1 the second switch group 88 will 
respond by closing a number of switches, counting from right to left, 
equal to the count from modulo N counter 124. The remainder of the 
switches in second group 88 are open and all of the switches in first 
group 86 are closed. Both the select switch group and switch control 
outputs are also coupled to threshold constant table 98 to indicate the 
number of closed switches, upon which the proper threshold constant is 
based. 
In the absence of a detected clutter transition, modulo N counter 124 is 
set at a count of 0 and toggle circuit 128 is providing a select switch 
group output of 0, thus closing all of the switches in both groups. Modulo 
2 counter 126 is also set at 0 and module N counter 124 is disabled. The 
transition threshold is chosen with regard to the anticipated clutter, the 
desired performance of the CFAR apparatus and the factors chosen for the 
transition detection function E. When a spike, either positive or 
negative, in E exceeds the transition threshold, comparator 120 is 
triggered and acts through flip-flop circuit 122 to enable modulo N 
counter 124. Each subsequent clock cycle, in addition to shifting the 
detected transition one cell further through the apparatus, increments the 
count in modulo N counter 124 by one and opens another switch in first 
group 86, thus preventing the transition from effecting the alarm 
threshold. Also, the threshold is updated to reflect the number of closed 
switches. At the Nth clock cycle, when the transition is shifted into the 
range cell immediately preceding the cell under test, modulo N counter 124 
rolls over and provides a carryover signal which changes toggle circuit 
128 to the 1 position and increments modulo 2 counter 126 by one. All of 
the switches in first group 86 are closed and all of the switches in 
second group 88 are opened in response to the new select switch group and 
switch control signals. At this point, the alarm threshold is calculated 
using only range cells following the transition. Modulo N counter 124 
continues to be enabled, so that subsequent clock cycles close successive 
switches in second group 88 and update the threshold constant. When modulo 
N counter 124 again reaches 0, the carryover output will roll over modulo 
2 counter 126, which provides a carryover output to reset modulo N counter 
124 and flip-flop circuit 122, thus returning the entire transition 
detection circuit to its initial state. 
While the invention has been particularly shown and described with 
reference to a preferred embodiment thereof it will be understood by those 
skilled in the art that various other modifications and changes may be 
made to the invention without departing from the spirit and scope thereof.