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Description  |
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CROSS-REFERENCE TO RELATED APPLICATION
Reference is made to a related copending U.S. application filed in the U.S.
Patent Office on Mar. 10, 1976, bearing Ser. No. 665,643, and assigned to
a common assignee. This application relates to an MTI radar system
utilizing variable interpulse periods and weighting with a cascaded two
and three pulse canceler.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to pulse doppler or moving target indicator
(MTI) radar systems; and more particularly, to an improved digital filter
bank signal processor utilizing variable interpulse periods and weighting.
2. Description of the Prior Art
Moving target indication (MTI) radar is provided to reject signals or
echoes from stationary and slowly moving objects, such as terrain, foliage
or surface vehicles; and to pass echoes from moving objects such as
aircraft. The radar receivers may utilize digital filters to suppress such
undesired echoes; and these filters are generally described as moving
target indicators. The MTI signal processor utilizes the doppler shift
caused by the reflected signal of a moving target to distinguish moving
targets from fixed targets. In a pulse-radar system this doppler shift
appears as a change of phase of received signals between consecutive radar
pulses. Assuming that the radar transmits a pulse of RF energy, which is
reflected by ground clutter and a moving target such as an airplane, the
reflected pulses return to the radar antenna within a certain length of
time. The radar then transmits a second pulse. The reflection from the
ground clutter occurs in exactly the same amount of time for both the
first and second transmitted pulses, but the reflection from the aircraft
occurs in more or less time, because the aircraft has moved either closer
to or away from the radar in the interval between transmitted pulses. The
time change between the first and second transmitted pulses is determined
by comparing the phase of the received signal with the phase of the
reference oscillator in the radar. If the target is fixed the relative
phase of consecutive received pulses does not change. For a target that
moves between pulses, the phase of the received pulses change.
In the event of both wind and rain, such moving rain may be detected as a
moving target rather than clutter. Wind conditions vary as a function of
altitude, a condition known as "wind shear", so rain echoes cover a band
of velocities. Particularly, when the radar antenna is scanning and is
pointed either directly into the wind or with the wind, the rain clutter
will present the greatest radial velocity relative to the radar, and this
could be in the order of 40-60 knots. Inasmuch as such a low velocity does
not often exist in the detection of flying aircraft, the system can be so
constructed to reject any clutter or interference that has a radial
velocity equal to that of the rain. A flying aircraft can create such low
radial velocity when the aircraft is flying nearly tengentially relative
to the antenna.
In the past, such systems have been constructed either as single channel
filtering systems, generally known as MTI circuits, or as multiple channel
filter systems, recently given the name of MTD circuits. In the single
channel or MTI approach it is necessary that the clutter rejection filters
be designed to reject clutter at all possible velocities simultaneously;
for example, the filter rejection notch might need to extend from -50
knots to +50 knots in order to cope with any possible wind condition in
the case of rain clutter, even though the actual rain clutter present at
any one instant, corresponding to a particular antenna pointing direction,
would be unlikely to extend over the entire notch region. To avoid this
restriction, the multiple channel or MTD approach may be employed to
provide a system of filters which is adaptive to the actual clutter
conditions present at any instant. Thus, for example, a bank of filters
may be used, which in aggregate cover the velocity range -50 to +50 knots
but each of which has a narrower velocity coverage over a small part of
that velocity range. Each filter in the bank may then be equipped with
Constant False Alarm Rate (CFAR) circuits, of a conventional nature, at
its output, such that in the presence of interfering clutter, such as rain
clutter, the particular filters, into which the rain echoes fall, are
desensitized by their CFAR circuits to the extent necessary to prevent
detection of the rain clutter, whereas the remaining filters, in which
rain clutter echoes are not present, retain their full sensitivity to
detect aircraft targets. Thus, the CFAR circuits of the multiple filter
approach enable the detection system to respond adaptively to a clutter
interference environment which is changing with time, as a result, for
example, of the effects of antenna scanning.
It may be noted that the conventional CFAR circuits referred to above for
the individual filter outputs may be implemented in a variety of
alternative ways; for example, suitable well known CFAR methods are:
cell-averaging CFAR, log CFAR, or hard-limiting types of CFAR such as
CPACS (Coded Pulse Anti-Clutter System).
There are times, when the received signal is shifted precisely 360.degree.,
or multiplies thereof, between pulses. Such as the case, when the targets
move 1/2, 1, 3/2, etc. wavelengths between consecutive transmitted pulses.
Thus, where the radar system is so structured to provide a zero output not
only for stationary targets or clutter but also from targets up to 50
knots for example, to reject wind blown rain, such problem is aggravated.
Because not only are the multiples of 360.degree. phase shift rejected,
but also a band of phase shifts adjacent to the multiples corresponding to
the wind and rain clutter for a particular area. This rejection of the
frequency multiples which are echoed from a moving target are known as
"blind speeds". Thus, blind speeds represent the frequency ambiguity
inherent in a sample data system when the interval between data samples
(interpulse period) is fixed. The echoes generated by an object moving an
integer number of half-wavelengths toward or away from the radar antenna
during the interpulse period are indistinguishable from those of a
stationary object. Therefore, if ground clutter interferences are rejected
by the filter bank, the system also is blind to aircraft speeds which
create these ambiguous doppler frequencies.
Heretofore, filters for such radars were implemented with analog devices
such as capacitors, inductors and resistors. However, more recently
digital filters have been utilized primarily because of lower cost of
implementation when a large number of range cells must be covered. In both
the analog and digital implementations, the echoes of the radar receiver
are sampled at an interval equal to or less than the range resolution of
the radar. Successive radar transmissions provide a multiplicity of
samples for each of range cell of interest, which create the inputs for a
bank of filters at each point in range.
Most digital processors or filters utilize the Discrete Fourier Transform
mathematical operation to convert time separated data inputs into
frequency dependent data outputs. Although the Fast Fourier Transform is a
practical configuration which reduces the number of mathematical
operations which must be performed, it requires the data input be
collected at a fixed interpulsed period, which does not eliminate the
"blind speed" deficiency. Also, analog filters suffer from the same blind
speed deficiency; in that they do not provide the desired rejection of
interference frequencies if the interpulse period is variable; and of
course, a fixed interpulse period creates blind speeds.
One of the virtues of digital implementation of MTI filters is the ability
to quickly shift from one pulse repetition frequency to another so that a
target that is blind to one pulse repetition frequency (PRF) is visible on
another. Unfortunately, desired azimuth beam widths and scan rates of the
antenna generally do not provide an adequate number of echoes as the beam
scans across the target for this solution to be effective.
The previously mentioned MTD system, implemented for an airport
surveillance radar operating at a frequency of 3 GHz., employs two
interpulse periods: a burst of ten pulses having a minimal interpulse
period for the desired range coverage, followed by a second burst of ten
pulses with a 25% longer interpulse period. The combination of azimuth
beam widths, scan rate, and PRF provide 23 hits per beam width, between -6
dB points of echo amplitude, which is barely enough for the use of two
different PRF's. The 25% spread of PRF's is the maximum tolerable, which
creates a first blind speed of approximately 560 knots over ground clutter
interference. Thus the system has a modest range such as 58 nmi, for
example, and a velocity coverage of approximately 500 knots. Such a
proposed system provides this coverage most effectively when the only
interference is ground clutter. However, when simultaneous rain and ground
clutter interference occur, severe degradation of sensitivity results at
certain aircraft velocities (dim speeds). Referring to FIG. 1 as an
example, the velocity response of such a proposed system with two pulse
repetition frequencies in a combination of ground clutter and a particular
case of rain clutter, is shown. In this example the velocity spectrum of
the rain 20 is chosen to extend from approximately 15 to 55 knots. The
portions of the curve that are cross hatched illustrate aircraft
velocities which are processed with good sensitivity. However, between
such cross hatched portions of the curve are velocities where sensitivity
is seriously degraded, referred to at 10, 11, 12, 13 and 14 as well as at
15, 16, 17, 18 and 19. These notches represent the result of the system
having adapted to the rain spectrum designated at 20, which is rejected by
the deep clutter notch at 10. The other notches, 11 through 19, are not
desired. Under these conditions, as shown in FIG. 1 the following dim
speeds correspond to the clutter notches 11 through 19 as follows:
______________________________________
Notch Number Dim Speed Region
______________________________________
11 125 to 181 knots
12 288 to 300 knots
13 350 to 362 knots
14 456 to 500 knots
15 -75 to -125 knots
16 -231 to -244 knots
17 -294 to -306 knots
18 -400 to -437 knots
19 -525 to -600 knots
______________________________________
Thus, it is desirable to provide an MTI system that provides detection of
all aircraft velocities of interest, except those velocities close to the
velocities of rain, chaff or ground clutter without severe degradation at
doppler frequencies which are multiples of the PRF; or in other words,
without blind speeds.
SUMMARY OF THE INVENTION
In accordance with the present invention, there is provided a doppler radar
system combining variable interpulse periods and weighting to provide a
plurality of filters, so constituted that the echo energy from desired
aircraft velocities is distributed uniformly among the filters. When rain
and ground clutter force the system to desensitize several of the filters,
through constant false alarm rate actions, small losses result at all
aircraft velocities other than the velocities corresponding to the
interference itself, rather than extreme losses at certain velocities.
Each filter is designed to suppress a designated band of interference, the
width of the band being less than the average pulse repetition frequency.
The time varying weights are employed in generating the filter outputs to
compensate for the effects of the variable interpulse periods.
The digital filter bank includes filters which individually provide high
attenuation of undesired signals over designated frequency bands, the
width of which are a large fraction of 1/T.sub.av where T.sub.av is the
average period between data samples, and little or no attenuation of
desired signals having doppler frequencies greater than 1/T.sub.av.
In one specific embodiment, the present invention provides for a method and
system wherein the digital filter bank is created by a cascade combination
of a two-pulse canceler and a filter bank employing time-varying weights
for processing (N-1) outputs of the canceler to reduce the complexity of
both the computational hardware and memory, when the dominant interference
is centered on zero velocity. The system and method may provide for a
digital filter bank created by a cascade combination of an M-pulse
canceler and filter bank processing (N-M+1) outputs of the canceler where
the canceler may employ either fixed or time-varying weights and the
filter bank employs time-varying weights and M may be 3, 4, etc.
The outputs of the individual filters must be individually processed by
CFAR devices, because the intensity of clutter interference in each filter
is unique. The CFAR outputs may be combined to form a single detection
decision or may be processed individually.
This generally involves post-detection integration of the number of echo
pulses generated as the antenna beam scans past the target, and a
detection is declared when the integrated amplitude exceeds a threshold
value.
In one specific embodiment, the individual filters of the filter banks are
combined at their outputs to form a single signal channel in which the
presence of a target echo may be determined by comparison against a
threshold level.
The system and method may also include means to selectively exclude or not
exclude from the combination, the outputs of those filters of the bank
which are designed to respond to zero or low velocity target or clutter
echoes, which exclusion is based on the history of detected zero or low
velocity echoes received over a multiplicity of previous radar scans in
the outputs of the filters to be excluded.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a graphical illustration of the estimated velocity response of a
prior art device having two different pulse repetition frequencies in the
presence of rain and ground clutter;
FIGS. 2A and 2B are a schematic block diagram of a system according to one
embodiment of the present invention;
FIG. 3 is a general block diagram of a doppler filter bank signal processor
according to the principles of the present invention;
FIG. 4 is a functional block diagram of a signal processor formed by two
transversal filters in cascade to aid in the understanding of the method
by which individual filters in the bank may be designed;
FIG. 5 illustrates the response of the individual VIP filters in a system
of the present invention;
FIG. 6 is a graph illustrating the response of one of the filters in a
system utilized with a preceding two-pulse canceler and a four-pulse
canceler;
FIG. 7 is a series of waveforms illustrating the responses of one of the
filters for eight successive starting points in the variable interpulse
period sequence;
FIGS. 8A through 8E are a series of waveforms showing the averages of the
responses of a typical filter of the filter bank of the present invention
with different starting points in the variable interpulse period sequence;
FIG. 9 is a graph illustrating the velocity response of a system utilizing
a doppler filter bank of the present invention in the presence of rain and
ground clutter; and
FIG. 10 illustrates the responses of the filter bank with various quantized
weights.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Prior to describing the specific embodiment illustrated in FIG. 2, it is
believed that the present invention will be more readily understood by
describing initially the general organization and function of the system.
With reference to FIG. 3, which is a block diagram of one embodiment of the
VIP doppler filter bank signal processor of the present invention, there
is included a total of seven different individual filters. The filters
referred to as filter No. 1 and filter No. 7 are assumed to respond to
zero velocity echoes and are used in conjunction with a CFAR system
designed to desensitize or completely blank the outputs therefrom in
ground clutter areas. This can be accomplished, for example, by a
conventional form of clutter map well known in the art. The velocity
response characteristic of filter No. 7 is a mirror image of the
corresponding characteristic of filter No. 1 and the outputs of each are
input to a gate 21, which functions to blank the filter outputs when so
designated by the contents of the clutter map. Each of the five filters
Nos. 2 through 6 provide a unique velocity response and are combined to
provide a composite velocity response. This composite velocity response is
dependent to a degree on the clutter interference which is suppressed by
the constant false alarm rate device at each of the filter outputs. These
devices, referred to at 22A through 22E are summed at their outputs by a
conventional summing device 23; and then integrated by a conventional
integrator 24. Although only one integrator 24 is shown in FIG. 3, a
separate integrator could be employed for each individual filter 1 through
7. In FIG. 2, hereinafter described, the CFAR system is represented by the
decoders 147 through 150, corresponding to a CPACS type of CRAR system,
although it is noted that other forms of CFAR, such as cell-averaging or
log CFAR would also be applicable.
The seven-filter system is used as one embodiment in that it represents a
processor design which could be applicable to a radar operating at a
transmitted carrier frequency of approximately 1.3 GHz. with a range of
100-150 nmi, for example. A typical VIP sequence as follows may be
utilized with eight interpulse periods in the order listed, and expressed
as percentage deviations from the average interpulse period:
-27.46%
-13.81%
+2.39%
+21.65%
-20.93%
-6.03%
+11.60%
+32.59%
The design of a bank of doppler filters to match the signal processor
system described herein requires the synthesis of a relatively large
number of different filters for any particular radar application.
Specifically, it is the product of the number of filters and the number of
different starting points in the VIP sequence for which each filter is
implemented. The design of such filters was based on optimization of the
individual filter responses to specific interference or clutter inputs
spectra, as described hereinafter.
The filter design was made general in the sense that an adjustable
parameter interference model was employed and also that the order of the
individual filters in the number of filters used in the bank are
selectable. The filters are synthesized in Finite Impulse Response (FIR)
or transversal filter form because, in general, Infinite Impulse Response
(IIR) or feedback filter forms, typically have an insufficient number of
degrees of freedom in their design or weight parameters to be compatible
with VIP operation.
The synthesis divides naturally into two phases, namely the synthesis of
"ideal" filters, with optimized weights, expressed to a large number of
significant numbers, and the approximation of these ideal filters by
practical filters with weights expressed to a finite number of bits,
optimized so that the required number is as low as possible. The
approximation method is described hereinafter.
In general, doppler filters exhibit non-symmetrical frequency response
characteristics, which require cross couplings between the in-phase (I)
and quadrature (Q) channels of the filters to be described in more detail
hereinafter. Equivalently, the VIP filter weights are of complex value.
However, in order to cancel ground clutter, which exhibits a narrow,
symmetrical spectrum, resulting primarily from antenna scan-modulation, it
is necessary that the associated filter responses also include a deep
symmetrical notch around zero frequency. Thus, the concept of preceding
the doppler filter bank processor with MTI canceler 25, which is common to
the filters 2 through 6 of the bank which are those filters that are
designed to respond to other than zero velocity returns. Such a canceler
25 would exhibit a symmetric characteristic and hence require only
real-valued weights, with a corresponding reduction in complexity of that
part of the processor. Cancellation of the ground clutter would also
reduce the dynamic range requirements of the subsequent filters.
Therefore, a preceding MTI canceler, with the capability of employing
pre-selected time varying canceler weights is employed. An MTI canceler of
the type shown and described is disclosed in detail in U.S. Pat. Nos.
3,560,972 and 3,566,402 to which reference is made for a more detailed
discussion thereof.
The following is an analysis of the general situation of an M-pulse
processor with pre-selected weights, preceding an N-pulse processor which
is to be optimized to match a given clutter model. With reference to FIG.
4, consider a processor in the form of two transversal filters referred to
within the dashed lines 26 and 27 connected in cascade and let the input
to these filters be a sequence of samples V.sub.1, V.sub.2, V.sub.3, etc.
occurring at the corresponding times T1, T2, T3, etc. T1 is greater than
T2 which is greater than T3 which is greater than the remaining times; and
V.sub.1 represents the sample entering the first filter at the time of
interest; that is, the time at which the output is to be taken. The first
filter 26 has time-varying weights, as indicated by the rotating switches
73, 74, and 75, where the set of weights used at times T1, T2, T3, etc.
are assumed to be known and represented by the matrix A, where the nth row
is the set of weights applicable at time T.sub.N. A is an N x M matrix,
when the first filter 26 has M weights and the second filter 27 has N
weights. Let G be the N .times. (N+M-1) matrix formed from the elements of
A (plus an appropriate number of zero elements) such that:
##EQU1##
Then the N data values, U.sub.1, U.sub.2, . . . U.sub.N, which reside in
the memory 28a, 28b, 28c (shift register) of the second filter at time
t.sub.1 to form the elements of a vector u, where u = Gv and the elements
of v are V.sub.1, V.sub.2, V.sub.3 . . . V.sub.(N+M-1). The output of the
second filter at time t.sub.1, is then y = b.sup.T u = b.sup.T Gv where b
is an N vector whose elements are the tap weights of the second filter.
Now consider an input comprising sampled values of a unit amplitude
sinusoid of frequency .omega. such that
V.sub.k = e.sup.-j.omega.t.sub.k, k = 1, 2, . . . (N+M-1).
the squared amplitude of the corresponding output y(.omega.) is:
##EQU2##
where .rho. = Gv and the asterisk indicates conjugation. Integrating over
the clutter frequency range (a,b), with weight W(.omega.), we obtain the
clutter output power:
##EQU3##
W(.omega.) is the assumed power spectral density of the clutter input and
the prime indicates conjugate transpose.
##EQU4##
The filter output is y = b.sup.T Gv. Thus the tap weights of an equivalent
single stage filter are b.sup.T. The filter noise gain is therefore,
##EQU5##
where the prime indicates conjugate transpose and the element (i,j) of the
matrix S is:
##EQU6##
The synthesis problem is thus to minimize the clutter output b'Zb subject
to the constraint b'Sb = 1, corresponding to noise gain normalization.
Forming the Lagrangian function,
F = b'Zb - 1/.lambda. (b'Sb -1)
and setting df/db = 2Zb - 2/.lambda. Sb = 0, we obtain the eigen value
problem
Z.sup.-1 Sb - .lambda. b = 0,
assuming that Z is non-singular.
Multiplying by b'Z we see that the clutter/noise output power ratio is
##EQU7##
and, thus, the minimum clutter/noise corresponds to the largest (real)
eigen-value of Z.sup.-1 S which is a Hermitian matrix. The optimum filter
tap weights are given by the associated eigen-vector, and will, in
general, be complex.
The optimum filter synthesis problem thus reduces to a standard eigen-value
problem which can be solved numerically by routine techniques. Preliminary
steps required in the calculation are the several integrations indicated
in equation (1) to form the matrix Z and the subsequent computation of its
inverse. A discussion of the practical problems encountered in performing
these computations is given hereinafter.
It may be noted that the special case corresponding to a single filter
implementation (i.e. no preceding canceler) is included in the general
case discussed above, with S equal to the identity matrix. In this case,
the eigen-value equation can be re-arranged so that it is unnecessary to
compute the inverse of Z prior to determining the eigen-vectors.
The foregoing synthesis produces "ideal", complex filter weights.
Normalization by means of the constraint equation can be employed to
achieve unity noise gain if desired. This is useful for purposes of
presenting and assessing the resulting filter frequency response
characteristics, but is of minor significance in the signal processor
application, because the individual filter outputs are subjected to
subsequent processing by the CFAR's (FIG. 3) which essentially removes all
amplitude information from their outputs. Similarly, the CFAR circuit
outputs are envelope detected, which effectively removes all phase
information, so that the specific filter output phase is of no
consequence. Thus, the filter outputs can be arbitrarily varied with
respect to phase and gain, with no effect on system behavior.
Equivalently, the filter weights may be arbitrarily scaled in amplitude or
rotated in phase through the same phase angle for all weights in a filter,
with no change in the overall signal processor behavior. Advantage can be
taken of this fact by using phase and scaling constants to minimize the
filter response errors resulting from the practical necessity of
approximating the filter weights by a finite number of bits in their I and
Q components. In effect, it is desirable to pick phase and scaling
constants for each filter to minimize the necessary number of bits used to
represent the ideal weights, while maintaining a good accuracy of
approximation in the resulting filter response.
There appears to be no straightforward analytical approach to determining
the best phase and scaling constants to use for a given accuracy of
approximation. A search procedure is, therefore, indicated as the best
practical way of determining the optimum constants. Since a phase rotation
of 90.degree. is equivalent to a simple interchange of I and Q weight
components, it is evident that the search procedure need only cover a
range of 0.degree. to 90.degree. in phase. Similarly, for binary
representation of the weights, it is clear that scaling by a factor of 2
or more, effectively increases by one, the number of bits required. Thus,
if one wishes to determine the best approximate filter, using weights
having a specific number of bits, then the search procedure need only
cover a 2:1 range in scaling, such that the most significant bit is always
required in at least one of the I or Q components of the filter weights.
In implementing a search procedure to determine optimum gain and phase
constants, the filter clutter/noise output ratio, as given by equation (2)
provides a suitable performance criterion and is recommended as the best
design procedure as compared to a least squares weight error criterion for
example.
Although the particular weights may be readily determined, the following
are a list of typical weights that may be employed for filters No. 2 and
filters No. 3, as shown in FIG. 3; and which are typical for the
interpulse periods as previously described.
Specifically, the weights are applied to the I and Q components of the
received echoes. These I and Q components are generated in the radar
receiver at the outputs of synchronous detector circuits as described in
greater detail hereinafter. The weights may thus be conveniently expressed
in terms of their I and Q components, but alternatively they may be
expressed in terms of magnitude A and phase .phi., where the magnitude A
is equal to the square root of the sum of the squares of the corresponding
I and Q components and the phase .phi. is equal to the four-quadrant arc
tangent of the ratio of the corresponding Q components to the
corresponding I components, i.e. .phi. = tan.sup.-1 (d/c) where d is a Q
component weight and c, is the corresponding I-component weight. Since the
CFAR circuits which process the filter outputs are insensitive to the
absolute amplitude and absolute phase of those outputs, the weights for
any one filter are effectively arbitrary, with respect to any non-zero
constant multiplier of each of their magnitude-components A, or to any
fixed phase added to each of their phase-components .phi.. In this
respect, the corresponding I and Q components are also arbitrary with
respect to the effects of these constant magnitude-multipliers and
additive phase constants. The column of numerals at the extreme left side
index the sequence of weights for the sequence of interpulse period
variations applicable to these specific filters. The two columns under the
heading "EXACT WEIGHTS" are the ideal or exact weights, as determined by
the synthesis procedure previously described, expressed as magnitude and
phase respectively. The Quantized Weights for the in-phase (I) and
quadraphase (Q) channels are listed in the fourth and fifth columns,
respectively. These quantized weights are the values actually used in the
filter implementation. The interpulse period variations from the average
interpulse period for the particular weights are shown in the extreme
right-hand column. The quantized weights preceded by the numerals c1
through c9 and d1 through d9 correspond to the appropriately numbered and
designated weights applied to the filter bank to be described in
connection with FIG. 2.
It is to be noted that the typical weights for the filters No. 2 and 3
include a portion titled Part 2. This portion of the Table includes
weights for a different starting point in the VIP sequence. Inasmuch as
eight different filter characteristics are employed, and as hereinafter
discussed, effective results can be obtained by utilizing only two such
filters simultaneously, each of the filters has but two different starting
points in the VIP sequence and thus only two different sets of weights are
required for each velocity filter. The filter No. 4 weights are the same
for both filters of FIG. 2. With the typical examples of weights given in
the Tables and the procedures hereindescribed, the weights for the other
filters are readily determined.
__________________________________________________________________________
FILTER #2
EXACT WEIGHTS
QUANTIZED WEIGHTS
INTERPULSE PERIOD
WEIGHT #
MAG PHASE I Q VARIATION
__________________________________________________________________________
1 .0490
37.55.degree.
(cl)
6. (dl)
12.
-6.03%
2 .0860
17.55 (c2)
-23.
(d2)
13.
11.60
3 .1438
193.33
(c3)
-25.
(d3)
-32.
32.59
4 .4053
267.17
(c4)
54. (d4)
-63.
-27.46
5 .4291
9.0 (c5)
60. (d5)
48.
-13.81
6 .3016
85.43 (c6)
-24.
(d6)
46.
2.39
7 .1870
163.29
(c7)
-34.
(d7)
-7.
21.65
8 .1649
251.58
(c8)
6. (d8)
-39.
-20.93
9 .0590
338.52
(c9)
15. (d9)
3.
Part 2
1 .0699
26.10.degree.
(C1)
3. (d1)
10.
2 .1396
112.61
(c2)
-19.
(d2)
7. -13.81%
3 .2095
192.70
(c3)
-15.
(d3)
-27.
2.39
4 .4284
272.10
(c4)
48. (d4)
-41.
21.65
5 .3969
0.0 (c5)
40. (d5)
43.
-20.93
6 .2708
79.57 (c6)
-24.
(d6)
32.
-6.03
7 .1795
152.57
(c7)
-25.
(d7)
-9.
11.60
8 .2054
240.00
(c8)
9. (d8)
-29.
32.59
9 .0810
331.82
(c9)
11. (d9)
4. -27.46
FILTER #3 EXACT WEIGHTS INTERPULSE PERIOD
WEIGHT # MAG PHASE VARIATION
__________________________________________________________________________
1 .0440 .202.65.degree.
2 .0919 340.60 -20.93%
3 .1210 107.71 -6.03
4 .1447 232.73 11.60
5 .3742 0.0 32.59
6 .3147 135.51 -27.46
7 .1701 265.97 -13.81
8 .0699 28.75 2.39
9 .0497 164.09 21.65
Part 2
1 .0805 198.53.degree.
2 .1604 331.52 -27.46%
3 .1894 103.93 -13.81
4 .2024 231.34 2.39
5 .3520 0.0 21.65
6 .2532 132.19 -20.93
7 .1261 258.85 -6.03
8 .0580 21.32 11.60
9 .0470 147.76 32.59
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As previously mentioned, the basic function of the filters which make up
the VIP doppler filter bank signal processor is to combat two distinct
forms of clutter interference; namely, rain and ground clutter. For the
purposes of filter synthesis by the methods previously discussed, these
interference sources can be adequately defined in terms of appropriate
power spectral density models.
In practice, the ground clutter spectrum is usually determined by antenna
scan modulation effects and is typically approximately gaussian in shape.
Rain clutter spectra are much more variable, being dependent primarily on
the distribution with height of wind shear and rain density, as well as on
the antenna elevation pattern and, to a lesser extent, scan modulation.
However, for synthesis purposes it is necessary to employ more simplified
models, in order that the required integrations, defined by equation (1)
herein can be performed without an excessive | | |
