MTI Radar comprising a processor selectively operable as a Weibull and a Rayleigh clutter suppressor

In an MTI radar receiver, a clutter suppressor (46, 47, 48) is switched (72), under the control of a discriminating device (71) responsive either to the shape parameter .eta. of the Weibull distribution or an average level of a clutter suppressed signal, to be selectively operable as a Weibull and a Rayleigh clutter suppressor for best possible LOG/CFAR processing with simple cell averaging circuitry. The suppressor may comprise a first processor (61) combined with an .eta. parameter calculator (48) for converting the Weibull clutter to the Rayleigh clutter, a second processor (89) for timing, and a simple suppressor (62) for the Rayleigh clutter. (FIG. 6).

BACKGROUND OF THE INVENTION 
This invention relates to an MTI (moving target indication) radar for use 
in combination with an antenna device at least in detecting a moving 
target in the presence of Weibull clutter that is known in the art and 
will later be discussed to some extent. Although not restricted, a radar 
according to this invention is suited to an air traffic control radar, 
such as an ASR (airport surveillance radar). 
As will later be described in detail with reference to one of several 
figures of the accompanying drawing, a general radar system that may be an 
ASR system comprising an antenna, comprises a transmitter for generating a 
succession of microwave pulses in order to make an antenna radiate the 
microwave pulses as a sharp directive beam into a space. The antenna is 
either mechanically or electrically controlled to make the beam repeatedly 
scan a predetermined solid angle of the space, such as the whole azimuth 
with a variable elevation angle, along a plurality of unit azimuth 
regions. The space scanned by the beam will often be called a 
predetermined space and may be a two-dimensional space with the antenna 
made to radiate the beam at a predetermined elevation angle. 
When an object is present in the scanned space, an echo returns as a return 
pulse in response to each of a certain number of the radiated microwave 
pulses either to the antenna or to another similarly controlled antenna 
for use in receiving such a return signal from each unit azimuth region. 
In order to facilitate detection of a target, namely, an object to be 
detected, a receiver output signal produced by a receiver of the radar 
system is usually used to produce a visual display in which the target is 
included. The display is used in deciding, with reference to the control 
of the antenna or antennae, the azimuth of the target or the longitude 
thereof, as called in terms of spherical polar coordinates, and the 
elevation angle of the target or the colatitude thereof. In general, the 
receiver output signal is used also for calculation or measurement of the 
range or distance of the target from the antenna or antennae with 
reference to that one of the radiated microwave pulses from which the 
return pulse is produced. It is possible to use the display in estimating 
the range. 
In practice, it is not seldom that at least one spurious object is present 
in the scanned space regardless of presence and absence of the target. 
Besides a target return or echo, namely, the return pulse from the target, 
such spurious objects produce spurious returns, which result in clutter in 
the visual display. Although the spurious objects are often referred to as 
clutter, the word "clutter" will be used in the instant specification 
primarily to mean the spurious returns irrespective of utilization or not 
of a visual display. As the case may be, signals produced in the receiver 
from the target return and the clutter will be called a target return and 
clutter, respectively. 
Examples of the clutter for an MTI radar are land or ground clutter 
resulting from buildings and undulating terrains, sea clutter arising from 
sea surface, weather clutter originating with rainfall and rain clouds, 
and angel echoes attributed to other foreign matters, such as large flocks 
of migratory birds and/or atmospheric discontinuity or hererogeneity. The 
difference between the target return and the clutter depends on the field 
of use of the radar. For instance, the weather clutter becomes the target 
returns for a weather or meteorological radar. The following description 
will therefore be limited to MTI radars. 
For an MTI radar, it is desirable that the receiver may respond to a moving 
target with an excellent S/C (signal or target return to clutter) ratio. 
In other words, the clutter should be suppressed in the receiver output 
signal to a level of the order of the noise inherent to the receiver. A 
known MTI (here, a moving target indicator) or MTI canceller is well 
adapted to discrimination of the moving target from the land clutter but 
is ineffective in rejecting the clutter caused by spurious objects having 
velocity components as, for example, the sea clutter, the weather clutter, 
and the angel echoes. Various proposals have therefore been made to raise 
the S/C ratio as will presently be described. 
By the way, the return signal has an amplitude that varies with time due to 
target returns and clutter. Furthermore, the clutter is also variable with 
time. It was formerly believed that the amplitude variation resulting from 
the clutter follows Rayleigh distribution, which will shortly be 
described. Later, most of the clutter was found to follow Weibull 
distribution. 
By the use of a variate x representative of the clutter amplitude, which is 
either zero or positive, the Weibull distribution is expressed by a 
probability density function (P.sub.W (x) as: 
EQU P.sub.W (x)=(.eta./.sigma.).multidot.(x/.sigma.).sup..eta.-1 
.multidot.exp[-(x/.sigma.).sup..eta. ], (1) 
wherein .sigma. and .eta. (sometimes denoted by .gamma.) represent a first 
or scale and a second or shape parameter, respectively. These parameters 
have values dependent of the clutter amplitude variation. The Rayleigh 
distribution is given by another probability density function P.sub.R (x) 
as: 
EQU P.sub.R (x)=(2x/.sigma..sup.2).multidot.exp[-(x/.sigma.).sup.2 ], (2) 
by the use of the first parameter of the Weibull distribution probability 
density function (P.sub.W (x) alone. The Rayleigh distribution is 
therefore the Weibull distribution of a special case where the second 
parameter behaves as an invariant having a specific value equal to two. 
The clutter having an amplitude that follows the Weibull distribution is 
named Weibull clutter. The clutter having an amplitude that is given by 
the Rayleigh distribution is called Rayleigh clutter. General guidelines 
about the Weibull clutter were discussed in detail by D. Curtis Schleher 
in his article contributed to IEEE Transactions on Aerospace and 
Electronic Systems, Vol. AES-12, No. 6 (November 1976), pages 736-743, and 
titled "Radar Detection in Weibull Clutter." 
Amongst the proposals for raising the S/C ratio, CFAR (constant false alarm 
rate) techniques are most promissing. The CFAR techniques are for 
attaining a constant false alarm rate or probability even in the presence 
of the clutter. Stated otherwise, the CFAR techniques are to render that 
false alarm rate constant which represents the probability that the 
clutter is erroneoulsly detected as a target return. 
CFAR processors or detectors for the Rayleigh clutter were reviewed in 
detail by Vilhelm Gregers Hansen and Harold R. Ward in an article they 
contributed to IEEE Transactions on Aerospace and Electronic Systems, Vol. 
AES-8, No. 5 (September 1972), pages 648-652, under the title of 
"Detection Performance of the Cell Averaging LOG/CFAR Receiver." The term 
"LOG/CFAR receiver" stands for a logarithmic amplification and CFAR 
processing receiver. A sophisticated cell averaging LOG/CFAR processor for 
the Rayleigh clutter of the type reviewed in the Hansen et al article is 
used in each of MTI radars according to the present invention and will 
therefore be described later in conjunction with another of the 
accompanying drawing figures. 
A CFAR processor for the Weibull clutter was proposed by Gene B. Goldstein 
in his article that appeared in IEEE Transactions on Aerospace and 
Electronic Systems, Vol. AES-9, No. 1 (January 1973), pages 84-92, and was 
titled "False-Alarm Regulation in Log-Normal and Weibull Clutter." Insofar 
as the Weibull clutter is concerned, the Goldstein processor is operable 
only in a specific case for which the parameters for the Weibull 
distribution are invariants of particular values. 
Hansen solely proposed another CFAR processor for the Weibull clutter in 
general in his report that was made public at International Conference on 
Radar-Present and Future, 23-25 October 1973. The report of Hansen is 
paged 1-8 and titled "Constant False Alarm Rate Processing in Search 
Radars." A processor according to the Hansen report is used in an MTI 
radar according to an aspect of the instant invention. The processor will 
therefore be described later with reference to still another of the 
accompanying drawing figures. Briefly speaking, the Hansen processor 
carries out suppression of the clutter by converting a variate 
representative of the clutter amplitude given by the Weibull distribution 
to a new variate z indicative of the clutter amplitude that follows a 
simple exponential distribution probability density function P.sub.E (z) 
given by: 
EQU P.sub.E (z)=exp(-z). (3) 
At any rate, an excellent S/C ratio is achieved by a CFAR processor of the 
type reported by Hansen. Inasmuch as the Rayleigh clutter is the Weibull 
clutter of a special case, the processor involves no problem in theory in 
treating the Rayleigh clutter as the Weibull clutter. The processor is, 
however, disadvantageous in practice when the clutter merely follows the 
Rayleigh distribution. This is because the processor must carry out more 
processes than a sophisticated cell averaging LOG/CFAR processor for the 
Rayleigh clutter alone. As a result, not only complicated hardware is 
indispensable but also an increase in error is inevitable to make a 
clutter residue appear in the receiver output signal when the clutter 
amplitude is given by the mere Rayleigh distribution. 
SUMMARY OF THE INVENTION 
It is therefore a general object of the present invention to provide an MTI 
radar comprising a receiver in which a signal processor is capable of 
sufficiently suppressing the Weibull clutter in general. 
It is a specific object of this invention to provide an MTI radar of the 
type described, in which the signal processor is capable of excellently 
suppressing the Rayleigh clutter as well as the Weibull clutter, both to a 
best possible degree. 
It is another specific object of this invention to provide an MTI radar of 
the type described, wherein the signal processor is operable for the 
Rayleigh clutter as a suppressor that is simple in structure and works 
with less steps and errors as compared with a conventional suppressor for 
the Weibull clutter in general. 
A moving target indication radar to which this invention is applicable is 
for use at least in detecting a moving target that is present in a 
predetermined space together with spurious objects. The radar comprises a 
transmitter and a receiver for use in combination with an antenna device. 
The transmitter is for generating a sequence of microwave pulses of a 
predetermined pulse width and a predetermined repetition frequency. The 
antenna device is for making a beam of the microwave pulses scan the 
predetermined space along a plurality of unit azimuth regions and for 
receiving a return signal from each unit azimuth region. The return signal 
is capable of comprising a target return and clutter produced by the 
target and the spurious objects in response to one of the microwave pulses 
of the beam, respectively. The clutter has a clutter amplitude that 
follows one of Weibull and Rayleigh distributions at a time. The Weibull 
distribution is given by a probability density function of the clutter 
amplitude by the use of a first and a second parameter having values 
variable with time. The Rayleigh distribution is given by another 
probability density function of the clutter amplitude by the use of the 
first parameter alone with the second parameter given an invariant value 
equal to two. The receiver comprises means responsive to the return signal 
for producing a detected signal and a signal processor for processing the 
detected signal into a processed signal for use at least in detecting the 
target. The detected signal has an envelope, an envelope amplitude of 
which is variable with time in response to a target return component and a 
clutter component introduced into the envelope amplitude from the target 
return and the clutter, respectively. 
According to this invention, the signal processor specified in the next 
preceding paragraph comprises parameter calculating means, first and 
second suppressing means, discriminating means, selecting means, a 
connection, and final processing means. The parameter calculating means is 
responsive to the detected signal for calculating the value of the second 
parameter to produce a parameter signal representative of the calculated 
second parameter value. Operatively coupled to the parameter calculating 
means, the first suppressing means is responsive to the detected signal 
for suppressing that first-kind component of the clutter component by the 
use of the parameter signal, which is introduced into the envelope 
amplitude from the clutter having a clutter amplitude following the 
Weibull distribution, to produce a first clutter suppressed signal having 
an amplitude that is kept below a first predetermined level unless at 
least one of the target return component and that second-kind component of 
the clutter component, which is introduced into the envelope amplitude 
from the clutter having a clutter amplitude following the Rayleigh 
distribution, is present in the envelope amplitude. Operatively coupled to 
the first suppressing means, the second suppressing means is responsive to 
the detected signal for suppressing the second-kind component to produce a 
second clutter suppressed signal having an amplitude that is kept below a 
second predetermined level unless at least one of the target return 
component and the first-kind component is present in the envelope 
amplitude. The discriminating means is responsive to a variable input 
signal variable in compliance with that one of the Weibull and the 
Rayleigh distributions, which the clutter amplitude follows at each 
instant, for discriminating the above-mentioned one distribution from the 
other to produce a discrimination signal at a particular instant a 
predetermined interval of time after the afore-said each instant. The 
discrimination signal is indicative of the Weibull and the Rayleigh 
distributions when the Weibull and the Rayleigh distributions are 
discriminated to be followed by the clutter amplitude, respectively. 
Coupled to the first and the second suppressing means, the selecting means 
is responsive to the discrimination signal for selecting the first and the 
second clutter suppressed signals when the discrimination signal indicates 
the Weibull and the Rayleigh distributions, respectively. The selecting 
means thereby produces a selected signal having an amplitude that is kept 
below a first preselected level when the first clutter suppressed signal 
is selected and furthermore unless at least one of the target return 
component and the second-kind component is present in the envelope 
amplitude and below a second preselected level when the second clutter 
suppressed signal is selected and furthermore unless at least one of the 
target return component and the first-kind component is present in the 
envelope amplitude. The connection is comprised between the discriminating 
means and a predetermined one of the parameter calculating means and the 
selecting means for supplying the discriminating means with one of the 
parameter signal and the selected signal as the variable input signal that 
is produced by the predetermined one of the parameter calculating means 
and the selecting means. The final processing means is responsive to the 
discrimination signal for processing the selected signal into the 
processed signal. 
The predetermined space may be variable when the radar accompanied by the 
antenna device is used to track a specific moving target. The expression 
"microwave pulses" is used to mean pulses of any frequency in a range in 
which an MTI radar is operable. Preferably, the microwave pulses are 
radiated from the antenna device cyclically into the respective unit 
azimuth regions. The antenna device may comprise either only one antenna 
for both transmission and reception or antennae separately for 
transmission and reception. The processed signal becomes a receiver output 
signal that has an amplitude variable in response to the target return 
substantially alone with the clutter rejected. 
The selecting means may either be connected as a whole to outputs of the 
first and the second suppressing means or partly placed in the first and 
the second suppressing means with the remaining part connected to the 
outputs of the suppressing means. According to an aspect of this 
invention, the first suppressing means comprises a novel processor by 
which the variate representative of the clutter amplitude given by the 
Weibull distribution is once converted according to a novel algorithm to a 
novel variate representative of a clutter amplitude that follows the 
Rayleigh distribution rather than the simple exponential distribution 
mentioned hereinabove.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring to FIG. 1, an MTI radar according to a first embodiment of the 
present invention will be described as applied to an ASR. The radar 
comprises a transmitter-receiver 11, a CFAR or signal processor 12, and a 
timing signal generator 13 and is accompanied by an antenna 15. The 
transmitter-receiver 11, the timing signal generator 13, and the antenna 
15 are of the known structure. The timing signal generator 13 is for 
supplying first and second timing signal generator output terminals 16 and 
17 with a first timing signal of a lower rate or repetition frequency of, 
for example, 1 kHz and a second timing signal of a higher rate, such as 
1.3 MHz, respectively. The signal processor 12 is partly novel and partly 
similar in structure to a conventional CFAR processor disclosed in the 
above-referenced Hansen report and to a sophisticated cell averaging 
LOG/CFAR processor of the type discussed in the above-cited Hansen et al 
article. Alternatively, the CFAR processor according to the Hansen report 
may be changed to a novel processor designed to operate in compliance with 
a novel algorithm. 
The transmitter-receiver 11 comprises a transmitter, a receiver, and 
circuit elements shared by the transmitter and the receiver. Among the 
common circuit elements, a frequency stabilized oscillator 21 is for 
generating an oscillating signal at a signal frequency f.sub.s in the 
microwave band. A coherent oscillator 22 is for generating a phase 
reference signal of a reference frequency f.sub.c in an intermediate 
frequency band. The transmitter comprises a transmitter mixer 26 for 
mixing the oscillating and the phase reference signals to produce a mixed 
signal of a microwave frequency f.sub.2 +f.sub.c. Responsive to the first 
timing signal, a trigger pulse generator 27 produces a train of trigger 
pulses of a predetermined pulse width at the lower rate. Pulse modulated 
by the trigger pulse train, a high-power amplifier 28, such as a klystron 
amplifier, amplifies the mixed signal to feed the antenna 15 with a 
sequence of microwave pulses of the microwave frequency f.sub.s +f.sub.c 
and of the predetermined pulse width through a duplexer 30 that is shared 
in common by the transmitter and the receiver. The pulse width is 
determined in cosideration of the higher rate. For the rate of 1.3 MHz, 
the pulse width is preferably about 0.8 microsecond. 
The antenna 15 radiates the microwave pulses in a sharp directive beam and 
is controlled as symbolized by an arcuate line with an arrowhead to make 
the beam scan the whole azimuth at a predetermined elevation angle. Return 
pulses from a moving target and spurious objects in the scanned space are 
received by the antenna 15. As a result of the Doppler effect, the 
frequency of the target return includes a Doppler shift f.sub.d, which may 
be plus, minus, or zero. 
As will later be described, a return signal that is received by the antenna 
15 and may or may not include the target return in addition to the 
clutter, is sampled in the receiver at the higher rate into analog radar 
data samples. It is usual for the ASR that the beam is rotated at a period 
of rotation of four seconds. The scanned space is therefore divided into 
four thousand unit azimuth regions, into which the respective microwave 
pulses are cyclically sent. Inasmuch as an interval of one millisecond of 
the successive microwave pulses is sampled at the higher rate of 1.3 MHz, 
each unit azimuth region is divided into about 769 unit range regions from 
which the respective samples are obtained. Each unit range region is equal 
to the width of radiated microwave pulses in air or about one sixteenth 
nautical mile. The total 769 unit range regions is about 48 nautical miles 
long. In practice, some successive ones of the samples, such as those 
obtained from the farthest unit range regions, are not used so that an 
interval of time may be interposed between those two successions of the 
samples which are obtained from two adjacent unit azimuth regions. At any 
rate, the antenna 15 produces a return signal from each unit azimuth 
region, which signal may comprise a target return and clutter. 
The receiver comprises a receiver mixer 31 supplied with the oscillating 
signal for converting the return signal to an intermediate frequency 
signal. The target return contained in the intermediate frequency signal 
has an intermediate frequency f.sub.c +f.sub.d variable with the Doppler 
shift f.sub.d. After amplified by an intermediate frequency amplifier 32, 
the intermediate frequency signal is amplitude detected by an amplitude 
detector 33. The detected signal has an envelope having an envelope 
amplitude X variable with time in response to a target return component 
and a clutter component introduced into the envelope amplitude from the 
target return and the clutter included in the return signal, respectively. 
Let the clutter component have an amplitude that is designated again by x 
merely for simplicity of denotation. The clutter component amplitude x is 
given by either of Equations (1) and (2). 
In the receiver, first and second phase detectors 36 and 37 are supplied 
with the phase reference signal directly and through a 90.degree. phase 
shifter 38, respectively, and carry out phase detection of the amplified 
intermediate frequency signal. The phase detectors 36 and 37 produce a 
pair of phase detected signals representative of information concerning 
the Doppler shift f.sub.d. 
The signal processor 12 is for processing the amplitude detected signal 
into at least one processed signal for use at least in detecting the 
target. The signal processor 12 comprises a logarithmic converter or 
amplifier 41 for subjecting the envelope amplitude X to logarithmic 
conversion to produce a logarithmic converter output signal. The clutter 
component amplitude x is converted to a logarithmic clutter component 
amplitude w according to: 
EQU w=log x, 
where (log x) represents preferably the natural logarithm of the clutter 
component amplitude x. Responsive to the second timing signal, a single 
analog-to-digital converter 42 samples the logarithmic converter output 
signal into a sequence of analog data samples having discrete analog 
amplitudes and produces a sequence of digital or digitized signals 
indicative of logarithms of digitized discrete amplitudes of the detected 
signal envelope. Each digital signal may be of ten bits. In general, the 
digital signals comprise a logarithmic target return component and 
logarithmic clutter components. The logarithms indicated by the 
logarithmic clutter components will be denoted by w(n), where n represents 
numbers given to the respective unit range regions in each unit azimuth 
region. The logarithmic clutter components will be designated also by w(n) 
merely for convenience of denotation. 
The signal processor 12 further comprises first and second 
analog-to-digital converters 43 and 44 for converting the phase detected 
signals to digitial signal pairs. Supplied with the digital signal pairs, 
a known MTI canceller 45 produces an MTI canceller output signal in which 
the clutter resulting from standstill objects are cancelled. The MTI 
canceller output signal serves as a processor output signal for use in 
dealing with the Doppler shift f.sub.d as, for example, for use in 
discriminating between the moving targets. 
The digital signal sequence is supplied to first or Weibull clutter and 
second or Rayleigh clutter suppressors 46 and 47 and also to a parameter 
calculator 48. The signal processor 12 still further comprises an 
antilogarithmic converter or amplifier 49 and a gate circuit 50. In the 
manner to be described in the following, the first and the second 
suppressors 46 and 47 produce a first and a second clutter suppressed 
signal, respectively. The antilogarithmic converter 49 is for producing an 
antilogarithmic converter output signal by subjecting either of the first 
and the second clutter suppressed signals that is supplied thereto at a 
time, to antilogarithmic conversion that is conjugate with the logarithmic 
conversion. The gate circuit 50 is for producing a processed signal by 
rejecting those portions of the antilogarithmic converter output signal 
which result from the clutter component. 
A combination of the second suppressor 47, the logarithmic and the 
antilogarithmic converters 41 and 49, and the gate circuit 50 may be a 
sophisticated cell averaging LOG/CFAR processor of the type discussed in 
the above-referenced Hansen et al article and suppresses the Rayleigh 
clutter. Another combination of the first suppressor 46, the parameter 
calculator 48, the converters 41 and 49, and the gate circuit 50 may be a 
CFAR processor revealed in the above-cited Hansen report. Alternatively, 
the first suppressor 46 may work in accordance with a novel algorithm to 
once convert the Weibull clutter to the Rayleigh clutter in cooperation 
with the parameter calculator 48. 
Turning to FIG. 2 for a short while, the first suppressor 46 comprises, as 
disclosed in the Hansen report, a first shift register 51 that has (-H)-th 
through minus first stages 51(-H) to 51(-1), a center or zeroth stage 
51(0), and first through H-th stages 51(1) to 51(H) and is supplied with 
the second timing signal as the shift pulses. Each stage, as called 
herein, is for a digital signal of the digital signal sequence. If no 
logarithmic target return component is present in successive digital 
signals, (2H+1) in number, the shift register 51 is loaded with 
logarithmic clutter components w(h-H), . . . , (w(h-1), w(h), w(h+1), . . 
. , and w(h+H) at a particular instant at which a particular or h-th 
logarithmic clutter component w(h) is stored in the center stage 51(0). It 
is possible to select the number H between twelve and sixteen. A first 
average calculator 52 is connected to the shift register stages except the 
center stage 51(0) so as to produce a first average signal E.sub.1 (h) 
representative of a first average E.sub.1 (h) given by: 
##EQU1## 
if no logarithmic target return component is included in the digital 
signals supplied to the first average calculator 52. The first average is 
for use as that mean value E(w) of the logarithmic clutter component 
amplitudes w which is mathematically calculated for the Weibull 
distribution to be equal to: 
EQU E(w)=log .sigma.-.gamma./.eta., (4) 
where .gamma. represents the Euler's or Euler-Mascheroni constant. 
The reason why a particular or h-th digital signal stored in the center 
stage 51(0) is excluded from calculation of the first average is already 
known. Briefly speaking, it is not preliminarily known which one of the 
digital signals of each sequence would be the logarithmic target return 
component. The particular digital signal is substantially real-time CFAR 
processed as will become clear as the description proceeds. The CFAR 
processing is of particular importance when the particular digital signal 
is the logarithmic target return component on which a logarithmic clutter 
component may or may not be superposed. In this event, the first average 
is calculated only as regards the logarithmic clutter components. This is 
advantageous in raising the S/C ratio. The reason applies to similar 
average calculation to be described in the following. 
The parameter calculator 48 shown in FIG. 2 comprises a square calculator 
53 responsive to the digital signal sequence for producing a sequence of 
squared signals representative of squares of the respective logarithms 
indicated by the successive digital signals. In the absence of the 
logarithmic target return component, both the squared signals and the 
squares represented thereby may be designated by w.sup.2 (n). A second 
shift register 54 has (-H)-th through minus first, zeroth or center, and 
first through H-th stages 54(-H), . . . , 54(-1), 54(0), 54(1), . . . , 
and 54(h). When the h-th logarithmic clutter component w(h) is stored in 
the first shift register center stage 51(0), the square of this h-th 
logarithmic clutter component w.sup.2 (h) is stored in the second shift 
register center stage 54(0). As was the case with the first average 
calculator 52, a second average calculator 55 produces a second average 
signal E.sub.2 (h) representative of a second average E.sub.2 (h) given 
by: 
##EQU2## 
provided that no logarithmic target return component in contained in the 
squared signals supplied to the second average calculator 55. The second 
average is for use as that square mean value E(w.sup.2) of the logarithmic 
clutter component amplitudes w which is known in mathematics as: 
EQU E(w.sup.2)=.pi..sup.2 /(6.eta..sup.2)+(log .sigma.-.gamma./.eta.).sup.2. 
On the other hand, the variance V(w) of the logarithmic clutter component 
amplitudes w is given according to mathematics by: 
EQU V(w)=E(w.sup.2)-[E(w)].sup.2 =.pi..sup.2 /(6.eta..sup.2), 
which is no more dependent on the first parameter .sigma. but only on the 
second parameter .eta.. It is now possible to know the value of the second 
parameter .eta. by the use of the first and the second averages E.sub.1 
(h) and E.sub.2 (h). The parameter calculator 48 therefore comprises a 
parameter meter 56 responsive to the first and the second average signals 
E.sub.1 (h) and E.sub.2 (h) for calculating an instantaneous value 
.eta.(h) of the second parameter .eta. at the particular instant. The 
parameter meter 56 produces a parameter signal, denoted also by .eta.(h), 
representative of the second parameter value calculated in compliance 
with: 
##EQU3## 
In FIG. 2, the first suppressor 46 comprises a parameter logarithm meter 57 
responsive to the first average signal E.sub.1 (h) and the parameter 
signal .eta.(h) for calculating a logarithm log.sigma.(h) of an 
instantaneous value that the first parameter .sigma. has at the particular 
instant. The parameter logarithm meter 57 produces a parameter logarithm 
signal, designated by log.sigma.(h), representative of the first parameter 
logarithm calculated according to: 
EQU log .sigma.(h)=E.sub.1 (h)+.gamma./.eta.. (6) 
Speaking now in general, let the detected signal amplitude X be converted 
to a new variate Z according to a specific function by which the clutter 
component amplitude x, dependent on the first and the second parameters, 
is converted to a new clutter variate z dependent on neither of the two 
parameters. The new clutter variate z be given by: 
EQU z=F(x, .sigma., .eta.), 
where F(x, .sigma., .eta.) represents the specific function. On the other 
hand, let a cumulative density function of the Weibull probability density 
function P.sub.w (x) be denoted by Q.sub.W (x). The cumulative density 
function Q.sub.W (x) is given by: 
##EQU4## 
according to mathematics. It is now understood that the new clutter 
variate z follows the simple exponential distribution defined by Equation 
(3) if the cumulative density function Q.sub.W (x) be used as: 
EQU z-=log [1-Q.sub.W (x)]=(x/.sigma.).sup..eta., 
in the specific function. A logarithmic clutter variate (log z) is given 
by: 
EQU log z=.eta.(log x-log .sigma.), 
which equation means that CFAR processing is feasible when those values of 
the new variate Z are taken out as the target returns which are greater 
than a threshold level prescribed relative to the variance of the new 
clutter variate z that is no more dependent on the parameters .sigma. and 
.eta. but only on the circuit constants of the circuits concerned. 
Reverting to FIG. 2, the first suppressor 46 comprises a subtractor 58 
responsive to the particular digital signal stored in the first shift 
register center stage 51(0) at the particular instant and to the parameter 
logarithm signal log .sigma.(h) for producing a difference signal 
representative of a difference resulting from subtraction of the 
instantaneous first parameter logarithm log .sigma.(h) from the logarithm 
indicated by the particular digital signal. If no logarithmic target 
return component is present in the particular digital signal, the 
logarithm is represented by w(h) or [log x(h)]. The difference is given by 
[log x(h)-log .sigma.(h)]. Responsive to the parameter signal .eta.(h) and 
the difference signal, a product calculator 59 produces the first clutter 
suppressed signal that includes at the particular instant a multiplied 
signal representative of a result of multiplication of the calculated 
second parameter value .eta.(h) and the difference. Such results of 
multiplication are representative of logarithmic clutter variate [log 
z(h)]given by: 
EQU log z(h)=.eta.(h).multidot.[log x(h)-log .sigma.(h)], 
in the absence of the logarithmic target return component. The first 
clutter suppressed signal has discrete amplitudes that are equal to the 
logarithms of the successive values of the new variate Z and are kept 
below a first predetermined level dependent only on the circuit constants 
unless at least one of the target return component and the clutter 
component resulting from the Rayleigh clutter is present in the detected 
signal. 
Before describing the remaining parts of the signal processor 12, the novel 
algorithm mentioned hereinabove will be described. Once converted to the 
Rayleigh clutter according to the novel algorithm, the Weibull clutter is 
CFAR processed by a sophisticated cell averaging LOG/CFAR processor. 
Let the variate x that follows the Weibull probability density function 
P.sub.W (x) be converted to a novel variate y in accordance with: 
EQU y=.sigma..multidot.(x/.sigma.).sup..eta./2. (7) 
A novel probability density function, designated by P.sub.N (y), of the 
novel variate y is given by: 
EQU P.sub.N (y)=P.sub.W (x)dy/dx. (8) 
By the use of Equations (1) and (7), Equation (8) is rearranged into: 
EQU P.sub.N 
(y)=(2/.sigma.).multidot.(y/.sigma.).multidot.exp[-(y/.sigma.).sup.2 ]. 
(9) 
Equation (9) is identical with Equation (2). When given by logarithmic 
expression, Equation (7) turns into: 
EQU log y=log .sigma.+(.eta./2).multidot.(log x-log .sigma.), (10) 
in which the values of the second parameter .eta. and the first parameter 
logarithm log .sigma. are already known from Equations (5) and (6). 
Turning now to FIG. 3, a first suppressor 46 that may be substituted for 
the first suppressor 46 illustrated with reference to FIG. 2, comprises a 
novel processor 61 for carrying out the novel algorithm and a simple 
suppressor 62 for the Rayleigh clutter. A combination of the novel 
processor 61 and the parameter calculator 48 comprises similar parts 
designated by like reference numerals as in FIG. 2 and is operable with 
corresponding signals denoted by like reference symbols. The product 
calculator 59, however, delivers the signal representative of the result 
of multiplication to a divider 64 that may be combined with the product 
calculator 59 into a combined multiplier. The output signal of the 
multiplier may be named a product signal that now represents a product of 
the second parameter value .eta.(h), 1/2, and the difference, which 
difference is equal to the second term in the right side of Equation (10) 
provided that the logarithmic target return component is absent in the 
digital signals supplied to the first average calculator 52. 
Representative to the product signal and the parameter logarithm signal 
log .sigma.(h), an adder 65 produces a digital sum signal indicative of a 
sum of the first parameter logarithm and the product, which sum is equal 
to [log y(h)] given according to Equation (10) in the absence of the 
last-mentioned logarithmic target return component. 
The novel processor 61 thus produces a sequence of the digital sum signals, 
which sequence may be designated by log Y. The digital sum signal sequence 
has discrete amplitudes equal to the sums indicated by the successive 
digital sum signals and is herein called a transform signal in which the 
logarithmic target return component appears as a target return transform 
with a predetermined delay related to the number of first shift register 
stages preceding the zeroth stage 51(0). The logarithmic clutter 
components are transformed into clutter transforms that may be denoted by 
[log y(m)], where m represents numbers equivalent to the numbers n, and 
that are what would be introduced into the transform signal through the 
envelope amplitude from imaginational Rayleigh clutter if the 
imaginational clutter were substituted for the Weibull clutter. 
In FIG. 3, the simple suppressor 62 is a sophisticated cell average 
subtraction circuit. More particularly, the suppressor 62 comprises a 
third shift register 66 having (-K)-th through minus first, zeroth or 
center, and first through K-th stages 66(-K), . . . , 66(-1), 66(0), 
66(1), . . . , and 66(K) for storing the digital sum signals, (2K+1) in 
number at a time. The number K may be an integer between twelve and 
sixteen. At a specific instant a preselected interval of time after the 
particular instant, the zeroth stage 66(0) is loaded with a specific 
digital sum signal that may be denoted by [log Y(k)] if no target return 
transform is included therein. As was the case with the first average 
calculator 52, a third average calculator 67 produces a third average 
signal E.sub.3 (k) representative of a third average E.sub.3 (k), which is 
given by: 
##EQU5## 
if no target return transform is included in the digital sum signals 
supplied to the third average calculator 67. Responsive to the specific 
digital sum signal and the third average signal E.sub.3 (k), a second 
subtractor 68 produces a second difference signal representative of a 
second difference obtained by subtracting the third average E.sub.3 (k) 
from the sum indicated by the specific digital sum signal. In the absence 
of the target return transform in the digital sum signal stored in the 
third shift register 66, the second difference is given by [log 
y(k)-E.sub.3 (k)]. When subjected to the antilogarithmic conversion at the 
antilogarithmic converter 49, such a second difference signal gives the 
new clutter variate z according to: 
EQU z=y(k)/exp[E.sub.3 (k)], 
which is independent of the two parameters .sigma. and .eta. originally had 
by the Weibull clutter and dependent only on the circuit constants of the 
related circuits. It is therefore possible by the use of the gate circuit 
50 to reject the Weibull clutter. 
The simple suppressor 62 thus produces a sequence of the second difference 
signals. The second difference signal sequence serves as the first clutter 
suppressed signal, which has discrete amplitudes equal to the successive 
second differences. 
The second suppressor 47 depicted in FIG. 1 is similar in structure to the 
simple suppressor 62. It is only necessary that the logarithmic target 
return component should appear in the second clutter suppressed signal 
simultaneously with the appearance thereof as either one of the multiplied 
signals (FIG. 2) or one of the second difference signals (FIG. 3) in the 
first clutter suppressed signal. With the Rayleigh clutter suppressed, the 
second clutter suppressed signal has an amplitude that is kept below a 
second predetermined level dependent on the circuit constants of the 
related circuits unless at least one of the target return component and 
the clutter component is present in the envelope amplitude. The second 
clutter suppressed signal has discrete amplitudes of the multiplied 
signals or of the second difference signals. 
It may be repeated here that the second clutter suppressed signal is given 
a somewhat higher level when the digital signals stored in the shift 
register of the second suppressor 47, include logarithmic clutter 
components derived from the Weibull clutter. When only the Rayleigh 
clutter is present, the first clutter suppressed signal is rendered a 
little higher than the second clutter suppressed signal because of the 
reason pointed out before. The signal processor 12 therefore comprises a 
discriminator 71A supplied with a reference signal indicative of two as 
the second parameter value for discriminating whether or not the 
instantaneous value .eta.(h) of the second parameter is in a predetermined 
range including a value equal to two. The discriminator 71A may be a 
read-only memory or a comparator and produces a discrimination signal 
indicative of the Weibull and the Rayleigh distributions when the 
instantaneous value is in the predetermined range and outside thereof, 
respectively. Responsive to the discrimination signal, a selector 72 
connected to the first and the second suppressors 46 and 47, selects the 
first and the second clutter suppressed signals as a selector output 
signal when the discrimination signal indicates the Weibull and the 
Rayleigh distributions, respectively. 
When the first processor 46 comprises the novel processor 61 and the simple 
suppressor 62, the target return transform and the clutter transforms 
appear as the second difference signals in the first clutter suppressed 
signal with a preselected delay related to the third shift register stages 
prior to the zeroth stage 66(0) as compared with production of the 
parameter signal .eta.(h) and hence the discrimination signal. It is 
therefore preferred that the selector 72 be operable with the preselected 
delay. 
In FIG. 1, the selector output signal is supplied to the antilogarithmic 
converter 49 as the above-mentioned "either" of the first and the second 
clutter suppressed signals. For convenience of an understanding of the 
present invention as a whole, the antilogarithmic converter 49 may be 
considered as an intermediate processor for processing the selector output 
signal into a selected signal and is a part of a selecting device that 
comprises the selector 72 as the remaining part. The selecting device is 
coupled to the first and the second suppressors 46 and 47 and is for 
selecting the first and the second clutter suppressed signals to produce 
the selected signal when the discrimination signal indicates the Weibull 
and the Rayleigh distributions, respectively. The selected signal has 
discrete amplitudes related to the discrete amplitudes of the selected one 
of the first and the second clutter suppressed signals. The discrete 
amplitudes of the selected signal are kept below a first preselected level 
related to the first predetermined level when the first clutter suppressed 
signal is selected and furthermore unless at least one of the target 
return component and the clutter component derived from the Rayleigh 
clutter is present in the envelope amplitude and below a second 
preselected level related to the second predetermined level when the 
second clutter suppressed signal is selected and furthermore unless at 
least one of the target return component and the clutter component 
resulting from the Weibull clutter is present in the envelope amplitude. 
In the meanwhile, the discrimination signal is supplied to a threshold 
setting circuit 73 for producing a variable threshold signal having a 
level variable to either of a first and a second threshold level when the 
discrimination signal indicates the Weibull and the Rayleigh 
distributions, respectively. The first and the second threshold levels are 
related to antilogarithms of the first and the second predetermined 
levels, respectively, and may be equal thereto. The gate circuit 50 serves 
as a final processor in combination with the threshold setting circuit 73. 
Responsive to the threshold signal, the gate circuit 50 produces the 
processed signal by making those portions of the selected signal, namely, 
the antilogarithmic converter output signal, pass therethrough which have 
discrete amplitudes higher than the first and the second threshold levels 
when the selected signal is produced from the first and the second clutter 
suppressed signals, respectively. The gate circuit 50 may be a comparator. 
Referring now to FIG. 4, an MTI radar according to a second embodiment of 
this invention is accomparied by an antenna 15 and comprises similar parts 
designated by the like reference numerals is in FIG. 1 except that a level 
monitor 71B to be presently described in detail is substituted for the 
discriminator 71A for production of the discrimination signal at a 
particular instant. Generally speaking, the level monitor 71B serves as a 
discriminating device and is supplied with a variable input signal 
variable in compliance with that one of the Weibull and the Rayleigh 
distributions which the clutter amplitude follows at each instant a 
predetermined interval of time before the particular instant. In contrast 
to the circuitry illustrated with reference to FIG. 1 wherein the 
discriminator 71A is supplied with the parameter signal as the variable 
input signal through a connection 75A, the level monitor 71B is supplied 
with the detected signal as the variable input signal through another 
connection 75B. 
Turning to FIG. 5, the level monitor 71B may comprise a first comparator 81 
supplied with the selected signal that has discrete amplitudes as pointed 
out heretobefore. The first comparator 81 compares the discrete amplitudes 
with a prescribed level indicated at 82 and selected in consideration of 
the receiver noise to produce a sequence of discrete output signals, each 
of which is given a predetermined one of binary levels, such as a logic 
"1" level, each time when the discrete amplitude is higher than the 
prescribed level. A resettable counter 83 is for counting those of the 
discrete output signals, each of which has the predetermined binary level, 
to produce a count signal representative of the number of those discrete 
output signals of the predetermined binary level which are supplied 
thereto during a prescribed interval of time. A second comparator 84 is 
for comparing the count represented by the count signal with a prescribed 
count indicated at 85 to produce a comparator output signal that is given 
a preselected one of binary values and the other, such as a logic "1" and 
a logic "0" value, when the count is greater and not greater than the 
prescribed count, respectively. By the binary values, the comparator 
output signal indicates whether an average level of the selected signal is 
increasing or not. The prescribed interval and the prescribed count are 
selected so that the rise of the average level which result from the 
target return component may not be discriminated as impertinent clutter 
suppression. 
Further referring to FIG. 5, an Exclusive OR circuit 86 has a first and a 
second input terminal for receiving the comparator output signal and a 
reference input signal having either of the binary values at a time, 
respectively. The Exclusive OR circuit 86 produces an Exclusive OR'ed 
signal given an output binary value that is the same as the Exclusive OR 
of the comparator output signal binary value and the reference input 
signal binary value. A register 87 is for registering the output binary 
value to produce a register output signal given a registered binary value 
that is the same as the output binary value registered therein. The 
register output signal is delivered to the second input terminal of the 
Exclusive OR circuit 86 as the reference input signal through a connection 
88. The registered binary value is therefore inverted and kept unchanged 
when the comparator output signal has the predetermined binary value and 
has not, respectively. The register output signal thus provides the 
discrimination signal. One of the Weibull and the Rayleigh distributions 
that is indicated by the discrimination signal is changed to the other 
only when the binary value represented by the discrimination signal are 
switched from one to the other, namely, either from the logic "1" value to 
the logic "0" value or from the logic "0" value to the logic "1" value. 
Otherwise, the indication is kept as it is. 
With the level monitor 71B, the selector 72 selects one of the first and 
the second clutter suppressed signals at least with a delay equal to the 
prescribed interval. This, however, is not serious. 
Turning now to FIG. 6, a combination of first and second suppressors 46 and 
47, a parameter calculator 48, and a selector 72 comprises similar parts 
designated by like reference numerals as in FIG. 3. A discriminating 
device 71 may be whichever of the discriminator 71A and the level monitor 
71B. Connected to the first processor 61 that is described hereinabove as 
a novel processor in conjunction with FIG. 3, the selector 72 selects the 
transform signal and delivers the same as a selector output signal to the 
simple suppressor 62 when the discrimination signal indicates the Weibull 
distribution. The suppressor 62 produces the first clutter suppressed 
signal. The second suppressor 47 shares a portion of the first shift 
register 51 with the novel processor 61 of the first suppressor 46. The 
first shift register portion serves as a second processor 89, which is 
merely for giving the predetermined delay to the digital signal sequence 
to produce a delayed signal comprising a target return delayed component 
and clutter delayed components into which the logarithmic target return 
component and the logarithmic clutter components are delayed, 
respectively. Coupled also to the second processor 89, the selector 72 
selects the delayed signal to supply the same to the simple suppressor 62 
as the selector output signal when the discrimination signal indicates the 
Rayleigh distribution. Under the circumstances, the simple suppressor 62 
produces the second clutter suppressed signal. The simple suppressor 62 is 
thus shared by the first and the second suppressors 46 and 47 in common. 
When the level monitor 71B is used as the discriminating device 71, the 
selector 72 selects the first and the second clutter suppressed signals 
with an appreciable delay particularly when coupled to the first and the 
second supressors 46 and 47 in the manner described with reference to FIG. 
6. The delayed operation of the selector 72 is, however, immaterial. 
Finally referring to FIG. 7, a parameter calculator shown therein may be 
substituted for the parameter calculator 48 described in conjunction with 
FIG. 2 and consequently for each of those depicted in FIGS. 3 and 6. The 
illustrated parameter calculator is supplied with the detected signal 
rather than with the digital signal sequence and is operable as follows 
when only the clutter component amplitude x is taken into consideration. 
It is known in mathematics that a mean value E(x) of the clutter component 
amplitude x and a square mean value E(x.sup.2) thereof are given by: 
##EQU6## 
respectively. Therefore, a ratio calculated according to: 
##EQU7## 
is dependent only on the second parameter .eta.. 
In FIG. 7, an analog-to-digital converter 91 converts the detected signal 
to a sequence of digitized signals having digitized discrete amplitudes 
x(n) of the envelope. A first cell averaging circuit comprises a first 
shift register 92 having first through L-th stages for storing the 
digitized signals, L in number at a time, and a first average calculator 
93 for producing a first mean value signal representative of a first mean 
value Ex(n) of the digitized amplitudes of the digitized signals stored in 
the first shift register 92 at a time. The number L may be selected 
between about twenty and thirty. It is now unnecessary to exclude one of 
the digitized signals that is stored in a prescribed stage. A first 
squaring circuit 94 is for producing a first squared signal representative 
of a square of the first mean value [Ex(n)].sup.2. Responsive directly to 
the digitized signal sequence, a second squaring circuit 95 produces a 
sequence of second squared signals representative of squares of the 
respective digitized amplitudes x.sup.2 (n). A second cell averaging 
circuit comprises a second shift register 96 having first through L-th 
stages for the second squared signals, L in number at a time, and a second 
average calculator 97 for producing a second mean value signal 
representative of a second mean value Ex.sup.2 (n) of the digitized 
amplitude squares, L in number at a time. A ratio calculator 98 produces a 
ratio signal representative of a ratio [Ex(n)].sup.2 /Ex.sup.2 (n). A 
parameter meter 99 produces the parameter signal representative of the 
second parameter value calculated by the use of Equation (11). The 
parameter meter 99 may be a read-only memory to which the ratio signal is 
supplied as an access signal. It is possible to refer to Equation (12) or 
to an inverse ratio on producing the parameter signal. 
While two preferred embodiments of this invention have thus far been 
described together with various modifications thereof, it is now obvious 
that this invention can be carried into effect in a number of other ways. 
For example, it is possible to supply, instead of the logarithmic 
converter output signal, the output signal of the MTI canceller 45 to the 
first and the second suppressors 46 and 47 and the parameter calculator 48 
through a logarithmic converter, such as that shown at 41 in each of FIGS. 
1 and 4. In this connection, it is convenient to deem that a first and a 
second clutter suppressor and a parameter calculator comprise a 
logarithmic and analog-to-digital converter, such as depicted at 41 and 42 
or 43, 44, and 41. The first shift register 51 or 92 may have a somewhat 
greater number of stages than the second shift register 54 or 96. The 
particular one of the signals stored in each of the first and the second 
shift registers 51 and 54 may be produced from any one of the stages 
provided that such particular signals are simultaneously produced from the 
respective shift registers. This applies to the third shift register 68 
and the corresponding shift register comprised by the second suppressor 
separately from the third shift register 68. The numbers of the first, the 
second, and the third shift register stages may therefore be designated by 
A, B, and C with the particular or specific stages called an a-th, a b-th, 
and a c-th stage, respectively. The number of stages of the first and the 
second shift registers 92 and 96 of the parameter calculator illustrated 
with reference to FIG. 7 may be denoted by D and E. The level monitor 71B 
may be connected to the outputs of the first and the second suppressors 46 
and 47 or to the simple suppressor 62 described in connection with FIG. 7. 
In this event, the intermediate processor may be a mere connection. When 
the discriminator 71A is used as the discriminating device with the novel 
processor resorted to, it is possible to put the gate circuit 50 into 
operation with a delay related to the number of third shift register 
stages preceding the zeroth stage 68(0).