Lll\tllTATIONS TO MTI PERFORMANCE

MTI AND PULSE DOPPLER RADAR

4.8 Lll\tllTATIONS TO MTI PERFORMANCE

The improvemenl in signal-to-clutter ratio or an MTI is affected

by

factors other than the design of the doppler signal processor. Instabilities or the transmitter and receiver, physical motions of the clutter, the finite time on target (or scanning modulation), and limiting in the receiver can all detract from the performance of an MTI radar. Before discussing these effects, some definitions will be stated.

MT/ improvement factor. The signal-to-clutter ratio at the output of the MTI system divided by the signal-to-clutter ratio at the input, averaged uniformly over all target radial veloci:

ties of interest.

Suhclutter visihility. The ratio by which the targ~t echo power may be weaker than the coincident clutter echo power and still be detected with specified detection and false- alarm probabilities. AIi target radial velocities are assumed equally likely. A subclutter visibility of, for example, 30 dB implies that a moving target can be detected in the presence or clutter even though the clutter echo power is 1000 times the target echo

power. Two radars with the same subclutter visibility might not have the same ability to detect targets in clutter if the resolution cell of one is greater than the other and accepts a greater clutter signal power; that is, both radars might reduce the clutter power equally, but one starts with greater clutter power because its resolution cell is greater and .. sees"

more clutter targets.

Clutter visibility factor. The signal-to·clutter ratio, after cancellation or doppler filtering, that provides stated probabilities of detection and false alarm.

Clutter attenuation. The ratio of clutter power at the canceler input to the clutter residue at the output, normalized to the attenuation of a single pulse passing through the unprocessed channel of the canceler. (The clutter residue is the clutter power remaining at the output of an MTI system.)

Cancellation ratio. The ratio of canceler voltage amplification for the fixed-target echoes received with a fixed antenna, to the gain for a single pulse passing thro11gh the un- processed channel of the canceler.

The improvement factor

(l)

is equal to the subclutter visibility (SCV) times the clutter visibility factor

(Voe),

In decibels, /(dB)= SCV(dB)

+

Voc(dB). When the MTI is limited by noiselike system instabilities, the clutter visibility factor should be chosen as is the signal-to- noise ratio of Chap. 2. When the MTI performance is limited by the antenna scanning fluctua- tions, Shrader⁸ suggests letting V0c = 6 dB. (Although not stated by Shrader,

it

seems this value is for a single pulse.) The improvement factor is the preferred measure of MTI radar performance.

Still another term sometimes employed in MT[ radar is the interclutter visibility. This describes the ability of an MTI radar to detect moving targets which occur in the relatively clear resolution cells between patches of strong clutter. Clutter echo power is not uniform, so if a radar has sufficient resolution

it

can see targets in the clear areas between clutter patches.

The higher the radar resolution, the better the interclutter visibility. Radars with "moderate"

resolution might require only enough improvement factor to deal with the median clutter power, which may be 20 dB less than the average clutter power.⁴⁵ According to Shrader a medium-resolution radar with a 2 µs pulse width and a 1.5° beam width, is of sufficient resolution to achieve a 20 dB advantage over low-resolution radars for the detection of targets in ground clutter.⁵⁰

Equipment instabilities. Pulse-to-pulse changes in the amplitude, frequency, or phase of the transmitter signal, changes in the stalo or coho oscillators in the receiver, jitter in the timing of the pulse transmission, variations in the time delay through the delay lines, and changes in the pulse width can cause the apparent frequency spectrum from perfectly stationary clutter to broaden and thereby lower the improvement factor of an MTI radar. The stability of the equipment in an MTI radar must be considerably better than that of an ordinary radar. It can limit the performance of an MTI radar if sufficient care is not taken in design, construction, and maintenance.

Consider the effect of phase _variations in an oscillator. If the echo from stationary clutter on the first pulse is represented

PY A

cos

wt

and from the second pulse is A cos (wt

+

At/>),

' ^'•

where A¢ is the change in oscillator phase between the two, then the difference between the two after subtraction is A cos wt - A cos (wt+ A¢)= 2A sin (A¢/2) sin (wt

+

A¢/2). For small phase errors, the amplitude of the resultant difference is 2A sin A¢/2 ::::: A A¢. Therefore the limitation on the improvement. fa~tor· due_ to oscillator instability is

.. / , , I ' ' :I. ; '• ; ' l .

I=

(A¢)2 ^(4.17)

This would arrly 10 the coho Jocking or to the phase change introduced by a power amplifier.

A phase change pulse-to-pulse of 0.01 radians results in an improvement-factor limitation of 40 dB. The limits to the improvement factor imposed by pulse-to-pulse instability are listed below:A.46.47

Transmitter frequency Sta lo or coho frequency Transmitter phase shift Coho locking

Pulse timing Pulse width Pulse amplitude

(m:\fr

r

²

(2rr llJTr²

(ll</J r

²

(ll<t> r

²

r² /(llt)²2Br r²/(llr}2Br

(A/llA)

²

where llf = interpulse frequency change, r

=

pulse width, T

=

transmission time to and from target. ll</> = interpulse phase change, llt = time jitter, Br = time-bandwidth product of pulse compression system ( = unity for simple pulses,)

llr

= pulse-width jitter, A = pulse amplitude, llA

=

intcrpulse amplitude change. In a digital signal processor the improvement factor is also limited by the quantization noise introduced by the A/D converter, as was discussed in Sec. 4.5. The digital processor, however, does not experience degradation due to time jitter of the transmitted pulse since the system clock controlling the processor timing may be started from the detected rf envelope of the transmitted pulse.

Internal fluctuation of clutter. ⁴⁸ Although clutter targets such as buildings, water towers, bare hills. or mountains produce echo signals that are constant in both phase and amplitude as a function of time, there are many types of clutter that cannot be considered as absc,lutely stationary. Echoes from trees, vegetation, sea, rain, and chaff fluctuate with time, and these fluctuations can limit the performance of MTI radar.

Because of its varied nature, it is difficult to describe precisely the clutter echo signal.

However, for purposes of analysis, most fluctuating clutter targets may be represented by a model consisting of many independent scatterers located within the resolution cell of the radar.

The echo at the radar receiver is the vector sum of the echo signals received from each of the individual scatters; that is, the relative phase as well as the amplitude from each scatterer innuences the resultant composite signal. If the individual scatters remain fixed from pulse to pulse, the resultant echo signal will also remain fixed. But any motion of the scatterers relative to the radar will result in different phase relationships at the radar receiver. Hence the phase and amplitude of the new resultant echo signal will differ pulse to pulse.

Examples of the power spectra of typical clutter are shown in Fig. 4.29. These data apply at a frequency of 1000 MHz. The experimentally measured power spectra of clutter signals may he approximated by

where W(f) = clutter-power spectrum as a function of frequency g(f) = Fourier transform of input waveform (clutter echo)

.f~

=

radar carrier frequency

a = a parameter dependent upon clutter

(4.18)

Values of the parameter a which correspond to the clutter spectra in Fig. 4.29 are given in the caption.

0.2

...

at 0.1 0.05

2 0.02 0.01

0 5 10 15

Frequency, Hz

20 25

Figure4.29 Power spectra of various clutter targets.

(I) Heavily wooded hills, 20 mi/h wind blowing (a= 2.3 x 10^17); (2) sparsely wooded hills, calm day (a

=

3.9 x 10^19); (3} sea echo, windy day (a= 1.41 x 10¹⁶); (4) rain clouds (a= 2.8 x 10¹⁵);

(5) chaff (a= l x 10¹⁶). (From Barlow,⁴⁹ Proc.

IRE.)

The clutter spectrum can also be expressed in terms of an rms clutter frequency spread cr, in hertz or by therms velocity spread <lv in m/s.⁴⁶ Thus Eq. (4.18) can be written

( r2) ( r2).2)

W(f) = W0 exp -

la;

^{= Wo} exp - · So} (4.19) where W₀

= l9ol2.

<I,= 2<Ivfl,). =wavelength= c/fo, and

c

= velocity of propagation.

It

can be seen that a= c²/8<I~. The rms velocity spread <Iv is usually the preferred method for describing the clutter fluctuation spectrum.

The improvement factor can be written as

I =

(So/Co)

=

(So) x

Ci =

(So) x CA (4

^.20)

S;/Cj

^ave

Si

^ave

Co Sj

^ave

where S0/C0 = output signal-to-clutter ratio, SdC; = input signal-to-clutter ratio, and

CA

= clutter attentuation. The average is taken over all target doppler frequencies of interest.

For a single-delay-line canceler, the clutter attentuation is

J:

^{W(.f) df}

CA=

s:

W(f)I H(f)l 2~7 (4.21)

where

H(.f)

is the frequency response function of the canceler. Since the frequency response function of a delay line of time delay T is exp (-j2nf T), II(!) for the single-delay-line canceler is

H(f)

=

1 -

exp ( - j2nf

T)

=

2j

sin (nf

T)

exp ( - jnf

T)

(4.22) Substituting Eqs.

(4.19)

and

(4.22)

into

Eq. (4.21)

and assuming that <I,~ l/T, the clutter attentuation is

f;

Wo exp (-f²

/2a;)

df CA = ~-·:::....:;._---'----

J0 W₀ exp

(-f

²

/2a;)4

sin² nf T df

0.5

(4.23)

If the exponent in the denominator of Eq. (4.23) is small, the exponential term can be replaced hy the first two terms of a series expansion, or

f/ f/ ).2 af/

CA=----= = - - (4.24)

· 4rr²

a;

^16rr2

a~

^2rr2

Ja2

where

f,,.

the pulse repetition frequency, has been substituted for 1/T. The average gain (So /S,)a,·• of the single delay-line-c:111celer can be shown to be equal to 2. Therefore. the improvement factor is

(4.25) Similarly. for a double canceler. whose average gain is 6, the improvement factor is

f/ J/

^{,l 4}

a2f/

l i e " ' - - · - - = - - ~ - = - -

- 8rr⁴a: 128n4<r! 2n⁴

f

₀^{4 (4.26)}

!\ plot of Fq. (4.26) for the double canceler is shown in Fig. 4.30. The parameter describing the curves is Jp).· Example prf's and rrequencies are shown. Several "representative" examples of clutter are indicated, based on published data for a11 , which for the most part dates back to World War 11.⁴⁶·49 Although each type of clutter is shown at a particular value of ^<Tv, nature is more variable than this. Actual measurements cover a range of values. The spectral spread in velocity is with respect to the mean velocity, which for ground clutter is usually zero. Rain and

ro u

60 -

50

2

_u ⁴⁰

0

OJ C

~ 30 -

>

0

..

0.

E 20 -

10 - Sparse woods

Wooded hills 10 knots

Wooded hills Seo echo Rain

40 knots Chaff

0 ' - - - ' - - - ' - - - ' - - ' - _ . _ ~ ~ - - - ~ ~ ~ ~ _ . _ ~ ~ ~ - - ~ - ~ - - ' - - ~ ~ ~

0 001 01 1·0 10

c,11 = rms velocity spread, mis

Figure 4.30 Plot of double-canceler clutter improvement factor [Eq. (4.26)] as a function of uv

=

rms velocity spread of the clutter. Parameter is the product of the pulse repetition frequency (/p) and the radar wavelength (,l).

chaff, however, as well as sea echo, can have a nonzero mean velocity^{4 7} which must be properly accounted for when designing MTI signal processors.

The frequency dependence of the clutter spectrum as given by Eqs. (4.25) and (4.26) cannot be extended over too great a frequency range since account is not taken of any variation in radar cross section of the individual scatterers as a function of frequency. The leaves and branches of trees, for example, might have considerably different reflecting proper- ties at K0 band (,.l = 0.86 cm), where the dimensions are comparable with the wavelength, from those at VHF (l = 1.35 m), where the wavelength is long compared with the dimensions.

The general expression for improvement factor for an N-pulse canceler with N₁ = N - I delay lines is⁶¹

(4.27)

Antenna scanning modulation. ⁴⁶.4⁹-52 As the antenna scans by a target, it observes the target for a finite time equal to t₀ = n_{8 /}

J,

= 8_{8 /()1}^, where n₈ = number of hits received,

J, =

pulse repetition frequency, ()₈ = antenna beamwidth and (J₁ = antenna scanning rate. The received pulse train of finite duration t₀ has a frequency spectrum (which can be found by taking the Fourier transform of the waveform) whose width is proportional to 1/t_{0 .} Therefore, even if the clutter were perfectly stationary, there will still be a finite width to the clutter spectrum because of the finite time on target. If the clutter spectrum is too wide because the observation time is too short, it will affect the improvement factor. This limitation has sometimes been called scanning fluctuations or scanning modulation.

The computation of the limitation to the improvement factor can be found in a manner similar to that of the clutter fluctuations described previously. The clutter attentuation is first found using Eq.

(4.21),

except that the power spectrum

JYs(f)

describing the spectrum produced by t~e finite time on target is used. The clutter attenuation is

C -

s: ^Ws(f)

^df

A -

J; ^Ws(f)

^I

^H(f)

^{12 df (}

^{4 .lS)}

where

H(f)

is the frequency response function of the MTI signal processor. If the antenna main-beam pattern is approximated by the gaussian shape, the spectrum will also be gaussian.

Therefore, the results previously derived for a gaussian clutter spectrum can be readily applied.

Equations

4.25

and

4.26

derived for the clutter fluctuation improvement factor apply for the antenna scanning fluctuations by proper interpretation of a,, the standard deviation, or the rms spread of the frequency spectrum about the mean.

The voltage waveform of the received signaJ is modulated by the square of the antenna electric-field-strength-pattern, which is equal to the (one-way) antenna power pattern G(O), described by the gaussian function as

(

2.7768²)

G(8)

=

G

0 exp -

D i

^(4.29)

Since the antenna is scanning at a rate of

tJ.

deg/s the time waveform may be found from

Eq. (4.29) by

dividing both the numerator and denominator of the exponent by {},. Letting 0/()₁ = t, the time variable, and noting that 0₈

/fJ

1 = t_{0 ,} the time on target, the modulation of the received signal due to the antenna pattern is

( )

k

(

^{2.776 t}

2)

s11 t = exp - ₂

to

(4.30)

where k constant. The angular frequency spectrum or this time waveform is found by taking its Fourier transform, which is

(l'.) (

2 776t

²)

S0(f)

=

k

J_ro

exp - ·

15

exp (-j2nft) dt

(4.31)

where

k

1

=

constant. Since this is a gaussian runction, the exponent is of the formf ²

/2a}

where a ₁

=

standard deviation. Therefore

(4.32)

This applies to the voltage spectrum. Since the standard deviation or the power spectrum is less than that of the voltage spectrum by

j2,

the power spectrum due to antenna scanning can be described by a standard deviation

1.178

1

(4.33)

50 rn

"O

I

0 40 ^-

u

J:'

c

_(I)

E 30 ^-

(I)

>

0 ....

0

E 20 ^-

o,

_{100 1000}

"9, number of hits wilhin 3 dB beomwidth

Figure 4.31 Limitation to improvement factor due to a scanning antenna. Antenna pattern assumed to be of gaussian shape.

This can be substituted for <J, in Eqs. (4.25) and {4.26) to obtain the limitation to the improve- ment factor caused by antenna scanning. These are

(single canceler) (4.34)

(double canceler) (4.35)

These are plotted in Fig. 4.31.

A stepped-scan antenna that dwells at a particular region in space, rather than scan continuously, also is limited in MTI performance by the finite time on target ^t0 • The time waveform is constant so that it will have a different spectral shape and a different improvement factor than that produced by the gaussian beam assumed in the above.

Limiting in MTI radar.⁸·53 -55

A limiter is usually employed in the IF amplifier just hcforc the MT( processor to prevent the residue from large clutter echoes from saturating the display.

Ideally an

MTI

radar should reduce the clutter to a level comparable to rece.ivcr noise.

60

50

0)

"O

...

I

0 40

ti 0 C/L 0 dB

- _c

C/L == 10 dB

(I)

E (I) _> 30

0

...

a.

E

20.

10

n₈ = 50 n₈ = 20 n₈ = 10 n₈ 5

o ~ ~ - - ' - ~ ~ - ' - ~ - - - - ' - ~ - - ' - ~ - ' - ~ ' - ' - ~ _ . _ _ _ . _ _ _ . ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

0·001 0 01

(a)

m u I

E

_u

l?

c _a.,

E a.,

>

0

0 E 50

40 -

30

20

10 "

0

0001 001

Figure 4.32 Effect or limit level on the improvement factor ror (a) two-pulse delay-line canceler and (b) three-pulse delay-line canceler. C/L

=

ratio of rms clutter power to limit level. (From Ward and Slirader,⁵³ Courtesy IEEE.)

However, when the MTI improvement factor is not great enough to reduce the clutter sufficiently.~the clutter residue will appear on the display and prevent the detection of aircraft targets whose cross sections arc larger than the clutter residue. This condition may be pre- vented hy selling the limit level L relative to the noise N, equal to the MTI improvement factor I; or L/N = /. If the limit level relative to noise is set higher than the improvement factor. clutter residue ohscures part of the display. Hit is set too low there may be a" black hole" effect on the display. The limiter provides a constant false alarm rate (CFAR) and is essential to usable MTI performance.⁵⁰

Unfortunately, nonlinear devices such as limiters have side-effects that can degrade performance. Limiters cause the spectrum of strong clutter to spread into the canceler pass- band, and result in the generation of additional residue that can significantly degrade MTI performance as compared with a perfect linear system.

An example of the effect of limiting is shown in Fig. 4.32, which plots the improvement factor for two-pulse and three-pulse cancelers with various levels of limiting.⁵³ The abscissa applies to a gaussian clutter spectrum that is generated either by clutter motion with standard deviation ^<r,. at a wavelength A. and a prf fp, or by antenna scanning modulation with a

gaussian-shaped beam and _{11 8} pulses between the half-power beamwidth of the one-way antenna pattern. The parameter C/L is the ratio of the rms clutter power to the receiver-IF limit level.

The loss of improvement factor increases with increasing complexity of the canceler.

Limiting in ·the three-pulse canceler will cause a 15 to 25 dB reduction in the performance predicted by linear theory.⁵⁰ A four-pulse canceler (not shown) with limiting is typically only 2 dB better than the three-pulse canceler in the presence of limiting clutter and offers little advantage. Thus the added complexity of higher-order cancelers is seldom justified in such situations. The linear analysis of MTI signal processors is therefore not adequate when limit-

ing,is employed and can lead to disappointing differences between theory and measurement of actual systems.

Limiters need not be used if the MTI is linear over the entire range of clutter signals and if the processor has sufficient improvement factor to reduce the largest clutter to tre noise level.

To accomplish this the signal processor must provide at least 60 dB improvement factor, which is a difficult task. ⁵⁶ Not only must the signal processor be designed to reduce the clutter by this amount, but the receiver must be linear over this range, there must be at least eleven bits in the A/D converter of the digital processor, the equipment must be sufficiently stable, and the number of pulses processed (for reducing antenna scanning modulation) must be sufficient to achieve this large value of improvement factor.