DELAY-LINE CANCELERS

MTI AND PULSE DOPPLER RADAR

4.2 DELAY-LINE CANCELERS

Duplexer

Mix

To

delay-line canceler

Magnetron oscillator

Pulse modulator RF locking pulse

Stoia

Coho

CW reference signal

Mix

IF locking pulse

Trigger generator

Figure 4.6 Block diagram of MTI radar with power-oscillator transmitter.

Each of these has its advantages and disadvantages, which are discussed in Chap. 6. A trans- mitter which consists of a stable· low-power oscillator followed by a power amplifier is sometimes called MqPA, which stands for master-oscillator power amplifier.

Before the development of the klystron amplifier, the only high-power transmitter avail- able at microwave frequencies for' radar application was the magnetron oscillator. In an oscillator the phase of the RF bears no relationship from pulse to pulse. For this reason the reference signal cannot be generated by a continuously running oscillator. However, a coher- ent reference signal may be readily obtained with the power oscill~tor by readjusting the phase of the coho at the beginning of each sweep according to the phase of the transmitted pulse. The phase of the coho is locked to the phase of the transmitted pulse each time a pulse is generated.

A block diagram of an MTI radar (with a power oscillator) is shown in Fig. 4.6. A portion of the transmitted signal is mixed with the stalo oµtput to produce an IF beat signal whose phase is directly related to the phase of the transmitter. This IF pulse is applied to the coho and causes the phase of the coho CW oscillation to "lock" in step with the phase of the IF reference pulse. The phase of the coho is then related to the phase of the transmitted pulse and may be used as the reference signal for echoes received from that particular transmitted pulse.

Upon the next transmission another IF locking pulse is generated to relock the phase of the

CW coho until the next locking pulse comes along. The type of MTI radar illustrated in

Fig. 4.6 has had wide application.

reasonable physical length since the velocity of propagation of acoustic waves is about 10-⁵ that of electromagnetic waves. After the necessary delay is introduced by the acoustic line, the signal is converted back to an electromagnetic signal for further processing. The early acoustic delay lines developed during World War ll used liquid delay lines filled with either water or mercury. ¹ Liquid delay lines were large and inconvenient to use. They were replaced in the mid-l 950s by the solid fused-quartz delay line that used multiple internal reflections to obtain a compact device. These analog acoustic delay lines were, in turn supplanted in the early 1970s by storage devices based on digital computer technology. The use of digital delay lines requires that the output of the MTI receiver phase-detector be quantized into a sequence of digital words. The compactness and convenience of digital processing allows the implementation of more complex delay-line cancelers with filter characteristics not practical with analog methods.

One of the advantages of a time-domain delay-line canceler as compared to the more conventional frequency-domain filter is that a single network operates at all ranges and does not require a separate filter for each range resolution cell. Frequency-domain doppler filter- banks are of interest in some forms of MTI and pulse-doppler radar.

Filter characteristics of the delay-line canceler. The delay-line canceler acts as a filter which rejects the d-c component of clutter. Because of its periodic nature, the filter also rejects energy in the vicinity of the pulse repetition frequency and its harmonics.

The video signal [Eq.

(4.3)]

received from a particular target at a range R₀ is

(4.4)

where

¢

0 = phase shift and k = amplitude of video signal. The signal from the previous transmission, which is delayed by a time T = pulse repetition interval, is

V₂ = k sin [2nfd(t - T) - <Po]

(4.5)

Everything else is assumed to remain essentially constant over the interval Tso that k is the same for both pulses. The output from the subtractor is

V =

V

^{1 -}

Vi

⁼

2k

^{sin nf4 T cos}

[2nf4(

^{t - ~) -}

<Po] ^(4.6)

It is assumed that the gain through the delay-line canceler is unity. The output from the canceler [Eq.

(4.6)]

consists of a cosine wave at the doppler frequency

f

4 with an amplitude 2k sin

nf,

T: Thus the amplitude of the canceled video output is a function of the doppler frequency shift and the pulse-repetition interval, or prf. The magnitude of the relative frequency-response of the delay-line canceler [ratio of the amplitude of the output from the delay-line canceler, 2k sin

(nf.t

T), to the amplitude of the normal radar video k] is shown in

Fig. 4.7.

(

o

1/r

2/r

3/r 4/r

5/r

Frequency

Figure 4. 7 Frequency response or the single delay-line canceler; T

=

delay time

=

1/f,,.

Blind speeds. The response of the single-delay-line canceler will be zero whenever the argu- ment rrJj Tin the amplitude factor of Eq. (4.6) is 0, n, 2n, ... , etc., or when

(4.7) where 11

=

0, 1, 2, ... , and j~

=

pulse repetition frequency. The delay-line cancela not only eliminates the d-c component caused by clutter (n = 0), but unfortunately it also rejects any moving target whose doppler frequency happens to be the same as the prf or a multiple thereof. Those relative target velocities which result in zero MTI response arc called hli11J speeds and are given by

n = 1, 2, 3, ... (4.8)

where lln is the nth blind speed. If ,1.. is measured in meters,.fP in Hz, and the relative velocity in knots, the blind speeds are

(4.9) The blind speeds are one of the limitations of pulse MTI radar which do not occur with CW radar. They are present in pulse radar because doppler is measured by discrete samples (pulses) at the prf rather than continuously. If the first blind speed is to be greater than the maximum radial velocity expected from the target, the product ^)JP must be large. Thus the MTI radar must operate at long wavelengths (low frequencies) or with high pulse repetition frequencies, or both. Unfortunately, there are usually constraints other than blind speeds which determine the wavelength and the pulse repetition frequency. Therefore blind speeds might not be easy to avoid. Low radar frequencies have the disadvantage that antenna bcam- widths, for a given-size antenna, are wider than at the higher frequencies and would not be satisfactory in applications where angular accuracy or angular resolution is important. The pulse repetition frequency cannot always be varied over wide limits since it is primarily determined by the unambiguous range requirement. In Fig. 4.8, the first blind speed _{ll 1} is plotted as a function of the maximum unambiguous range

(Runamb =

c1 /2), with radar frequency as the parameter. If the first blind speed were 600 knots, the maximum unambiguous range would be 130 nautical miles at a frequency of 300 MHz (UHF), 13 nautical miles at 3000 MHz (S band), and 4 nautical miles at 10,000 MHz (X band). Since commercial jet aircraft have speeds of the order of 600 knots, and military aircraft even higher, blind speeds in the MTI radar can be a serious limitation, .. ,

In practice, long-range MTI radars that operate in the region of Lor S band or higher and are primarily designed for the detection of aircraft must usually operate with ambiguous doppler and blind speeds if they are to operate with unambiguous range. The presence of blind speeds within the doppler-frequency band reduces the detection capabilities of the radar. Blind speeds can sometimes be traded for ambiguous range, so that in systems applications which require good MTI performance, the first blind speed might be placed outside the range of expected doppler frequencies if ambiguous range can be tolerated. (Pulse-doppler radars usually operate in this manner). As .will be described later, the effect of blind speeds can be significantly reduced, without incurring range ambiguities, by operating with more than one pulse repetition frequency. This is called a staggered-pr_{ MT/. Operating at more than one RF frequency can also reduce the effect of blind speeds.

V,

0 C --"'

.

"CJ Q.) OJ a

V,

"CJ 1,000

C

Li

+- V, L

ii:

10 100 1,000

Maximum unambiguous range, nautical miles

Figure 4.8 Plot of MTI radar first blind speed as a function of maximum unambiguous range.

Uouble cancellation. The frequency response of a single-delay-line canceler (Fig. 4.7) does not always have as broad a clutter-rejection null as might be desired in the vicinity or d-c. The clutter-rejection notches may be widened by passing the output of the delay-line canceler through a second delay-line canceler as shown in Fig. 4.9a. The output of the two single-delay- line cancelers in cascade is the square of that from a single canceler. Thus the frequency response is 4 sin² nfd T. The configuration or Fig. 4.9a is called a double-delay-line canceler, or simply a double canceler. The relative response of the double canceler compared with that of a single-delay-line canceler is sho..yn in Fig. 4.10. The finite width of the clutter spectrum is also shown in this figure so as to illustrate the additional cancellation of clutter offered by the double canceler.

The two-delay-line configuration of Fig. 4.9b has the same frequency-response character- istic as the double-delay-line canceler. The operation of the device is as follows. A signal!

(t)

is inserted into the adder along with the signal from the preceding pulse period, with its ampli- tude weighted by the factor - 2, plus the signal from two pulse periods previous. The output of the adder is therefore

Input

---

Input

- ~

f(t) - ~f(t

+

T)

+

f(t

+

2T)

Deloy line T=¹/fp Deloy line T=lffp

(al

+1 Deloy line T = 'lfp 1---.----i--1·Deloy line T= ¹11p t---+-'-t -

-2 (b)

figure 4.9 (a) Double·delay·line canceler; (b) three·pulse canceler.

Output

Output

1.0

(I.>

::'.! 0.8

0

la 0. 0.6

L.

.~ 0.4

-

⁰

£

^0.2

Clutter spectrum

Single cancellation

I

I

I I

I

/

I I

Double

cancellation---""\

\ \

Clutter l o / d o v e r ~

/

"

I '-

/ \

I \

I \

I \

I \

I \

O~'..LL~~~~---1..~~~~_L~....,CLL~~~~...L~~~~_..l-J-D,,"""":...J...~~

0 fp =Yr ^{2 Ip}

Frequency

Figure 4.10 Relative frequency response of the single-delay-line canceler (solid curve) a9d the double- delay-line canceler (dashed curve). Shaded area represents clutter spectrum.

which is the same as the output from the double-delay-line canceler.

/(t) -

f(t

+ T) - f(t + T) + f(t + 2T)

This configuration is commonly called the three-pulse canceler.

Tramversal

·filters.

The three-pulse canceler shown in Fig. 4.9b is an example of a transversal filter. Its general form with N pulses and N - 1 delay lines is shown in Fig. 4.11. It is also sometimes known as afeedforward filter, a nonrecursive filter, a.finite memory filter or a tapped delay-line filter. The weights w₁ for a three-pulse canceler utilizing two delay lines arranged as a transversal filter are l,

-2,

1. The/requency response function is proportional to sin²

nh

^T.

A transversal filter with three delay lines whose weights are 1, - 3, 3, - I gives a sin ³

nf,

T response. This is a four-pulse'canceler. Its response is e~uivalent to a triple canceler consisting of a cascade of three single-delay-line cancelers. (Note the potentially confusing nomenclature.

A cascade configuration of three delay lines, each con.nected as a single canceler, is called a triple canceler, but when connected as. a transversal fi1ter it is called a four-pulse canceler.) The weights for a transversal filter with n delay lines that gives a response sin" nf,, T are the coefficients of the expansion of (1 ...:..

xY,,

which are the bi~omial coefficients with alternating signs:

Input Deloy

r,

( )1-1

n!

Wi=

-l (n-i+l)!(i-1)!'

Deloy Tz

Deloy T3

Summer

Output

Deloy

9-/-1

i = 1, 2, ... , n

+

1

(4.10)

Figure 4.11 General form of a trans- versal ( or nonrecursivc) filter for MTI signal processing.

The transversal filter with alternating binomial weights is closely related to the filter which maximizes the average or the ratio le=

(S/C)

0

u

1

/(S/C)in,

where

(S/C)our

is the signal-to- clutter ratio at the output of the filter, and

(S/C);n

is the signal-to-clutter ratio at the input.³•4

The average is taken over the range of doppler frequencies. This criterion was first formulated in a limited-distribution report by Emerson. ⁵ The ratio le was called in the early literature the reference gain, hut it is now called the improvement factor for clutter. It is independent of the target velocity and depends only on the weights wi, the autocorrelation function (or power spectrum) describing the clutter, and the number of pulses. For the two-pulse canceler (a single delay line). the optimum weights based on the above criterion are the same as the binomial weights, when the clutter spectrum is represented by a gaussian function.⁶ The differenc~

between a transversal filter with optimal weights and one with binomial weights for a three- pulse canceler (two delay lines) is less than 2 dB.⁴·5 The difference is also small for higher- order cancelers. Thus the improvement obtained with optimal weights as compared with binomial weights is relatively small. This applies over a wide range of clutter spectral widths.

Similarly, it is found that the use of a criterion which maximizes the clutter attenuation (ratio of input clutter power to the output clutter power) is also well approximated by a transversal filter with binomial weights of alternating sign when the clutter spectrum can be represented hy a gaussian function whose spectral width is small compared to the pulse repetition frequency. ⁷ Thus the delay line cancellers with response sin" 1t/& Tare" optimum" in the sense that they approximate the filters which maximize the average signal-to-clutter ratio or the average clutter attentuation. It also approximates the filter which maximizes the probabil- ity of detection for a target at the midband doppler frequency or its harmonics.⁶

In spite of the fact that such filters are" optimum" in several senses as mentioned above, they do not necessarily have characteristics that are always desirable for an MTI filter. The notches at de, at the prf, and the harmonics of the prf are increasingly broad with increasing number of delay lines. Although added delay lines reduce the clutter, they also reduce the number of moving targets detected because of the narrowing of the passband. For example, if the

-10

dB response of the filter characteristic is taken as the threshold for detection and if the targets are distributed uniformly across the doppler frequency band, 20 percent of all targets will be rejected by a two-pulse canceler (single delay-line canceler), 38 percent will be rejected by a three-pulse canceler (double canceler), and 48 percent by a four-pulse canceler (triple canceler). These filters might be "optimum" in that they satisfy the specified criterion, but the criterion might not be the best for satisfying MTI requirements. (Optimum is not a synonym fo.r best; it means the best under the given set of assumptions.) Maximizing the signal-to-clutter ratio over all doppler frequencies, which leads to the binomial weights and sin" 1tf& T filters, is not necessarily a pertinent criterion for design of an MTI filter since this criterion is independent of the target signal characteristics. ³-5 It would seem that the MTI filter should be shaped to reject the clutter at d-c and around the prf and its harmonics, but have a flat response over the region where no clutter is expected. That is, it would be desirable to have the freedom to shape the filter response, just as with any conventional filter.

The transversal, or nonrecursive, filter of Fig. 4.11 can be designed to achieve filter responses suitable for MT1¹- 10 but a relatively large number of delay lines are needed for filters with desirable characteristics. An N - 1 delay-line canceler requires N pulses, which sets a restriction on the radar's pulse repetition frequency, beamwidth, and antenna rotation rate, or dwell time.

Figure 4.12²⁶ shows the amplitude response for (1) a classical three-pulse canceler with sin²

nf&

T response, (2) a five-pulse" optimum" canceler designed to maximize the improve- ment factor³ and

(3)

a 15-puJse canceler with a Chebyshev filter characteristic. (The amplitude

N

is normalized by dividing the output of each tap by the square root of

L wf,

^where

'"' I

2 . 0 . - - - . - - - - . - - - . - - - , - - - . - - - - . - - - - , - - - ~ - ~ - ~

1.6

lJ..

I I

<1> 1.2

VI C 0 a.

VI

<1>

~

...

0.8

~ C.

4 E 0.4

( 1)

Frequency

Figure 4.12 Amplitude responses for three MTI delay-line cancelers. (1) Classical three-pulse canceler, (2) five-pulse delay-line canceler with "optimum" weights, and (3) 15-pulse Chebyshev design. ( Afcer fl outs and Burlage.²⁶)

W; = weight at the ith tap.) A large number of delay lines are seen to be required of a nonrecursive canceler if highly-shaped filter responses are desired. It has been suggested, ²⁶ however, that even with only a five-pulse c·anceler, a five-pulse Chebyshev design provides significantly wider bandwidth 'tha'n the. five-pulse "optimum" design. To achieve the wider band the Chebyshev design has··a lower improvement factor (since it is not "optimum"), but in many cases the trade is worthwhile especially if the clutter spectrum is narrow. However, when only a few pulses are available fo'r' processing ~here is probably little that can be done to control the shape of the filter characteristic. Thus, there is ~ot much to be gained in trying to shape the nonrecursive filter response for three- or four-pulse cancelers other than to use the classical sin² or sin³ response· of the," optimum,, canceler.

The N-pulse nonrecursive delay-line canceler allows the designer N zeros for synthesizing the frequency response. The result is that many delay lines are required for.highly-shaped filter responses. There are limits to the' n'umber of delay lines (and pulses) that can he emplGyed.

Therefore other approaches to MTI filter implementation are sometimes desired.

Shaping the frequency responsi Nonrecursive filters employ only feedforward loops. If feed- back loops are used, as well as feedfcirward. loops, each delay line can provide one pole as well as one zero for increased design flexibility. The canonical configuration of a time-domain filter with feedback as well

as

feedforward loops is illustrated in Fig. 4.13. When feedback loops are

> I '

Deloy Deloy Deloy Deloy Vout

Figure 4.13 Canonical-configuration comb filter. (After White and Ruvin,² IRE Natl. Conv. Record.)

used ti1e filter is called recursive. Using the Z-Lransform as the basis for design it is possible in principle to synthesize almost any frequency-response function.^2•11-13

The canonical configuration is useful for conceptual purposes, but it may not always be desirable to design a filter in this manner. White and Ruvin² state that the canonical configuration may be broken into cascaded sections, no section having more than two delay elements. Thus no feedback or feed forward path need span more than two delay elements. This type of configuration is sometimes preferred to the canonical configuration.

The synthesis technique described by White and Ruvin may be applied with any known low-pass filter characteristic, whether it is a Butterworth, Chebyshev, or Bessel filter or one of the filters based on the elliptic-function transformation which has equal ripple in the rejection band as well as in the passband. An example of the use of these filter characteristics applied to the design of a delay-line periodic filter is given in either of White's papers.²•12 Consider the frequency-response characteristic of a three-pole Chebyshev low-pass filter having 0.5 dB ripple in the passband (Fig. 4.14). The three different delay-line-filter frequency-response char- acteristics shown in Fig. 4.14b to d were derived from the low-pass filter characteri!.tic of Fig. 4.14a. This type of filter characteristic may be obtained with a single delay line in cascade with a double delay line as shown in Fig. 4.15. The weighting factors shown on the feedback paths apply to the characteristic of Fig. 4.14c.

The additional degrees or freedom available in the design of recursive delay-line filters olTer a steady-state response that is superior to that or comparable nonrecursive filters. How- ever the feedback loops in the recursive filter result in a poor transient response. The presence

-1 0

0.5

10[

0 I

0

(l)

"' ^C ₀ 5t 1 0 -

t .

~ 0.5 -

2 3 Angular frequency, w

(a)

4

-:\,[

1/T

(b)

5

·g O _ _ L _ _ _ _ _ _ . l . _ ~ 1 - - ~ ~ ~ - ~

~ 0

1/T

(c)

r:\,L

1/T

Frequency (d)

Figure 4.14 (a) Three-pole Chebyshev low-pass filter characteristic with 0.5 dB ripple in the passband; ^(b-d) delay-line filter ·;haracteristics derived from (a). (After White.12)