OIGITAL SIGNAL PROCESSING

MTI AND PULSE DOPPLER RADAR

4.5 OIGITAL SIGNAL PROCESSING

The introduction of practical and economical digital processing to MTI radar allowed a significant increase in the options open to the signal processing designer. The convenience of digital processing mcaus Iha\ multiple .~t!lay-li11~ canc~l-~rs_with ta_iloreJL[rco~1:1cncy-response characteristics can he readily achieved. /\ digital MTI processor does not, in prindple-;doany helter than a well-designed analog canceler; hut it is more dependable, it requires less adjust- ments and attention, and can do some tasks easier. Most of the advantages of a digital MTI processor are due to its use of digital

~ J i ~

rather than analog delay lines which are characterized by variations due to temperature, critical gains, and poor on-line availability.

A simple block diagram of a digital MTJ processor is shown in Fig. 4.21. From the output/

of the IF amplifier the signal is split into two channels. One is denoted/, for in-phase cltannel. \ The other

is

denoted Q,

for

quadrature channel, since a 90° phase change

(n/2

radians) is\

introduced into the coho reference signal at the phase detector. This causes the outputs of the '\

two detectors to be 90° out of phase. The purpose of the quadrature channel

is

to eliminate the elTects of hlind phases, as will be described later. It is desirable to eliminate blind phases in any ) MTI processor. but it is seldom done with analog delay-line cancelers because of the complex- - ity of the added analog delay lines of the second channel. The convenience of digital processing allows the quadrature channel to be added without significant burden so that it is often included in digital processing systems. It is for this reason

it

is shown in this block diagram, but was not included in the previous discussion of MTI deb.y-line cancelers.

Following the phase detector the bipolar video signal is sampled at a rate sufficient to ohtain one or more samples within each· range resolution cell. These voltage samples are converted to a series of digital words by the analog-to-digital (A/D) converter.^23•24 The digital

Pho~~

det~ctor

Coho From

--

JF

Phase deteclor

!, or m - phase, channel

Sample _A/0

and

...

_converter

hold

Sample A/0

and converter hold

0, or quadrature, channel

Digital Sub- store tractor

Magnitude {/2 + 02,112

Digital Sub- s lore I roe tor

Figure 4.21 Block diagram of a simple digital MTI signal processor.

0/A To

converter display

words are stored in a digital memory for one pulse repetition period and are then suhtracred from the digital words of the next sweep. The digital outputs of the I and Q channels are combined by taking the square root of /²

+ Q

^2• An alternative method of combining, which is adequate for most cases, is to take

I

^I

I + IQ j.

The combined output is then converted to an analog signal by the digital-to-analog (D/A) converter. The unipolar video output is then ready to be displayed. The digital MTI processor depicted in Fig. 4.21 is that of a single-delay- line canceler. Digital processors are likely to employ more complex filtering schemes, but the simple canceler is shown here for convenience. Almost any type of digital storage device can be used. A shift register is the direct digital analogy of a delay line, but other digital computer memories can also be used effectively.

The A/D converter has been, in the past, one of the critical parts of the MTI signal processor. It must operate at a speed high enough to preserve the information content of the radar signal, and the number of bits into which it quantizes the signal must be sufficient for the precision required. The number of bits in the A/D converter determines the maximum im- provement factor the MTI radar can achieve. ^{8• 7 5• 76} Generally the A/D converter is designed ^to cover the peak excursion of the phase detector output. A limiter may be necessary to ensure this. An N-bit converter divides the output of the phase detector into 2N

1

discrete intervals.

According to Shrader,⁸ the quantization noise introduced by the discrete nature of the A/D converter causes, on the average, a limit to the improvement factor which is

Io.N

= 20

log [(2N -

l )j0.75]

(dB)

(4.12)

This is approximately equal to 6 dB per bit since each bit represents a factor of two in amplitude resolution.²² When a fixed signal of maximum level is present, a possible error of one quantization interval is possible. A 9-bit A/D converter therefore has a maximum di:,cri- mination of 1 out of 511 levels; or approximately 54 dB. (Equation (4.12) on the other hand, predicts 52.9 dB for 9-bit quantization.)

In the above

it

was said that the addition of the Q channel removed the problem of reduced sensitivity due to blind phases. This is different than the blind speeds which occur when the pulse sampling appears at the same point in the doppler cycle at each sampling instant, as shown in Fig. 4.22a. Figure 4.22b shows the in-phase, or /, channel with the pulse train such

Doppler frequency ,....""' > ' /

'\

I \

01 Oz

/ -

<I)

u I '\

::, I \.

a. E

<l

\ I

' _'

_/ ^/

\ \

....__

I I

Rodar echo ,...-,, / pulses I _,,.,.,...--

/ _.--- \ I

Time

\ ' ^{, __}

^/

(a)

(b)

{c) Figure4.22 (a) Blind speed in an MTI radar.

The target doppler frequency is equal to the prf. (b) Effect of blind phase in the l channel, and (c) in the Q channel.

that the signals are of the same amplitude and with a spacing such that when pulse a1 is subtracted from pulse a_{2 ,} the result is zero. However, a residue is produced when pulse a3 is subtracted from pulse _{a4 ,} but not when a₅ is subtracted from a4, and so on. In the quadrature channel, the doppler-frequcncy signal is shifted 90° so that those pulse pairs that were lost in the I channel are recovered in the Q drnnnel, and vice versa. The combination or the I and Q channels thus results in a uniform signal with no loss. The phase of the pulse train relative to that of the doppler signal in Fig. 4.22b and c is a special case to illustrate the effect. With other phase and frequency relationships, there is still a loss with a single channel MTI that can be recovered by the use of both the I and Q channels. An extreme case where the blind phase with only a single channel results in a complete loss of signal is when the doppler frequency is half the prf and the phase relationship between the two is such that the echo pulses lie on the zeros

or

the doppler-frequency sine wave. This is not the condition for a blind speed but nevertheless there is no signal. However, if the phase relationship is shifted 90°, as it is in the Q channel, then all the echo pulses occur at the peaks of the doppler-frequency sine wave. Thus, to ensure the signal

will

be obtained without loss, both I and Q channels are desired.

Digital signal processing has some significant advantages over analog delay lines, parti- cularly those that use acoustic devices. As with most digital technology,

it

is possible to achieve greater stability, repeatability, and precision with digital processing than with analog delay- line cancelers. Thus the reliability is better. No special temperature control is required, and

it

can be packaged in convenient size. The dynamic range is greater since

digital

MTI processors do not experience the spurious responses which limit signals in acoustic delay lines to about 35

to 40 dB above minimum detectable signal level.²⁵ (A major restriction on dynamic range in a digital MTI is that imposed by the A/D converter.) In an analog delay-line canceler the delay time and the pulse repetition period must be made equal. This is si~plified in a digital MTI since the timing or the sampling of the bipolar video can be controlled readily by the timing of the transmitted pulse. Thus, different pulse repetition periods can be used without the necessity of switching delay lines of various lengths in and out. The echo signals for each interpulse period can be stored in the digital memory with reference to the time of transmission. This allows more elaborate stagger periods. The flexibility of the digital processor also permits more freedom in the selection and application of amplitude weightings for shaping the filters. It has also allowed the ready incorporation of the quadrature channel for elimination of blind phases. In short, digital MTI has allowed the radar designer the freedom to take advantage of the full theoretical capabilities of doppler processing in practical radar systems.

The development of digital processing technology

has

not only made the delay-line canceler a more versatile tool for the MTI radar designer, but it has also allowed the applica- tion or the contiguous filter bank for added flexibility in MTI radar design. One of the major factors in this regard has been the introduction of digital devices for conveniently computing the Fourier transform.

Digital filter banks and the FFT. A transversal filter with N outputs (N pulses and N 1 delay lines) can be made to form a bank of N contiguous filters covering the frequency range from O lo fr, where fr= pulse repetition frequency. A filter bank covering the doppler frequency range is of advantage in some radar applications and offers another option in the design or MTI signal processors. Consider the transversal filter that was shown

in

Fig. 4.11 to have N -

1

delay lines each with a delay time T =

1/f,,.

Let the weights applied to the outputs of the N taps be:

W _ e-1121t(i-1)k/NJ

ik -

(4.13)

where i = 1, 2, ... , N represents the ith tap, and k is an index from Oto N - 1. Each value of k corresponds to a different set of N weights, and to a different doppler-filter response. The N filters generated by the index k constitute the filter bank. Note that the weights of Eq. (4.13) and the diagram of Fig. 4.11 are similar in form to the phased array antenna as described in Sec. 8.2.

The impulse response of the transversal filter of Fig. 4.11 with the weights given by Eq. (4.13) is

N

hk(t) =

L

^{b[t -}

^{(i -}

l)T]e-jlrr(i-l)k/N _(4.14)

i"= I

The Fourier transform of the impulse response is the frequency response function

H.(.f) = e- j2rtfl

L

N ej2n(i- l)(fT-k/NI (4.15)

i == I

The magnitude of the frequency response function is the amplitude passband characteristic of the filter. Therefore

I

H ( f)

I = I r,

ei2rr<i- llffT-k/NI

I= I

^{si~ [nN(.IT - ~{N)J}

I

k · i == 1 sm [ n(.fT - k/ N)] ^(4.16)

By analogy to the discussion of the array antenna in Sec. 8.2, the peak response of the filter occurs when the denominator of Eq. (4.16) is zero, or when n(.IT - k/N) = 0, n, 2n, .... For k = 0, the peak response of the filter occurs at

f

= 0, 1/T, 2/T, ... , which defines a filter centered at de, the prf, and its harmonics. This filter passes the clutter component at de, hence it has no clutter rejection capability. (Its output is useful, however, in some MTI radars for providing a map of the clutter.) The first null of the filter response occurs when the numerator is zero, or when/= 1/NT. The bandwidth between the first nulls is 2/NT and the half-power bandwidth is approximately 0.9/NT (Fig. 4.23).

When k = 1, the peak response occurs atf= 1/NT as well asf= 1/T

+

1/NT, 2/T

+

l/NT, etc. Fork= 2, the peak response is at

f

^{= 2/NT,} and so forth. Thus each value of the index k defines a separate filter response, as indicated in Fig. 4.23, with the total response covering the region from

f=

0 to

f

= 1/T =fp· Each filter has a bandwidth of 2/NT as measured between the first nulls. Because of the sampled nature of the signals, the remainder of the frequency band is also covered with similar response, but with ambiguity. A bank of filters, as in Fig. 4.23, is sometimes called a coherellt integratio11 filter.

To generate the N filters simultaneously, each of the taps of the transversal filter of Fig. 4.11 would have to be divided into N separate outputs with separate weights correspond-

Ill 'O ::,

a. E

<t

1 2 3 4 5 6 7

O NT NT NT NT NT NT NT Frequency

T 1

Figure 4.23 MTI doppler filter bank resulting from the processing of N

=

8 pulses with the weights of Eq. (4.13), yielding the response

or

Eq. (4.16). Filter sidelobes not shown.

ing to the k =Oto N - 1 weighting as given by Eq. (4.13). (This is analogous to generating N independent beams from an N-elemcnt array by use of the Blass multiple-beam array as in Fig. 8.26.) When generating the filter bank by digital processing it is not necessary literally to subdivide each of the N taps. The equivalent can be accomplished in the digital computations.

The generation by digital processing of N filters from the outputs of N taps of a transver- sal filter requires a total of (N - l )² multiplications. The process is equivalent to the computa- 1 io11

or

a disnl'tl' Fo11ri1•r trc111sfiJ1m. 1 lowcver, when N is some power of 2, that is, N = 2, 4, 8,

16 ... an algorithm is available that requires approximately (N/2) log2 N multiplications instead of (N I

)2.

wlticlt results in a considerable saving in processing time. This is the.f<1st Fo11ria trw1sfi1r111 (FFT), which has been widely described in the literature.1^{1·27 29}

Since each filter occupies approximately 1/Nth the bandwidth of a delay-line canceler, its signal-to-noise ratio will be greater than that of a delay-line canceler. The dividing of the f rcqucncy band into N independent parts by the N filters also allows a measure of the doppler frequency to be made. Furthermore if moving clutter, such as from birds or weather, appears at other-than-zero frequency, the threshold of each filter may be individually adjusted so as to adapt to the clutter contained within it. This selectivity allows clutter to be removed which would be passed by a delay-line canceler. The first sidelobe of the filters described by Eq. (4.16) has a value of - 13.2 dB with respect to the peak response of the filter. If this is too high for proper clutter rejection, it may be reduced at the expense of wider bandwidth by applying amplitude weights wi. Just as is done in antenna design, the filter sidelobe can be reduced by using Chebyshev, Taylor, sin² x/x^2, or other weightings.³⁹ (In the digital signal processing literature, filter weighting is called windowing.⁸⁰ Two popular forms of windows are the Hamming and hanning.) It may not be convenient to display the outputs of all the doppler filters of the filter bank. One approach is to connect the output of the filters to a greatest-a,(

circuit so that only a single output is obtained, that of the largest signal. (The filter at de which contains clutter would not be included.)

the improvement factor for each of the 8 filters of an 8-pulse filter bank is shown in Fig. 4.24 as a function of the standard deviation of the clutter spectrum assuming the spectrum to he represented by the gaussian function described by Eq. (4.19). The average improvement for all filters is indicated by the dotted curve. For comparison, the improvement factor for an N-pulse canceler is shown in Fig. 4.25. Note that the improvement factor of a two-pulse canceler is almost as good as that of the 8-pulse doppler-filter bank. The three-pulse canceler is even better. (As mentioned previously, maximizing the average improvement factor might not

be the only criterion used in judging the effectiveness of MTI doppler processors.)

If a two- or three-pulse canceler is cascaded with a doppler-filter bank, better clutter rejection is provided. Figure 4.26 shows the improvement factor for a three-pulse canceler and an eight-pulse filter bank in cascade, as a function of the clutter spectral width. The upper figure assumes uniform amplitude weighting (

-13.2

dB first sidelobe) and the lower figure shows the effect of Chebyshev weighting designed to produce equal sidelobes with a peak value of - 25 dB. It is found that doubling to 16 the number of pulses in the filter bank does not offer significant -advantage over an eight-pulse filter.³⁰ More pulses do not necessarily mean more gain in signal-to-clutter ratio, because the filter widths and sidelobe levels change relative to the clutter spectrum as the number of pulses (and number of filters) is varied. If the sidelobes of the individual fllters of the doppler filter bank can be made Jow enough, the inclusion of the delay-line canceler ahead of it might not be needed.

I 60 --- --- ·-- - -

+ ^-t--

al 50 - - - - -

-0

u

0 40 2

20

10

01...~~~-L-~~J.-~l-...!_-L..-L...J-...Jl---~~~-L-~~.L.-~1..-'""""::::i:::...L_L_.l__J

0.001 0.01 0.1

Clutter spectral width/radar prf

. 5 4, 6 3, 7 2,8

Figure 4.24 Improvement factor for each filter of an 8-pulse doppler filter bank with uniform weighting as a function of the clutter spectral width (standard deviation). The average improvement for all filters is indicated by the dotted curve. (From Andrews.³⁰)

140

120

al 100

-0

0 80 2 u c _<1J

E 60 ^-

<1J ::,,

e

a.

_§

40

20

0 0.001

- - -- --·---

0.01

I

I· ^{.. t -}

I ^I

·---·---j-·

_L ___

J_.

~ - 1

0.1 Clutter spectral width /radar prf

Figure 4.25 Improvement factor for an N-pulse delay-line canceler with optimum weights (solid curves) and binomial weights (dashed curves), as a function of the clutter spectral width. (Afcer Andrews.³1.32)

ro "CJ

140

120

100

O 80

E

~ ~ 60 - -- - - ,

>

e

0

_E

40

20 ^{. I·}

0 0 001

140

120

ID 100

"CJ I

£

_u

.!:! 80

c

_Cl)

E 60

Cl)

>

a

0

E 40

20

0 0 001

0.01

Clutter ~,rectrol width I radar prf (a)

I -·

5

· -- ave. 4,6 3, 7 2,8 0.1

-- · - - - - - - - t - - - + - - l · - - l - 1 - - 1 - - - + - l

001

Cluller spectral width /radar prf (h)

0 l 5 ove, 4, 6 3 , 7

2,8

Figure 4.26 Improvement factor for a 3-pulse (double-canceler) MTI cascaded with an 8-pulse doppler filter hank. or integrator. (a) Uniform amplitude weights and (h) 25-dB Chebyshev weights. The average improvement for all filters is indicated hy the dotted curve. (From Andrews.³⁰⁾