solving radar detection problems using simulation

8/3/2019 Solving Radar Detection Problems Using Simulation

http://slidepdf.com/reader/full/solving-radar-detection-problems-using-simulation 1/5

Solving Radar Detection ProblemsUsing Simulation

D. Curtis SchleherNaval Postgraduate School

ABSTRACT

Simulation is a well-known but often misunderstood

method for predicting the detection range of radars. Recent

advances n computer software and hardware have made

simulation easier to apply and use. Users are putting increased

reliance on computer simulation n lieu of more expensive test

and evaluation.

In this paper, a simulation example is given of a

complex radar detection problem which is not solvable using

conventional procedures. It is shown how this problem is

easily solved using a MATLAB simulation on a personal

computer (PC).

INTRODUCTION

The ability of radar to detect small targets at long range

is one of its most important characteristics. This has led to the

development of systematic procedures which provide an

accurate estimate of the maximum detection range of a radar.

These procedures in the form of curves, work sheets and

computer algorithms can be found in radar handbooks and

Author’s Current Address:

Naval Postgraduate School,Monterey, CA

Manuscript received February 15, 1995

0885-8985/95/ $4.000 1995 IEEE

36

textbooks [l].Computer software packages implementing

these procedures are also available [ 2 ] .

procedures is that they were developed on the basis that the

limitation on the maximum target range is imposed by the

ever present receiver noise. Thus, while they accurately

predict the maximum range of a radar which is exercised

against a balloon-borne sphere, they generally provide

inaccurate results when the detection limitation is based uponcompeting scatterers n the vicinity of the target called clutter.

This has led to the incorporation of a clutter model into the

specificationsby most users of modern radars [3]. In general,

the available procedures and software are inadequate to

provide accurate predictionsof the maximum radar range

when radar clutter is present. A similar conclusion applies to

radars exposed to intentional (i.e,, ECM) or unintentional

interference.

and software is to simulate the detection problem. Most radar

detection problems involving receiver noise, clutter and

jamming can be solved using this method. Accuracy generally

depends upon how well the clutter and interference statistics

can be modeled. Simulation is the preferred method when theclutter or interferencestatistics are non-Gaussian or if the

radar signal processing is nonlinear. In addition, simulation

can be used to evaluate the effect of complex signal

processing or radar waveforms on the radar’s detection range.

One of the deficiencies with the present radar detection

An alternative o using the available radar handbooks

IEEE AESS SystemsMagazine, April 1995



Several questions arise when simulation is being

considered. The first is the practicality of determining ow

error probabilities associated with false alarm statistics. This

generally involves the generationof millions of random

variables and their propagation through the radar’s signal

processor. The second is the difficulty of generating the

required computer code to represent the radar’s detection and

environmental processes and to retrieve the desired statistical

data. A third is the fidelity of radar waveform simulation

necessary to determine the desired radar performance data. Allof these questions relate to the size and capacity of the

computer necessary to perform the simulation and the

computer language used in the simulation.

Fortunately, recent developments n personal

computers (PC’s), increasing their speed and memory

capacity, have made these computers suitable for simulating

radar detection problems. An inherent advantage is that these

machines can be dedicated to a particular problem and ru n for

long periods until the problem is solved. Of course, it is

prudent to estimate the run-time to solve a particular problem.

If this is too long, the general solution is then to reduce the

fidelity of the simulationor to use variance reduction

techniques such as importance sampling [4] to reduce the

number of computer operations required.In addition, a number of software packages have

become available which make programming simulations

relatively easy. One of the more capable is MATLAB. It uses

a higher order language (i.e., programming is done in English

commands), contains commands for most functions used in

radar signal processors, allows the generation of random

variables with various probability distributions, provides

histograms and other statistical data associated with the

signals, and also provides a graphic capability to examine

signals as they propagate through the radar.

SIMULATION FUNDAMENTALS

Determining a radar’s maximum range by simulation

on a digital computer involves a series of experiments

performed on a model of the radar to be evaluated. The

outcome of each experiment is different due to the statistical

nature of receiver noise, clutter, interference and target

fluctuations.However, generally a simple binary decision

defines the outcome of each experiment. If the detection

threshold is exceeded; either a target detection or a false alarm

is declared, depending upon whether a target was simulatedor

not. The probability of detection (Pd) is then the number of

declared targets divided by the number of simulated target

trials while the probability of false alarm (Pfa)is the number

of false target declarations divided by the number of trials

with no target simulated.

The most critical phase of the simulation involvesselection of the models used to represent the system under

evaluation.The two issues are the accuracy and efficiency of

the simulation.

IEEE AESS Systems Magazine, April 1995

I N P U TI I D f CFAR PLRAYETERI N P U T

N O S A M P L E SN K

4 4

1 0 0- D I B T R l B U T E D-URIADLCO +

N O 1 8 1

Q C N E R A T E I N P U T C I N R A T I O

Un1ADt.S * V

OWL B I Q M A L

W O I B B . I N C U T S / ND I 0 T I ) I B U T L DRIAOLC

W O l O t - X

R A T I O

I Y . V I

Fig. 1. Distribution Free CFAR Simulation

Several rules apply to the efficiencyof the simulation.

A general rule is to use analytic formulations wherever

possible for quantities represented by mathematical

relationships (i.e., such as the radar range equation). Also, the

fidelity of the simulation model should be minimized

wherever possible consistent with accuracy requirements.

models selected and the variance of the simulation result.

Random clutter, target and interference models should be

selected to closely emulate the expected environmentor in

some cases, these are provided in the radar specification.The

simulation accuracy is related to the number of trials (n) used

in the simulation. The normalized variance (a ) of the

simulation estimate is given by:

The accuracy of the simulation depends on both th e

2

where p = probability estimated.

accuracy, then n Pfa>> 1.For example, to estimate a Pfa=

loe6, hen the order of lo7 rials would be required.

generate the large number of trials required to obtain accurate

results. When this occurs, then variance reduction techniques

such as importance sampling must be used [4]. Importance

sampling distorts the input distributions n such a way that low

probability events occur much more frequently. The results

are then weighted to compensate for the distortion whileproviding the desired accuracy. Using this technique, the

number of trials can often be reduced by three-to-four orders

of magnitude.

Equation 1 indicates hat to estimate Pfawith high

In complex simulations, t might be impractical to

37



As an example of simulation methodology, consider

the problem of determining the detection characteristics of a

distribution-free CFAR for a steady target in K-distributed

clutter. The simulation is relatively straightforward as

indicated by the flow chart depicted in Figure 1. Solution by

analysis would be very difficult.

The distribution-free CFAR shown in Figure 1 uses a

sliding window (128 cells wide) to determine an adaptive

threshold. It determines the adaptive threshold by first ranking

the 128 signal amplitudes within the window from the lowest

90

80

70

60

scan-to-scan basis. Since the clutter returns decorrelate on a

scan-to-scan basis, while the target returns remain correlated;

it is possible to extract targets using scan-to-scan integration.

The most difficult component to model is the radar

clutter. As the resolution of the radar increases, reflections

from individual wave facets can return high amplitudes called

sea spikes which significantly exceed target returns. The

composite surface model postulates that sea clutter is due to

the compound effect of reflections from the many small wave

facets modulated by the underlying sea swell structure. Each

CNR=20dB

RESOLUTION=8 FEET

-

-

-

-8

Gd4

I I

20

10

n"0 100 200 300 400 500 600 700 800 900 1000

SAMPLE TIME

Fig. 2. Simulation of Sea Spikes

value to the highest value. It then selects that value k ranks

displaced from the highest value. The test cell is then

compared against the adaptive threshold when clutter (Pf,

determination) and clutter plus a target (Pd determination) are

present. The detection statistics are determined by counting

th e number of threshold crossings and dividing by the number

of trials.

of these components responds differently to the use of

frequency agility by the radar.

Although this form of sea clutter representation

accurately represents experimentally determined sea clutter

statistics, its properties are difficult to quantify analytically.

Fortunately, it is relatively straightforward to simulate this

form of sea clutter by emulating its physical model. Using this

approach provides the added advantage that the effects of both

frequency agility and high range resolution on the maximum

detection range are automatically embedded in the model.

To simulate this detection problem, the K-distributed

clutter voltage in receiver noise is simulated by:

SIMULATION EXAMPLE

To illustrate the ease with which complicated radar

detection problems can be simulated, we will describe the

simulation of a radar which functions to detect small targets in

sea clutter. Most radars of this class work on the sameprinciple. They transmit a wide bandwidth providing high

range resolution matched as closely as possible to the physical

dimensions of the target. A rapid scanning antenna (150-300r/min) is used to sample target and clutter returns on a

where RND is a uniformly distributed random variable 0-1, U

is a root gamma (chi) variable and Pn is the noise power. The

38 IEEE AESS Systems Magazine, April 1995



inphase and quadrature components of the interference are

given by

x, = r, * cos (2% * RND)

xe = rn * sin (2% * RND) (3)

resulting in a signal-plus-interference andom variable given

by

(4)

where Vs is the steady or fluctuating target random variable.

series generated for K-distributed clutter and receiver noise.

The spiky nature of the simulated sea clutter is apparent. Also

apparent is the difficulty of detecting small fluctuating targets

whose magnitudes are significantly ess than that of the sea

spikes.

signal processing block diagram depicted in Figure 3. High

range resolution (e.g., 8 feet), matched to the expected target

extent, is transmitted to minimize the clutter patch size.

Pulse-to-pulse requency agility is used to transmit a total

bandwidth of500

MHz through a combination of pulsecompression and frequency agility. Frequency agility is used

to reduce target fluctuation loss by integrating target retums

received within an antenna beam dwell and to decorrelate he

distributed sea clutter component.

Figure 2 depicts a MATLAJ3 simulation of the time

A potential detection strategy is illustrated by the radar

P ULS E - TO - P ULS EFRE O UE NCY

AG IL ITY

INTE G RATE CO NTRO LS P E RFO RMS CO NTRO LSN-PULSES FALSE ALARM SCAN-TO-SCAN OVERAL L FAR

FAST HIGHS CANNING RANG EANTE NNA RE S O LUTIO N RE TURNE D RATE INDE P E DE NT B INARV E O P E R HO UR

WITHIN O F CLUTTE R INTE G RATIO N

BEAM DWELL VELOCIT Y TARGETSANTE NNA D IS TRIBUTIO N O N L INE AR

Fig. 3. Radar Signal Processing BlockDiagram

Final detection is accomplished using a binary

integrator which performs scan-to-scan integration after

CFAR processing. A minimum target exposure time of 5

seconds resulting in 10antenna scans is assumed. Detection

occurs when at least 8 target responses are achieved in the

detection cell within the observation time. Similarly,a false

alarm is declared when at least 8 random noise or sea spikes

fall within the detection cell and a target is not present.

determined for the radar illustrated in Figure 3. A transmitter

average power of 500watts, an antenna gain of 33 dB, a scan

rate of 2 r/second and a Swerling3 target is assumed. Figure 4

illustrates the effect of radar resolution on the ability to detectsmall radar targets at low grazing angles. It assumes that the

Figure 4 depicts the maximum range performance

TARGET RCS SO M)0.6

0.25 1I) FOOT

RESOLUTION

o::l0.1 1FOOT

I RESOLUTION0.05 r

0 1 2 3 4 5 6 7 8 9 10 11 1 2 1 3

RANGE (NMI)

Fig. 4. Small Target Detection Performance

for Various Resolutions

target extent is always less than the radar’s resolution and that

500MHz radar bandwidth is transmitted through a

combination of pulse compression and frequency agility.

Scan-to-scan integration over a 5 second period is employed

to capture the minimum expected target exposure time. The

curve illustrates the advantage of increased resolutionin

detecting small targets whose range resolution extent is less

than the target’s extent.

CONCLUSION

Most real world radar detection problems are too

complex to be solved using the conventional procedures found

in radar handbooks and available software programs. A viable

alternative is to solve these problems using simulation

techniques. Recent advances n PC’s support this trend as does

recent initiatives of users to put a greater reliance on

simulation in lieu of more expensive test and evaluation.

The overall conclusion is that simulation can be used to

solve most radar detection problems. Its use is increasing both

to confirm solutions obtained by standard procedures, and also

to solve complex problems not otherwise solvable by analytic

methods. Rapid advances in computer science and hardware

will further accelerate the use of this important tool.

REFERENCES

[ l ] M.1. Skolni k, “Radar Handbook,” 2nd Ed., M cGraw -Hill, New York, 1990.

[2] D . Barton and W. Barton, “Modem Radar System Analys is Software andUsers Manual,”version 2.0, Artech House, Norwood, MA, 1993.

[3] R. Lay, J. Taylor and G . Bruning, “AR SR-4Unique Solutions to LongRecognized Radar Problems,”IEEE Int. Radar Conf., Washington, D.C. ,May 1990.

[4] R. Mitchell, “Importance Sampling Applied to Simulation of FalseAlarm

Statistics,” EEE Trans. Aerospace and Electronic Systems, Vol. AES-17,No . 1, Jan. 1981 .

IEEE AESS Systems Magazine, April I995 39

~-_ _ _ _ _ _ _ __ _ _ _ ~ ___ _ _ _ - __



D. CurtisSchleher is Professor of Electrical and Computer Engineering at the Naval Postgraduate School. Formerly, he was Vice President of

Engineering at Telephonics Corporation, D irector of Research and Development at AIL Division of Eaton Corporation, and Manager of the

Advanced Development Laboratories at Raytheon Corporation. He is a Fellow of the IEEE and author of four books: MTI Radar, Automatic

Detection and Radar Data Processing, Introduction to Electronic Warfare and M TI and Pulsed D oppler R adar. Dr. Schleher holds BEE, M EE and

Ph.D degrees from Polytechnic University.

INSIDE AESS

NJ Coast Joint AES/EM Chapter

Robert Doto, Speaker, Deputy PM Combat ID

Subject: ‘Battlefield Combat ID Program”

28 November 1994

Demo of Combat ID Display Models

(From left to right):

Seymour Krevsky, Secretary, NJ Coast Joint

AES/EM Chapter;

Robert Doto, Speaker;

Seymour Hirsch of Questech, Inc.;

Samuel Sequer, Chairman NJ Coast Joint

AES/EM Chapter; and

George Hessel, Treasure r, NJ Coast Joint

AES/EM Chapter

Presentation of Plaque to the General

for the Presentation of the Talk

‘State of Cecom”

30 November 1994

at

Gibbs Hall, Fort Monmouth, NJ

(From left to right):

Major General Oho J. Guenther;

NJ Coast Chapter AES/EM Vice Chairman,

John Van Savage

40 IEEE AESS Systems Magazme, April 1995

~ ~- _ _ _ _ ~ _ _ ~~ _ _

solving radar detection problems using simulation

Documents