Computer Generation of Signal, Noise, and Clutter - IEEE Xplore

Synthetic Radar-Signal Environment: Computer Generation of Signal, Noise, and Clutter Levent Sevgi Do~u§ University, Electronics and Communication Eng. Dept. Zeamet Sokak, No 21, Acibadem - Kadikoy, Istanbul - Turkey E-mail: [email protected] .tr, [email protected]

Abstract Computer simulations are widely used in multi-sensor system tests. Algorithms for detection, tracking, classification, identification, intent/threat evaluation, etc., are tested either by using measured real data, or with synthetically generated computer data. Real data is expensive to record and can only be available for simple, sample scenarios. Therefore, a synthetic representation of the radar signal environment is essential. How realistic the synthetic data is depends on the physical and statistical understanding of the radar signal environment, and its stochastic modeling based on random-number generation. This tutorial briefly reviews the generation of a synthetic radar-signal environment. Keywords: Radar; multisensor systems; radar signal analysis; radar signal processing; noise; clutter; SNR; CNR; coherent integration; stochastic modeling; random signals; Doppler effect; Bragg scattering; CFAR detection

1. Introduction with tens or even erformance tests of multi-sensor systems hundreds of targets can only be done in a synthetic environment, so computer simulations are almost mandatory [1-4]. A typical multi-sensor surveillance system is pictured in Figure 1. The country may be Italy, or any other country such as Turkey, Greece, Egypt, England, Germany, Spain, or France in the same (Mediterranean) region, or the USA, Canada, China, Japan, Sri Lanka, India, etc., somewhere else. The mission may be national or international, commercial or military. The aim is to monitor surface and air activity continuously under all weather conditions.

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Finally, how do you do all these with a limited budget and time? Obviously, a real-world test of this problem is almost an impossible task. Therefore numerical simulations are of great importance. Once everything is moved onto a computer, problems related to studying in a non-physical, numerical environment become important. Tables 1 and 2 list fundamental system-level simulation requirements and challenges. Even if these requirements are satis-

Suppose you want to do real tests for the performance of such a system: *How do you design characteristic scenarios? * How many air and surface test targets should you use? * How do you specifyr their routes, and why? * Under what environmental conditions do you repeat tests, and why? * How do you synchronize targets and personnel? * How do you design and switch to plan B when something goes wrong? 192

Figure 1. A typical multi-sensor surveillance system (HF: highfrequency, MtW: microwave, PR: profiling, SAR: syntheticaperture radar, 0CC: operation control center). IEEE Antennas and Propagation Magazine, Vol. 49, No. 5, October 2007

Table 1. System-level simulation requirements. * Understanding and modeling (deterministic or stochastic, mathematical or numerical) of different types of sensors with different sets of parameters (such as power, frequency, coverage, capacity, accuracy, etc.) * Repetitious runs in order to gain confidence and/or establish the sensitivity of the simulator output data on variations in each of the assumed parameters or conditions * A tradeoff between simulation run time and model accuracy in an intelligent way to balance model fidelity and intended applications * A design decision on a choice between online or off-line simulations partially as standalone sensors or subsystems.

Table 2. System-level simulation challenges. optimum number and type DesignAvailable sensors, sensors, optimum locations, etc. Designof Software Communication Test Performance

Detection and tracking algorithms, level of sensor or data fusion, etc. Types of communication, data flow over communication lines, etc. Calibration, verification and validation Performance, success/failure criteria

evaluation_____________

System integration

____

Communication between subsystems, input/output relations, etc.

fled and the challenges are taken care of, there are still important questions left for clarification [5]: * How do you design characteristic/typical realistic test scenarios? * How many times should you repeat these tests? * How do you define evaluation/performance criteria? * How and when do you say the system works successfully? * How do you judge the performance difference between 80% success and 85% success? What does this mean? Keeping in mind all of these issues and questions, this short tutorial aims to present stochastic modeling (random generation) of the signal environment.

2. Radar Signal Environment A radar signal usually contains echoes from objects under investigation (targets), unwanted objects' echoes (clutter), noise, IEEE Antennas and Propagation Magazine, Vol. 49, No. 5, October 2007

and other interfering signals [6, 7]. All fluctuate randomly with time, so the signal environment is stochastic. Usually, the target signal is embedded within a background (noise + clutter) signal, and/or obscured by interference: i.e., the target signal's power level is much less than the others. The process of extracting target information from the total echo is called (stochastic) signal processing, and it is performed via powerful, intelligent algorithms. The power of these algorithms comes from (1) the physical and statistical understanding of the target, noise, clutter, and interfering signals; and (2) computer generation of the synthetic signal environment. The first step is to generate random numbers with a probability density function (PDF) that represents the statistical characteristics of the physical event.

2.1 Random Number Generation Random processes with different statistical characteristics (such as PDF, mean, variance, etc.) are numerically represented by using random-number generation [8]. The four well-known probability distributions in radar and communication simulations are the uniform, Gaussian, Raleigh, and exponential distributions. Table 3 lists short MATLABI scripts that create an array of random numbers that obey these four distributions. Note that an array of random numbers with Gaussian, Raleigh, and exponential distributions can be generated using the uniform distribution. This is illustrated in Table 3. In other words, all other distributions can be realized using the rand command. The rand command generates random numbers uniformly distributed between zero and one. A transformation of a + (b - a)rarnd is required if random numbers uniformly distributed between a and b are of interest. Similarly, Raleigh-distributed random numbers, with standard deviation o, can be generated using the rand command via V2o' n (rand) transformation [8]. Similar to rand, a random array with a Normal distribution can be generated using the randn command. A normal distribution is a Gaussian distribution with zero mean and unit standarddeviation. A normally distributed random array and its PDF are given in Figure 2 (on the right and left, respectively). The PDF of a random array can be plotted directly by using the AMTLAB hist () comTable 3. MA TLAB scripts for random-number generation. function out = randUNIFORM(a~b,n) for k =1 :n out(k) =a + (b-a) * rand; End function out = randGAUSS(mean,var~n) for k =1 :n out(k) =sqrt(var)*randn + mean; End function out = randRALEIGH(var~n) for k = 1:n out(k) = sqrt(var)*sqrt(-2*log(rand)); End function out = randEXPO(a,n) fork= 1:n out(k) =-log(rand)/a; End

Crates an n-element uniformly distributed random variable between "a7' and "b." Creates n-element Gaussian random variable with mean "mean"' and variance "var." Creates ni-element Raleigh random variable with variance "'var."1 Creates ni-element exponentially distributed random variable with parameter ,a, 193

X

KVoltage

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[VI

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A

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V I V

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I

Randn() Sample No

Figure 2. A normally distributed random array and its histogram. mand. The Gaussian PDF is maximum at zero value and falls off away from zero, as shown (rotated 90') on the left. Any Gaussian random array with a given mean and standard deviation may then be produced by shifting and re-scaling, as given in the randGAUSS function in Table 3. The reader may produce similar figures using this three-line MATLAB script: x =randn(1,5000); plot(x); hist(x). Here, the size of the array with normal distribution is 5000.

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Figure 3. A synthetically generated sinusoidall signal plus noise (SNR = 10 dB): solid line: uniform noise; dashed line: Gaussian noise.

2.2 Noise Generation Noise is a random signal and is handled in a stochastic manner [9]. Its amplitude-distribution characteristics, average value, deviation, frequency characteristics (power spectrum), etc., must be well understood when dealing with communication/radar theory. The distinguishing characteristic of the noise is that it is a sampleto-sample (pulse-to-pulse) uncorrelated signal (usually called while or Gaussian noise). The signal correlation in the time domain and the power spectrum in the frequency domain form a Fourier pair. This means that the autocorrelation function of a random array, e.g., as generated by the rand command, will be a delta function. A delta function in the time domain corresponds to a constant value in the frequency domain (noise is present at all frequencies). Therefore, the wider the (receiver) bandwidth, the higher the noise level in radar receivers.

Figure 4. Signal plus noise for SNR = 0 dB: dashed line: single generation; solid line: over-sampled and averaged.

Table 4 lists a short MA TLAB script that generates a 192element array containing a sinusoidal signal between 0 and 6Z, and Gaussian-distributed noise with a SNR (signal-to-noise ratio) of 10 dB. The signal level is set to 0 dB (1 W).

Table 5. The MA TLAB AWGN command.

90

plot(Y,'r--'); hold on; plot(Sigtot) xlabel('Sample No'); ylabel('Signal+Noise Voltage [V]')

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150

AwGN(X,SNR)

Adds white Gaussian noise to X. The SNR is in dB. The power of X is assumed to be 0 dBW. If X is complex then AWGN adds complex noise.

AwGN(X,SNR,XPOW)

When XPOW is numeric, it represents the signal power in dBW. When SIGPOWER is "measured," AWGN measures the signal power before adding noise.

Table 4. MATLAB script for signal plus noise generation. clear all; etc; SNRdB input (SNR: Signal to noise ratio [dB]') SNR=10^(SNRdB/10); Vs sqrt(2); Psignal=0.5*VsA2; X =Vs*sin(0:.pi/32:6*pi); % Signal array %Noise Power Pnoise=Psignal/SNR; %Noise Voltage Vn--sqrt(Pnoise); [nn nSample]=size(X); % Random numbers Nk-randn(l ,nSample); %Noise array Noise=Vn*Nk; % Total signal Sigtot--X+Noise;

120

Sample No

Example: X sqrt(2)*sin(0:piI8:6*pi); Specifies the power of X to be 0 dBW and adds noise to produce Y =AwGN(X, 13,0); SNR = 13dB. IEEE Antennas and Propagation Magazine, Vol. 49, No. 5,October 2007

Fignre 3 shows the time variation of the signal plus noise for SNR =10 dB. Solid and dashed curves correspond to uniformly and normally distributed noise, respectively. Note that signal plus noise for a given SNR can be performed with a single MATLAB command, AWGN. Table 5 explains the use of the AWGN command. The noise is uncorrelated, meaning that it can be reduced or filtered out by simply over-sampling and averaging. This is illustrated in Figure 4. Roughly speaking, the SNR increases by a factor of -,[I--, where in is the number of samples averaged (in this example, the SNR is improved by 10 dB).

2.3 Signal Generation A useful signal can be generated as explained above in Section 2.2 if the carrier signal of a communication/radar system is of interest. When the radar cross section (RCS) of a radar target is of interest, there may be spatial or temporal fluctuations (or both), which differ from target to target [6]. The fluctuations may be slow (correlated over seconds, even minutes, e.g., a tanker ship navigating on a calm ocean) or fast (correlated only over milliseconds, e.g., a maneuvering high-speed fighter aircraft). The fluctuating RCS values may be distributed, or they may accumulate around a few dominant scatterers. These situations are categorized in terms of the PDFs, and are grouped into three sets [5-7]: * Steady targets, such as mountains, buildings, etc. (Type 0) * A group of small scatterers (without a dominant contribution): (slow, Type 1, and fast, Type 2) * A group of scatterers with a few dominant scatterers: (slow, Type 3, and fast, Type 4)

signals, so elimination by just averaging (post-detection integration, as done for noise) is not possible. Usually, clutter elimination is performed in the frequency domain. Land clutter occupies a very low frequency range, around zero Doppler frequency. On the other hand, ocean clutter has different Doppler characteristics at different radar frequencies. Ocean clutter is the result of the interaction of the radiated electromagnetic wave with ocean waves [5-7], and has a quite interesting Doppler spectrum. The dominant contribution is produced by scatter from ocean waves having a wavelength half that of the radar wavelength, and moving radially toward and away from the radar site. This first-order resonant scatter results in two dominant peaks, called Bragg lines [10-12]. These occur at two distinct Doppler frequencies, fb =± rglrA 0. 102JfM., in Hz, corresponding to the velocities of the propagation of these ocean waves [10]. Here, A is the radar wavelength, f is the radar frequency in MHz, and g is the acceleration due to gravity. A typical ocean spectrum is pictured in Figure 5. Ocean parameters and their effects on the spectra are A: surface wind direction, B: radial current, C,D: wind speed and E,F: scalar wave spectrum. Ocean spectra are also used in inverse problems, and surface-current and wind maps are prepared, especially near economically important harbors and narrow straits (see, for example, [11 ]). Ocean clutter is modeled as an ensemble of N complex elements that have a specified amplitude distribution and are pulse-to-pulse correlated. This correlation is established through imposition of a specified shape of the power spectrum. A few available empirical ocean-wave models are the NeumannPierson spectrum, the Phillipsi spectrum, the Pierson-Moskowitz spectrum, and JONSWAP [10, 12, 13]. The spectral density (power spectru~m), S,, (w), of a stationary random process , pu(t), and its correlation function, K. (r) , are Fourier pairs [9]:

These types are also called the Swerling types (SW), and determine the radar waveform as well as the echo-integration process in radar receivers. For example, since SW 1 and SW 3 targets (which have a decorrelation time of seconds) are sample-to-sample stationary, pulse-to-pulse coherent integration can be applied.

S,,,(wo)

f Sp (co) e'dco.

fJKý(r)e-Jtudt++Kp,(r)

(1) For example,

2.4 Clutter Generation

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2~ Cali

S,(C) r(0 +a Clutter is a word used to describe all unwanted echoes in a radar receiver [6]. Unlike noise, which inherently is present at the receiver, clutter is a target-like echo signal that comes from many small scatterers, such as rain droplets, birds, ocean waves, terrain irregularities, vegetation, aurora, meteors, etc. It is therefore parameter- and range-dependent. When clutter power dominates over noise, the radar is said to operate in a clutter-limited condition. Unwanted echoes usually occur as distributed clutter, as surface clutter (such as land and sea echoes), or as volume clutter (such as rain, chaff, etc.). They depend on many factors, such as the type of the terrain observed, the direction of illumination and observation, the radar wavelength, and the polarization. For example, ocean clutter (usually described as RCS density) depends on ocean-wave height, wind characteristics (direction and speed), and wave direction [6]. Land clutter depends on soil type, surface roughniess, foliage cover, etc. Both are sample-to-sample coherent IEEE Antennas and Propagation Magazine, Vol. 49, No. 5, October 2007

Sea wave spectra

-1Hz

42n

1)u.z Do~pper shift

(2)

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f

1Hz

Figure 5. A typical HF radar ocean-wave spectrum [5]. 195

Once the input parameters for this example (ar, a, and At) are supplied, signal coherency can be imposed by using either of the expressions in Equation (2).

0.05 Hz bandwidth around 0.25 Hz; Bragg peaks, and a Swerling11-type fluctuating target echo with a 5 dB fluctuation margin and a Doppler shift of 0.75 Hz.

The generation of a Gaussian stationary process with a correlation function given by Equation (2) starts with the generation of the first normally distributed random number, z0 . This could be done in MATLAB, by using either the randn or rand commands:

The Bragg peaks (fb ýý±0. 1021ffM,ýý) around ±0.25 Hz correspond to the radar carrier frequency of 6 MiHz. Assume this carrier frequency is removed at the front end of the receiver, after a demodulation. The frequency spectrum should cover ±0.25Hz; of the Bragg peaks and 0.75 Hz; of Doppler shift caused by the radial component of the moving target. Therefore, the maximum frequency (fmx may, for example, be set to ±1.0Hz or ±2.0Hz. For N =512, these two values yield frequency resolutions of Af ;:ý0.004 Hz and Af ; 0.008 Hz, respectively. The signal integration time (i.e., the recording period) is inversely proportional to the frequency resolution, and is equal to (T = l/Af ) 250s for Af --0.004 Hz (see [14] for a DFT and EFT tutorial).

z0 =

2 I(rand) cos (27r rand),

(3a)

or (3b)

o =randn.

The first clutter sample is then produced by imposing the correlation via

The other samples, Zk via zk

(4)

0.

l-e =az

flk, k =

1,2....N, are obtained iteratively

-2 In (rand) cos(27r rand),

(5)

2 eI-_A Zk.

(6)

pk = ea Pk1I+a I

An alternative procedure for the clutter generation is as follows [7]: Two Gaussian-distributed unit-amplitude phasor as generated are g2k* 91k, arrays,

* The Gaussian-shaped power spectrum, Sp~ (A),~ of the ocean clutter around the dominant Bragg frequencies is generated at KFFT points (at fi ,f2 f,,, where f,,, is the maximum frequency in ... the Doppler spectrum). * The width of the Gaussian-shaped power spectrum is related to the ocean-wave height. The ensemble of KFFT elements, Xk, is generated via Xk = 4

SX(f) ,(k=l, 2,..,KFFT).

* The inverse Fourier transform is utilized via an FFT to obtain the complex elements p t

3. Total Radar Signal The quiz in the August 2007 issue was about the specification of the threshold level for a constant-false-alann-rate (CFAR) detector, if the total signal recorded contains a normally distributed, uncorrelated environmental noise with 13 dB SNR, a coherent ocean clutter having 30 dB CNR with a Gaussian-type amplitude distribution and a Gaussian-shaped frequency spectrum with 196

The target is of Swerling-Il type, with a fluctuation margin of 5 dB. A 5 dB power fluctuation corresponds to approximately 2.5 V fluctuations in amplitude (i.e., voltage). A Swerling-il type of target means a target with small scatterers, without a dominating scatterer. Therefore, either a uniform or Gaussian distribution may be used (actually, this example belongs to a high-frequency radar, where the radar signal, i.e., electromagnetic waves, interact with a target as a whole. It is in the resonance RCS regime. Therefore, target-amplitude fluctuations may be neglected. However, for microwave radars, i.e., for the optical RCS regime, target fluctuations must be taken into account). The total received echo signal is synthetically generated as follows: * Produce the environmental noise first. Produce an array of N elements (e.g., N = 512) of normally distributed noise samples. Set the noise power (i.e., the variance of the array) to a specified value (e.g., 30d0). * Add N discrete target samples using a sinusoidal signal: Vmnsin (27rfDoppjrnAz') 2 for n=l1,2 , 3 ,..,51 and At = T1512.

* Normalize the array as explained in Table 3 in order to obtain a SNR of 13 dB. * Generate an N-element clutter array using either of the methods explained in Section 2.4. Do this either directly in the time domain, using the autocorrelation function, or in the frequency domain, using a specified power spectrum. Form two Gaussianshaped power spectra around the two Bragg peaks. * Normalize the array as explained in Table 3, and set the CNR to 30 dB. Figures 6 and 7 present the total signal environment in the time and frequency domains, respectively. Since SNR=13 dB and CNR - 30 dB, the target is embedded in the clutter signal. As observed in Figure 6, it is impossible to detect the target in the time domain, in this case. Therefore, the detection procedure is carried IEEE Antennas and Propagation Magazine, Vol. 49, No. 5, October 2007

out in the frequency domain, as observed in Figure 7 (note that the horizontal scale is normalized to the Brag Frequency).

Voltage [V] 3

CNR=30 dB SNR=13 dlB

2-

In Figure 7, the two Bragg peaks around ±1 and the target around ±3 (normalized frequencies), respectively, are clearly identified. If the CFAR threshold in the detection algorithm is set to around -15 dB (let's say), the target will be detected. Note that there may be afew ghost detections also, because of the Gaussian

1

o0fl

WIH

noise (e.g., the noise sample denoted with a question mark will be falsely recognized by the detection algorithm). Fortunately, noise is

1

uncorrelated from sample-to-sample as well as from spectrum-todetection decision is made after averaging a few Doppler spectra. This is illustrated in Figure 8. Although Figures 7 and 8 belong to

-2-

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the same parameter sets, the ghost target in Figure 7 does not

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45aperiFgue8

Time [s]aperiFiue8 Figure 6. Signal plus noise plus clutter as a function of time (I channel).

On the other hand, Bragg peaks and ocean clutter are present at all Doppler spectra, so spectral averaging will not work for the

elimination of the clutter. Targets with slow radial velocities (i.e., low Doppler shifts) fall in this high-clutter region, which makes them invisible [3,5].

Doppler Spectrum [dB]______ 10

Multi-sensor system simulation necessitates synthetic genera-

of a radar-signal environment that is as realistic as possible.

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This can only be achieved by a good understanding of the physical as well as statistical behaviors of the radar target, noise, clutter, and

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interference. There are no generally accepted performance-evaluacriteria for the tests of multi-sensor systems. Therefore, not

Nise loortion

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only the design of a simulator design but also its application are challenges.

Itoreal

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4. References

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Normalized Frequency [f/f,3] Figure 7. A typical HF-radar Doppler spectrum (SNR CNR = 30 dB, noise floor was set to -30 dB).

=

13 dB,

1. N. Ince, E. Topuz, E. Panayirci, and C. Isik, Principles of Integrated Maritime Surveillance Systems, Boston, Kluwer Academic,

2000. 2. L. Sevgi, A. M. Ponsford, and H. C. Chan, "An Integrated Manitime-Surveillance System Based on Surface-Wave HF Radars, Part 1: Theoretical Background and Numerical Simulations," IEEE Antennas and PropagationMagazine, 43, 4, August 2001, pp. 28-

Doppler Spectrum [dB] 10

Brag-- pak: ~Target

43.

0

3. A. M. Ponsford, L. Sevgi, H. C. Chan, "An Integrated MaritimeSurveillance System based on Surface-Wave HF Radars, Part 2: Operational Status and System Performance," IEEE Antennas and PropagationMagazine, 43, 5, October 2001, pp. 52-63.

_10-20-

.--

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4L.Sevgi, "Target Reflectivity and RCS Interaction in Integrated Maritime Surveillance Systems Based on Surface-Wave HF Radars," IEEE Antennas and PropagationMagazine, 43, 1, Febru-

Noise floor ------

00 1 pp.36-5 1.

-40-ary

Gaussian Noise - -3

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0 -1 Noralze

1

2

Frqec [f/f]-

3

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Figure 8. Another spectrum with the same parameters as given in Figure 7. IEEE Antennas and Propagation Magazine, Vol. 49, No. 5, October 200719

5. L. Sevgi, Chapter 1: Radars, in Rajeev Banisal (ed.), Engineering Electromagnetics: Applications, Boca Raton, CRC Press

Taylor &Francis Group, 2006.

6. M. L. Skolnik, Introduction to Radar Systems, New York, McGraw Hill, 1985. 197

7. L. Sevgi, Complex Electromagnetic Problems & Numerical Simulation Approaches, New York, IEEE Press/John Wiley & Sons, 2003. 8. D. C. Montgomery and G. C. Runger, Applied Statistics & Probabilityfor Engineers, New York, John Wiley & Sons, 2003. 9. S. Haykin and M. Moher, Introduction to Analog & digital Communications, Second Edition, New York, John Wiley & Sons, 2007. 10. D. E. Barrick, "Theory of HF and VHF Propagation Across the Rough Sea, 1, The Effective Surface Impedance for a Slightly Rough Highly Conducting Medium at Grazing Incidence," Radio Science, 6, 5, 197 1, pp. 5 17-526.

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11. H. Gunther et al., "The EuroROSE Project," Proceedingsof the 16th International Conference of the American Meteorological Society on "InteractiveInformation and Processing Systems (7IPS) for Meteorology, Oceanography and Hydrology," California, USA, January 2000, pp. 214-217. 12. B. Kinsman, Wind Waves, Englewood Cliffs, NJ, Prentice Hall, 1965. 13. 0. M. Phillips, Dynamics of the Upper Ocean, London, Cambridge University Press, 1966. 14. L. Sevgi, "Numerical Fourier Transforms: DFT and FFT," IEEE Antennas and PropagationMagazine, 49, 3, June 2007, pp. 238-243 l

IEEE Antennas and Propagation Magazine, Vol. 49, No. 5, October 2007