Radar systems

1. Radar systems Some of this material is derived from Microwave Remote Sensing—Vol II, by Ulaby, Moore, and Fung • Chris Allen (callen@eecs.ku.edu) • Course website URL people.eecs.ku.edu/~callen/823/EECS823.htm

2. Outline • Radar measurements Radar equation Range resolution Doppler shift and velocity resolution Signal fading Spatial discrimination • Radar system types Side-looking airborne radar (SLAR) Synthetic-aperture radar (SAR) Inverse SAR Interferometers Scatterometers • Scattering mechanisms and characteristics

3. Radar system • Like a radiometer, radar systems use very sensitive receivers to output a voltage that contains information about the target. • Unlike a radiometer, the signal that the radar receives does not originate from the target (emission), rather it is a scattered version of a signal transmitted by the radar. • Therefore the characteristics of the signal received by radar may be fundamentally different from the radiometer signal.

4. Radar system • Radar is an acronym for radio detection and ranging. • Detection addresses the question of whether a target is present or changing. • Ranging, the ability to measure the range to a target, is possible as radar provides its own illumination (the transmitter) unlike a radiometer that provides no range information.

5. Radar system • The transmitted radar signal may be coherent, polarized, and modulated in frequency, phase, amplitude, and polarization. In addition, the transmit antenna determines the spatial distribution of the transmitted signal. • While radar system measures only the received signal voltage as a function of time, signal analysis enables the extraction of new information about the target including location, velocity, composition, structure, rotation, vibration, etc. • Radar images of 3.5-km asteroid 1999 JM8 at a range of 8.5x106 km with ~ 30-m spatial resolution

6. Radar equation • Extraction of useful information using signal analysis requires that the signal be discernable from noise, interference, and clutter. • Noise usually originates inside the receiver itself (e.g., receiver noise figure) though may also come from external sources (e.g., thermal emissions, lightning). • Interference is another coherent, spectrally-narrow emission that impedes the reception of the desired signal (e.g., a jammer). [May originate internal or external to radar] • Clutter is unwanted radar echoes that interfere with the observation of signals from targets of interest.

7. Radar equation • Received signal power, Pr, is an essential radar parameter. • The radar range equation, used to determine Pr, involves the geometry and system parameters. • Bistatic geometry

8. Radar equation • The power density incident on the scatterer, Ss, is Pt is the transmit signal power (W) Gtis the transmit antenna’s gain in the direction of the scatterer Rt is the range from the transmitter to the scatterer (m) • The power intercepted by the scatterer, Prs, is Ars is the scatterer’s effective area (m2) • The power reradiated by the scatterer, Pts, is fa is the fraction of intercepted power absorbed

9. Radar equation • The power density at the receiver, Sr, is Gts is the gain of the scatterer in the direction of the receiver Rr is the range from the receiver to the scatterer, (m) • The power intercepted by the receiver, Pr, is Ar is the effective area of the receiver aperture, (m2) • Combining the pieces together yields

10. Radar equation • The terms associated with the scatterer may be combined into a single variable, , the radar scattering cross section (RCS). • The RCS value will depend on the scatterer’s shape and composition as well as on the observation geometry. • For bistatic observations • where (q0, f0) = direction of incident power (qs, fs) = direction of scattered power (p0, ps) = polarization state of incident and scattered fields

11. Radar equation • In monostatic radar systems the transmit and receive antennas are collocated (placed together, side-by-side) such that 0 = s, 0 = s, and Rt = Rr so that the RCS becomes • The radar range equation for the monostatic case is • Monostatic geometry

12. Radar equation • If the same antenna or identical antennas are used in a monostatic radar system then • and recognizing the relationship between A and G • we can write • Monostatic geometry

13. Radar equation • Receiver noise power, PN k is Boltzmann’s constant (1.38  10-23 J K-1) T0 is the absolute temperature (290 K) B is receiver bandwidth (Hz) F is receiver noise figure • Signal-to-noise ratio (SNR) is • may be expressed in decibels

14. Radar range equation example • Example Radar center frequency, f = 9.5 GHz Transmit power, PT = 100 kW Bandwidth, B = 100 MHz Receiver noise figure, FREC = 2 (F = 3 dB) Antenna dimensions, 1 m x 1 m(square aperture) Range to target, R = 20 km (12.5 miles) Target RCS,  = 1 m2(small aircraft or boat) • Find the Pr , PN , and the SNR First derive some related radar parameters Wavelength, = 3.15 cm Antenna gain, G = 4A/2(assuming  = 1)A = 1 m2G = 12,600 or 41 dBi

15. Radar range equation example • Find Pr Solve in dB • Pr(dBm) = Pt(dBm) + 2G(dBi) + 2  (dB) + (dBsm) – 3  4(dB) – 4  R(dB) Pt(dBm) = 80 G(dBi) = 41 (dB) = -15 (dBsm) = 0 4(dB) = 11 R(dB) = 43 Pr(dBm) = -76 dBm or 25 pW • Find PN Solve in dB • PN(dBm) = kT0(dBm) + B(dB) + F(dB) kT0(dBm) = -174 B(dB) = 80 F(dB) = 3 PN(dBm) = -91 dBm or 0.8 pW • Find SNR SNR = – 76 – (– 91) = 15 dB or 31

16. Radar range equation example • Several options are available to improve the SNR. • Increase the transmitter power, Pt Changing Pt from 100 kW to 200 kW improves the SNR by 3 dB • Increase the antenna aperture area, A, and gain, G Changing A from 1 m2to 2 m2 improves the SNR by 6 dB • Decrease the range, R, to the target Changing R from 20 km to 10 km improves the SNR by 12 dB • Decrease the receiver noise figure, F Changing F from 2 to 1 improves the SNR by 3 dB • Decrease the receiver bandwidth, B Changing B from 100 MHz to 50 MHz improves the SNR by 3 dB only if the received signal power remains constant • Change the operating frequency, f, and wavelength,  Changing f from 9.5 GHz to 4.75 GHz degrades the SNR by 6 dB Changing f from 9.5 GHz to 19 GHz improves SNR by 6 dB

17. Range resolution • The radar’s ability to discriminate between targets at different ranges, its range resolution, rR or r or r, is inversely related to the signal bandwidth, B. where c is the speed of light in the medium. • The bandwidth of the received signal should match the bandwidth of the transmitted signal. A receiver bandwidth wider than the incoming signal bandwidth permits additional noise with no additional signal, and SNR is reduced. A receiver bandwidth narrower than the incoming signal bandwidth reduces the noise and signal equally, and the radar’srange resolutionis reduced. • Therefore to achieve an rR of 1.5 m in free space requires a 100-MHz bandwidth in both the transmitted waveform and the receiver bandwidth.

18. Velocity resolution • The signal from a target may be written as • and the relative phase of the received signal,  • A target moving relative to the radar produces a changing phase (i.e., a frequency shift) known as the Doppler frequency,fD • where vr is the radial component of the relative velocity. • The Doppler frequency can be positive or negative with a positive shift corresponding to target moving toward the radar.

19. Velocity resolution • The received signal frequency will be • Example • Consider a police radar with a operating frequency, fo, of 10 GHz. ( = 0.03 m) • It observes an approaching car traveling at 70 mph (31.3 m/s) down the highway. (v = -31.3 m/s) • The frequency of the received signal will be • fo – 2v/ = fo+ 2.086 kHz or 10,000,002,086 Hz • Another car is moving away down the highway traveling at 55 mph (+24.6 m/s). The frequency of the received signal will be • fo – 2v/ = fo– 1.64 kHz or 9,999,998,360 Hz

20. Velocity resolution • ^ • uR = u cos(q) • fD = 2 u cos(q) / l • Given the position, P, and velocity, u, both the radar and the target, the resulting Doppler frequency can be determined • The ability to resolve targets based on their Doppler shifts depends on the processed bandwidth, B, that is inversely related to the observation (or integration) time, T • Instantaneous position and velocity • Relative velocity, u • Radial velocity component

21. Radar equation for specular surfaces • Reflection from a smooth, specular surface produces a significantly different received power level than backscattering. • For a sufficiently large specular surface area, the scattering characteristics involves a delta function (x) • where a is a non-zero value. • For a monostatic radar configuration, the radar cross section of a specular surface is • where sp is the Fresnel power reflection coefficient and  is the incidence angle at the specular surface.

22. Radar equation for specular surfaces • Furthermore due to the properties of the specular surface the receiver essentially “sees” an image of the transmitter at a distance of 2R. • This configuration can be modeled as a point-to-point communication link (i.e., R2 dependence instead of an R4). • For this special case the radar range equation becomes

23. Radar equation for specular surfaces • Using this concept, large surfaces of calm (still) water may be used to measure the antenna’s radiation pattern by varying the antenna’s orientation relative to the specular surface. • How large of an area is required to implement this concept? • The flat area must be two or more Fresnel zones across.

24. Radar equation for specular surfaces • How large of an area is required to implement this concept? • The flat area must be two or more Fresnel zones across. • So what is a Fresnel zone? The set of points on the surface such that the path difference from the illumination source and the observing point varies by no more than /2. The first Fresnel zone is bounded by an ellipse on the surface centered on the specular point.Subsequent Fresnel zones are also elliptical and the average phase of radiation from each zone bounded by neighboring ellipses will differ from the adjacent zone by /2. • The radius, A, of the 1st Fresnel zone is

25. Radar equation for extended targets • The preceding development considered point target with a simple RCS, . • The point-target case enables simplifying assumptions in the development. Gain and range are treated as constants • Now consider the case of extended targets including surfaces and volumes. • The backscattering characteristics of a surface are represented by the scattering coefficient, , • where A is the illuminated area.

26. Radar equation for extended targets • For an extended target there are multiple independent, randomly located scatterers that each contribute to the overall backscattered signal. • While the amplitude of the scatterers may be comparable, the received phase of these scatterers are strongly dependent on the observation geometry and the observation wavelength (frequency). • Slight changes in observation geometry or wavelength will produce a different interference of the signals from these scatterers.

27. Radar equation for extended targets • To analyze signal characteristics we first make some simplifying assumptions many point scatterers randomly located no single scatterer dominates the return • The received signal (E field) is the summation of the individual fields from each scatterer • where i is the phase associated with scatterer i Ri is the exact distance from the radar to scatterer i • Since the scatterers are randomly located, the 2kRi term represents a random phase thus producing noise-like characteristics.

28. Radar equation for extended targets • As with noise, we can treat this as an incoherent process and therefore we will focus on the average received power, Pr • where Pri is the average power from each scatterer, or • where i is the RCS of each individual scatterer. • In many cases Gi and Ri will be constant over the illuminated area resulting in

29. Radar equation for extended targets • The area of illumination to be used in the analysis is dependent on the system characteristics. • Different illumination areas result depending on whether the system is beam limited, pulse (or range) limited, Doppler (or speed) limited, or a combination of these.

30. Radar equation for extended targets

31. Radar equation for extended targets • For homogeneous extended area targets (e.g., grass, bare soil, forest, water, sand, snow, etc.)  constant (though still dependent on , , and polarization). • Substituting this relationship leads to • where A is determined by the system’s spatial resolution. • The scattering coefficient, , contains target information. Soil moisture Surface wind speed and direction over water Ground surface roughness Water equivalent content of a snowpack • Therefore the accuracy and precision of  measurements are important.

32. Accuracy and precision • As we saw earlier with radiometers, measurement accuracy and precision are essential for effective remote sensing applications. • In the context of measuring the target’s backscattering coefficient, , accuracy will be achieved through calibration and measurement uncertainty will determine the precision. • An understanding of the factors affecting measurement uncertainty is required before steps to reduce the uncertainty can be taken. • Assuming an acceptable signal-to-noise ratio is achieved (and sources of interference and clutter have been reduced to acceptable levels) the primary factor affecting uncertainty in  measurement is signal fading.

33. Signal fading • For extended targets (and targets composed of multiple scattering centers within a resolution cell) the return signal (the echo) is composed of many independent complex signals. • The overall signal is the vector sum of these signals. • Consequently the received voltage will fluctuate as the scatterers’ relative magnitudes and phases vary spatially. • Consider the simple case of only two scatters with equal s separated bya distance d observed at a range Ro.

34. Signal fading • As the observation point moves along the x direction, the observation angle  will change the interference of the signals from the two targets. • The received voltage, V, at the radar receiver is • where • The measured voltage varies from 0 to 2, power from 0 to 4.Single measurement will not provide a good estimate of the scatterer’s . • Note: Same analysis used for antenna arrays.

35. Fading statistics • Consider the case of Ns independent scatterers (Ns is large) where the voltage due to each scatterer is • The vector sum of the voltage terms from each scatterer is • where Ve and  are the envelope voltage and phase. • It is assumed that each voltage term, Vi and i are independent random variables and that i is uniformly distributed. • The magnitude component Vi can be decomposed into orthogonal components, Vxand Vy • where Vxand Vy are normally distributed.

36. Fading statistics • The fluctuation of the envelope voltage, Ve, is due to fading although it is similar to that of noise. • The models for fading and noise are essentially the same. • Two common envelope detection schemes are considered, linear detection (where the magnitude of the envelope voltage is output) and square-law detection (where the output is the square of the envelope magnitute). • Linear detection, VOUT = |VIN| = Ve • It can be shown that Ve follows a Rayleigh distribution • where 2 is the variance of the input signal

37. Fading statistics (linear detection) • For a Rayleigh distribution • the mean is • the variance is • The fluctuation about the meanis Vac which has a variance of • So the ratio of the square of the envelope mean to the variance of the fluctuating component represents a kind of inherent signal-to-noise ratio for Rayleigh fading.

38. Fading statistics (linear detection) • An equivalent SNR of 5.6 dB (due to fading) means that a single Ve measurement will have significant uncertainty. • For a good estimate of the target’s RCS, , multiple independent measurements are required. • By averaging several independent samples of Ve, we improve our estimate, VL • where • N is the number of independent samples • Ve is the envelope voltage sample

39. Fading statistics (linear detection) • The mean value, VL, is unaffected by the averaging process • However the magnitude of the fluctuations are reduced • And the effective SNR due to fading improves as N • As more Rayleigh distributed samples are averaged the distribution begins to resemble a normal or Gaussian distribution.

40. Fading statistics (square-law detection) • Square-law detection, Vs = Ve2 • The output voltage is related to the power in the envelope. It can be shown that Vs follows an exponential distribution • Again the mean value is found • and the variance is found(note that ) • Again for a single sample measurement yields a poor estimate of the mean. • where 2 is the variance of the input signal

41. Fading statistics (square-law detection) • An equivalent SNR of 0 dB (due to fading) means that a single Vs measurement will have significant uncertainty. • For a good estimate of the target’s RCS, , multiple independent measurements are required. • By averaging several independent samples of Vs, we improve our estimate, VL • where • N is the number of independent samples • Vs is the envelope-squared voltage sample

42. Fading statistics (square-law detection) • The mean value, VL, is unaffected by the averaging process • However the magnitude of the fluctuations are reduced • And the effective SNR due to fading improves as N. • As more exponential distributed samples are averaged the distribution begins to resemble a 2(2N)distribution.For large N, (N > 10), the distribution becomes Gaussian.

43. Independent samples • Fading is not a noise phenomenon, therefore multiple observations from a fixed radar position observing the same target geometry will not reduce the fading effects. • Two approaches exist for obtaining independent samples change the observation geometry change the observation frequency (more bandwidth) • Both methods produce a change in  which yields an independent sample. • Estimating the number of independent samples depends on the system parameters, the illuminated scene size, and on how the data are processed.

44. Independent samples • In the range dimension, the number of independent samples (NS) is the ratio of the range of the illuminated scene (R) to the range resolution (rR)

45. Independent samples • When relative motion exists between the target and the radar, the frequency shift due to Doppler can be used to obtain independent samples. • The number of independent samples due to the Doppler shift, ND, is the product of the Doppler bandwidth, fD, and the observation time, T • The total number of independent samples is • In both cases (range or Doppler) the result is that to reduce the effects of fading, the resolution is degraded.

46. Independent samples • N = 1 • N = 10 • N = 50 • N = 250

47. Spatial discrimination • Consider an airborne radar system flying at a constant speed along a straight and level trajectory as it views the surface beneath. • For a point on the ground the range to the radar and the radial velocity component can be determined as a function of time. • Radar position = (0, vt, h), Target position = (xo, yo, 0), Range to target, R(t)

48. Example radar data icebergs in open water

49. Spatial discrimination • Now solve for R and fD for all target locations and plot lines of constant range (isorange) and lines of constant Doppler shift (isodops) on the surface.

50. Spatial discrimination • Isorange and isodoppler lines for aircraft flying north at 10 m/s at a 1500-m altitude.R = 2 m, V = 0.002 m/s, fD = 0.13 Hz @ f = 10 GHz,  = 3 cm