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

Outline Radar measurements Radar system types 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

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.

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.

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

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.

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

Radar equation The power density incident on the scatterer, Ss, is Pt is the transmit signal power (W) Gt is 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

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

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

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

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

Radar equation Receiver noise power, PN Signal-to-noise ratio (SNR) is 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

Radar range equation 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 m2 G = 12,600 or 41 dBi

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 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

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 m2 to 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

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’s range resolution is 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.

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.

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

Velocity resolution 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 uR = u cos(q) fD = 2 u cos(q) / l ^ Radial velocity component

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.

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.

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.

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

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.

Radar equation for extended targets

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.

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.

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 by a distance d observed at a range Ro.

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.

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, Vx and Vy where Vx and Vy are normally distributed.

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

Fading statistics (linear detection) For a Rayleigh distribution the mean is the variance is The fluctuation about the mean is 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.

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

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.

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

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

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.

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.

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)

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.

Independent samples N = 1 N = 10 N = 50 N = 250

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)

Example radar data icebergs in open water

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.

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

Spatial discrimination Spatial discrimination relates to the ability to resolve signals from targets based on spatial position or velocity. angle, range, velocity Resolution is the measure of the ability to determine whether only one or more than one different targets are observed. Range resolution, rR, is related to signal bandwidth, B Two targets at nearly the same range Short pulse  higher bandwidth Long pulse  lower bandwidth

Spatial discrimination

Spatial discrimination Factors complicating target resolution include differing signal strength (RCS), phase differences between targets, noise, and fading effects.

Spatial discrimination The ability to resolve targets is somewhat subjective. In microwave remote sensing a more objective definition of resolution is: the distance (angle, range, speed) between the half-peak-power response.

Spatial discrimination The ability to discriminate between targets is better when the resolution distance is said to be finer (not greater) Fine (and coarse) resolution are preferred to high (and low) resolution Various combinations of resolution can be used to discriminate targets

Spatial discrimination

Range resolution Short pulse radar The received echo, E(t) is where p(t) is the pulse shape S(t) is the target impulse response  denotes convolution To resolve two closely spaced targets, rR Example rR = 1 m    6.7 ns rR = 1 ft    2 ns

Range resolution Clearly to obtain fine range resolution, a short pulse duration is needed. However the amount of energy (not power) illuminating the target is a key radar performance parameter. Energy, E, is related to the transmitted power, Pt by Therefore for a fixed transmit power, Pt, (e.g., 100 W), reducing the pulse duration, , reduces the energy E. Pt = 100 W,  = 100 ns  rR = 50 ft, E = 10 J Pt = 100 W,  = 2 ns  rR = 1 ft, E = 0.2 J Consequently, to keep E constant, as  is reduced, Pt must increase.

Range resolution

PRF and ambiguous ranges Alternatively, a series of pulses are used to illuminate the target and the pulse repetition frequency (PRF) is another key radar parameter. So by increasing the PRF (i.e., reducing Tp) more pulses can be used to illuminate the target in a given time interval (thus overcoming the energy reduction associated with shorter pulses). However a new problem emerges, range ambiguity. An ambiguous range implies uncertainty about which transmit pulse the incoming target range is resulting from. Uniquely identifying each pulse by “coding” is possible but adds additional complexity and challenges.

PRF and ambiguous ranges

PRF and ambiguous ranges Time domain

PRF and ambiguous ranges The maximum unambiguous range, Ru is Examples PRF = 1 kHz, Tp = 1 ms  Ru = 150 km PRF = 20 kHz, Tp = 50 s  Ru = 7.5 km Combining received signal energy from multiple consecutive transmitted pulses requires additional receiver complexity and imposes new requirements on the transmitter (i.e., coherence). But it can be done. More on PRFs later.

PRF and ambiguous ranges

FM-CW radar Alternative radar schemes do not involve pulses, rather the transmitter runs in “continuous-wave” mode, i.e., CW. FM-CW radar block diagram

FM-CW radar Linear FM sweep Bandwidth: B Repetition period: TR= 1/fm Round-trip time to target: T = 2R/c fR = Tx signal frequency – Rx signal frequency If 2fm is the frequency resolution, then the range resolution rR is The maximum unambiguous range, Ru is

FM-CW radar The FM-CW radar has the advantage of constantly illuminating the target (complicating the radar design). It maps range into frequency and therefore requires additional signal processing to determine target range. Targets moving relative to the radar will produce a Doppler frequency shift further complicating the processing.

Chirp radar Blending the ideas of pulsed radar with linear frequency modulation results in a chirp (or linear FM) radar. Transmit a long-duration, FM pulse. Correlate the received signal with a linear FM waveform to produce range dependent target frequencies. Signal processing (pulse compression) converts frequency into range. Key parameters: B, chirp bandwidth , Tx pulse duration

Chirp radar Linear frequency modulation (chirp) waveform for 0  t   fC is the starting frequency (Hz) k is the chirp rate (Hz/s) C is the starting phase (rad) B is the chirp bandwidth, B = k

Stretch chirp processing LO

Challenges with stretch processing Reference chirp Received signal (analog) Digitized signal Low-pass filter A/D converter To dechirp the signal from extended targets, a local oscillator (LO) chirp with a much greater bandwidth is required. Performing analog dechirp operation relaxes requirement on A/D converter. Echos from targets at various ranges have different start times with constant pulse duration. Makes signal processing more difficult. LO near Tx B Rx near time frequency frequency far far time

Correlation processing of chirp signals Avoids problems associated with stretch processing Takes advantage of fact that convolution in time domain equivalent to multiplication in frequency domain Convert received signal to freq domain (FFT) Multiply with freq domain version of reference chirp function Convert product back to time domain (IFFT) FFT IFFT Freq-domain reference chirp Received signal (after digitization) Correlated signal

Signal correlation examples Input waveform #1 High-SNR gated sinusoid, no delay Input waveform #2 High-SNR gated sinusoid, ~800 count delay

Signal correlation examples Input waveform #1 High-SNR gated sinusoid, no delay Input waveform #2 Low-SNR gated sinusoid, ~800 count delay

Signal correlation examples Input waveform #1 High-SNR gated chirp, no delay Input waveform #2 Low-SNR gated chirp, ~800 count delay

Analog chirp signal processing chirp generation and compression Dispersive delay line is a SAW device SAW: surface acoustic wave

Chirp pulse compression and sidelobes Peak sidelobe level can be controlled by introducing a weighting function -- however this has side effects.

Window functions and their effects Time sidelobes are an side effect of pulse compression. Windowing the signal prior to frequency analysis helps reduce the effect. Some common weighting functions and key characteristics Less common window functions used in radar applications and their key characteristics

Window functions Basic function: a and b are the –6-dB and - normalized bandwidths

Window functions

Detailed example of chirp pulse compression received signal dechirp analysis which simplifies to sinusoidal term chirp-squared term quadratic frequency dependence linear frequency dependence phase terms after lowpass filtering to reject harmonics

Pulse compression Chirp waveforms represent one approach for pulse compression. Radar range resolution depends on the bandwidth of the received signal. The bandwidth of a time-gated sinusoid is inversely proportional to the pulse duration. So short pulses are better for range resolution Received signal strength is proportional to the pulse duration. So long pulses are better for signal reception c = speed of light, rR = range resolution,  = pulse duration, B = signal bandwidth

More Tx Power?? Why not just get a transmitter that outputs more power? High-power transmitters present problems Require high-voltage power supplies (kV) Reliability problems Safety issues (both from electrocution and irradiation) Bigger, heavier, costlier, …

Pulse compression, the compromise Transmit a long pulse that has a bandwidth corresponding to a short pulse Must modulate or code the transmitted pulse to have sufficient bandwidth, B can be processed to provide the desired range resolution, rR Example: Desired resolution, rR = 15 cm (~ 6”) Required bandwidth, B = 1 GHz (109 Hz) Required pulse energy, E = 1 mJ E(J) = P(W)· (s) Brute force approach Raw pulse duration,  = 1 ns (10-9 s) Required transmitter power, P = 1 MW ! Pulse compression approach Pulse duration,  = 0.1 ms (10-4 s) Required transmitter power, P = 10 W

Simplified view of pulse compression Energy content of long-duration, low-power pulse will be comparable to that of the short-duration, high-power pulse 1 « 2 and P1 » P2 time t1 Power P1 P2 t2 Goal:

Pulse coding Long duration pulse is coded to have desired bandwidth. Various ways to code pulse. Linear frequency modulation (chirp) for 0  t   fC is the starting frequency (Hz) k is the chirp rate (Hz/s) B = k = 1 GHz Phase code short segments Each segment duration = 1 ns Choice driven largely by required complexity of receiver electronics t 1 ns

Phase coded waveform

Analog signal processing

Binary phase coding

Receiver signal processing phase-coded pulse compression time Correlation process may be performed in analog or digital domain. A disadvantage of this approach is that the data acquisition system (A/D converter) must operate at the full system bandwidth (e.g., 1 GHz in our example). PSL: peak sidelobe level (refers to time sidelobes)

Binary phase coding Various coding schemes Barker codes Low sidelobe level Limited to modest lengths Golay (complementary) codes Code pairs – sidelobes cancel Psuedo-random / maximal length sequential codes Easily generated Very long codes available Doppler frequency shifts and imperfect modulation (amplitude and phase) degrade performance

Pulse compression effects on SNR and blind range SNR improvement due to pulse compression: B Case 1: Pt = 1 MW,  = 1 ns, B = 1 GHz, E = 1 mJ For a given R, Gt, Gr, l, s: SNRvideo = 10 dB B = 1 or 0 dB SNRcompress = SNRvideo = 10 dB Blind range = c/2 = 0.15 m Case 2: Pt = 10 W,  = 0.1 ms, B = 1 GHz, E = 1 mJ For a same R, Gt, Gr, l, s: SNRvideo = -40 dB B = 100,000 or 50 dB SNRcompress = 10 dB Blind range = c/2 = 15 km

Pulse compression effects on SNR and blind range Okay, so that is what the math tells us, but what is really going on? Case 1: Pt = 1 MW,  = 1 ns, B = 1 GHz, E = 1 mJ Pulse duration is 1 ns  B = 1 GHz Find noise power using F = 4 dB and B = 1 GHz (90 dB) PN = kT0BF = -174 + 90 + 4 dBm = -80 dBm Case 2: Pt = 10 W,  = 0.1 ms, B = 1 GHz, E = 1 mJ Pulse duration is 100 s but B = 1 GHz Range is mapped into frequency, so my ability to resolve frequencies is related to my range resolution With 100 s echo duration, the frequency resolution is 10 kHz Spectral analysis of the echo from a point target with 10-kHz frequency resolution maximizes the SNR Again find noise power using F = 4 dB but now B = 10 kHz (40 dB) PN = kT0BF = -174 + 40 + 4 dBm = -130 dBm

Pulse compression effects on SNR and blind range Okay, but what about the 15-km blind range? The blind range issue concerns adverse impacts on radar performance that result from transmissions while receiving. Issues include: Dynamic range limitations Saturation in the receiver chain It is possible (though perhaps not trivial) to accommodate transmission while receiving thus avoiding the blind range constraint.

Pulse compression Pulse compression allows us to use a reduced transmitter power and still achieve the desired range resolution. The costs of applying pulse compression include: added transmitter and receiver complexity must contend with time sidelobes increased blind range The advantages generally outweigh the disadvantages so pulse compression is used widely.

Short pulse vs. pulse compression A comparison of short pulse (impulse) systems with compressed pulse systems reveals several performance benefits for the compressed pulse approach, including: Noise rejection Pulse energy Electromagnetic interference (EMI) The examples below were developed to compare a compressed-pulse ground-penetrating radar (GPR) system with an conventional impulse GPR. Impulse GPR systems typically involve short-duration pulses whose bandwidth ~ center frequency.

Short pulse vs. pulse compression Noise rejection Received broadband noise is dependent on bandwidth as noise is present over the entire spectrum. The bandwidth of the compressed pulse waveform is the inverse of the pulse duration, e.g., 100 s yields 10-kHz bandwidth; the bandwidth of a conventional impulse radar is the signal center frequency (e.g., 3.3 GHz). The noise rejection advantage of the pulsed-chirp system is the ratio of these bandwidths, 3.3 GHz/10 kHz = 3.3  105 or 55 dB. Typical impulse radars have a transmit waveform bandwidth that is the reciprocal of the impulse duration. The receiver bandwidth should match the transmit waveform bandwidth. Therefore, a system with a transmit pulse duration of about 300 ps will produce a waveform with about 3.3 GHz of bandwidth (extending from 1.6 GHz to 4.9 GHz) and the receiver bandwidth should likewise be 3.3 GHz and this figure is used to compute received noise power.

Short pulse vs. pulse compression Noise rejection Illustration of the simple operating geometry showing response of impulse and compressed pulse GPRs. Signal power versus depth from surface and shallow target for both impulse and compressed-pulse systems. Signal power versus depth of surface and deeper target, signal power from impulse and compressed-pulse systems. Simple two-antenna geometry indicating echoes from both surface and shallow buried target.

Short pulse vs. pulse compression Pulse energy The pulse energy of the pulsed-chirp system is the product of the pulse duration (100 s) and the peak output power (1 W) yielding a pulse energy of 10–4 J; the pulse energy for the impulse system is the product of 300 ps and 1 kW or 3  10–7 J. Thus the pulse energy of the compressed pulse system is more than 330 times (25 dB) greater than that of the impulse system.

Short pulse vs. pulse compression Electromagnetic interference (EMI) The spectral energy content of the GPR waveform determines its potential for adversely impacting susceptible electronic systems nearby (e.g., radios, TV receivers, cell phones, etc.), termed electromagnetic interference or EMI. With digitally produced waveforms, the compressed pulse GPR can readily modify its spectral content thereby avoiding sensitive frequency bands to mitigate its impact on susceptible systems often with minimal impact on GPR performance. By their very nature impulse systems produce energy bursts with broad spectral extent, thus producing significant EMI challenges.