Radar Measurements II Chris Allen

Radar Measurements II Chris Allen (callen@eecs.ku.edu)
Course website URL people.eecs.ku.edu/~callen/725/EECS725.htm

Ground imaging radar In a real-aperture system images of radar backscattering are mapped into slant range, R, and along-track position. The along-track resolution, y, is provided solely by the antenna. Consequently the along-track resolution degrades as the distance increases. (Antenna length, ℓ, directly affects along-track resolution.) Cross-track ground range resolution, x, is incidence angle dependent where p is the compressed pulse duration slant range slant range along-track direction y R cross-track direction ground range ground range x cross-track direction x

Slant range vs. ground range
Cross-track resolution in the ground plane (x) is the projection of the range resolution from the slant plane onto the ground plane. At grazing angles (  90°), r  x At steep angles (  0°), x   For  = 5°, x = 11.5 r For  = 15°, x = 3.86 r For  = 25°, x = 2.37 r For  = 35°, x = 1.74 r For  = 45°, x = 1.41 r For  = 55°, x = 1.22 r

Real-aperture, side-looking airborne radar (SLAR) image of Puerto Rico
~ 40 x 100 miles Mosaicked image composed of 48-km (30-mile) wide strip map images Radar parameters modified Motorola APS-94D system X-band (3-cm wavelength) altitude: 8,230 m (above mean sea level) azimuth resolution: 10 to 15 m Digital Elevation Model of Puerto Rico

Another SLAR image SLAR image of river valley
5-m (18 feet) SLAR antenna mounted beneath fuselage SLAR image of river valley SLAR operator’s console X-band system Civilian uses include: charting the extent of flood waters, mapping, locating lost vessels, charting ice floes, locating archaeological sites, seaborne pollution spill tracking, various geophysical surveying chores.

Limitations of real-aperture systems
With real-aperture radar systems the azimuth resolution depends on the antenna’s azimuth beamwidth (az) and the slant range, R Consider the AN/APS 94 (X-band, 5-m antenna length) az = 6 mrad or 0.34 For a pressurized jet aircraft altitude of 30 kft (9.1 km) and an incidence angle of 30 for a slant range of 10.5 km R = h/cos  = 9100 / cos 30 = m y = 63 m (coarse but useable) Now consider a spaceborne X-band radar (15-m antenna length) az = 2 mrad or 0.11 500-km altitude and a 30 incidence angle (27.6 look angle) for a km slant range y = 1.1 km (very coarse) The azimuth resolution of real-aperture radar systems is very coarse for long-range applications

Radar equation for extended targets
Since A = x y we have Substituting these terms into the range equation leads to note the range dependence is now R-3 whereas for a point target it is R-4 This is due to the fact that a larger area is illuminated as R increases.

SNR and the radar equation
Now to consider the SNR we must use the noise power PN = kT0BF Assuming that terrain backscatter, , is the desired signal (and not simply clutter), we get Solving for the maximum range, Rmax, that will yield the minimum acceptable SNR, SNRmin, gives

Radar altimetry Altimeter – a nadir-looking radar that precisely measures the range to the terrain below. The terrain height is derived from the radar’s position.

Altimeter data Radar map of the contiguous 48 states.

Altimeter

TOPEX/Poseidon A - MMS multimission platform B - Instrument module 1/Data transmission TDRS 2/Global positioning system antenna 3/Solar array 4/Microwave radiometer 5/Altimeter antenna 6/Laser retroreflectors 7/DORIS antenna Dual frequency altimeter (5.3 and 13.6 GHz) operating simultaneously. Three-channel radiometer (18, 21, 37 GHz) provides water vapor data beneath satellite (removes ~ 1 cm uncertainty). 2-cm altimeter accuracy 100 million echoes each day 10 MB of data collected per day French-American system Launched in day revisit period (66 orbit inclination) Altitude: km Mass: ~ 2400 kg

Altimeter data Global topographic map of ocean surface produced with satellite altimeter.

Altimeter data

Mars Orbiter Laser Altimeter (MOLA)
Laser altimeter (not RF or microwave) Launched November 7, 1996 Entered Mars orbit on September 12, 1997 Selected specifications 282-THz operating frequency (1064-nm wavelength) 10-Hz PRF 48-mJ pulse energy 50-cm diameter antenna aperture (mirror) 130-m spot diameter on surface 37.5-cm range measurement resolution

Mars Orbiter Laser Altimeter (MOLA)

Radar altimetry The echo shape, E(t), of altimetry data is affected by the radar’s point target response, p(t), it’s flat surface response, S(t), which includes gain and backscatter variations with incidence angle, and the rms surface height variations, h(t). Analysis of the echo shape, E(t), can provide insight regarding the surface. From the echo’s leading we learn about the surface height variations, h(t), and from its trailing edge we learn about the backscattering characteristics, ().

Signal integration Combining consecutive echo signals can improve the signal-to-noise ratio (SNR) and hence improve the measurement accuracy, or it can improve our estimate of the SNR and hence improve our measurement precision. Two basic schemes for combining echo signals in the slow-time dimension will be addressed. Coherent integration Incoherent integration Coherent integration (also called presumming or stacking) involves working with signals containing magnitude and phase information (complex or I & Q values, voltages, or simply signals that include both positive and negative excursions) Incoherent integration involves working with signals that have been detected (absolute values, squared values, power, values that are always positive) Both schemes involve operations on values expressed in linear formats and not expressed in dB.

Coherent integration Coherent integration involves the summation or averaging of multiple echo signal records (Ncoh) along the slow-time dimension. Coherent integration is commonly performed in real time during radar operation. Coherent integration affects multiple radar parameters. It reduces the data volume (or data rate) by Ncoh. It improves the SNR of in-band signals by Ncoh. It acts as a low-pass filter attenuating out-of-band signals.

Coherent integration

Coherent integration Signal power found using Noise power found using
where vs is the signal voltage vector Noise power found using where vs+n is the signal + noise voltage vector SNR is then note that [std_dev]2 is variance

Coherent integration Summing Ncoh noisy echoes has the following effect Signal amplitude is increased by Ncoh Signal power is increased by (Ncoh)2 Noise power is increased by Ncoh Therefore the SNR is increased by Ncoh Noise is uncorrelated and therefore only the noise power adds whereas the signal is correlated and therefore it’s amplitude adds. This is the power behind coherent integration. Averaging Ncoh noisy echoes has the following effect Signal amplitude is unchanged Signal power is unchanged Noise power is decreased by Ncoh Noise is uncorrelated and has a zero mean value. Averaging Ncoh samples of random noise reduces its variance by Ncoh and hence the noise power is reduced.

Coherent integration Underlying assumptions essential to benefit from coherent integration. Noise must be uncorrelated pulse to pulse. Coherent noise (such as interference) does not satisfy this requirement. Signal must be correlated pulse to pulse. That is, for maximum benefit the echo signal’s phase should vary by less than 90 over the entire integration interval. For a stationary target relative to the radar, this is readily achieved. For a target moving relative to the radar, the maximum integration interval is limited by the Doppler frequency. This requires a PRF much higher than PRFmin, that is the Doppler signal is significantly oversampled. Ncoh = 10

Coherent integration Coherent integration filters data in slow-time dimension. Filter characterized by its transfer function.

Coherent integration Impact on SNR
Coherent integration improves the SNR by Ncoh. For point targets For extended targets SNRvid SNRcoh

Coherent integration So what is going on to improve the SNR ?
Is the receiver bandwidth being reduced ? No By coherently adding echo signal energy from consecutive pulses we are effectively increasing the illumination energy. This may be thought of as increasing the transmitted power, Pt. Again returning to the ACR 430 airfield-control radar example The transmitter has peak output power, Pt, of 55 kW and a pulse duration, , of 100 ns, (i.e., B = 10 MHz). Hence the transmit pulse energy is Pt  = 5.5 mJ Coherently integrating echoes from 10 pulses (Ncoh = 10) produces an SNR equivalent to the case where Pt is 10 times greater, i.e., 550 kW and the total illumination energy is 55 mJ. Alternatively, coherent integration permits a reduction of the transmit pulse power, Pt, equivalent to the Ncoh while retaining a constant SNR.

Incoherent integration
Incoherent detection is similar to coherent detection in that it involves the summation or averaging of multiple echo signal records (Ninc) along the slow-time dimension. Prior to integration the signals are detected (absolute values, squared values, power, values that are always positive). Consequently the statistics describing the process is significantly more complicated (and beyond the scope of this class). The improvement in signal-to-noise ratio due to incoherent integration varies between  Ninc and Ninc, depending on a variety of parameters including detection process and Ninc. How it works: For a stable target signal, the signal power is fairly constant while the noise power fluctuates. Therefore integration consistently builds up the signal return whereas the variability of the noise power is reduced. Consequently the detectability of the signal is improved.

Incoherent integration
Example using square-law detection

More on coherent integration
Clearly coherent integration offers tremendous SNR improvement. To realize the full benefits of coherent integration the underlying assumptions must be satisfied Noise must be uncorrelated pulse to pulse Signal phase varies less than 90 over integration interval The second assumption limits the integration interval for cases involving targets moving relative to the radar. Coherent integration can be used if phase variation is removed first. Processes involved include range migration and focusing. For a 2.25-kHz PRF, Ncoh = 100,000 or 50 dB of SNR improvement 2 km 1 km l = 30 cm 90 m/s

Tracking radar In this application the radar continuously monitors the target’s range and angular position (angle-of-arrival – AOA). Tracking requires fine angular position knowledge, unlike the search radar application where the angular resolution was el and az. Improved angle information requires additional information from the antenna. Monopulse radar With monopulse radar, angular position measurements are accomplished with a single pulse (hence the name monopulse). This system relies on a more complicated antenna system that employs multiple radiation patterns simultaneously. There are two common monopulse varieties amplitude-comparison monopulse phase-comparison monopulse Each variety requires two (or more) antennas and thus two (or more) receive channels

Amplitude-comparison monopulse
This concept involves two co-located antennas with slightly shifted pointing directions. The signals output from the two antennas are combined in two different processes  (sum) output is formed by summing the two antenna signals  (difference) output is formed by subtracting signals from one another These combinations of the antenna signals produce corresponding radiation patterns ( and ) that have distinctly different characteristics / (computed in signal processor) provides an amplitude-independent estimate of the variable related to the angle

Phase-comparison monopulse
This concept involves two antennas separated by a small distance d with parallel pointing directions. The received signals are compared to produce a phase difference, , that yields angle-of-arrival information. For small , sin   

Dual-axis monopulse Both amplitude-comparison and phase-comparison approaches provide angle-of-arrival estimates in one-axis. For dual-axis angle-of-arrival estimation, duplicate monopulse systems are required aligned on orthogonal axes.

Dual-axis monopulse

Monopulse Conventional monopulse processing to obtain the angle-of-arrival is valid for only one point target in the beam, otherwise the angle estimation is corrupted. Other more complex concepts exist for manipulating the antenna’s spatial coverage. These exploit the availability of signals from spatially diverse antennas (phase centers). Rather than combining these signals in the RF or analog domain, these signals are preserved into the digital domain where various antenna patterns can be realized via ‘digital beamforming.’

Frequency agility Frequency agility involves changing the radar’s operating frequency on a pulse-to-pulse basis. (akin to frequency hopping in some wireless communication schemes) Advantages Improved angle estimates (refer to text for details) Reduced multipath effects Less susceptibility to electronic countermeasures Reduced probability detection, low probability of intercept (LPI) Disadvantages Scrambles the target phase information Changing f changes  To undo the effects of changes in f requires precise knowledge of R Pulse-to-pulse frequency agility is typically not used in coherent radar systems.

Pulse compression Pulse compression is a very powerful concept or technique permitting the transmission of long-duration pulses while achieving fine range resolution.

Pulse compression Pulse compression is a very powerful concept or technique permitting the transmission of long-duration pulses while achieving fine range resolution. Conventional wisdom says that to obtain fine range resolution, a short pulse duration is needed. However this limits the amount of energy (not power) illuminating the target, 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  R = 50 ft, E = 10 J Pt = 100 W,  = 2 ns  R = 1 ft, E = 0.2 J Consequently, to keep E constant, as  is reduced, Pt must increase.

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, …

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 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 Solution: Transmit a long-duration pulse that has a bandwidth corresponding to that of a short-duration pulse c = speed of light, R = range resolution,  = pulse duration, B = signal bandwidth

Pulse compression, the compromise
Transmitting a long-duration pulse with a wide bandwidth requires modulation or coding the transmitted pulse to have sufficient bandwidth, B can be processed to provide the desired range resolution, R Example: Desired resolution, R = 15 cm (~ 6”) Required bandwidth, B = 1 GHz (109 Hz) Required pulse energy, E = 1 mJ E(J) = Pt(W)· (s) Brute force approach Raw pulse duration,  = 1 ns (10-9 s) Required transmitter power, Pt = 1 MW ! Pulse compression approach Pulse duration,  = 0.1 ms (10-4 s) Required transmitter power, Pt = 10 W

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

Phase coded waveform

Analog signal processing

Binary phase coding

Receiver signal processing phase-coded pulse compression
time Correlation process may be performed in the 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

Chirp waveforms and FM-CW radar
To understand chirp waveforms and the associated signal processing, it is useful to first introduce the FM-CW radar. FM – frequency modulation CW – continuous wave This is not a pulsed radar, instead the transmitter operates continuously requiring the receiver to operate during transmission. Pulse radars are characterized by their duty factor, D where  is the pulse duration and PRF is the pulse repetition frequency. For pulsed radars D may range from 1% to 20%. For CW radars D = 100%.

FM-CW radar Simple FM-CW block diagram and associated signal waveforms. 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 The beat frequency fb = fTx– fRx The beat signal observation time is TR/2 providing a frequency resolution, f = 2 fm Therefore the range resolution R = c/2B [m] = k

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

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

Stretch chirp processing

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. Echoes 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

Pulse compression example
Key system parameters Pt = 10 W,  = 100 s, B = 1 GHz, E = 1 mJ , R = 15 cm Derived system parameters k = 1 GHz / 100 s = 10 MHz / s = 1013 s-2 Echo duration,  = 100 s Frequency resolution, f = (observation time)-1 = 10 kHz Range to first target, R1 = 150 m T1 = 2 R1 / c = 1 s Beat frequency, fb = k T1 = 10 MHz Range to second target, R2 = m T2 = 2 R2 / c = s Beat frequency, fb = k T2 = MHz fb2 – fb1 = 10 kHz which is the resolution of the frequency measurement

Pulse compression example (cont.)
With stretch processing a reduced video signal bandwidth is output from the analog portion of the radar receiver. video bandwidth, Bvid = k Tp where Tp = 2 Wr /c and Wr is the swath’s slant range width for Wr = 3 km, Tp = 20 s  Bvid = 200 MHz This relaxes the requirements on the data acquisition system (i.e., analog-to-digital (A/D) converter and associated memory systems). Without stretch processing the data acquisition system must sample a 1-GHz signal bandwidth requiring a sampling frequency of 2 GHz and memory access times less than 500 ps.

Correlation processing of chirp signals
Avoids problems associated with stretch processing Involves time-domain cross correlation of received signal with reference signal. {Matlab command: [c,lag] = xcorr(a,b)} Time-domain cross correlation can be a slow, compute-intensive process. Alternatively we can take 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

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

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

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

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

Superposition and multiple targets
Signals from multiple targets do not interfere with one another. (negligible coupling between scatterers) Free-space propagation, target interaction, radar receiver all have linear transfer functions  superposition applies. Signal from each target adds linearly with signals from other targets. r is range resolution

Why time sidelobes are a problem
Sidelobes from large-RCS targets with can obscure signals from nearby smaller-RCS targets. Related to pulse duration, , is the temporal extent of time sidelobes, 2. Time sidelobe amplitude is related to the overall waveform shape. fb = 2 k R/c fb

Window functions and their effects
Time sidelobes are a 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 sinusoidal term after lowpass filtering to reject harmonics

Pulse compression effects on SNR and blind range
SNR improvement due to pulse compression is the waveform’s time-bandwidth product: B (regardless of pulse compression scheme used) Case 1: Pt = 1 MW,  = 1 ns, B = 1 GHz, E = 1 mJ, R = 15 cm 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,  = 100 s, B = 1 GHz, E = 1 mJ , R = 15 cm For the same R, Gt, Gr, l, s: SNRvideo = – 40 dB B = 100,000 or 50 dB SNRcompress = 10 dB Blind range = c/2 = 15 km (point target range equation)

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.

Radar range equation (revisited)
We now integrate the signal-to-noise ratio improvement factors from coherent and incoherent integration as well as pulse compression into the radar range equation for point and distributed targets. Point targets Extended targets

Dynamic range example The SNR improvements discussed (coherent and incoherent integration, pulse compression) also expand the radar’s dynamic range. In modern radars these SNR improvements occur in the digital domain. Consequently the overall dynamic range is not limited by the ADC. To illustrate this fact consider the following example. A radar uses a Linear Technologies LT2255 ADC Specs: 14-bit, 125 MS/s, 2-V full scale, 640-MHz analog bandwidth It samples at 112 MHz (fs) a signal centered at 195 MHz with 30 MHz of bandwidth. At 200 MHz the ADC’s SNR is ~ 70 dB (per the product specifications) indicating an effective number of bits, ENOB = 11.7. 2 Vpp  10 dBm in a 50- system To realize the SNR improvement offered by coherent integration, the thermal noise power must be 3 to 5 dB above the ADC’s quantization noise floor.

Dynamic range example Radar center frequency is 195 MHz.
Radar bandwidth is 30 MHz. Radar spectrum extends from 180 MHz to 210 MHz. Sampling frequency is 112 MHz. Satisfies the Nyquist-Shannon requirement since fs = 112 MHz > 60 MHz Undersampling is used, therefore analysis is required to ensure signal is centered within a Nyquist zone.

Dynamic range example The radar system has a 10-kHz PRF, a 10-s  with 30-MHz bandwidth, and performs 32 presums (coherent integrations) prior to data recording. During post processing pulse compression is applied followed by an additional 128 coherent integrations are performed (following phase corrections or focusing). These processing steps have the following effects Signal Noise Dynamic power power range ADC 10 dBm -55 dBm 65 dB presum: Ncoh = dB 15 dB 15 dB pulse compression, B = dB 0 dB 25 dB coherent integration: Ncoh = dB 21 dB 21 dB Overall 107 dBm -19 dBm 126 dB Thus the radar system has an instantaneous dynamic range of 126 dB despite the fact that the ADC has a 65-dB dynamic range.

Level set by adjusting receiver gain
Dynamic range example Level set by adjusting receiver gain

0/ modulation Coherent noise limits the SNR improvement offered by coherent integration. Using interpulse binary phase modulation (which is removed by the ADC), the SNR improvement range can be improved significantly. On alternating transmit pulses, the phase of the Tx waveform is shifted by 0 or  radians. Once digitized by the ADC, the phase applied to the Tx waveform is removed (by toggling the sign bit), effectively removing the interpulse phase modulation and permitting presumming to proceed. This scheme is particularly useful in suppressing coherent signals originating within the radar. Interpulse phase modulation can also be used to extend the ambiguous range. +waveform waveform +waveform waveform

0/ modulation Graphical illustration of 0/ interpulse phase modulation to suppress coherent interference signals. +waveform waveform +waveform waveform +int +int +int +int +waveform +waveform +waveform +waveform +int int +int int Coherent integration produces [+waveform +int] + [+waveform int] + [+waveform +int] + [+waveform int] = 4 [+waveform]

0/ modulation Measured noise suppression as a function of the number of coherent averages both with and without 0/ interpulse phase modulation.

FM-CW radar Now we revisit the FM-CW radar to better understand its advantages and limitations. CW  on continuously (never off)  Tx while Rx Tx signal leaking into Rx limits the dynamic range OR

FM-CW radar Circulator case (in on port 1  out on port 2, in on port 2  out on port 3) Leakage through circulator, port 1  port 3 isolation maybe as good as 40 dB Reflection of Tx signal from antenna back into Rx “good antenna” has S11 < -10 dB Separate antenna case Antenna coupling < - 50 dB isolation enhancements (absorber material, geometry) Leakage signal must not saturate Rx

FM-CW radar FM – frequency modulated Unmodulated CW radar
Frequency modulation required to provide range information Unmodulated CW radar No range information provided, only Doppler Useful as a motion detector or speed monitor Leakage signal will have no Doppler shift (0 Hz), easy to reject the DC component by placing a high-pass filter after the mixer FM-CW radar applications Short-range sensing or probing A pulsed system would require a very short pulse duration to avoid the blind range Altimeter systems Nadir looking, only one large target of interest FM-CW radar shortcomings Signals from multiple targets may interact in the mixer producing multiple false targets (if mixing process is not extremely linear)

FM-CW radar Design considerations
Range resolution, R = c/(2 B) [m] Frequency resolution, f = 2/TR [Hz] Noise power, PN = k T0 B F [W] But the bandwidth is the frequency resolution, f, so PN = k T0 f F [W] Example – snow penetrating FM-CW radar

FM-CW radar Example – snow penetrating FM-CW radar
B = 2000 – 500 MHz = 1500 MHz  R = 10 cm Frequency resolution, f = 1/sweep time = 1/4 ms = 250 Hz PN = -140 dBm Rx gain = 70 dB PN out = -140 dBm + 70 dB = -70 dBm ADC saturation power = + 4 dBm Rx dynamic range, +4 dBm – (-70 dBm) = 74 dB Consistent with the ADC’s 72-dB dynamic range FM slope (like the chirp rate, k), 1500 MHz/4 ms = 375 MHz/ms So for target #1 at 17-m range, t = 2R1/c = 113 ns Beat frequency, fb = 113 ns  375 MHz/ms = 42.5 kHz fb - f = kHz  range to target #2, R2 = 16.9 m  R = 10 cm Note: MHz bandwidth, 42-kHz beat frequency

FM-CW radar block diagram
LPF HPF

FM-CW radar – RF circuitry
9” x 6.5” x 1” module

Measured radar data from Summit, Greenland in July 2005
Laboratory test data Measured radar data from Summit, Greenland in July 2005

Bistatic / multistatic radar
Bistatic radar one transmitter, one receiver, separated by baseline L, and bistatic angle, , is greater than either antenna’s beamwidth OR L/RT or L/RR > ~20% The three points (Tx, Rx, target) comprising the bistatic geometry form the bistatic triangle that lies in the bistatic plane. Multistatic radar more than one transmitter or receiver separated

Bistatic / multistatic radar
Why use a bistatic or multistatic configuration? Covert operation no Tx signal to give away position or activity Exploit bistatic scattering characteristics forward scatter » backscatter Passive radar or “hitchhiker” exploit transmitters of opportunity to save cost example transmitters include other radars, TV, radio, comm satellites, GPS, lightning, the Sun Counter ARM (ARM = anti-radiation missile) missile that targets transmit antennas by homing in on the source Counter retrodirective jammers high-gain jamming antenna directing jamming signal toward the transmitter location Counter stealth some stealth techniques optimized to reduce backscatter, not forward scatter Homing missile transmitter on missile launcher, receiver on missile (simplifies missile system) Unique spatial coverage received signal originates from intersection of Tx and Rx antenna beams

Bistatic radar geometry
For a monostatic radar the range shell representing points at equal range (isorange) at an instant forms a sphere centered on the radar’s antenna. For a bistatic radar the isorange surface forms an ellipse with the Tx and Rx antennas at the foci. That is, RT + RR = constant everywhere on the ellipse’s surface. Consequently, echoes from targets that lie on the ellipse have the same time-of-arrival and cannot be resolved based on range.

Bistatic range resolution
The bistatic range resolution depends on the target’s position relative to the bistatic triangle. For targets on the bistatic bisector the range resolution is RB For targets not on the bisector the range resolution is R Therefore for target pairs on the ellipse,  = 90 and R  , i.e., negligible range resolution. Note: For the monostatic case,  = 0 and R = c/2.

Bistatic Doppler The Doppler frequency shift due to relative motion in the bistatic radar geometry is found using For the case where both the transmitter and receiver are stationary while the target is moving, the Doppler frequency shift is Note: For the monostatic case,  = 0 and fd = 2 VTGT cos ()/

Bistatic Doppler For the case where both the transmitter and receiver are moving while the target is stationary, the Doppler frequency shift is Another way to determine the Doppler shift for the general case where the transmitter, receiver, and target are moving is to numerically compute the ranges (RT and RR) to the target position as a function of time. Use numerical differentiation to find dRT/dt and dRR/dt that can then be used in This approach can also be used to produce isodops (contours of constant Doppler shift) on a surface by numerically computing fB to each point on the surface. Matlab’s contour command is particularly useful here.

Example plots Monostatic example
Aircraft flying straight and level x = 0, y = 0, z = 2000 m vx = 0, vy = 100 m/s, vz = 0 f = 200 MHz

Example plots Bistatic example
Tx (stationary atop mountain): x = -6 km, y = -6 km, z = 500 m vx = 0, vy = 0, vz = 0 Rx (aircraft flying straight and level): x = 0, y = 0, z = 2 km vx = 0, vy = 100 m/s, vz = 0 f = 200 MHz

Radar Measurements II Chris Allen

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Radar Measurements II Chris Allen

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