Detection of Targets in Noise and Pulse Compression Techniques

Transcription

1 Introduction to Radar Systems Detection of Targets in Noise and Pulse Compression Techniques Radar Course_1.ppt ODonnell

2 Disclaimer of Endorsement and Liability The video courseware and accompanying viewgraphs presented on this server were prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor the Massachusetts Institute of Technology and its Lincoln Laboratory, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, products, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors or the Massachusetts Institute of Technology and its Lincoln Laboratory. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or any of their contractors or subcontractors Radar Course_2.ppt

3 Detection and Pulse Compression Propagation Medium Transmitter Waveform Generator Target Cross Section Antenna Receiver A / D Pulse Compression Signal Processor Doppler Processing Main Computer Detection Tracking & Parameter Estimation Console / Display Recording Radar Course_3.ppt

4 Outline Detection of Target Echoes in Noise Basic Concepts Integration of Pulses Fluctuating Targets Issues Adaptive Thresholding Techniques Pulse Compression Radar Course_4.ppt

5 Target Detection in the Presence of Noise Relative Power (db) Detectable Marginal Undetectable Noise Targets Threshold Radar Course_5.ppt DPC 9/8/ Range Gate The radar return is sampled at regular intervals with A/D (Analog to Digital) converters The sampled returns may include the target of interest and noise A threshold is used to reject noise

6 The Detection Problem Probability Density Noise Detection Threshold The area under the noise probability curve, from the detection threshold to infinity (way, way out to the right) is the probability of false alarm. The entire area under the noise density curve is 1..1 Radar Course_6.ppt Probability of False Noise Voltage Alarms

7 The Detection Problem.6 Probability Density Noise Detection Threshold P D = Detection Probability Signal + Noise SNR = 15 db.1 Radar Course_7.ppt Probability of False Alarms Voltage

8 Detection Examples with Different SNR Signal-to-Noise Ratio = 15 db Signal-to-Noise Ratio = 2 db Probability Density Noise Detection Threshold Signal + Noise P D (Detection Probability) Voltage Noise Detection Threshold Signal + Noise Voltage Higher P D (Detection Probability) Probability of False Alarm For a fixed threshold, a higher SNR (or S/N) will result in a higher of probability of detecting the target Radar Course_8.ppt

9 Probability of Detection vs. SNR Numbers to Remember Figure by MIT OCW. Radar Course_9.ppt

10 Outline Detection of Target Echoes in Noise Basic Concepts Integration of Pulses Fluctuating Targets Issues Adaptive Thresholding Techniques Pulse Compression Radar Course_1.ppt

11 Integration of Radar Pulses Improve ability of radar to detect targets by combining the returns from multiple pulses Coherent Integration No information lost (amplitude or phase) Non-coherent integration techniques Some information lost (phase) Non-coherent (video) Integration Binary Integration Cumulative detection For most cases, coherent integration is more efficient than noncoherent integration Radar Course_11.ppt

12 Coherent Integration Real and Imaginary (In-phase and Quadrature) parts of the complex radar return are added, and the magnitude of the voltage is calculated V=(I 2 + Q 2 ) 1/2 This quantity is then thresholded The coherent integration gain is equal to the number of pulses coherently integrated 2 pulses 3 db 1 pulses 1 db 2 pulses 13 db For this gain to be realized, the noise samples, from pulse to pulse must be independent The background noise is white Gaussian noise Radar Course_12.ppt

13 Noncoherent Integration Steady Target Normalized Power Single Pulse 8 Pulses Noncoherently Averaged Range Gates SNR Unchanged Noise Variance Reduced after Integration (Allows Lower Threshold) Radar Course_13.ppt

14 Different Types of Non-Coherent Integration Non Coherent Integration General (aka video integration) Generate magnitude for each of N pulses Add magnitudes and then threshold Binary Integration Generate magnitude for each of N pulses and then threshold Require at least M detections in N scans Cumulative Detection Generate magnitude for each of N pulses and then threshold Require at least 1 detection in N scans Radar Course_14.ppt

15 Outline Detection of Target Echoes in Noise Basic Concepts Integration of Pulses Fluctuating Targets Issues Adaptive Thresholding Techniques Pulse Compression Radar Course_15.ppt

16 Target Fluctuations Swerling Models Fluctuation Interval scan-to-scan (multiple pulses/scan) pulse-to-pulse similar amplitudes Nature of Scatterers p 1 σ σ av ( σ) = e σ av one amplitude much larger than others Swerling I Swerling II Swerling III Swerling IV p 2σ 4σ σ av ( σ) = e σ 2 av Radar Course_16.ppt

17 Non-fluctuating Target RCS Variability for Different Target Models Radar Course_17.ppt DPC 9/8/28 Swerling I/II Swerling III/IV Measured RCS (dbsm) Sample #

18 Detection Statistics for Fluctuating Targets Single Pulse Detection Radar Course_18.ppt Figure by MIT OCW. Fluctuating Targets Require More SNR than Non-fluctuating Targets to Maintain a High Probability of Detection

19 Outline Detection of Target Echoes in Noise Basic Concepts Integration of Pulses Fluctuating Targets Issues Adaptive Thresholding Techniques Pulse Compression Radar Course_19.ppt

20 Constant False Alarm Rate (CFAR) Thresholding Problem: Must know (or estimate) noise floor to set threshold Solution: Estimate noise floor using noise-only samples Adaptive thresholding Absolute threshold Noise floor Signal False alarm Power (db) CFAR thresholding: 1 test cell noise floor estimate > threshold Time (µs) Radar Course_2.ppt

21 The Mean Level CFAR Use mean value of surrounding range cells to determine threshold for cell under test Window Slides Through Data Cell Under Test Guard Cells Data Cells for Mean Level Computation Nearby targets can raise threshold and suppress detection Radar Course_21.ppt

22 Effect of Rain on CFAR Thresholding Radar Backscatter (Linear Units) Range Cells Rain Cloud 2.2 db Receiver Noise 2.6 Slant Range, nmi 9 db C Band 55 MHz Receiver Noise 4.5 Window Slides Through Data Cell Under Test Guard Cells Data Cells for Mean Level Computation Radar Course_22.ppt

23 Effect of Rain on CFAR Thresholding Amplitude (Linear Units) 2.2 db Receiver Noise Range Cells Rain Cloud 9 db C Band 55 MHz Receiver Noise 2.6 Slant Range, nmi 4.5 Window Slides Through Data Sharp Clutter or Interference Boundaries Can Lead to Excessive False Alarms Radar Course_23.ppt Cell Under Test Guard Cells Data Cells for Mean Level Computation

24 Greatest-of Mean Level CFAR Find mean value of N/2 cells before and after test cell separately Use larger noise estimate to determine threshold Window Slides Through Data Data Cells for Mean Level 1 Cell Under Test Data Cells for Mean Level 2 Guard Cells Use Larger Value Helps reduce false alarms near sharp clutter or interference boundaries Nearby targets still raise threshold and suppress detection Radar Course_24.ppt

25 Outline Detection of Target Echoes in Noise Pulse Compression Introduction Phase Coded Waveforms Linear Frequency Modulation Waveforms Radar Course_25.ppt

26 Pulsed CW Radar Fundamentals Range Resolution 3 1 μsec pulse Frequency spectrum of pulse 2 Amplitude 2 1 Pulsewidth T Power (db) 1 Bandwidth 1 T Time (μsec) Range Resolution ( Δ r ) Proportional to pulse width (T) Inversely proportional to bandwidth (B = 1/T) Frequency (MHz) Δ r c T = 2 Δ r c = 2 1 MHz Bandwidth => 15 m of range resolution B Radar Course_26.ppt

27 Pulse Width, Bandwidth and Resolution for a Square Pulse Resolution: Pulse Length is Larger than Target Length Cannot Resolve Features Along the Target Pulse Length is Smaller than Target Length Can Resolve Features Along the Target Δ Δ r r c T = 2 c = 2 B Example : Relative RCS (db) -2-4 Relative Range (m) High Bandwidth Δr =.1 x Δ r BW = 1 x BW Low Bandwidth Shorter Pulses have Higher Bandwidth and Better Resolution Radar Course_27.ppt

28 Motivation for Pulse Compression Hard to get good average power and resolution at the same time using a pulsed CW system Higher average power is proportional to pulse width Better resolution is inversely proportional to pulse width A long pulse can have the same bandwidth (resolution) as a short pulse if the long pulse is modulated in frequency or phase These pulse compression techniques allow a radar to simultaneously achieve the energy of a long pulse and the resolution of a short pulse Radar Course_28.ppt

29 Matched Filter Concept E = Pulse Energy (Power Time) Matched Filter 2E N Fourier Transform Pulse Spectrum Matched Filter Noise Spectrum Amplitude Phase Amplitude Phase Amplitude N Frequency Frequency Frequency Matched Filter maximizes the peak-signal to mean noise ratio For rectangular pulse, matched filter is a simple pass band filter Radar Course_29.ppt

30 Frequency and Phase Modulation of Pulses Resolution of a short pulse can be achieved by modulating a long pulse, increasing the time-bandwidth product Signal must be processed on return to pulse compress Square Pulse Pulse Width, T Binary Phase Coded Waveform Pulse Width, T Linear Frequency Modulated Waveform Pulse Width, T Bandwidth = 1/T T CHIP Bandwidth = 1/T CHIP Frequency F1 Frequency F2 Bandwidth = ΔF = F2-F1 Time Bandwidth = 1 Time Bandwidth = T/T CHIP Time Bandwidth = TΔF Radar Course_3.ppt

31 Binary Phase Coded Waveforms Binary Phase Coded Waveform Pulse Width, T T CHIP Bandwidth = 1/ T CHIP Changes in phase can be used to increase the signal bandwidth of a long pulse A pulse of duration T is divided into N sub-pulses of duration T CHIP The phase of each sub-pulse is changed or not changed, according to a binary phase code Phase changes or π radians (+ or -) Pulse compression filter output will be a compressed pulse of width T CHIP and a peak N times that of the uncompressed pulse Pulse Compression Ratio = T/ T CHIP Radar Course_31.ppt

32 Implementation of Matched Filter Matched filter is implemented by convolving the reflected echo with the time reversed transmit pulse 1 Reflected echo Time reversed pulse Convolution process: Move digitized pulses by each other, in steps When data overlaps, multiply samples and sum them up Radar Course_32.ppt No overlap Output Output of Matched Filter Time

33 Implementation of Matched Filter Matched filter is implemented by convolving the reflected echo with the time reversed transmit pulse 1 Reflected echo Time reversed pulse Convolution process: Move digitized pulses by each other, in steps When data overlaps, multiply samples and sum them up Radar Course_33.ppt No overlap Output Output of Matched Filter Time

34 Implementation of Matched Filter Matched filter is implemented by convolving the reflected echo with the time reversed transmit pulse 1 Reflected echo Time reversed pulse Convolution process: Move digitized pulses by each other, in steps When data overlaps, multiply samples and sum them up Radar Course_34.ppt One sample overlaps 1x1 =1 Output of Matched Filter Time

35 Implementation of Matched Filter Matched filter is implemented by convolving the reflected echo with the time reversed transmit pulse 1 Reflected echo Time reversed pulse Convolution process: Move digitized pulses by each other, in steps When data overlaps, multiply samples and sum them up Two samples overlap (1x1) + (1x1) = 2 Radar Course_35.ppt Output of Matched Filter Time

36 Implementation of Matched Filter Matched filter is implemented by convolving the reflected echo with the time reversed transmit pulse 1 Reflected echo Time reversed pulse Convolution process: Move digitized pulses by each other, in steps When data overlaps, multiply samples and sum them up Radar Course_36.ppt Output of Matched Filter Three samples overlap (1x1) + (1x1) + (1x1) = Time

37 Implementation of Matched Filter Matched filter is implemented by convolving the reflected echo with the time reversed transmit pulse 1 Reflected echo Time reversed pulse Convolution process: Move digitized pulses by each other, in steps When data overlaps, multiply samples and sum them up Two samples overlap (1x1) + (1x1) = 2 Radar Course_37.ppt Output of Matched Filter Time

38 Implementation of Matched Filter Matched filter is implemented by convolving the reflected echo with the time reversed transmit pulse 1 Reflected echo Time reversed pulse Convolution process: Move digitized pulses by each other, in steps When data overlaps, multiply samples and sum them up Radar Course_38.ppt One sample overlaps 1x1 =1 Output of Matched Filter Time

39 Implementation of Matched Filter Matched filter is implemented by convolving the reflected echo with the time reversed transmit pulse 1 Reflected echo Time reversed pulse Convolution process: Move digitized pulses by each other, in steps When data overlaps, multiply samples and sum them up Radar Course_39.ppt Output of Matched Filter Use of Matched Filter Maximizes S/N Time

40 Pulse Compression Binary Phase Modulation Example Radar Course_4.ppt Figure by MIT OCW.

41 Linear FM Pulse Compression Because range is measured by a shift in Doppler frequency, there is a coupling of the range and Doppler velocity measurement Radar Course_41.ppt Figure by MIT OCW.

42 Summary Detection of Targets in Noise Both target properties and radar design features affect the ability to detect signals in noise Coherent and non-coherent integration pulse integration can improve target detection Adaptive thresholding (CFAR) techniques are needed in realistic environments Pulse compression offers a means to simultaneous have high average power and good resolution A long pulse can have the same bandwidth (resolution) as a short pulse, if it is modulated in frequency or phase Phase-encoded pulse compression divides long pulses into binary encoded sub-pulses With frequency-encoded pulse compression, the radar frequency is increased linearly as the pulse is transmitted Radar Course_42.ppt

43 References Skolnik, M., Introduction to Radar Systems, New York, McGraw-Hill, 3 rd Edition, 21 Toomay, J. C., Radar Principles for the Non-Specialist, New York, Van Nostrand Reinhold, 1989 Radar Course_43.ppt