Session 1: General Radar Background

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2 Session 1: General Radar Background What you will learn: What and why is radar Multiple radar examples and explanations Key radar sub-systems Key issues concerning radar sub-systems performance Principal digital signal processor functions Key functions of the radar control program in the back-end computer Basic principles preliminaries Electromagnetic radiation in free space Frequency, frequency designations, and performance implications Transmission and reception Range measurement, pulse spectrum, and instantaneous bandwidth Transmitter peak and average power Range measurement, range resolution, minimum range, and range ambiguities Radar range equation: development, forms, losses, receiver noise, pattern propagation factor, radar cross section, Blake charts Detection threshold, range/angle/doppler measurement process and accuracies Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 2

3 Radar Photos PSR and SSR of the UK Watchman ATC radar Ground based, fixed PSR: Primary surveillance radar, also known as an ASR (airport surveillance radar): 2D, S-band, reflector array SSR: Secondary surveillance radar: it is a transponder based communication device also known, in military applications, as an IFF (identification friend foe): 2D, L-band ATC: Air traffic control; Surveillance, tracking, and identifications of aircraft in the vicinity of airports. Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 3

4 Radar Photos AN/TPS-80 Ground/Air Task Oriented Radar (G/ATOR) Ground based, mobile Multi-mission, search, track, engage, and fire finder radar. Future missions include ATC. Full AESA, 3D, S-band, multiple Simultaneous beams, two dimensional electronic steering Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 4

5 Radar Photos F22 Raptor s AN/APG-77 AESA radar Airborne, multi-mode, fire-control Multi-mode, 3D, fully active ESA, airborne fire control radar Typical missions include surveillance and tracking, fire control, ground mapping, and GMTI Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 5

6 Radar Photos AEGIS AN/SPY-1 ESA radar Shipboard, multi-mode Long range search, track, and engage radar. 3D, S-band Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 6

7 Key Radar Sub-systems Transmitter Pulse Modulator Waveform Generator Duplexer Antenna Receiver/ADC Signal Processor Data Processor and Radar Controller Communications Operator Displays Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 7

8 Principal Digital Signal Processor Functions (Typical Organization) ADC-Σ ADC-Δ AZ ADC-Δ EL Adaptive Sidelobe Cancellation Pulse compression Centroiding Doppler Filtering Sidelobe Blanking Thresholding (CFAR) Detection ADC-SLB ADC-Aux 1 ADC-Aux N W 1 W N Weight Computation Angle Estimation Ambiguity Resolution Prioritization Report Formation Higher Throughput; Simple Logic Lower Throughput; Complex Logic Pulse Compression and Doppler Filtering in Monopulse and Blanker Channels, and CFAR and Detection in Blanker Channel are not Shown Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 8

9 Major Functions of the Radar Control Program Accept Target Reports from Signal Processor Correlate Reports against existing Tracks Update Tracks with correlated Reports Initiate Tracks with uncorrelated Reports Major Track Processing Functions Perform Track maintenance Functions Prioritize Tracks and assign dedicated Track Status, Track Rates, etc. Select Dwells by Priority Select Waveforms and other Parameters Especially demanding in Electronically Steered Array Systems Schedule Dwells e.g., dedicated Tracks, Track-whilescan, Calibration, BIT/FIT, etc. Key Resource Management Functions Generate Displays Communicate with Internal Systems Process Operator Control Communicate with External Systems Key Control and Communication Functions Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 9

10 PRELIMINARIES Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 10

11 Electromagnetic Radiation in Free Space (1/2) Sinusodial Electric (E) and H(Magnetic) Components Each ^ to the other and direction of travel All EM Waves Travel at Speed of Light, C C = 3X10 8 Meters/Sec = 300,000 KM/Sec = 186,000 Miles/Sec Definition of Wavelength, LAMBDA (l) and Frequency (f) f l = c l Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 11

12 Electromagnetic Radiation in Free Space (2/2) The Electromagnetic Power Density in Free Space is Given By Energy Per Unit Volume Where 2 2 0E 0H = = ε 0 =Free Space Electric Permitivity=8.854*10-12 Farad/m μ 0 =Free Space Magnetic Permiability=4π*10-7 Henry/m c= 1/ =300m/microsecond=Speed of light 0 0 E= 0 H = Z 0 H Z 0 = The Free Space Impedance =377Ω 0 Power Density (Per Unit Area) = ε 0 E 2 c=e 2 /Z 0 = Z 0 H 2 Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 12

13 Radar Bands and Some Related Applications Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 13

14 Transmit/Receive Operations PRI = Pulse Repetition Interval Duplexer switch provides receiver isolation from powerful transmission Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 14

15 Single Pulse spectrum (1/2) The Single Pulse Spectrum is Given by: A Voltage Spectrum = The Power Spectrum is Given by: e j c t e jt = sin A sin y y Power Spectrum 2 sin y y 2 When y =, 2 then sin 2 y y Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 15

16 Single Pulse spectrum (2/2) The Half-Power Spectral Width, or Bandwidth, B, is Given by: B Spectral Width 1/2 = 2 f 1 = 2 1 Where f 1 is Determined from 2 y 1 2 = = f 1 2 = 2 ; i.e., f 1 2 = 1 2 When the received noise is matched filtered to the signal spectrum, B becomes also the Noise bandwidth The B τ ~ 1 is a direct consequence of the Fourier transform relationship between the pulse temporal and spectral aspects. It hold for any pair of entities related by the same transform. Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 16

17 Simple Form of Range Equation P P G A t t e r =, R WATTS P t, P r = Peak Transmit and Receive Powers G t = Antenna Transmit Gain A e = Antenna Effective Receive Aperture σ = Target s Radar Cross Section R = The Slant Range from Radar to Target Useful as a reference, and for rough performance calculations For accuracy and realism must include Propagation Composite Background (Thermal Noise, Clutter, and ECM) Losses Simple Equation Includes Power radiated toward target Flux density at target Power reflected by target Flux density at radar Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 17

18 Propagation of Reflected Power Density from Target back to Radar in free Space A e = Effective area of radar antenna Power density at radar antenna 1 = [P T G T / (4πR 2 )] σ t / (4πR 2 ) = (P T G T σ t )/ (4πR 2 ) 2 = (P T G T σ t )/ [(4π) 2 R 4 ] R Reflected Power Shell Power intercepted by radar antenna = Received Signal = Power density at radar antenna x A e = (P T G T σ t )/ [(4π) 2 R 4 ] A e = S = (P T G T A e σ t )/ [(4π) 2 R 4 ] 1 Assuming perfectly conducting spherical target Transmitting Antenna Radar Target Transmitted Power Shell Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 18

19 Key Radar Sub-systems and Typical Losses: A High Level, simplified Example L radiator L line1 L BF,Tx Transmitter Pulse Modulator Waveform Generator L radome L line2 L circulator Circulator Antenna L BF,Rx L line3 L RP Receiver T RX Signal Processor L proc Data Processor and Radar Controller L Tx = L line1 + L BF,Tx + L circulator + L line2 +L radiator + L radome L Rx = L radome +L radiator + L line2 +L circulator + L line3 + L BF,Rx + L RP + L proc Some receive plumbing losses are traditionally accounted for in the System s Noise Temperature Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 19

20 Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 20 Thermal Noise in the Radar Range Equation The Radar Range Equation in its Simple Form is Given by: It Can be Solved for Range as Follows: Multiplying and Dividing by the Thermal Noise Power ( N ): R A P G P t e t t r = Where, P min = S min = The Minimum Detectable Signal and R max = The Maximum Detection Range for this Target 4 1 min 2 max 4 = P A P G R t e t t 4 1 min 2 4 = S A G P t e t t 4 1 min 2 max 4 = N S N A P G R t e t t 4 1 min 2 4 = N S N A G P t e t t 4 1 min 2 4 = N S ktb A G P t e t t

21 What you will learn: Session 2: Noise in Receiving Systems and Detection Principles Noise in receiving systems What is the system s noise temperature The origin and justification of the ktb expression Elements of receiver thermal noise analysis The referral principle and its role Active and passive transducers Detailed thermal noise analysis The role of low noise amplifier in reducing the system s noise temperature Detection Principles The detection process as a statistically based decision Signal and noise statistics False alarm probability, false alarm time, false alarm number: definition and role Single pulse detection process and statistics Multiple pulse integration: purpose and alternative techniques Fluctuating target, and target-plus-noise, statistics and their role in multi-pulse integration process Frequency diversity, frequency agility, and their roles in improving detection statistics Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 21

22 The Origin of KTB Planck s Formula for thermal Noise per unit Bandwidth P N, UnitBand = e hf hf kt 1 kt ( At Microwave Frequencies ) Where h = Planck s Constant = 6.63 x Watt-Second 2 k = Boltzmann s Constant = 1.38 x Watt-Second/deg f = frequency (Hz) T = Ambient Temperature (degree Kelvin) Clearly, though locally flat, when f becomes large, the Noise Power Density diminishes Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 22

23 The Referral Principle Antenna Reference Point Target Detection Point Incoming Signal S N forward Incoming Noise Transmission Line Rx Transmission Line ADC N referred back S N = S N forward N referred back Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 23

24 Entire Receiver Analysis The entire Receiver can be summarized at high Level as follows: T ant T amb, L trans G rx, NF Reference Point Transmission Line R x Input Receiver Or, T = T T T * L sys sys a a tran amb Rx tran L 1 T NF 1 L tran 0 tran T = T T * Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 24

25 The Role of A Low Noise Amplifier When the System Noise Temperature is too high, a Low Noise Amplifier after the reference Point is indicated: Antenna Reference G LNA, NF LNA T amb, L tran G R, NF T ant Transmission Line Receiver T sys = T ant T NF 1 T L 1 T NF 1* L / G LNA amb tran 0 R tran LNA 0 The down-stream Contributions are reduced by the LNA gain The LNA s own Noise is added, and must therefore be low Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 25

26 Thermal Noise Statistics (1/3) Receiver Thermal Noise is Caused by Very Large Numbers of Electrons Oscillating Independently within Conductors and Dialectrics - Inside and Outside the Radar Because the Contributions are Many and Independent, the Thermal Noise Voltage is Governed by a Normal (i.e., Gaussian) Probability Density Function P x = 1 exp 2 x Where, x = V = Noise Voltage; α = σ v = Standard Dev. ; σ v 2 = Variance; and μ = Mean = 0 The Noise Voltage Density: (a) Has a Symethrical Bell Shape, and (b) Has Positive and Negative Values about a Zero Mean 1 As per the Central Limit Theorem Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 26

27 Probability Density Single Pulse Detection Probability Density Functions and Detection Threshold for a Single Pulse Noise Alone PFA Threshold Signal Plus Noise N : (1 Pulse) S+N : (1 Pulse) Amplitude PD Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 27

28 Probability Density Non-Coherent Integration Probability Density Functions and Detection Thresholds for Single and Non-Coherently Integrated Pulses T 100 N 100 (S+N) 100 T 1 N : (1 Pulse) S+N : (1 Pulse) N : (100 Pulses) S+N : (100 Pulses) N 1 (S+N)1 Normalized Voltage Amplitude Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 28

29 Probability Density Coherent Integration Probability Density Functions and Detection Thresholds - for Single and Coherently Integrated Pulses N 1 (S+N) 1 T 1 T 10 N 10 (S+N) 10 N : (1 Pulse) S+N : (1 Pulse) N : (10 Pulses) S+N : (10 Pulses) Scaled Sample Voltage Amplitude Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 29

30 S/N Requirement Versus # Pulses Integrated (PD=0.5) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 30

31 Integration Improvement Factor (Non-Coherent- Integration) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 31

32 Single-Pulse Fluctuation Loss for Swerling Targets Figure 2.23 Additional signal-to-noise ratio required to achieve a particular probability of detection. When to target cross section fluctuates, as compared with a nonfluctuating target single hit, n = 1. (To be used in conjunction with Fig. 2.7 to find (S/N) Source: Skolnik, Introduction to Radar Systems Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 32

33 Integration Improvement Factor for Swerling Targets Source: Skolnik, Introduction to Radar Systems. Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 33

34 Session 4: Radar Propagation in the Troposphere What you will learn: Principal Propagation Issues The Pattern Propagation Factor (PPF) Effects of the Earth Surface: Interference (Multipath), Intermediate region, Diffraction Effects of spherical Earth, surface type, antenna pattern polarization, frequency, Effects of the atmospheric refractivity Refractive index, Refractivity, Modified Refractivity Refraction and propagation Standard and anomalous propagation conditions Evaporation and surface based propagation ducts Modified Earth radius modeling technique Modern computational tools: The Parabolic Equation coupled with the Split Step technique Combined effects of refractivity and variable terrain Effects of propagation on angle measurement Effects of propagation on both surface based and on airborne radars Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 34

35 The Pattern Propagation Factor One-way, voltage domain: PPF = F = E Actual E Free Space, at Max Gain One-way, power domain: PPF = 2 F Two-way, power domain: PPF = F2 2 1 F 2 E Actual The electric field actually experienced at the target, or the electric field experienced a the radar antenna due to unit stated transmission from the target E free Space, at Max Gain The corresponding electric fields above, that would be experienced under free-space conditions when the maximum antenna gain is pointed directly at the target Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 35

36 Radar Range Equation with Pattern Propagation Factor P RCV = P t G t A e F 2 t R F 2 r Where F t 2 = The one-way Pattern Propagation Factor (PPF) on Transmit (power domain), and F r 2 = The one-way Pattern Propagation Factor (PPF) on Receive (power domain) When the antenna patterns are identical on transmit and receive: P RCV = P t G t A e F R 4 Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 36

37 The Presence of the Earth s Surface: Classical Propagation Regions Three regions of propagation: Interference (multipath) region: well within the target horizon; Ray Theory is valid Deep shadow region: far beyond the target horizon: mechanism is diffraction; classical solutions are available Intermediate region: straddling the target horizon: mechanism is diffraction; classical solutions are tedious Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 37

38 Multipath Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 38

39 Detection Contour Plot (1) f=100mhz h a =20feet e =0 degrees R0=100 nmi HH BW =90 0 Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 39

40 Detection Contour Plot (2) f=100mhz h a =80feet e =0 degrees R0=100 nmi HH BW =90 0 Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 40

41 Detection Contour Plot (3) f=1000mhz h a =80feet e =0 degrees R0=50 nmi HH BW =10 0 Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 41

42 Reflection Coefficient of Sea Water Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 42

43 Pattern Propagation Factor (db) PPF at Various Sea States for a 100 Foot Target PPF for VARIOUS SEA 100 ft SS SS 4-25 SS 2-30 Range (nmi) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 43

44 Effective Earth Radius Effective Earth Radius Is Used Compensate For Refractive Effects. Simpler to Compute Refractive Effects In Terms of Straight Rays Accomplished (as an Approximation) by Replacing Actual Earth Radius With and Effective Earth Radius k eff 1 = dn 1 a dh Where, K eff = the ratio between the effective Earth radius and the mean Earth radius a = the mean actual Earth radius, and dn/dh = the derivative of the refractive index wrt height near sea level 4/3 is used for the Standard Atmosphere 1.6 is used routinely as a maritime Keff Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 44

45 Standard Propagation Coverage Diagram Generated by VTRPE (S-Band) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 45

46 40 Foot Duct Coverage Diagram Generated by VTRPE (S-Band) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 46

47 Refractivity Profile Representing a 300 Meter Surface Based Duct Measured in the Adriatic Sea Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 47

48 Coverage Diagram Generated by VTRPE for the 300 Meter Surface Based Duct Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 48

49 Standard Propagation, 1000 Target Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 49

50 Session7: Radar Waveforms What you will learn: Physical principles of pulse compression Bandwidth and range resolution The time-bandwidth product Pulse coding as methods to simultaneously obtain desired time and bandwidth Pulse compression processing Codes and filters Matched and mismatched filters; matched lengths and mismatched length filters Convolution between codes and filters in the range and Doppler domains Measures of performance for codes and filters Mismatch loss; Peak and Integrated sidelobe levels; Doppler tolerance; Cross-correlation in code families; Target broadening; Spectral behavior Example Codes description Pseudo-random-number (PRN); Linear FM; Lewis-Kretschmer P4; Non-linear FM; Single and nested Barker Optimal codes and mismatched filters: Temporal and spectral constraints; Optimal codes and code families Multiple-Input-Multiple-Output (MIMO) Radar and code families Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 50

51 Pulse Compression Issues Pulse Compression Consists of Generating a Phase Code (Discrete or Continuous) on Transmit and Removing it on Receive The Compressed Waveform Generally has a Response Region outside the Main Response, Entitled Time Sidelobes An Adequate Design should Provide High Peak Gain High Range Resolution Low Time Sidelobes Low Sensitivity to Target Doppler The Above is Obtainable through the Combination of Good Compression Codes Effective Compression Filters (Matched or Mismatched) Doppler Compensation in the Processing Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 51

52 Pulse Compression Coding Conceptually: Some characteristic of the waveform is progressively changed over the transmitted pulsewidth typically the pulse is phase or frequency modulated (coded) This gives the radar receiver a method for differentiating target returns that overlap Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 52

53 The Correlation Function Time Domain: R ( n) = C( m) b( n m) m Frequency Domain: 1 R( n) = N N 1 k= 0 l C( l) e 2nl j N l b( l) e 2nl j N * e 2nk j N R = Cross-correlation (mismatched filter), or auto-correlation (matched filter) function C = transmitted pulse compression code (amplitude and phase) b = Compression filter coefficients (matched or mismatched) m = Correlation delay Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 53

54 Phase Coded Pulse Compression Resolution and Accuracy The phase code determines the overall shape of the pulse compressed output Good phase codes produce a thumbtack response in range Isolated peak at target range The peak is easier to locate than in the uncompressed case - improves range accuracy The width of the peak, and range resolution, is determined by the coding rate (1/) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 54

55 Some Common Types of Phase Codes Barker codes Peak sidelobe is 1 Longest known code is 13 Not long enough for most applications High Doppler Sensitivity Pseudo-random (maximal length) PN codes Exist in lengths 2N - 1 Number of 1 s and -1s differ by 1 1/2 the runs are length 1, 1/4 are length 2, 1/8 are length 3, etc.. Generated using a shift register with feedback Used in live radar eliminates need to store codes in memory Minimum peak sidelobe codes Found by exhaustive search for a given N N-49 is the longest code completely searched Custom codes picked for application Found by random search for given N, search until enough are found Picked for cross-correlation properties, sidelobe structure, etc.. Optimal codes Found by optimal search subject to multiple, suitably chosen constraints, in multiple dimensions Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 55

56 Mismatched Filtering: Second Example Better control of time sidelobes can be achieved with increasing mismatched filter length Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 56

57 Mismatched Filtering: Third Example Mismatched filters can provide fine and adaptive control over time sidelobes to adaptively counteract clutter behavior Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 57

58 Doppler Tolerance Examples PN Code P4 Code Time-Frequency Ambiguity Diagrams Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 58

59 Figures of Merit (FOM) Definition: The broadening of the pulse compressed peak response beyond its inverse bandwidth value. Matched filter introduces no broadening The least squares filter introduces no broadening Classical amplitude tapers (Hamming, Taylor, etc.) have moderated broadening Phase weighting (non-linear FM waveforms) have large intrinsic broadening Impact: -Degrades range resolution -Increases clutter levels Target Broadening Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 59

60 Code Comparisons Peak Sidelobes-Matched Length Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 60

61 Abundance of codes High performance code/filter pairs can be generated very quickly & efficiently Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 61

62 Pulse 4 Pulse 3 Pulse 2 Pulse 1 Orthogonal Codes 0 Pulse 1 0 Pulse 2 0 Pulse 3 0 Pulse x x x x x x x x x x x x x 10 5 x 10 5 x 10 5 x 10 5 Matched filter properties of four codes optimized to have -55 db autocorrelation & cross-correlation sidelobes Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 62

63 Power (db down from peak) Spectrum Control 0 No spectral control Careful spectral control Frequency offset from carrier (MHz) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 63

64 Magnitude (db down from the autocorrelation peak) Temporal Control 0 Correlation of waveform1 with filter 2-10 Loss= 0.98 db Correlation delay (samples) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 64

65 Multiple Input Multiple Output (MIMO) Radar (2 of 4) A typical MIMO Scheme WF 1 WF 2 WF 3 WF Receive Array N Transmit Array WF j, j=1,n, are N orthogonal waveforms MF j, j=1,n, are N corresponding matched filters MF 1 M 2 MF 3 MF N Transmit Beamformer for L-beams The Transmit and Receive Array can be the same array (monostatic) or different arrays (bistatic) Receive Beamformer for one beam Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 65

66 Session 8: Electronically Scanned Antennas What you will learn: Fundamental concepts Advantages of phased array antenna over reflector antennas Radiation from an isotropic source; antenna directivity and gain Radiation in free space; antenna pattern in the radiating near field and in the far field Element factor and array factor Antenna pattern and the illumination function: a Fourier transform relationship Multiple examples including effects of illumination function errors Beamwidth approximations Low sidelobes antennas: illumination functions; error noise floor; error budgets Array bandwidth Array steering with variable phase shifters and with true time delay lines Sub-array implementations Element separation and grating lobes Phase monopulse angle measurement: Taylor sum and Bayliss difference illuminations Amplitude and phase quantization Implementation examples Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 66

67 Advantages of a Phased Array Antenna over a Reflector Beam Agility Electronic Scanning i.e., no Mechanical Inertia Flexible Search: Different Search Patterns and Update Rates at Different Sectors Multi-target Tracking, Concurrent with Search, at Flexible Rates across broad Volume Multiple simultaneous beams Potential for multiple independent or clustered beams implementation Wideband Potential for wide band implementation Reduced Antenna Radar-Cross-Section (RCS) relative to reflector arrays Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 67

68 Radiation from an Isotropic source R Radiation Intensity (I) = Radiated Power per Unit Solid Angle [ W / Ω ] I = Transmitted Power (Watts) 4 (Radians) An Isotropic Source Serves and a Reference for Measuring the Directivity of Other Antennas Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 68

69 Antenna Directivity A Radar Antenna Concentrates Transmitted Energy into a Beam Favoring one Narrow Solid Angle Sector over all Others Increases the Radiation Intensity in the Beam Direction Decreases the Radiation Intensity in other Directions Antenna Directivity (it s Directive Gain ) is Measured by Comparing its Radiation Intensity Relative to that of an Isotropic Antenna Directivity = 0 10 Log 10 ( ) = Directivity in dbi 0 Typical Maximum Antenna Directivity = 4 A Where A = Array Size ; l = Radar Wavelength l 2 Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 69

70 Phase of Electric Field Electric and Magnetic fields are 90 Degrees out of Phase E = ( E 0 [D()] 1/2 / R ) e j ( t - k R ) = 2 / T = 2 x frequency k = 2 / l l I f R E 0 e j f = E 0 ( cos( f ) + j sin( f ) ) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 70

71 POWER, db POWER, db Pattern Multiplication : Array Factor Element Pattern 5 0 Element Pattern Array Factor sin( ) sin( ) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 71

72 APERTURE ILLUMINATION FIELD STRENGTH POWER, db APERTURE ILLUMINATION FIELD STRENGTH POWER, db A Smaller Array, Operating at the Same Frequency, has a Wider, Lower Power Beam Physical Position in Array Antenna Physical Position in Array Antenna sin( ) sin( ) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 72

73 Array Bandwidth DEFINITION: Array instantaneous bandwidth (IBW) is the band over which the array can maintain its nominal steering angle within predetermined constraints. Steering with phase shifters: Instantaneous bandwidth depends on the steering angle» At array boresight (no steering) the instantaneous array bandwidth is infinite» As the steering angle increases, the instantaneous array bandwidth decreases» The instantaneous array bandwidth is normally taken to be determined by what happens at the 60 degree steering angle.» The percent bandwidth is than roughly equal to the degrees beamwidth at boresight Percent BW = 100 IBW/f carrier = θ deg (boresight); where f carrier is the carrier frequency» It can also be roughly estimated from the following relationship IBW (MHz) = 150 MHz-m / L; where L is the largest linear array dimension in meters. Steering with true time delays at the element level:» The instantaneous array bandwidth is infinite in every steering direction Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 73

74 Element Separation: Too Large a Separation Causes Grating Lobes to Form Normally Accepted Element Separation is near half wavelength: i.e., λ/2 Boresight Beam λ Grating Lobe Beam Boresight Beam Grating Lobe Beam It allows Grating- Lobe-Free Steering to, at least, 60 degrees off Boresight λ λ Grating Lobes degrade Performance in two major Ways - Loss of Power and Sensitivity - Ambiguous Measurement Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 74

75 Phase Monopulse Angle Measurement: Simplified Σ =Sum =V 1 + V 2 Array Boresight direction f = 2 x l Target direction x V 1 V 2 Array Left Half V 2 V 2 Σ V 1 V 1 Array Right Half Δ =Difference =V 1 V 2 R = = Measure of angular location Δ Difference Channel Sum Channel Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 75

76 Receive Power, Relative to (Taylor) Pattern Peak (db) Sum and Difference Power Patterns for Taylor/Bayliss Weights Taylor Pattern (Sum) Bayliss Pattern (AZ) Bayliss Pattern (Difference Taylor Pattern (EL) Off-Boresight Angle (degrees) Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 76

77 Comparison of Receive (Sum) Array Elements Amplitude Quantization Effects on Array Illumination ( Original Illustrations are in Color) Coarse Amplitude Quantization Fine Amplitude Quantization Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 77

78 Amplitude Quantization: Comparison of Receive (Sum) Patterns Coarse Amplitude Quantization Fine Amplitude Quantization Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 78

79 Search Beam 2- Way Gain Do Not Reproduce Without Written Permission from the Author or Applied Technology Institute. 79