Principles of Modern Radar - Volume 2 1891121537

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17.2 Evaluation of the 2D-CCF for the Passive Radar Coherent Integration 747DMRDNRDOADOFDSSSDVB-TECAECA-BECA-B&SFFTFIRFMFUSCGALHFIDFTIFFTMFMFCMTINLMSOFDMPBRPNFRPSDPSKPSLRPUSCRxS-CMASFCSNRST-CMAT-CMATPSTxUHFULWiMAXdirect signal-to-multipath ratiodirect signal-to-noise ratiodirection of arrivaldegrees of freedomdirect sequence spread spectrumdigital video broadcasting - terrestrialextensive cancellation algorithmECA batchesECA batches & stagesfast Fourier transformfinite impulse responsefrequency modulationfully used sub-channelizationgradient adaptive latticehigh frequencyinverse discrete Fourier transforminverse fast Fourier transformmultiple-frequencymultiple-frequency configurationmoving target indicationnormalised least mean squaresorthogonal frequency-division multiplexingpassive bistatic radarpeak-to-noise floor ratiopower spectral densityphase-shift keyingpeak-to-sidelobe ratiopartially used sub-channelizationreceiverspace constant modulus algorithmsingle frequency channelsignal-to-noise ratiospace-time constant modulus algorithmtime constant modulus algorithmtransmission parameter signallingtransmitterultra-high frequencyup-linkworldwide interoperability for microwave access17.2 EVALUATION OF THE 2D-CCF FOR THEPASSIVE RADAR COHERENT INTEGRATIONThe evaluation of the bistatic range-velocity 2D-CCF is the key step in the PBR processingchain. It corresponds to the implementation of a bank of matched filters, each one tunedto a specific target bistatic velocity. Typically the values of velocity are chosen witha separation approximately equal to the bistatic velocity resolution. Therefore, the set
748 CHAPTER 17 Advanced Processing Methods for Passive Bistatic Radar Systemsof filters covers all the possible target velocities. The filter where the target is detectedprovides the estimates of the bistatic Doppler shift of each target echo. Similarly, theestimate of the bistatic range is given by the sample along range where it is detected.Assuming that the signal s ref (t) collected at the reference antenna is a perfect copy (or atleast good enough as discussed in a later section) of the transmitted signal, the 2D-CCFfor a PBR is evaluated as∫ ∞χ(τ,f D ) = s surv (t) s ∗ ref (t − τ)e− j2π f Dt−∞dt (17.1)wheres surv (t) = the complex envelope of the signal collected at the surveillance antennaτ = R B /c = the bistatic time difference of arrival of interest, where R B is the relativebistatic range, or the difference between the two-way path length and the baselinebetween the transmitter (Tx) and the receiver (Rx)f D = v B /λ = the Doppler shift of interest, v B , being the bistatic velocity (i.e., the rateof change of Tx – target – Rx range)The integral is limited in practice to the coherent processing interval (CPI) T int .Assuming that the signals are sampled at frequency f s , equation (17.1) can be easilyexpressed in discrete time notation aswhereN−1∑χ[l,m] = s surv [n] · s ∗ mnj2πref[n − l] · e− N (17.2)n=0N = ⌊T int f s ⌋ = the number of integrated samplesl = the time bin corresponding to time delay τ = l/f sm = the Doppler bin corresponding to Doppler shift f D = mf s /NThe evaluation of the 2D-CCF for a PBR represents one of the most costly operations interms of computational burden [4,27,28]. In fact, the exploited waveform of opportunitytypically has a low power level for radar purposes, so a very long integration time isusually required to obtain an acceptable signal-to-noise ratio (SNR). Moreover, large2-D maps might be required depending on the desired surveillance region extent in bothrange (0, R Bmax ) and Doppler dimensions (–|v B | max , |v B | max ), where R B max and |v B | maxare the maximum relative bistatic range and the maximum bistatic velocity of interest,respectively. This implies that a huge amount of data has to be managed and a largenumber of complex operations has to be performed that might require very fast hardwarefor real-time processing. As a reference, the direct evaluation of (17.2) over N τ time binsand N f Doppler bins requires N(N τ + 1)N f complex multiplications and (N − 1)N τ N fcomplex additions, where, assuming that the 2D-CCF is not oversampled, we haveN τ =⌈RB maxcf s⌉⌈ 2|vB |and N f = maxλ⌉Nf s(17.3)
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Principles of Modern Radar
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Published by SciTech Publishing, an
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Brief ContentsPreface xvPublisher A
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xContents3.6 Adaptive MIMO Radar 10
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xiiContents9.3 Adaptive Jammer Canc
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xivContents15.3 Multisensor Trackin
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xviPrefacehas always been the unlik
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Publisher AcknowledgmentsTechnical
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Editors and ContributorsVolume Edit
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xxiiEditors and ContributorsDr. Lis
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xxivEditors and ContributorsMr. Ara
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2 CHAPTER 1 Overview: Advanced Tech
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1.3 Radar and System Topologies 5FI
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1.4 Topics in Advanced Techniques 7
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1.6 References 15TABLE 1-1Summary o
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PART IWaveforms and SpectrumCHAPTER
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20 CHAPTER 2 Advanced Pulse Compres
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2.2 Stretch Processing 35is applied
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2.2 Stretch Processing 37TABLE 2-1
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2.5 Stepped Frequency Waveforms 61T
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2.5 Stepped Frequency Waveforms 63w
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2.5 Stepped Frequency Waveforms 69I
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2.9 References 812.7.4 SummaryWhile
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2.9 References 83[27] Taylor, Jr.,
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2.10 Problems 85shift across the pu
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88 CHAPTER 3 Optimal and Adaptive M
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3.2 Optimum MIMO Waveform Design fo
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3.4 Optimum MIMO Design for Target
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3.4 Optimum MIMO Design for Target
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3.5 Constrained Optimum MIMO Radar
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108 CHAPTER 3 Optimal and Adaptive
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3.6 Adaptive MIMO Radar 111SINR Los
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3.10 Problems 115[22] W. Y. Hsiang,
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3.10 Problems 1179. A constrained o
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120 CHAPTER 4 MIMO Radarperformance
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4.3 The MIMO Virtual Array 123separ
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4.4 MIMO Radar Signal Processing 12
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134 CHAPTER 4 MIMO RadarFIGURE 4-7T
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136 CHAPTER 4 MIMO Radar4.5.2 MIMO
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138 CHAPTER 4 MIMO Radarnamely, R
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140 CHAPTER 4 MIMO RadarTABLE 4-2 P
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142 CHAPTER 4 MIMO RadarSINR Loss (
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144 CHAPTER 4 MIMO Radar[10] H. V.
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Radar Applications of SparseReconst
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5.1 Introduction 149δ = M/N, the u
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152 CHAPTER 5 Radar Applications of
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5.2 CS Theory 163While the notion o
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5.2 CS Theory 165as , where is a b
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5.3 SR Algorithms 167than the norm
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5.3 SR Algorithms 169the value of o
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5.3 SR Algorithms 171takes special
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5.3 SR Algorithms 173The function f
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5.3 SR Algorithms 175of the TV norm
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5.3 SR Algorithms 177One can argue
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5.3 SR Algorithms 179probability ma
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5.3 SR Algorithms 181only a subset
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5.4 Sample Radar Applications 183pr
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5.4 Sample Radar Applications 185We
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5.4 Sample Radar Applications 187th
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5.4 Sample Radar Applications 189tu
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5.4 Sample Radar Applications 191Ra
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5.4 Sample Radar Applications 193Ta
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Spotlight SyntheticAperture RadarCH
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6.1 Introduction 213• Image quali
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6.2 Mathematical Background 215andf
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6.2 Mathematical Background 2172π
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220 CHAPTER 6 Spotlight Synthetic A
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6.4 Sampling Requirements and Resol
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6.4 Sampling Requirements and Resol
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6.5 Image Reconstruction 239FIGURE
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6.6 Image Metrics 241The contrast r
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6.6 Image Metrics 243Along-track am
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6.7 Phase Error Effects 245TABLE 6-
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260 CHAPTER 7 Stripmap SAR3 m SAR O
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262 CHAPTER 7 Stripmap SAR• RMA i
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264 CHAPTER 7 Stripmap SARH 0 (ω)
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268 CHAPTER 7 Stripmap SARTABLE 7-1
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274 CHAPTER 7 Stripmap SARFIGURE 7-
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276 CHAPTER 7 Stripmap SAR−500Sce
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7.3 Doppler Beam Sharpening Extensi
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288 CHAPTER 7 Stripmap SARand in th
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7.4 Range-Doppler Algorithms 291to
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7.4 Range-Doppler Algorithms 293For
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296 CHAPTER 7 Stripmap SAR−150Col
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300 CHAPTER 7 Stripmap SAR33 cycles
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302 CHAPTER 7 Stripmap SARCrossrang
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304 CHAPTER 7 Stripmap SARfrom freq
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7.5 Range Migration Algorithm 307r,
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310 CHAPTER 7 Stripmap SARkx (rad/m
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316 CHAPTER 7 Stripmap SARThe diffe
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320 CHAPTER 7 Stripmap SARLet us re
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322 CHAPTER 7 Stripmap SARThe resul
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324 CHAPTER 7 Stripmap SARscene. Th
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326 CHAPTER 7 Stripmap SARdriven by
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328 CHAPTER 7 Stripmap SARTABLE 7-3
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330 CHAPTER 7 Stripmap SARFIGURE 7-
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332 CHAPTER 7 Stripmap SAR7.10 REFE
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334 CHAPTER 7 Stripmap SAR6. [MATLA
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Interferometric SAR andCoherent Exp
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8.1 Introduction 3398.1.1 Organizat
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8.1 Introduction 341Rsabnv rw x ,w
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8.2 Digital Terrain Models 343FIGUR
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8.3 Estimating Elevation Profiles U
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352 CHAPTER 8 Interferometric SAR a
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8.5 InSAR Processing Steps 365ξ ta
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8.5 InSAR Processing Steps 3670.1 0
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8.5 InSAR Processing Steps 373While
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8.6 Error Sources 375The second met
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8.6 Error Sources 377If sufficient
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Adaptive Digital BeamformingCHAPTER
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9.1 Introduction 403c k = clutter s
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408 CHAPTER 9 Adaptive Digital Beam
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9.2 Digital Beamforming Fundamental
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9.3 Adaptive Jammer Cancellation 42
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9.5 Wideband Cancellation 447FIGURE
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454 CHAPTER 10 Clutter Suppression
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10.2 Space-Time Signal Representati
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10.5 STAP Fundamentals 4810−5−1
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10.6 STAP Processing Architectures
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10.7 Other Considerations 4911 CPIM
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10.9 Summary 49310.7.3 Computationa
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10.10 References 495[12] Fenner, D.
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10.11 Problems 497the PSD in Figure
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11.2 Colored Space-Time Exploration
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11.2 Colored Space-Time Exploration
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506 CHAPTER 11 Space-Time Coding fo
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11.8 References 525Cost reduction o
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11.9 Problems 52711.9.2 Equivalence
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530 CHAPTER 12 Electronic Protectio
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12.2 Electronic Attack 535TABLE 12-
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12.2 Electronic Attack 541variation
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12.5 Antenna-Based EP 557are adjust
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12.6 Transmitter-Based EP 561polari
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12.11 Summary 583TABLE 12-4Summary
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12.14 Problems 585[9] Stimson, G.W.
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Introduction to RadarPolarimetryCHA
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13.1 Introduction 591and precipitat
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13.1 Introduction 593S: target scat
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13.2 Polarization 597After substitu
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13.2 Polarization 599zFIGURE 13-4Po
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13.3 Scattering Matrix 601left-hand
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604 CHAPTER 13 Introduction to Rada
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13.4 Radar Applications of Polarime
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13.4 Radar Applications of Polarime
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13.5 Measurement of the Scattering
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13.5 Measurement of the Scattering
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13.8 References 623• Lee, Jong-Se
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13.8 References 625[32] Kraus, J.D.
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13.9 Problems 627with the result in
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Automatic Target RecognitionCHAPTER
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14.2 Unified Framework for ATR 633P
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14.3 Metrics and Performance Predic
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14.3 Metrics and Performance Predic
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14.4 Synthetic Aperture Radar 639TA
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14.4 Synthetic Aperture Radar 641Te
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14.4 Synthetic Aperture Radar 645Un
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14.4 Synthetic Aperture Radar 64714
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14.4 Synthetic Aperture Radar 649se
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14.4 Synthetic Aperture Radar 651th
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14.5 Inverse Synthetic Aperture Rad
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14.5 Inverse Synthetic Aperture Rad
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14.6 Passive Radar ATR 657radar sys
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14.7 High-Resolution Range Profiles
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14.9 Further Reading 661take a targ
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14.10 References 663[19] Q. H. Pham
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14.10 References 665[56] M. Martore
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14.10 References 667[92] E. Libby,
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Multitarget, MultisensorTrackingCHA
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15.1 Review Of Tracking Concepts 67
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15.1 Review Of Tracking Concepts 67
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678 CHAPTER 15 Multitarget, Multise
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15.2 Multitarget Tracking 683TABLE
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15.2 Multitarget Tracking 685remove
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15.5 Further Reading 69515.4 SUMMAR
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17.6 Multichannel Processing for De
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810 CHAPTER 17 Advanced Processing
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17.10 References 815While far from
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17.10 References 817[20] Chetty, K.
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17.11 Problems 819[52] Gao, Z., Tao
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17.11 Problems 8215. Using the sign
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824 Appendix A: Answers to Selected
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ResolutionResolution withDimension
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830 IndexASAR. See Advanced SAR (AS
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832 IndexCross-polarization (XPOL),
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834 IndexExciter-based EP (cont.)fr
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836 IndexInterferencecolored noise,
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838 IndexMoving target indication (
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840 IndexPOI. See Probability of in
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842 IndexSaturated (constant amplit
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844 IndexStripmap SAR (cont.)remote
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846 IndexWWald sequential test, com
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