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Kei Suwa, Toshio Wakayama, Masafumi Iwamoto Mitsubishi Electric Co.

A Study on The Resolution Limit of Polarimetric Radar and The Performance of Polarimetric Bandwidth Extrapolation Technique. Kei Suwa, Toshio Wakayama, Masafumi Iwamoto Mitsubishi Electric Co. Information Technology R&D Center. Outline.

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Kei Suwa, Toshio Wakayama, Masafumi Iwamoto Mitsubishi Electric Co.

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  1. A Studyon The Resolution Limit of Polarimetric Radarand The Performance of Polarimetric Bandwidth Extrapolation Technique Kei Suwa, Toshio Wakayama, Masafumi Iwamoto Mitsubishi Electric Co. Information Technology R&D Center

  2. Outline • Background -- SAR resolution, PRF, and Polarimetry -- • Polarimetric Bandwidth Extrapolation (PBWE) • The Signal Model • Statistical Resolution Limit (SRL) • The Cramér-Rao Bound (CRB) • SRL and The Performance of PBWE • Conclusion

  3. Background -- SAR resolution, PRF, and Polarimetry -- Higher resolution with smaller aperture size . Range resolution : signal bandwidth / Azimuth resolution : synthetic aperture length • Range resolution is determined by the signal bandwidth. • Azimuth resolution is determined by the synthetic aperture length. FT : Signal Bandwidth : Speed of light range freq. : wave length : Synthetic Aperture length : Range orbit Strip map mode Spotlight mode

  4. Background -- SAR resolution, PRF, and Polarimetry Doppler Freq. Time PRF Due to PRF limitation, Polarimetric SAR often give up the resolution. orbit • Conditions of the PRF • PRF must be higher than the signal Doppler bandwidth, which is determined by the azimuth beam width. • PRF must be low enough so that the range ambiguity is sufficiently low. • The problem with Polarimetry • Polarimetry requires sending H-polarization pulse and V-polarization pulse. • PRF gets lower for each polarization channel, so polarimetric SAR often need to give up the resolution. Beam Illumination area Platform trajectory It would be nice if polarization information helps enhancing the resolution

  5. Background -- SAR resolution, PRF, and Polarimetry Dr. Mihai Datcu “Semantic Content Extraction from High Resolution Earth Observation Images”

  6. Background -- SAR resolution, PRF, and Polarimetry What is “resolution”? … resolution refers to separate two or more nearby targets, i.e., to determine that there are two instead of one. ~Radar Handbook (1970) 4-2~

  7. Background -- SAR resolution, PRF, and Polarimetry It seems to be possible that polarization information helps improving the “resolution”. 1. Flat plate and dihedral corner reflector case HH Polarization vector range Two vectors are orthogonal to each other. VV 2. Two flat plates case HH range Polarization information would not help VV polarization vectors Shh Shv Svv 1 0 1 1 0 -1 Dihedral corner reflector = Flat plate

  8. Polarimetric Bandwidth Extrapolation (PBWE) c 2B c 2B’ • A polarimetric linear prediction model is fitted to the spectral data. • Then the HH,HV,VV spectral data is extrapolated up to B’. B i ii FFT VV HV VV HH iii freq. HV HH range Polarimetric Linear Prediction Model Estimation v B’ iv IFFT VV VV HV HV HH HH range freq.

  9. Polarimetric Bandwidth Extrapolation (PBWE) We have empirically shown that Polarization information does contribute to the resolution enhancement azimuth range Storebaelt : the great belt EMISAR : dual frequency (L- and C-band) polarimetric Synthetic Aperture Radar (SAR) system developed at Technical University of Denmark. http://www.emi.dtu.dk/research/DCRS/Emisar/emisar.html

  10. Resolution Quantitative analysis on the influence of polarization information on the resolution is provided in this presentation. “Nominal” Resolution does not reflect polarization properties range azimuth • Fourier analysis would give the nominal resolution. • Parametric spectrum analysis would achieve higher resolution. --- e.g. PBWE, MUSIC, ESPRIT, MVM, MEM, etc We are interested in the resolution achievable by “polarimetric” parametric spectrum analysis method such as PBWE.

  11. Statistical Resolution Limit (SRL) SRL is a simple metric that provides the highest resolution achievable by any unbiased parametric spectral estimator. • “Statistical Resolution” : Δd • “Statistical Resolution Limit” : min(Δd) true target separation = d The estimate of target separation contains error due to noise. If the expected error is sufficiently small compared to the real separation, we can claim that these targets are resolvable. [1] S.T.Smith, “Statistical Resolution Limits and the Complexified Cramér-Rao Bound,” IEEE Trans. Signal Process., vol. 53, no. 5, pp1597—1609, May 2005

  12. The Signal Model The signal at each resolution cell is represented by a polarization vector. target clutter scene range Polarization property power VV Polarimetric channels HV HH

  13. The Signal Model Two closely located point targets signal model is considered. B target #2 target #1 VV VV HH HH freq. range d n: Gaussian noise V: matrix of steering vectors a: complex amplitudes of the targets N: the number of samples The probability density function of the data z is: denotes the long column vector formed by concatenating the columns of X.

  14. The Cramér-Rao Bound (CRB) The CRB for the parameters are derived. • Likelihood function of the parameters • Fisher Information Matrix • Cramér-Rao Bound on the covariance of the estimator of the parameters • Convert the CRB to the lower bound of the target separation d

  15. The Cramér-Rao Bound (CRB) The CRB for 2 polarimetric channels case is derived. • The lower bound for the target separation (Polarimetric / 2 channels / White Gaussian noise) • cf) when ∆φ→large (two targets are far away)

  16. SRL and the Performance of PBWE a a VV HH range d The PBWE achieves CRL and SRL fairly well. Δd=0.4 Δd=0.15 (a) ∆Ψ = 0 (b) ∆Ψ = π/6 • Monte Carlo iteration 1,000 times. • N=50 / SNR=40dB / order of the linear prediction filter = 6 • If the polarization properties of the two targets are the samepolarization information does not help (a).

  17. SRL and the Performance of PBWE a a VV HH range d The SRL is minimum when the polarization properties of the two targets are orthogonal (c) ∆Ψ = π/2 (d) ∆Ψ = π • The SRL is improved to ¼ by using polarization information, when the polarization properties of the two targets are orthogonal (d). • (d) corresponds to a case where two targets are trihedral and dihedral corner reflectors.

  18. Conclusion • The SRL of polarimetric radar is derived and compared with that of single polarization radar • It has been shown analytically that the polarization information helps improving the resolution when the polarization properties of the two closely located targets are different, and thus on the average, the polarimetric radar outperforms single polarization radar. • e.g. If the polarization properties of the two closely located targets are orthogonal to each other, the SRL is improved to ¼ by using polarization information. • It has been shown that the resolution of the PBWE previously proposed by the authors almost achieves the SRL.

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