Ensemble Scattering and RFI Speckle Caused by Collision Avoidance Radar

1
Ensemble Scattering and RFI Speckle Caused by
Collision Avoidance Radar
College of Engineering Department of
Atmospheric, Oceanic Space Sciences
2005 URSI National Radio Science Meeting Boulder,
CO 5-8 January 2005

• Chris Ruf
• Departments of Atmospheric, Oceanic Space
  Sciences
• and Electrical Engineering and Computer Science
• University of Michigan
• 734-764-6561 (V), 734-936-0503 (F),
  cruf_at_umich.edu (E)

2
Outline

• Statement of Problem
• How to estimate the effect on Earth Exploration
  Satellite Service (EESS) microwave radiometers of
  a large populations of automotive collision
  avoidance radars (CARs)
• Given Detailed characterization of the frequency
  and directional dependence of scattering of radar
  transmission from a single CAR
• Previous Work
• A recent peer reviewed publication has done the
  single CAR characterization and has attempted to
  do the large population analysis
• (Younis et al., Interference from 24-GHz
  Automotive Radars to Passive Microwave Earth
  Remote Sensing Satellites, IEEE Trans. Geosci.
  Remote Sens., 42(7), 1387-1398, July 2004)
• This presentation
• Significant simplifications are identified in the
  method by which the large population analysis is
  performed
• A revised analysis lowers the upper limit on
  radar transmit power above which significant
  degradation results to the satellite measurements

3
Review of TGRS article by Younis et al.
(2004)(slide 1 of 4)

• Characterization of scattering by a single car
  illuminated by a CAR
• Frequency is swept from 22.0 to 26.0 GHz to
  represent the Ultra Wide Band nature of CAR
  operation
• Measurements at each frequency are made versus
  elevation and azimuth angle

CAR horn antenna
Sketch of experimental setup (ref. Younis et al.,
2004, Fig. 2)
Photograph of experimental setup (ref. Younis et
al., 2004, Fig. 3)
4
Review of TGRS article by Younis et al.
(2004)(slide 2 of 4)

• Characterize RFI to EESS observations from CAR
  transmitter as
• where N is the number of CARs per unit area
  m-2, PTx is the CAR transmitter equivalent
  isotropic radiated power density Wm-2Hz-1, C is
  the coupling constant between the ensemble of
  CARs and the EESS radiometer, k is Bolzmanns
  constant 1.38E-23 J/K , DT is the brightness
  temperature of allowable interference K, l is
  the RF wavelength m, t is the zenith normalized
  atmospheric opacity Np, and q is the incidence
  angle from nadir of the EESS radiometers antenna
  beam
• The value of C for a single CAR has been measured
• A small component of C is determined by the
  direct coupling between the CAR sidelobes and the
  EESS radiometer mainbeam
• C is generally dominated by indirect scattering
  from nearby targets (e.g. other automobiles)
• The effective value of C for an ensemble of CARs
  is derived statistically to estimate the RFI
  level in real world conditions

5
Review of TGRS article by Younis et al.
(2004)(slide 3 of 4)

• Results of single car scattering characterization
  at one frequency Dynamic range of the coupling
  constant covers -45 dB to -5 dB versus
  elevation azimuth

Finite element modeling roughly reproduces
measurements
Measured front (top) and rear (bot) coupling
consant
6
Review of TGRS article by Younis et al.
(2004)(slide 4 of 4)

• Large variability expected in coupling constant
  vs. frequency due to very large electrical extent
  of scattering targets
• No quantitative description of variability given
• Authors average over 22 lt f lt 26 GHz to get
  average coupling
• Large variability reported in coupling constant
  vs. azimuth and elevation angles
• e.g. dynamic range of -45 dB to -5 dB in
  previous figures
• Authors average over azimuth and elevation to get
  average coupling
• ltCgt -22.9 dB averaged over frequency, azimuth
  and elevation

7
Ensemble Summation of Scattered Fields(slide 1
of 3)

• The total power, S, scattered by N individual
  CARs is an incoherent (power) sum of individual
  signals, si
• For independent individual scatterers (e.g.
  randomly oriented cars in an urban setting), if
  p(si) is the pdf of the scattered power from an
  individual CAR then the pdf of S is
• where denotes convolution
• Evaluate nested convolutions numerically to
  derive p(S) from empirical p(si) or perform
  analytical convolutions if p(si) has an
  analytical form
• Form of p(S) is significantly altered by nested
  convolution
• For fully correlated individual scatterers (e.g.
  parallel cars on a freeway), p(S) has the same
  form as p(si) with S Nsi

8
Ensemble Summation of Scattered Fields(slide 2
of 3)

• EXAMPLE
• Assume p(si) is exponentially distributed
• Consistent with Rayleigh distributed envelope of
  scattered electric field strength
• Then S will be Gamma distributed as
• where ltsigt is the average power scattered by an
  individual CAR
• NOTE Central Limit Theorem implies that p(S)
  N(m,s) as

9
Ensemble Summation of Scattered Fields(slide 3
of 3)

• Relevant statistics of coupling constant
  associated with individual CAR scattered signal,
  si
• ltsigt-38.0 dB and si,max-10.6 dB
• ref. Table IV of Younis et al. (2004)
• Assuming an exponential distribution for si
• Prsi gt si,max e-550 0 (from Prsi gt t
  exp(-t/ltsgt) )
• StdDev(si) ltsigt
• Relevant statistics of coupling constant
  associated with total scattered signal, S
• ltSgt Nltsigt
• This is the value used in Younis et al. 2004 as
  the effective coupling constant of the total
  scattered signal
• Smax Nsi,max (maximum possible interference)
• StdDev(S) N1/2StdDev(si) (analogous to speckle
  variability in radar fading statistics)

10
Testing Central Limit Theorem on Threshold
Statistics of Ensemble Summation

• Using the exact Gamma pdf for S
• PrS gt t0.01 at t/ltsigt 4.6(N1), 18.8(N10),
  124.7(N100)
• PrS gt t0.0001 at t/ltsigt 9.2(N1),
  26.2(N10), 141.5(N100)
• Assuming N(mNltsigt,sN1/2ltsigt) pdf for S
• PrS gt t0.01 at t/ltsigt 17.4(N10),
  123.3(N100)
• PrS gt t0.0001 at t/ltsigt 21.8(N10),
  137.2(N100)
• Central Limit Theorem valid within a few percent
  for Ngt10

11
Allowable Interference Level Assuming
Independent Rayleigh Scatterers

• Assume PrS gt t 10-5 as an acceptable
  frequency of occurrence. Then t ms 4.265sS
  if S N(ms, sS)
• Surface area of Europe 9,938,000 km2
• Surface area of AMSR footprint at 23 GHz 242
  km2
• Ratio of areas is 6x10-5 gt 17 chance of single
  pixel interference
• Then t Nltsigt 4.265N1/2ltsigt

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Allowable Interference Level Assuming
Independent Uniform Scatterers

• Assume p(si) U(0, si,max)
• Use Central Limit Theorem with
• ltSgt ms Nltsigt and StdDev(S) sS
  N1/2(2ltsigt/121/2)
• Assume PrS gt t 10-5 as an acceptable
  frequency of occurrence. Then t ms 4.265sS
  if S N(ms, sS)
• Then t Nltsigt 4.265 N1/2(2ltsigt/121/2)
• Compare to t Nltsigt 4.265N1/2ltsigt for
  Independent Rayleigh Scatterers
• Compare to t Nltsigt from Younis et al. (2004)

13
Allowable Interference Level Assuming Correlated
Uniform Scatterers

• Assume p(si) U(0, si,max)
• Central Limit Theorem does not apply
• Assume p(S) U(0, Smax)
• Smin 0 and Smax Nsi,max
• Assume PrS gt t 10-5 as an acceptable
  frequency of occurrence. Then t 0.99999 Smax
  if S U(0, Smax)
• Then t 0.99999Nsi,max
• Compare to t Nltsigt 4.265 N1/2(2ltsigt/121/2)
  for Independent Uniform Scatterers
• Compare to t Nltsigt 4.265N1/2ltsigt for
  Independent Rayleigh Scatterers
• Compare to t Nltsigt from Younis et al. (2004)
• With correlated uniform scatterers, the coupling
  constant associated with the ensemble sum is 500
  times larger than the Younis et al. (2004) model

14
Allowable Number Density of CARs True Ensemble
Summation vs. Younis et al. 2004 Model