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Modeling and Simulation Analysis of an FMCW Radar for Measuring Snow Thickness Sudarsan Krishnan April 02, 2004 Committee Dr. Glenn Prescott Dr. Prasad Gogineni Dr. David Braaten Slide 1 Outline Snow cover

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Modeling and Simulation Analysis of an FMCW Radar for Measuring Snow Thickness Sudarsan Krishnan April 02, 2004 Committee Dr. Glenn Prescott Dr. Prasad Gogineni Dr. David Braaten Slide 1 Outline Snow cover over sea-ice KU snow radar Research goal Approach System modeling Propagation modeling Simulation methodology Results Summary and future work Slide 2 Snow Cover Over Sea Ice Sea ice extent and thickness Important indicator of global climate change Snow layer affects sea ice thickness Low thermal conductivity insulates sea-ice High Albedo reflects energy Snow layer thickness measurement - important Properties of snow Mixture air, ice and water Forms dielectric contrast with sea ice layer Measurable by radar Slide 3 Measurement of Snow Thickness Usually measured using in-situ measurements. Not practical over large areas like polar regions. Solution satellite based measurements. Validation of satellite measurements needed. High resolution needed. KU snow radar. 2-8 GHz FMCW radar ~ 3 4 cms resolution. Prototype radar ground based. Next step airborne radar. Slide 4 FMCW Radar Transmits sweep Tx f ( t) = f + α t t T Transmit wave phase Beat frequency 0 1 φ( t) = 2π f ( t) dt = 2π ( f t + α 2 2RB f B = ct Plotted in freq domain One peak = one target 2 0 t ) f b f LPF τ f b X f T (t) f R (t) Dly t Slide 5 Simulated Ideal FMCW Radar Data Slide 6 KU Snow Radar Radar specifications Characteristic Value Unit Frequency choice Radar Type FMCW Bandwidth choice Sweep Frequency 2 8 GHz Functional block diagram Range Resolution 4 cm Sweep Time 10 msec Osc Dir. Coup LO Tx Ant. Transmit Power PRF dbm Hz A/D Dynamic Range 12 bit, 72 db A/D IF Rx Ant. Sampling Rate 5 MHz Slide 7 KU Snow Radar Data Slide 8 Research Goal Snow radar return is not ideal. Affected by. System effects radar components. Propagation effects surface and volume scattering. Goal. Simulate radar. Include system effects. Include propagation effects. Helps in understanding and removing effects. Slide 9 Radar System Modeling Goal: to include effects of system into simulation How? Determine point spread function By measurement By calibration Modeling by measurement Source modeling System transfer function modeling Modeling by calibration Calibration target Slide 10 Modeling by Measurement V I YIG D IV From DDS To DAQ System LO Slide 11 Modeling by Measurement Source modeling Modeling amplitude and phase errors of sweep Amplitude vs. Frequency non constant Frequency vs. Time non linear V Voltage Sweep Oscillator Section Constant Amplitude Chirp f v 1 f 1 v_sweep t B f 0 t 0 T 0 T Slide 12 Amplitude Error Modeling Output power vs. Sweep voltage measured No amplitude errors output power a constant Output power not constant Choose significant components as model How? Determine DCT of the amplitude errors Select significant peaks (amerr) Compute IDCT Slide 13 Amplitude Error Modeling Slide 14 Phase Error Modeling Output frequency vs. Sweep voltage measured Sweep voltage proportional to sweep time Express frequency as a function of time 3 2 f ( t) = a t + a t + a t + a 3 The phase is then given by φ( t) = 2π f ( t) dt = b3t + b2t + b1t + b0t This phase includes phase error 1 To generate chirp with amplitude and phase errors ( 1+ idct( amerr )) cos( φ( )) x( t) = t 0 Slide 15 Phase Error Modeling Slide 16 Transfer Function Other section characterized by transfer function Transfer function determined from s-parameter (s 21 ) S 21 determined using network analyzer and interpolated System modeled as a input output relationship Output is the product of input and transfer function Y ( f H ( f ) S ) = = 21 = X ( X ( = V V V V o i V ( f ) ( f ) + 2 = 0 f )* H ( f ) f )* S 21 ( f ) Slide 17 Modeling by Calibration Calibration target is used usually screen The return should ideally be a single peak in Freq. domain IFFT of obtained peak = Point Spread Function Slide 18 Propagation Modeling Goal: determine return given transmit waveform and geophysical data Transmit waveform simulated from source model Modeling involves Determining reflected power Determining backscattered power Combining the two and introducing noise What is geophysical data? Slide 19 Geophysical Data Geophysical data: defines the medium. Constituent media, depth, density, temperature etc. Roughness information also included. Depth (m) Medium Density (gm/cc) Temperature ( C) Salinity PPT 1 Air Snow Sea-Ice Snow layer roughness: rms height = 1cm, correlation length = 40cm Sea-Ice layer roughness: rms height = 1mm, correlation length = 10cm Slide 20 Dielectric Profile For radar EM properties are needed Convert geophysical data to dielectric profile Determine dielectric constant of every layer Dielectric contrast can be seen to form 2 interfaces Air (ε r = 1) Snow (Temp. -5C, Density 500 gm/cc) (ε r = j) Sea Ice Half Space (Temp. -10C, Density 914 gm/cc) (ε r = j) Slide 21 Return Power Due to Reflection Assuming plane surfaces, Γ can be determined Γ = Then Γ is reduced to accommodate for surface roughness The return power due to reflection is determined P ε ε Γ = Γ r = spe Pλ t 2 G ε ε k σ h 2 Γ 2 ( 4π ) 2 ( 2R) 2 Slide 22 Surface Scattering Coefficient Surfaces not smooth cause surface scattering Power reflected from various angles Depends on rms height and correlation length rms height standard deviation of surface height Correlation length autocorrelation = (1/e) Modeled using Kirchhoff model for large roughness Special case of IEM for small roughness Slide 23 Volume Scattering Media not homogenous volume scattering Scattering and extinction occurs between interfaces Volume scattering coefficient computed as sum of contributions of scattering and extinction ( θ ) ( θ ) σ = v cos 1 1 2κ e L θ o σ v 2 ( ) Here σ 0 v is the volume backscattering coefficient, L the loss factor and k e is the extinction coefficient Slide 24 Slide 25 Backscattered Power Combine scattering coefficients using Here σ ss is the snow surface scattering coefficient, σ sv the snow volume scattering coefficient, σ is is the ice surface scattering coefficient, T s the transmission coefficient and L the loss factor Using this the back scattered power is computed as + + = ) ( ) ( 1 ) ( ) ( ) ( ) ( θ σ θ θ σ θ θ σ θ σ is sv s ss L T ( ) ( ) R A G P P t r π σ λ = Simulation Methodology Start Generate transmit wave Simulation, Radar and Target Information Find reflection coefficient Transmit Wave Determine reflected power Reflection Coefficient Scattering Coefficient Find scattering coefficient Reflected Wave Multiple Backscattered Waves Determine scattered power Include PSF Include PSF Introduce noise Add up powers Compute distance axis Plot distance vs. Power Mix Compute Power Sum Compute Distance Axis Plot Mix Compute Mean Power Stop Slide 26 Results Delay line simulation and measurement setup Delay line simulation results Comparison of simulation and measurement Snow over sea-ice simulation setup Snow over sea-ice simulation results Snow over sea-ice measurement setup Comparison of simulation and measurement Slide 27 Delay Line Setup Tx Osc Dir. Coup LO Delay Line A/D IF Rx Slide 28 Delay Line Simulation Result Slide 29 Simulation and Measurement Comparison Slide 30 Snow Over Sea Ice Simulation Setup Dir. Coup LO Tx Rx IF A/D Osc Ant. Snow Sea Ice Slide 31 Snow Over Sea-ice Results Slide 32 Snow Over Sea-ice Field Trial Setup Dir. Coup LO Tx Rx IF A/D Osc Ant. Snow Sea Ice Slide 33 Simulation and Measurement Comparison Slide 34 Summary and Future Work Simulation of snow radar System model By measurement with source model By calibration Propagation model With surface and volume scattering Results Future work IF section effects need to be simulated Deconvolution needs to be applied Forward scattering models need to be included Slide 35 Questions?? Slide 36 Modeling and Simulation Analysis of an FMCW Radar for Measuring Snow Thickness Sudarsan Krishnan April 02, 2004 Committee Dr. Glenn Prescott Dr. Prasad Gogineni Dr. David Braaten Slide 37

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