The University of Calgary - Focal Plane Field Calculator (UC-FPFC) and Its Applications

Transcription

1 The University of Calgary - Focal Plane Field Calculator (UC-FPFC) and Its Applications Thushara Gunaratne & Dr. Len Bruton MDSP Group Department of Electrical and Computer Engineering Shulich School of Engineering University of Calgary, Canada. 18 June 2009 Dominion Radio Astrophysical Observatory (DRAO)

2 Outline Introduction & Motivation Focal plane arrays (FPAs) for SKA Why an accurate model for the focal field is required? Calculation of focal region electric field in UC-FPFC Physical optics approximation Sampling density of the reflector surface Comparison with GRASP Applications of UC-FPFC Spectral analysis of the synthesized field Broadband conjugate field matching (BB-CFM) Conclusions and future work 18 June 2009 DRAO 2

3 Focal Plane Arrays (FPAs) for the Square Kilometer Array (SKA) The proposed receiver technology for the SKA for the bandwidth GHz. Combines the Large collection area of a paraboloidal reflector Multi-beam synthesis capability of a phased array The complete 180-element PHAD array assembly DRAO. ae/features/ska/ska.htm 18 June 2009 DRAO 3

4 Motivations for Focal Field Modeling Accurate modeling of focal field is essential Predict the best achievable selectivity with FPAs Predict suitable receiver elements for FPAs Predict suitable arrangements of elements of FPAs Predict the maximum power recovery by FPAs Ways of achieving optimum SNR and radio interference mitigation through FPA signal processing TICRA GRASP9 is the industry standard for focal field calculations involving parabolic reflectors But!!.it is too Expensive!!.. 18 June 2009 DRAO 4

5 University of Calgary Focal Plane Field Calculator (UC-FPFC) UC-FPFC is a custom MATLAB based software tool that evaluates the electromagnetic fields in the focal region of a prime focus paraboloidal reflector in response to an impinging monochromatic plane-wave. Uses the physical-optics approximation in determining the reflector currents Enables straight-forward secondary analysis of fields Agree well with the calculated fields with GRASP9 18 June 2009 DRAO 5

6 Orientation of the Objects & Notations Used 18 June 2009 DRAO 6

7 Calculating the Electric Field in the Focal Region jkρ kη ()= ( ( )-(( ) ˆ) ˆ ) e Er j Jr Jr RR ds 4π ρ refl R inc Physical Optics Approximation inc Jr ( ) = 2ˆ n H inc e jk ( r R ) z x r ˆn inc Jr ( ) = 2ˆ n E R e ( ) inc inc jk ( r R ) r y ˆ ρr 18 June 2009 DRAO 7

8 Sampling the Reflector Surface Solve by 2D numerical integration jkρ ( ) mn, kη ˆ ˆ e Er ()= j Jr (, )-(( Jr, ) R, ) R, J 4π mn mn mn mn Σ m n m n ρmn, There is no direct application of sampling theory for the sampling of induced currentdensity on the reflector surface. Hence, m and n can be changed to have a tread off between the accuracy and the computational complexity. Sample grid on the reflector surface 18 June 2009 DRAO 8

9 Some Results Achieved with UC-FPFC Parabolic Reflector : F = 6m; D = 10m: Plane Wave : Pol = [0,1,0]; f = 1.5 GHz; θ = 1.5 ; φ = 0. FPA m 2 Sampled into a grid of June 2009 DRAO 9

10 Comparing UC-FPFC and GRASP Plane Wave : Pol = [0,1,0]; f = 1 GHz; θ = 1.5 ; φ = 0. Comparison for Co-polar components Maximum relative error of Ey = June 2009 DRAO 10

11 Comparing UC-FPFC and GRASP Plane Wave : Pol = [0,1,0]; f = 1 GHz; θ = 1.5 ; φ = 0. Comparison for cross-polar components Maximum relative error of Ex = June 2009 DRAO 11

12 Comparing UC-FPFC and GRASP Plane Wave : Pol = [0,1,0]; f = 1 GHz; θ = 1.5 ; φ = 0. Comparison for longitudinal components Maximum relative error of Ez = June 2009 DRAO 12

13 Comparing UC-FPFC and GRASP Angle θ in degrees (φ = 0 ) Co-Polar Component Percentage Maximum Relative Error (%) Cross-Polar Component Longitudinal Component Note: Sample grid size on the reflector surface is (32 32). 18 June 2009 DRAO 13

14 Comparing UC-FPFC and GRASP Different Sampling Grids on the Reflector Surface Sample Grid Size for the Reflector (11 11) Percentage Maximum Relative Error for the Normal Incident (θ = 0 ; φ = 0 ) (%) Co-Polar Component To GRASP To ( ) Cross-Polar Component To GRASP To Longitudinal Component To GRASP To ( ) ( ) (21 21) (35 35) (63 63) ( ) ( ) ( June 1023) 2009 DRAO

15 Applications of UC-FPFC 18 June 2009 DRAO 15

16 Verification of the Conjectured Model for the Focal Field θ 8(F/D) = tan 16(F/D) 1 1 max 2 18 June 2009 DRAO 16

17 Conjectured Region of Support (ROS) of the Spectrum of the Focal Field θ [ θ, θ ] φ [0,360 ] α max max = tan (sin( θ )) 1 1/2 max FP (,, ) 0.1 UC-FPFC ωx ωy ω t = As predicted, the iso-surface of the spectrum of the focal-field synthesized for the band GHz using UC-FPFC resembles a section of a cone. 18 June 2009 DRAO 17

18 Conjectured ROS of the Spectrum of the Focal Field (Contd.) F/D=0.6 F/D= June 2009 DRAO 18

19 Broadband - Conjugate Field Matching (BB-CFM) An extended CFM method is proposed where the spectral components of the desired signal is added in-phase compared to the spectral components of the interfering signals and AGWN. Given the sampled focal field P x( n) = w ( n) + AWGN ; n= ( n, n, n ) p= 1 C p According to the Cauchy-Schwartz inequality the best possible SNR is achieved in recovering w ( ) C 1 n from x( n ) is when the 3D coefficient matrix y( n) has the frequency response Y e e e W e e e y w jω 1 jω 2 jω3 * jω 1 jω 2 jω3 3D * (,, ) = (,, ) ( n) = ( n) C 1 DDFT C 1 18 June 2009 DRAO 19

20 Determination of Best Possible Selectivity with BB-CFM BB-CFM achieves optimum SNR with AWGN, but how would it perform with interference? Given w w x T 4 wc p p= 1 ( n) = ( n); ( n) ( θ = 0, φ = 0 ), w ( n) ( θ = 1, φ = 0 ), ( n) ( θ = 2, φ = 0 ), w ( n) ( θ = 3, φ = 0 ). C 1 C 2 C 3 C 4 In order to enhance wc p ( n); p= 1,2,3,4 with respect to other signals, four 3D coefficient matrices were evaluated such that * * y ( n) = w ( n), y ( n) = w ( n), y ( n) = w ( n), y ( n) = w ( n). 1 C 1 2 C 2 * * 3 C 3 4 C 4 18 June 2009 DRAO 20

21 T Results of BB-CFM Test sequence x ( n) of size ( ) Filter coefficients y p ( n) of size ( ) wc p ( n) correspond to far-field sinc functions 18 June 2009 DRAO 21

22 Conclusions and Future Work Conclusions UC-FPFC results agree very well with GRASP The primary conjecture on the ROS is verified Best possible selectivity for FPA under BB- CFM is determined Future Work Combine element response patterns GP-GPU implementation for possible speed up Performance comparison with low-complexity frequency transformed 3D FIR filters 18 June 2009 DRAO 22

23 Thank You. 18 June 2009 DRAO 23