1. Applying a Composite Pattern Scheme to Clutter Cancellation with the Airborne POLARIS Ice Sounder Keith Morrison 1, John Bennett 2, Rolf Scheiber 3 k.morrison@cranfield.ac.uk 1 Department of Informatics & Systems Engineering Cranfield University, Shrivenham, UK. 2 Private Consultant, UK. 3 Microwaves and Radar Institute German Aerospace Research Center, Wessling, Germany.

2. C OLLABORATORS Matteo Nannini - DLR Pau Prats - DLR Michelangelo Villano - DLR Hugh Corr - BAS ESA-ESTEC Contract: 104671/11/NL/CT Nico Gebert Chung-Chi Lin Florence Heliere

3. P RESENTATION ProblemProblem Composite PatternComposite Pattern - convolution - array polynomial ApplicationApplication ResultsResults

4. H dh r ice bedrock air R R z POLARIS P ROBLEM

5. Geometric alignment and dimensions of the 4 independent receive apertures of the POLARIS antenna A NTENNA A RRAY

6. Test-IDBandwidth [MHz] Remarks p110219_m155222_jsew1 85 & 30 MHzFrom east: grounded ice, then crossing the glacier tongue, frozen grounded ice in the middle, ice shelf in the west p110219_m155222_jswe185 & 30 MHz p110219_m155222_jsns185 & 30 MHzcross-track slopes with grounded ice p110219_m180339_jsns2 85 & 6 MHzprofile along the glacier tongue I CE G RAV 2011

7. P ROCESSING S CHEME

8. Rx Pattern Rx Array & Element Pattern

9. Phased-array nulling traditionally optimizes performance by utilising available array elements to steer a single null in the required direction. However, here we exploit the principle of pattern multiplication. With different element excitations, nulls in differing angular directions are generated. Composite array is produced by the convolution of two sub-arrays. The angular response of the composite array is the product of those generated by the individual sub-arrays. C OMPOSITE A RRAY

10. C ONVOLUTION The building block is the 2-element array. To generate a null at angle θ A the excitation of the array is required to be: Similarly to generate a null at angle θ B the excitation of the array is required to be: 1.0

11. 3-E LEMENT : 2-Null To preserve these nulls we must generate the product of the two patterns and this is achieved by convolving the two distributions to give the following 3-element distribution: 1a+bab where: a = -exp[jkdsin A ] b = -exp[jkdsin B ]

12. 4-E LEMENT : 2-Null 1ab0b0 ab 0 where: a = -exp[jkdsin A ] b = -exp[jkdsin B ] b 0 =-exp[jk2dsin B ]

13. 4-E LEMENT : 3-Null To generate a third null at angle, θ C, requires convolution of the result from the 3-element, 2-null case with an additional 2-element array, with the distribution : 1.0

14. S IMULATION Wavelength Range bandwidthNoise power Chirp durationClutter attenuation Range sampling frequency 150m 300m 500m 0m 700m 1000m H=3000m

15. C OMPOSITE – 3 NULL Double-null with 2° separation centred at left-hand clutter angle

16. C OMPOSITE – 2 NULL

17. This is done using Schelkunoff scheme. Array excitation represented by the array polynomial and its representation as zeros on the unit circle. Computationally straightforward because there are only three zeros for the four element array. A RRAY P OLYNOMIAL Array factor: If substitute (where αd is a linear phase term to account for beam steering) thenθ

18. Factorizing For the 4-element case factorizes to (z-a) (z-b) (z-c) Providing coefficients 1, -(a+b+c), (ab+ac+bc), (-abc)

19. A RRAY P OLY. – A LT. 3- NULL Ensured maximum amplitude contribution from this zero in the nadir direction. Remaining two zeros were used to position the pair of nulls at the clutter angles.

21. N ADIR R ESPONSE

22. F INAL R ECOMMEDATION 1a + b + 1ab + (a+b)ab a+b+1

23. R ESULTS

24. C OUNTERACTING N ADIR N ULLS

25. Considered two and three-nulling scenarios using convolution. “Best Result” obtained from a modified 3-null approach: » Array Polynomial: third null located 180° on the unit circle. Nadir null can be avoided by allowing points to move off the unit circle. C ONCLUSIONS