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Transmit beam - pattern synthesis

Transmit beam - pattern synthesis. Waveform design for active sensing Chapters 13 – 14. Introduction. Problem Receive beampattern === transmitt beampattern ( technical issues !! ). MIMO radar. Beam-pattern to covariance. Signal at target : . Power at a specific . .

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Transmit beam - pattern synthesis

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  1. Transmit beam-patternsynthesis Waveform design for activesensing Chapters 13 – 14

  2. Introduction • Problem Receivebeampattern === transmitt beampattern (technicalissues !! ) MIMO radar

  3. Beam-pattern to covariance Signal at target: Power at a specific .

  4. The transmit beampatterncan be designed by chosingR. ( Individual radiator) The power constraint ( Total Power )

  5. Goals: Match a transmit beampattern. Minimize cross correlationbetweenprobing signals. Minimizesidelobelevel. Achieve a requiredmain-bembandwidth. For a MIMO radar with K targets. A correlatedscattered signal willcreateambiguities!!

  6. How to design the signal xknowingR ? When the covariancematrix of w is the identitymatrix. Optimal Design Assumetargets of interest

  7. Ifthere is no information on the targetlocations Optimize for J With solution is: The MIMO radar creates a spaciallywhite signal.

  8. Optimal Design for knowntargetlocations • An estimate of is available. The problem becomes: However: is the lefteigenvector of

  9. Problems with previous design: • Element power uncontrolled. • Power reachingeachtargetuncontrolled. • No controll in Cross-correlation Any design with phaseshiftedarraywillhavecoherenttargetscattering. • Advantage : • The same approach maximizes SINR. (different B)

  10. Beampatternmatching design & cross-correlationminimization Assume a desiredbeampattern A L-targetslocated at Are weigths to the costfunction. Allowsmatching a scaled version of the beampattern.

  11. Previous problem is a SQP Havingr the vector of Rmm and Rmp This can be solved using SQP solvers !

  12. How to obtain ? Use: A spatiallywhite signal . Use the Generalizedlikelyhoodratio test (GLRT) and/or CAPON. GLRT, has good features for targetdetection, jammeravoidance, and trade-offbetwenrobustness and resolution.

  13. Minimun sidelobebeampattern design Interestingly a relaxation seems to producebetter solution than the strict!

  14. Phasearraybeampattern • All the radiators contain the same scaled version of the signal x. • Problem becomesnon-convex = > hard!! Introduce a constraint An approach is to use the same solution as MINO (relaxed version) followed by a Newton-like algorithm.

  15. 3 targets: 0o, -40o and 40o. Strong jammer at 25o Numericalexample

  16. CAPON technique

  17. Using = 1 = 0.

  18. Beampattern design (robust phase)

  19. Beampattern design (robust phase) Usingphaseshiftedarray

  20. Reducing the cross-correlation

  21. Effect of samplecovariancematrix HavingR a design of x ? The samplecovariance of w has to be identity….. Error 1000 Monte-Carlo

  22. Minimun sidelobelevel design MIMO array

  23. Phasearray

  24. Relax the individualenergyconstraint from 80% to 120% c/M while the total energy is still fixed.

  25. Covariance to MatrixWavefrom The uni-modularconstraintcan be replaced by a low PAR. This with a energyconstraintwillproduce:

  26. Assume: Samplecovariance Result of unconstraintminimization Weneed to includegoodcorrelationproperties:

  27. With this notation the goal is: Using the idea of decomposingX intotwomatrixmultyiplicationthenwecansolve:

  28. Thus: • For unimodular signal design === MultiCAO • replaced • For low PAR constraint CA algorithm

  29. Constraining the PAR becomes the independent minimization problems With the ”p-th” element of z as:

  30. NumericalResults M=10 P=1 N = 256

  31. M=10 P=10 N = 256

  32. M=10 P=1 N = 256

  33. M=10 P=10 N = 256

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