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Beamforming

Beamforming. Tx1. Tx1. Tx2. Tx1. +. Tx2. Tx1. Rx. Destructive superimposition. Tx2. Tx1. Zero signal. +. Rx. Tx2. Tx1. Constructive superimposition. Amplified signal (twice amplitude). Tx2. Tx1. Receiver at arbitrary location. Rx. +.

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Beamforming

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  1. Beamforming

  2. Tx1

  3. Tx1

  4. Tx2 Tx1

  5. + Tx2 Tx1 Rx

  6. Destructive superimposition Tx2 Tx1 Zero signal

  7. + Rx Tx2 Tx1

  8. Constructive superimposition Amplified signal (twice amplitude) Tx2 Tx1

  9. Receiver at arbitrary location Rx + Tx2 Tx1

  10. Arbitrary location, what’s the path difference Path difference = ??

  11. Path difference Rx + Tx2 Tx1

  12. Path difference and phase difference Rx + Path difference = Tx2 Tx1

  13. Radiation pattern: Rx amplitude as a function of angle

  14. Radiation pattern: Rx amplitude as a function of angle

  15. Radiation pattern: Rx amplitude as a function of angle

  16. Radiation pattern: Rx amplitude as a function of angle +

  17. Radiation pattern: Rx amplitude as a function of angle The initial phases can be controlled +

  18. Radiation pattern: Rx amplitude as a function of angle + =0 =-x A non zero initial phase can change the radiation pattern =0 =-x

  19. Multiple antennas

  20. Rx . . . Tx2 Tx1 Tx(N) Tx(N-1) ……..

  21. +

  22. Radiation pattern

  23. Rotating the beam + + A maxima occurs in the direction of

  24. Rotating the beam

  25. Networking applications

  26. Acoustic Beamforming – noise suppression Silent zone Audible Zone

  27. Other applications • Localization • Gesture tracking • RF Imaging

  28. Reception

  29. Sensing Angle of Arrival (AoA) Tx Path difference = Rx1 Rx2

  30. Antenna array Tx . . . Rx2 Rx1 Rx(N) Rx(N-1)

  31. Steering vector

  32. Multiple transmitters Tx2 Tx1 . . . Rx2 Rx1 Rx(N) Rx(N-1)

  33. Multiple transmitters Output is a linear combination of steering vectors from different directions

  34. Multiple transmitters Steering Matrix (N x K) K sources (Input Vector) N receivers (Output vector)

  35. Detecting AoA of K sources simultaneously

  36. Multiply by conjugate of steering vector of source 1 .. ..

  37. ..

  38. A = .. All energy from direction have been aggregated and amplified

  39. A = .. All energy from direction have been aggregated and amplified

  40. A = .. The resultant output is very low .. since multiplied steering vector does not match with any of the incoming signals

  41. Construct a graph of for all values of • Any active source from direction should have a peak in the above graph .. • This is called delay and sum beamforming A

  42. Detecting multiple AoA A AoA Spectrum Suc

  43. Close by AoAs cannot be resolved

  44. MUSIC algorithm has sharp peaks to resolve close AoA Based on eigen decomposition and PCA – reference to be provided

  45. Degrees of freedom for beamforming • Antenna separation • Initial phases of antenna sources • Number of antennas

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