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Properties of the MIMO Radar Ambiguity Function

Properties of the MIMO Radar Ambiguity Function. Chun-Yang Chen and P. P. Vaidyanathan. California Institute of Technology Electrical Engineering/DSP Lab. ICASSP 2008. Outline. Review of the background Radar ambiguity function and its properties MIMO radar MIMO radar ambiguity function

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Properties of the MIMO Radar Ambiguity Function

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  1. Properties of the MIMO Radar Ambiguity Function Chun-Yang Chen and P. P. Vaidyanathan California Institute of Technology Electrical Engineering/DSP Lab ICASSP 2008

  2. Outline • Review of the background • Radar ambiguity function and its properties • MIMO radar • MIMO radar ambiguity function • Properties of the MIMO ambiguity function • Signal component • Energy • Symmetry • Linear frequency modulation (LFM) • Conclusion Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  3. Review: Ambiguity function and MIMO radar 1

  4. Radar Ambiguity Function t: delay n: Doppler u(t-t)ej2pnt u(t) Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  5. Radar Ambiguity Function t: delay n: Doppler u(t-t)ej2pnt u(t) Matched filter output Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  6. Radar Ambiguity Function t: delay n: Doppler u(t-t)ej2pnt u(t) Matched filter output Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  7. Radar Ambiguity Function t: delay n: Doppler u(t-t)ej2pnt u(t) Matched filter output Radar ambiguity function Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  8. Radar Ambiguity Function • Ambiguity function characterizes the Doppler and range resolution. t: delay n: Doppler u(t-t)ej2pnt u(t) Matched filter output Radar ambiguity function Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  9. Radar Ambiguity Function Multiple targets (tk,nk) Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  10. Radar Ambiguity Function Multiple targets (tk,nk) Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  11. Radar Ambiguity Function Multiple targets (tk,nk) Matched filter output Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  12. Radar Ambiguity Function Multiple targets (tk,nk) Matched filter output n target 1 (t1,n1) target 2 (t2,n2) t Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  13. Radar Ambiguity Function Multiple targets (tk,nk) Matched filter output n target 1 (t1,n1) target 2 (t2,n2) t Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  14. Radar Ambiguity Function • Ambiguity function characterizes the Doppler and range resolution. n target 1 (t1,n1) target 2 (t2,n2) t Ambiguity function Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  15. Radar Ambiguity Function • Ambiguity function characterizes the Doppler and range resolution. n target 1 (t1,n1) target 2 (t2,n2) t Ambiguity function Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  16. Properties of Radar Ambiguity Function • Signal component n t Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  17. Properties of Radar Ambiguity Function • Signal component • Energy n t Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  18. Properties of Radar Ambiguity Function • Signal component • Energy • Symmetry n t Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  19. Properties of Radar Ambiguity Function • Signal component • Energy • Symmetry • Linear frequency modulation (LFM) n t Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  20. The radar systems which emits orthogonal (or noncoherent) waveforms in each transmitting antennas are called MIMO radar. MIMO Radar MIMO radar SIMO radar (Traditional) w2f(t) f2(t) w1f(t) f1(t) w0f(t) f0(t) • Advantages • Better spatial resolution [Bliss & Forsythe 03] • Flexible transmit beampattern design [Fuhrmann & San Antonio 04] • Improved parameter identifiability [Li et al. 07] Chun-Yang Chen, Caltech DSP Lab | ICASSP 2007 student paper contest

  21. Ambiguity Function in MIMO Radar t:delay n:Doppler f: Spatial freq. (t,n,f) TX … dT u0(t) u1(t) uM-1(t) Chun-Yang Chen, Caltech DSP Lab | Asilomar Conference 2007

  22. Ambiguity Function in MIMO Radar t:delay n:Doppler f: Spatial freq. (t,n,f) (t,n,f) TX RX … … dT dR u0(t) u1(t) uM-1(t) MF MF MF … … … Chun-Yang Chen, Caltech DSP Lab | Asilomar Conference 2007

  23. Ambiguity Function in MIMO Radar t:delay n:Doppler f: Spatial freq. (t,n,f) (t,n,f) TX RX … … dT dR u0(t) u1(t) uM-1(t) MF MF MF … … … Chun-Yang Chen, Caltech DSP Lab | Asilomar Conference 2007

  24. Ambiguity Function in MIMO Radar t:delay n:Doppler f: Spatial freq. (t,n,f) (t,n,f) TX RX … … dT dR u0(t) u1(t) uM-1(t) MF MF MF … … … Matched filter output Chun-Yang Chen, Caltech DSP Lab | Asilomar Conference 2007

  25. Ambiguity Function in MIMO Radar t:delay n:Doppler f: Spatial freq. um(t): m-th waveform xm: m-th antenna location n: receiving antenna index Matched filter output Receiver beamforming Chun-Yang Chen, Caltech DSP Lab | Asilomar Conference 2007

  26. Ambiguity Function in MIMO Radar t:delay n:Doppler f: Spatial freq. um(t): m-th waveform xm: m-th antenna location n: receiving antenna index Matched filter output Receiver beamforming Cross ambiguity function Chun-Yang Chen, Caltech DSP Lab | Asilomar Conference 2007

  27. Ambiguity Function in MIMO Radar t:delay n:Doppler f: Spatial freq. um(t): m-th waveform xm: m-th antenna location n: receiving antenna index Matched filter output Receiver beamforming [San Antonio et al. 07] MIMO ambiguity function Chun-Yang Chen, Caltech DSP Lab | Asilomar Conference 2007

  28. Properties of the MIMO ambiguity function 2

  29. Properties of the signal component • Ambiguity function: • Signal component: Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  30. Properties of the signal component • Ambiguity function: • Signal component: For orthogonal waveforms, Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  31. Properties of the signal component • Ambiguity function: • Signal component: For orthogonal waveforms, If the waveforms are orthogonal, the signal component will be a constant for all angle. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  32. Properties of the signal component • Ambiguity function: • Signal component: For general waveforms, For orthogonal waveforms, Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  33. Properties of the signal component • Ambiguity function: • Signal component: For general waveforms, For orthogonal waveforms, • If is integer, The integration of the signal component is a constant if dT is a multiple of the wavelength. dT is the spacing between the transmitting antennas Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  34. Properties of the signal component dT is the spacing between the transmitting antennas • Ambiguity function: • Signal component: For general waveforms, For orthogonal waveforms, • If is integer, • For the general case, In general, the integration of the signal component is confined. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  35. Energy of the cross ambiguity function • Cross ambiguity function: • Energy of the cross ambiguity function: Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  36. Energy of the cross ambiguity function • Cross ambiguity function: • Energy of the cross ambiguity function: Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  37. Energy of the cross ambiguity function • Cross ambiguity function: • Energy of the cross ambiguity function: Parserval relation Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  38. Energy of the cross ambiguity function • Cross ambiguity function: • Energy of the cross ambiguity function: The energy of the cross ambiguity function is a constant. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  39. Energy of the MIMO ambiguity function • MIMO ambiguity function: • Energy of the ambiguity function Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  40. Energy of the MIMO ambiguity function • MIMO ambiguity function: • Energy of the ambiguity function dT is the spacing between the transmitting antennas Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  41. Energy of the MIMO ambiguity function • MIMO ambiguity function: • Energy of the ambiguity function dT is the spacing between the transmitting antennas If dT is a multiple of the wavelength, we can apply Parserval relation for 2D DFT. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  42. Energy of the MIMO ambiguity function • MIMO ambiguity function: • Energy of the ambiguity function Cross ambiguity function has constant energy dT is the spacing between the transmitting antennas Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  43. Energy of the MIMO ambiguity function • If dT is a multiple of the wavelength, dT is the spacing between the transmitting antennas If dT is a multiple of the wavelength, the energy of the MIMO ambiguity function is a constant. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  44. Energy of the MIMO ambiguity function • If dT is a multiple of the wavelength, • Recall that the signal component satisfies, • Because energy and the signal component are both constants, we can only spread the energy to minimize the peak. dT is the spacing between the transmitting antennas Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  45. Energy of the MIMO ambiguity function • If dT is a multiple of the wavelength, • In general, the energy satisfies, dT is the spacing between the transmitting antennas In general, the energy of the MIMO ambiguity function is confined in a certain range. Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  46. Energy of the MIMO ambiguity function • If dT is a multiple of the wavelength, • In general, the energy satisfies, • In general, the signal component satisfies, dT is the spacing between the transmitting antennas Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  47. Symmetry properties • Symmetry of the cross ambiguity function Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  48. Symmetry properties • Symmetry of the cross ambiguity function • Symmetry of the MIMO ambiguity function It suffices to show only half of the ambiguity function (t>0). Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  49. Linear frequency modulation (LFM) • Linear frequency modulation Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

  50. Linear frequency modulation (LFM) • Linear frequency modulation • Cross ambiguity function Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

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