Radar ambiguity function презентация

California Institute of Technology
Electrical Engineering/DSP Lab

ICASSP 2008

Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

τ: delay
ν: Doppler

τ: delay
ν: Doppler

Radar ambiguity
function

τ: delay
ν: Doppler

Radar ambiguity
function

Ambiguity function characterizes the Doppler and range resolution.

τ: delay
ν: Doppler

Matched filter
output

τ

ν

target 2 (τ2,ν2)

target 1 (τ1,ν1)

Multiple targets
(τk,νk)

τ

ν

target 2 (τ2,ν2)

target 1 (τ1,ν1)

Multiple targets
(τk,νk)

τ

ν

target 2 (τ2,ν2)

target 1 (τ1,ν1)

Ambiguity function

τ

ν

target 2 (τ2,ν2)

target 1 (τ1,ν1)

Ambiguity function

τ

ν

τ

ν

τ

ν

τ

ν

SIMO radar (Traditional)

w2φ(τ)

w1φ(τ)

w0φ(τ)

Advantages
Better spatial resolution [Bliss & Forsythe 03]
Flexible transmit beampattern design [Fuhrmann & San Antonio 04]
Improved parameter identifiability [Li et al. 07]

u0(t)

u1(t)

uM-1(t)

…

(τ,ν,f)

TX

τ:delay
ν:Doppler
f: Spatial freq.

dT

…

…

MF

…

MF

…

MF

…

(τ,ν,f)

(τ,ν,f)

TX

RX

τ:delay
ν:Doppler
f: Spatial freq.

u0(t)

u1(t)

uM-1(t)

dT

dR

…

…

MF

…

MF

…

MF

…

(τ,ν,f)

(τ,ν,f)

TX

RX

τ:delay
ν:Doppler
f: Spatial freq.

u0(t)

u1(t)

uM-1(t)

dT

dR

…

…

MF

…

MF

…

MF

…

(τ,ν,f)

(τ,ν,f)

Matched filter output

TX

RX

τ:delay
ν:Doppler
f: Spatial freq.

u0(t)

u1(t)

uM-1(t)

dT

dR

Matched filter output

Receiver beamforming

τ:delay
ν:Doppler
f: Spatial freq.
um(t): m-th waveform
xm: m-th antenna location
n: receiving antenna index

Matched filter output

Receiver beamforming

τ:delay
ν:Doppler
f: Spatial freq.
um(t): m-th waveform
xm: m-th antenna location
n: receiving antenna index

Cross ambiguity function

Matched filter output

Receiver beamforming

[San Antonio et al. 07]

τ:delay
ν:Doppler
f: Spatial freq.
um(t): m-th waveform
xm: m-th antenna location
n: receiving antenna index

MIMO ambiguity function

Ambiguity function:

Signal component:

Ambiguity function:

Signal component:

For orthogonal waveforms,

Ambiguity function:

Signal component:

For orthogonal waveforms,

If the waveforms are orthogonal, the signal component will be a constant for all angle.

For orthogonal waveforms,

For general waveforms,

For orthogonal waveforms,

If is integer,

For general waveforms,

dT is the spacing between the transmitting antennas

The integration of the signal component is a constant if dT is a multiple of the wavelength.

For orthogonal waveforms,

If is integer,


For the general case,

For general waveforms,

dT is the spacing between the transmitting antennas

In general, the integration of the signal component is confined.

Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

Parserval relation

Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

The energy of the cross ambiguity function is a constant.

MIMO ambiguity function:


Energy of the ambiguity function

MIMO ambiguity function:


Energy of the ambiguity function

dT is the spacing between the transmitting antennas

MIMO ambiguity function:


Energy of the ambiguity function

If dT is a multiple of the wavelength, we can apply Parserval relation for 2D DFT.

dT is the spacing between the transmitting antennas

MIMO ambiguity function:


Energy of the ambiguity function

Cross ambiguity function has constant energy

dT is the spacing between the transmitting antennas

If dT is a multiple of the wavelength,

If dT is a multiple of the wavelength, the energy of the MIMO ambiguity function is a constant.

dT is the spacing between the transmitting antennas

Energy of the MIMO ambiguity function

Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

dT is the spacing between the transmitting antennas

Energy of the MIMO ambiguity function

Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

In general, the energy of the MIMO ambiguity function is confined in a certain range.

dT is the spacing between the transmitting antennas

Energy of the MIMO ambiguity function

Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

dT is the spacing between the transmitting antennas

Chun-Yang Chen, Caltech DSP Lab | ICASSP 2008

It suffices to show only half of the ambiguity function (τ>0).

Shear off

ν

ν

Shear off

For orthogonal waveforms,

If the waveforms are orthogonal, the signal component will be a constant for all angle.

If is integer,

For general waveforms,

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

For the general case,

In general, the integration of the signal component is confined in a certain range.

dT is the spacing between the transmitting antennas