BEIHANG UNIVERSITY 201 LAB

PARALLEL FREQUENCY RADAR

VIA COMPRESSIVE SENSING

You Yanan, Li Chunsheng, Yu Ze

IGARSS 2011

OUTLINE

1. INTRODUCTION

2. BACKGROUND OF COMPRESSIVE SENSING

3. PARALLEL FREQUENCY RADAR BASED ON COMPRESSIVE SENSING

4. SIMULATION RESULTS

5. CONCLUSION

1. INTRODUCTION

Traditional radar utilizes Shannon-Nyquist theorem for high bandwidth signal sampling, which induces the complicated system.

Compressive sensing (CS) indicates that the compressible signal using a few measurements can be reconstructed by solving a convex optimization problem.

1. INTRODUCTION

The structure of compressive sensing radar with frequencies transmitted in parallel is firstly presented in On compressive sensing applied to radar

Parallel frequency radar theoretically cannot degrade the resolution compared with a traditional radar system and effectively reduces the sampling rate.

2. BACKGROUND OF COMPRESSIVE SENSING

S x

y S x

1ˆ arg min{ }Nx x x R y x ： ,

Basis Pursuit (BP) , Matching Pursuit (MP) and Orthogonal Matching Pursuit (OMP) can solve this convex problem

sparse scene S

convex problem

Sparse scene S can be reconstructed by the above algorithms.

3. PARALLEL FREQUENCY RADAR BASED ON COMPRESSIVE SENSING

3.1 Observation mode

Transmit/Receive antenna

Target

Phase shift echo

V a

f1

f2

fM

The radar platform moves along track (azimuth) direction with constant velocity.

two-dimension observation scene is limited with the along track (azimuth) direction and the cross track (range) direction.

Parallel frequency radar synchronously transmits M single frequency pulses in each azimuth and then received the phase shift echoes.

Range resolution of traditional pulse compressive radar

Parallel frequency radar synchronously transmits M single frequency pulses in each azimuth with the constant .

Range resolution of parallel frequency radar via compressive sensing

2R c B

R c M f

fConclusion ： If we set the appropriate M and

2R c B R c M f

f

Range

Azimuth

Ground observation grid

3. PARALLEL FREQUENCY RADAR BASED ON COMPRESSIVE SENSING

3.2 Resolution and sampling rates

≈

QDM

High-rate A/D

Transmit/Receiveantenna

Match filter

QM

Chirp signal

f

f0

t

The sampling rate of parellel frequency radar is M/T complex samples per second. Define the time-bandwidth product to be D=BT, B is the total bandwidth of M single frequency pulses. Then, the sampling rate is shown as BM/D.

Conclusion： If we set the appropriate M and D

BBM/DTraditional radar

system

3. PARALLEL FREQUENCY RADAR BASED ON COMPRESSIVE SENSING

QDM

Phase Detecter

Transmit/Receive antenna

Parallel Transmitter

…

CS algorithm

…

QM

Δf

f1 …

2Δf MΔf

f2 fM

f1 f2 fM

f0

Parallel frequency radar system

＞3.2 Resolution and sampling rates

The kth echo in a certain azimuth is

The phase information of the target is

The discrete representation is

22 ( )2( ) ( ) kRi f tcRr t Arect t e

c

22 kRi fc

ky Ae

22

1

nk

RN i fc

k nn

y e x

Y S x x

3. PARALLEL FREQUENCY RADAR BASED ON COMPRESSIVE SENSING

3.3 Imaging based on compressive sensing

The phases of echo signal contain the information of the targets.

Phase demodulation

Azimuth phase compression

Constructing measurement y

OMP recovery

Ka estimating

Constructing measurementmatrix Φ

Raw echo

Image

is identity matrix

Ka estimation

3. PARALLEL FREQUENCY RADAR BASED ON COMPRESSIVE SENSING

The targets will be focused on the respective zero Doppler by Ka. Ka is calculated precisely before compressing the azimuth phases.

Ka varies with the range cells and the signal frequencies.

2set2a aK V R

construction

Prior

1D observation grid

M single frequency pulses

M echoes phasedetector

M frequencies 1

Nn n

22Tn 1{ }k

n Ri f Mcke

Measurement matrix is constructed by prior phase information using discrete grids.

3. PARALLEL FREQUENCY RADAR BASED ON COMPRESSIVE SENSING

3D prior

Observation scene Observation grids

Na×Nr

Prior

M frequencies M×Nr

M single frequency pulses

M echoesphase

detector M frequencies

recover

OMP 1×Nr

Observation scene reconstruction

3. PARALLEL FREQUENCY RADAR BASED ON COMPRESSIVE SENSING

Raw echo Phase demodulation

Azimuth phase compression

Constructing measurement y

OMP recovery

Ka estimating Constructing measurement matrix Φ

Image

Echo equation 1

Instantaneous range

Approximate representation

Echo equation 2

Demodulating and detecting the phase shift

2 ( )2 ( )2 ( )( , ) ( ) ( )Ri f tc

a cRr t Arect t ec

2 2 20( ) aR R V

2 22 2 2

0 00

( )2a

aVR R V R

R

2 20

0

22222 ( )( , ) ( ) ( )

aVR ii fi f t Rca c

Rr t Arect t e e ec

2 20

0

22 ( ) 22 2aVRR i fi f i f cRc cy Ae Ae e

Illation

3. PARALLEL FREQUENCY RADAR BASED ON COMPRESSIVE SENSING

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Imaging result of point target of the parellel frequency radar via compressive sensing

4. SIMULATION RESULTS

Range cross section(amplitude)

The parameters in simulations: M = 30, △f = 5MHz, RMAX = 20km and N = 512.

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Pulse compression radar Parallel frequency radar via compressive sensing

RD algorithm of pulse compression radar

Compressive sensing algorithm of parallel

frequency radar

4. SIMULATION RESULTS

Imaging results of pulse compression radar and parallel frequency radar via compressive sensing with single or several point targets

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4. SIMULATION RESULTS

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Imaging results of traditional SAR and parallel frequency radar via compressive sensing with the same data amount

Traditional SAR Parallel frequency radar via compressive sensing

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4. SIMULATION RESULTS

Pulse compression radar Parallel frequency radar via compressive sensing

Conclusion: Sampling rate is reduced by narrow-bandwidth of single frequency pulse. The sparse scene is reconstructed using 10% original data. Side lobes of the range disappear via compressive sensing.

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4. SIMULATION RESULTS

The ability of distinguishing the adjacent targets in the range direction

Pulse compression radar Parallel frequency radar via compressive sensing

5. CONCLUSION

This presentation introduces parallel frequency radar and imaging approach based on compressive sensing.

The novel radar can reduce data rate and maintain range resolution with the premise of the appropriate parameters.

The measurement matrix is composed of the priori phases. The observation scene is reconstructed by OMP.

5. CONCLUSION

The imaging approach based on compressive sensing avoids side lobes of the range.

The noise in received signal is not taken into account in the simulations, it is not ignored in practice.

More researches are required on the capability resisting the noise interference of the signal processing based on compressive sensing in the future.

BEIHANG UNIVERSITY 201 LAB

Thank you for your attention!

IGARSS 2011