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http://www.girdsystems.com Direction of Arrival Estimation (DOA) in Interference & Multipath Propagation Dr. H. Howard Fan GIRD Systems, Inc. 310 Terrace Ave. Cincinnati, Ohio 45220 This presentation is based on publicly available information only, some copyright restrictions may apply, not for commercial use.

Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Page 1: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Direction of Arrival Estimation (DOA)

in Interference & Multipath Propagation

Dr. H. Howard Fan

GIRD Systems, Inc.

310 Terrace Ave.

Cincinnati, Ohio 45220

This presentation is based on publicly available information only, some copyright

restrictions may apply, not for commercial use.

Page 2: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Scope

• There are many location methods

Source location vs. Self-location (Navigation)

Active vs. Passive

Network based (GPS) vs. Single platform (DOA or AOA)

• We will concentrate on source location with a single

platform equipped with a sensor array, passive

• Emphasis on DOA estimation

• Narrowband signals only

Page 3: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Outline

• Basics of DOA Estimation

Beamforming Type

High Resolution Type

• Adaptive Beamforming DOA Estimation in Strong

Interference

• High Resolution DOA Estimation in Multipath

• Smoothing Method

• Source Association and Locating the Sources

Page 4: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Outline

• Basics of DOA Estimation

Beamforming Type

High Resolution Type

• Adaptive Beamforming DOA Estimation in Strong

Interference

• High Resolution DOA Estimation in Multipath

Smoothing Methods

• Source Association and Locating the Sources

Page 5: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Objective of DOA Estimation

• To find DOA (relative to the array orientation) of all

incident RF rays

• Could have multipath propagation and interference

DOA Est /

Tracking

Page 6: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Narrowband Signal Sources

• A complex sinusoid

( ) j j t j ts t e e e

• A real sinusoid is a sum of two sinusoids

1 2cos( )2 2

j j t j j t j t j tt e e e e e e

• A delay of a sinusoid is a phase shift

0 0

0( ) ( )j t j tj ts t t e e e s t

• Apply approximately to narrowband signals

Page 7: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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A Uniform Linear Array

1( ) ( )x t s t• If the received signal at sensor 1 is

• Then the received signal at sensor i is

0( 1) sin

1( ) ( ) ( ) ( )i i

i dj

j j cix t e x t e s t e s t

• Then it is delayed at sensor i by 0( 1) sini

i d

c

0A signal source

“impinges” on the array

with an angle

c: propagation speed

( ) j ts t e

0

Page 8: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Outline

• Basics of DOA Estimation

Beamforming Type

High Resolution Type

• Adaptive Beamforming DOA Estimation in Strong

Interference

• High Resolution DOA Estimation in Multipath

Smoothing Methods

• Source Association and Locating the Sources

Page 9: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Beamforming

• Delay-and-sum type

• Reverse the delay/phase on each sensor to “line-up”

the received signal phase

• Adding all phase-shifted sensor outputs to enhance the

received SNR in that direction

Page 10: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Beamforming

• By adjusting the delay or phase shifts, we electronically steer the

beam through all look directions to find DOA of an incident signal

• Received signal at the ith sensor:

0( 1) sin

1( ) ( ) ( ) ( )i i

i dj

j j cix t e x t e s t e s t

• is the incidence angle of the received signal

• The delay or phase shift of the beamformer on the ith sensor is computed according to a “look angle” to get the output:

0

0

( 1) sin

*

1 1

( 1) [sin sin ]

1

( ) ( ) ( )

( )

i dN N jc

i i i

i i

i dN jc

i

y t w x t e x t

e s t

Page 11: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Beamforming

• If , then the output becomes

0

0

0

( 1) [sin sin ]

1 1

( ) ( ) ( ) ( )

i dN Njc

i i

y t e s t s t Ns t

• I.e., the output is enhanced N times

• Since noise is not correlated, noise is not enhanced

• So SNR is enhanced N times

• At other steering angles, the complex weights may cancel so the output is not enhanced or even degraded

• This is the designed purpose of a beamformer

0

Page 12: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Beamforming

• Beam pattern: A gain pattern as a function of the steering angle

0( 1) [sin sin ]

0

1

( , )

i dN jc

i

G e

0 0 o

0 30

Page 13: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Beamforming

• Sensor spacing is usually wavelength/2

• Larger spacing creates “grating lobes” that confuse with

the main lobe

• Smaller spacing

reduces the total

aperture – lower

spatial resolution

Page 14: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Beamforming

• Number of sensors (array aperture) are directly related to

spatial resolution

4-element (aperture = 1.5 wavelength) 7-element (aperture = 3 wavelength)

Page 15: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Beamforming

• Problem 1: A wide mainlobe causes poor spatial

resolution Two targets 10 degrees apart Cannot distinguish them

Page 16: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Beamforming

• Problem 2: A strong interferer can come into a sidelobe

and completely swamp weak signal in the look direction

Beamformer output:

• Control sidelobes by Dolph-Chebyshev shading, w. limited effect

Page 17: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Pros/Cons of Beamforming

• Can find only one DOA at a time

• Spatial resolution determined by number of sensors in

an array, but generally not very good unless having a

large number of sensors

• Works for other array shapes also, need to know

sensor positions in an array

• Sensitive to sensor position, gain, and phase errors,

must calibrate carefully to make it work well

• Interference is a big problem

• Multipath is a much lesser problem

Page 18: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Outline

• Basics of DOA Estimation

Beamforming Type

High Resolution Type

• Adaptive Beamforming DOA Estimation in Strong

Interference

• High Resolution DOA Estimation in Multipath

Smoothing Method

• Source Association and Locating the Sources

Page 19: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

MUSIC

• Able to find DOAs of multiple sources in “one-shot”

• High spatial resolution compared with beamforming

methods (I.e., a few antennas can result in very high

spatial resolution)

• MUSIC stands for Multiple Signal Classifier

Page 20: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Narrowband Signal Sources

• Consider I narrowband signal sources

1 2

1 1 2 2( ) , ( ) , , ( ) Ij t j t j t

I Is t e s t e s t e

• Assume that all amplitudes are uncorrelated

2;{ }

0;

i

i j

i jE

i j

• Recall received signal on the ith sensor:

0( 1) sin

1( ) ( ) ( ) ( )i i

i dj

j j cix t e x t e s t e s t

Page 21: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Signal Model

• Put received signals at all N sensors together:

• is called a “steering vector”

sin1

22 sin

3

( 1) sin

1

( )

( )

( ) ( ) ( ) ( ) ( )

( )

dj

c

dj

c

N dN jc

x tex t

t x t s t s te

x t

e

x a

( )a

Page 22: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Signal Model

• If there are I source signals received by the array, we get

a “signal model”:

x(t) --- received signal vector ( N by 1 )

s(t) --- source signal vector ( I by 1 )

n(t) --- noise vector ( N by 1 )

( N by I )

1( ) [ ( ), , ( )]T

It s t s ts

• Sources are independent, noises are uncorrelated

• Column of A can also be normalized

Page 23: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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The MUSIC Algorithm

• Compute the N x N correlation matrix

sR

2 2

1{ ( ) ( )} .{ , , }H

IE t t diag sR s s

2

0{ ( ) ( )}H HE t t x sR x x AR A I

where

• If the sources are somewhat correlated so is not

diagonal, it will still work if has full rank.

• If the sources are correlated such that is rank deficient,

then it is a problem. A common solution is “spatial

smoothing”.

Q: Why is the rank of (being I) so important?

A: It defines the dimension of the signal subspace.

sR

sR

sR

Page 24: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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The MUSIC Algorithm

• For N > I, the matrix is singular, i.e., H

sAR A

2 ; 1,2, ,i i i i N xR u u

• But this implies that is an eigenvalue of

• Since the dimension of the null space of is N-

I, there are N-I such eigenvalues of

• Since is non-negative definite, there are I other

eigenvalues such that

• Let be the ith eigenvector of corresponding to

2 2

0 0i

2

0

2

0

2

i

2

0det[ ] det[ ] 0H s xAR A R I

xR

H

sAR A

xR

iuxR

2

i

xR

2 2 2 2

0 0, 1, , ; , 1, ,i ii I i I N

Page 25: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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The MUSIC Algorithm

• This implies

• Partition the N-dimensional vector space into the

signal subspace and the noise subspace sU nU

2 2

0[ ] ; 1,2, ,H

i i i i i N x sR u AR A I u u

2 2

0( ) ; 1,2, ,H

i i i i N sAR A u u

2 2

0( ) ; 1,2, ,

0; 1, ,

H i i

i

i I

i I N

s

uAR A u

2 2 2

0

1 1

: , : ,

[ ]

i i

I I N

i I i I

s n

s n

U U

U U u u u u

Page 26: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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The MUSIC Algorithm

• The steering vector is in the signal subspace

• Signal subspace is orthogonal to noise subspace

sU

nU

( )ia

(1) means I linear combinations of columns of A equal the signal subspace spanned by columns of

(2) means the linear combinations of columns of A, i.e., the signal subspace, is orthogonal to

2 2

0( ) ; 1,2, , (1)

0; 1, , (2)

H i i

i

i I

i I N

s

uAR A u

Page 27: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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The MUSIC Algorithm

• The steering vector is in the signal subspace

• Signal subspace is orthogonal to noise subspace

• This implies that

• So the MUSIC algorithm searches through all angles , and plots the “spatial spectrum”

( )H

i na U 0

( )ia

1( )

( )HP

na U

• Wherever exhibits a peak

• Peak detection will give spatial angles of all incident sources

, ( )i P

Page 28: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

The MUSIC Algorithm

1. Compute the signal correlation matrix

2. Perform SVD/EVD on and separate the smallest eigenvalues from larger eigenvalues

3. Eigenvectors corresponding to the smallest eigenvalues form a noise subspace

4. Search through all angles in the MUSIC spatial spectrum

5. Peaks correspond to DOAs

1( )

( )HP

na U

xR

xR

nU

Page 29: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

The MUSIC Algorithm

MUSIC spatial spectrum compared with other methods

Blackberry

to go to??

Blackberry

to go to??

Blackberry

to go to?

S you ca?

Blackberry

to go to??

Blackberry to go to??

Blac

kberr

y to

go t

Page 30: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Pros/Cons of The MUSIC Algorithm

• Can find multiple DOAs with high resolution

• Number of sensors must be more than number of sources

• Works for other array shapes also, need to know sensor positions in an array

• Very sensitive to sensor position, gain, and phase errors, need careful calibration to make it work well

• Searching through all could be computationally expensive

• Interference is not much a problem, just another source whose DOA can be found with other sources

• Multipath is a big problem

Page 31: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Outline

• Basics of DOA Estimation

Beamforming Type

High Resolution Type

• Adaptive Beamforming DOA Estimation in Strong

Interference

• High Resolution DOA Estimation in Multipath

Smoothing Methods

• Source Association and Locating the Source

Page 32: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

http://www.girdsystems.com

Adaptive Beamforming

• Rather than fixed weights/phase, adapt the weights according to the signal environment

• The generalized sidelobe canceller (GSC) achieves this w. flexible constraints

• Delay-and-sum beamformer output y(t):

0( ) ( ) ( ) ( ) ( ) ( )H Hy t t s t a x a a

• The GSC output y(t):

0( ) ( ) ( ) ( )H Hy t t s t w x w a

w is a vector of complex weights, more general

Page 33: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Adaptive Beamforming

• Q: How do we choose the weights w?

• A: By some constrained optimization

• Constraints:

1) Array gain at the look direction should be preserved

When

2) Array gain at some other directions may need to be zero

This is also called null-steering

1 1( ) ( ) 1H H w a a w

2 2( ) ( ) 0H H w a a w

0( ) ( ) ( ) ( )H Hy t t s t w x w a

1 0 we have, ( ) ( )y t s t

Page 34: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Adaptive Beamforming

• Jointly, we write these constraints as

1

1 2

2

1( )( ) ( )

0( )

HH H

H

aw a a w C w g

a

• More constraints, other constraints, can be imposed

• The cost function is:

2{| ( ) | } { ( ) ( )}H H HE y t E t t xw x x w w R w

• The optimization problem is:

min subject to H H x

w

w R w C w g

Page 35: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Adaptive Beamforming

• The solution to this optimization problem is:

• Since we minimize the output energy, a strong interferer will result in a deep notch in its direction

ab ab

1 1 1( )H x xw R C C R C g

Page 36: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Adaptive Beamforming

• Another interpretation: Decompose w into

G I w w Bw

is the orthogonal compliment of : H B C C B 0

B

Gw

Iw

Iw

( )tx( )y t

• Upper branch: Main channel; Lower branch: Auxiliary channel

Page 37: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Adaptive Beamforming

• I.e., allows gain (null) in the desired directions – main channel

• Since , the matrix B is a “blocking matrix” that blocks the signal (null) in the desired directions – auxiliary channel

• is designed to produce a replica of interference leaking into the main channel to subtract it out

1( ) so that H H

G G

w C C C g C w g

Gw

H C B 0

Iw

1( )H H

I G

x xw B R B B R w

Page 38: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Adaptive Beamforming

• Advantages of adaptive beamforming

– Able to reduce effect of interferences from unknown angles

– Can steer look direction and multiple null directions

– Get a signal copy easily

• Shortcomings of adaptive beamforming

– Spatial resolution is still low

– Need enough weights (antenna channels) to obtain enough degrees of freedom: At least # of constraints + 1

– Sidelobe levels may not be controlled perfectly

Page 39: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Outline

• Basics of DOA Estimation

Beamforming Type

High Resolution Type

• Adaptive Beamforming DOA Estimation in Strong

Interference

• High Resolution DOA Estimation in Multipath

Smoothing Methods

• Source Association and Locating the Sources

Page 40: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Multipath Propagation Issue

• Urban areas have a lot of multipaths

• Beamforming DOA algorithms are not affected by

this much

• MUSIC fails in multipath!

• This is because if there is multipath, two or more

DOAs will be from the same source – i.e., some

sources in MUSIC signal model are correlated

• Now with I DOAs there are less than I sources

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Multipath Propagation Issue

• Correlated sources disable MUSIC!

• E.g.:

• This is called rank deficiency

– The rank of will be less than I

– The signal subspace has dimension less than I

– There are less than I peaks in the MUSIC spectrum

– Which of the I DOAs will give less than I peaks?

• In fact all peaks will be wrong.

1 1( ) [ ( ), ( )]Tt s t as ts2 2

1 1

2 2 2

1 1

{ ( ) ( )}H aE t t

a a

sR s s Rank 1

H

sAR A

Page 42: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Multipath Propagation Issue

• Remedy: Spatial Smoothing, still find I DOAs

– L overlapping subarrays

– M sensors in each subarray, M > I

– N total sensors

– N = M + L − 1

. . . . . . . . .1 2 L M M+1 N

• Let be the received signal vector of the ith subarray ( )i tx

Page 43: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Multipath Propagation Issue

• One signal case:

sin1

22 sin

3

( 1) sin

1

( )

( )

( ) ( ) ( ) ( ) ( )

( )

dj

c

dj

c

N dN jc

x tex t

t x t s t s te

x t

e

x a

sin

1 2( ) ( ) ( ), ( ) ( ) ( ), etc.d

jc

M Mt s t t e s t

x a x a

• In general ( 1) sin

( ) ( ) ( )i d

jc

i Mt e s t

x a

( 1) sin

( ) ( ) ( )i d

jc

i Mt e s t

x a

Page 44: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Multipath Propagation Issue

• With I DOAs:

1

1

( 1) sin ( 1) sin

1 1

( 1) sin

1

( 1) sin

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

I

IM

i

i d i dj j

c ci M M I I

i dj

c

M M I

i dj

c

t e s t e s t

e

t

e

A

D

x a a

O

a a s

O

( ) ( )i M it tx A D s (Noise has been ignored so far)

Page 45: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Multipath Propagation Issue

• Compute correlation matrix of each subarray

2

0{ ( ) ( )}H H H

i i i M i i ME t t x sR x x A D R D A I

• Now average the correlation matrices of all subarrays

2

0

1 1

1 1{ ( ) ( )}

L LH H H

L i i M i i M

i i

E t tL L

x sR x x A D R D A I

• Note the dimension of is M by I

• The dimension of the matrix in the brackets is I by I

MA

Page 46: Direction of Arrival Estimation (DOA) in Interference ... Interference & Multipath Propagation Dr. H. Howard Fan ... •Adaptive Beamforming DOA Estimation in Strong ... •Signal

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Multipath Propagation Issue

• The matrix in the brackets has full rank I if L is large

enough, i.e.,

• Provided M > I, there is a noise subspace in

• Now can apply MUSIC to

• Will detect I DOAs with this spatial smoothing

• Price paid is that more sensors are required: M > I,

M + L = N L more sensors to “de-correlate”

LxR

2

0

1 1

1 1{ ( ) ( )}

L LH H H

L i i M i i M

i i

E t tL L

x sR x x A D R D A I

LxR

L I

L I

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Outline

• Basics of DOA Estimation

Beamforming Type

High Resolution Type

• Adaptive Beamforming DOA Estimation in Strong

Interference

• High Resolution DOA Estimation in Multipath

Smoothing Methods

• Source Association and Locating the Sources

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Source Association Under Multipath

• Several paths belong to one source, multiple sources

• Can detect all DOAs of multiple paths and multiple

sources

• But how many sources are there?

• Need to know which DOAs can be associated to which

sources – source association

• Then locate the sources in several ways

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Source Association Under Multipath

• Once sources are associated with DOAs

– Locate the sources by using multipath if we know the

reflection geometry – back tracing

• Multipath works

to our advantage

in this case

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Source Association Under Multipath

• Alg. works for any DOA method, easier with MUSIC

1. Compute the received signal correlation matrix based

on all sensors, as in MUSIC but un-smoothed

2. Compute the noise subspace matrix whose rank is

the number of sources J, not the number of paths I

3. Based on the estimated DOAs, compute the overall

steering matrix A

4. Find minimum eigenvalues of and their

corresponding eigenvectors , the number of these

eigenvalues is the number of sources J

5. Construct I by J matrix

nU

H H

n nA U U A

iq

1[ ]JQ q q

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Source Association Under Multipath

6. Find J groups of rows of

that are independent among the groups but dependent

within each group, these correspond to groups of paths

associated with each source

• Dependency test can be done by, e.g., dividing the

corresponding elements in two rows and compute the

variance of the ratios

1[ ]JQ q q

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Source Association Under Multipath

• E.g.: 15 antennas in a ULA, two sources, 5 paths

– DOA from Source 1:

– DOA from Source 2:

– We only know 5 DOAs rank ordered as:

o o30 and 60 o o o5 , 25 , and 55

o o o o o60 , 30 , 5 , 25 , 55

• Put them into A in this order

• Computed eigenvalues of which are

{20.0559, 17.9585, 14.8226, 0.0430, 0.0088}

• Obviously I = 5 but J = 2

H H

n nA U U A

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Source Association Under Multipath

• Dependency test on

the rows of Q

1 & 2 belong to one

3, 4, 5 belong to the

other

1 2

0.4152 + j0.4824 0.2656 + j0.1121

0.4062 + j0.4989 0.2913 + j0.1122

[ ] -0.2290 + j0.0746 0.3954 - j0.3430

-0.2429 + j0.0498 0.3883 - j0.3502

-0.2210 + j0.1123 0.2770 - j0.4418

Q q q

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Source Association Under Multipath

• When reflection geometry is unknown

– Identify the LOS paths from the reflected paths if either the

source or the receiver is moving

• Once LOS paths are identified, the sources can be more

easily located by

– Ray back tracing

– Several different angles of LOS DOA to triangulate

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Source Association Under Multipath

• Stationary receiver: All paths have fixed DOAs;

• Moving receiver: Paths have varying DOAs, DOA

variations differ between LOS path and reflected paths.

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Source Association Under Multipath

• All DOAs need to

be tracked

• Reflected paths may

be eliminated over

time by choosing

the longest

continuous path as

the LOS path

• Most likely, reflected paths appear and disappear

intermittently as one travels, but not the LOS paths

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Source Association Under Multipath

• Caution: If not tracked properly, two DOAs may be

erroneously identified after they cross

• Special measures are needed to prevent this

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Conclusions

• Beamforming (adaptive)

– Can reduce effect of interferences from unknown DOAs

– Can steer look direction and multiple null directions

– Spatial resolution is low

– Resilient to multipath propagation

• MUSIC (with smoothing)

– Can find multiple DOAs with high resolution

– Very sensitive to sensor position, gain, and phase errors,

need careful calibration to make it work well

– Spatial smoothing is difficult to achieve on other than ULA

• Source association can be applied to both methods

• Source location done by ray back trace/triangulation

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About GIRD Systems, Inc.

• Founded in 2000 - based in Cincinnati

• Specializes in communications and

signal processing, especially

developing novel algorithms to solve

challenging problems

• As of Jan. 2010, won more than 15

Phase I awards and 7 Phase II awards

from Navy, Air Force, Army

• Partnerships with many large

contractors including Northrop

Grumman, L-3 Communications, etc.

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About GIRD Systems, Inc.

• Key Technology Areas

– Interference Mitigation (no reference, in-band)

– Direction Finding (wideband, high-resolution)

– Location/Navigation (Assisted GPS, GPS denied,

signals of opportunity)

– Wireless Network Security (physical layer)

– Power Amplifier Linearization

– Novel Communications systems/modeling

• Contact Information: GIRD Systems, Inc. Phone: (513) 281-2900

310 Terrace Ave. Fax: (513) 281-3494

Cincinnati, OH 45220 E-mail: [email protected]

USA Web: www.girdsystems.com