EFFECTS OF MUTUAL COUPLING AND DIRECTIVITY ON DOA ESTIMATION USING MUSIC

LOPAMUDRA KUNDU & ZHE ZHANG

Outline of the Presentation

What is DOA? MUSIC Parameter study:

Signal-to-noise ratio (SNR) Inter-element spacing Mutual coupling Directivity

Why DOA? Applications Scopes of future work

Direction of Arrival (DOA) Estimation

Estimation of direction finding signals in the form of electromagnetic/acoustic waves impinging on a sensor or antenna array.

High resolution DOA can resolve closely spaced frequencies.

Most popular technique is “Subspace method” Used for locating and tracking signal sources

in both military and civilian communications.

4

Multiple Signal Classification (MUSIC)

Steering vectors:

Data model of M signals incident on an array of N elements:

Where, k=1,…,K (number of snapshots)

1

( ) [ ( )]( ) ( )M

m mm

x k s k n k

2 2( ) sin ( )( 1) sin

1 2[ ( ) ( )... ( )] , ( ) [1, ,..., ]m mj d j N dT T

M mS s s s s e e

2 2H H HR S S I SAS I

Correlation matrix of x:

A: signal correlation matrixσ2: noise variance

1 2 NAntenna array

d

Msignals

Φn

MUSIC (contd.) Eigen value decomposition of R

Since (signal subspace) (noise subspace), DOAs are the peak locations ⊥of MUSIC power spectrum

2

1

1( )

( )N

Hm

m M

Pv s

2 2

1 1

( )M N

H Hi i i i i

i i M

R v v v v

signal subspace noise subspace

M N-M M N-M

v vH

Parameters Affecting the Performance of MUSIC

Signal-to-Noise Ratio (SNR) Inter-element Spacing Mutual Coupling Antenna Directivity

Normalized Power Spectrum For Different SNR Levels (AWGN)

Simulation Parameters: Array size=5 (ULA) Element Spacing=𝝺 Number of Signals=2 AOA= 20 and 80⁰ ⁰ Number of Snapshots=3 Conclusion: Broad peaks for SNR<15 dB. Sharp peaks at SNR ≥ 15 dB

and both the signal directions are estimated correctly.0 10 20 30 40 50 60 70 80 90

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

angle () in degree

Nor

mal

ized

pow

er s

pect

rum

P() vs. for DOA estimation using MUSIC for different snr

SNR = -10dB

SNR = 15dBSNR = 30dB

Normalized Power Spectrum For Various Inter-Element Spacing (No Coupling)

Simulation Parameters: Array size=5 (ULA) SNR level=30 dB (AWGN) Number of Signals=2 AOA=20 and 80⁰ ⁰ Number of Snapshots=3

Conclusion: Broad peaks for d<0.5 .𝝺 Sharp peaks at d≥0.5 and 𝝺

both the signal directions are estimated correctly.

0 10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

angle () in degree

Nor

mal

ized

pow

er s

pect

rum

P() vs. for DOA estimation using MUSIC

d= 0.1

d= 0.5

d=

Normalized Power Spectrum in the Presence of Mutual Coupling

Simulation Parameters: Array size=5 (ULA) SNR level=50 dB Number of Signals=3 (LP) AOA=20 , 50 and 80⁰ ⁰ ⁰ Number of Snapshots=10

Conclusion: Broad peaks for d<0.5 .𝝺 Sharp peaks at d ≥ 0.5 and 𝝺

all the three signal directions are estimated correctly.

0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

angle () in degree

Nor

mal

ized

pow

er s

pect

rum

P() vs. for DOA estimation using MUSIC

d=1

d=0.5

d=0.1

Comparison Between NEC Simulation and MALTLAB Simulation

Simulation Parameters: Array size=5 (ULA) SNR level=50 dB Number of Signals=3 (LP) AOA=20 , 50 and 80⁰ ⁰ ⁰ Number of Snapshots=10

Conclusion: The algorithm works better for

no coupling scenario. Mutual coupling degrades the

direction estimation efficiency considerably for same spacing.

0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

angle () in degree

Nor

mal

ized

pow

er s

pect

rum

P() vs. for DOA estimation using MUSIC

NEC simulation for d=0.1

Matlab simulation for d=0.1

Directivity of Antenna

DOA estimation is related not only with the mutual coupling, but also with the directivity of the antennas.Isotropic antenna: radiates uniformly in all directions.Directional antenna: radiates more efficiently in some

directions than others.Steering vector would be modified by the gain of directional

antenna

Goal is to compare the performance of isotropic antenna arrays and directional antenna arrays in DOA estimation.

( ) ( ) ( )ds G s

Structure of Antenna arrays in NEC

Isotropic Directional

Simulation Result for Isotropic Array

Analysis: Incident signals at 3 angles :

20⁰, 50⁰ and 80⁰ All 3 signals are detected

accurately. Isotropic array could detect

all the incident signals simultaneously.

0 10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Nor

mal

ized

Pow

er S

pect

rum

(P

())

angle () in degree

Simulation Result for Directional Array

0 10 20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Nor

mal

ized

Pow

er S

pect

rum

(P

())

angle () in degree

Analysis: Incident signals at 3 angles:

20⁰, 50⁰ and 90⁰. Only incoming signal at 90⁰

is detected. Directional array could only

detect the signals that fall within the range of its main beam position.

The gain of directional antenna may make the result more accurate.

Why DOA: Applications

DOA ESTIMATION

radar

SonarSeismic Exploration

Electronic Surveillance

Wireless Communication

Applications Involving Coupling and Directivity

Applications involving mutual coupling: MIMO system with closely spaced antennas.

Applications involving directivity: Indoor environment with intensive multipath effect and interferences.

Scopes of Future Work

Other types of arrays and antennas. Effects of other parameters like polarization, antenna

gain, delay and ground effects.

THANK YOU!