Angle of Arrival (AoA)CALEN CARABAJAL

EECS 823

Introduction to Angle of Arrival Physics

“Angle between propagation direction of an incident wave and some reference direction” (orientation)

Plane wave impinging upon array

Visual Understanding

Plane wave impinges on array of antennas with the same orientation and radiation pattern

Time delay corresponds to a phase shift between antennas

To the right, red lines represent wave front, each with the same relative phase

Red dot corresponds incidence of wave front

Results in a zero-valued response for this phase

Wave Propagation and Antenna: Specific Case

Constant amplitude assumed

Received signal for each antenna is

Summing signals together results in

Observations

– broadside vs boresight

Cancellation k*r

Frequency dependence

Antenna Arrays, Steering Vector

For identical antennas with radiation pattern and orientation , the overall radiation pattern is

Wave number

Steering vector can take various forms Specified to arbitrary point of origin

Represents relative phases at each antenna

Applications of Angle of Arrival Estimation: Wireless Sensor Networks Wireless Sensor Networks

May use antenna array on each sensor node

Geodesic location of cell phones

Emergency phone calls

Applications of Angle of Arrival: Remote Sensing

AoA estimation provides also allows further characterization of target. Adaptive processes can take advantage of this knowledge

Beamsteering/Nullsteering

Angle-of-arrival-assisted Radio Interferometry

Ground moving objects

Coupled with other data (range, Doppler), can extract target location

Limitations of Angle of Arrival Estimation: The Cramer-Rao Bound CRB provides lower bound on variance in estimations

Provides a theoretical limit on ability to discern angle of arrival

Considers corrupting noise on the signal

The Cramer-Rao Bound for AoA estimation is

: covariance of noise vector

N : number of elements in array

d : distance between array elements

Limitations of Angle of Arrival Estimation: Effect of Multipath

Consider either a smooth surface or rough surface

Specular surface results in two components—direct component and image component

Rough surface results in both the above components as well as diffuse components

Fading

In extreme case, may result in signal cancellation

Approach: Multi-taper Method

Limitations in Angle of Arrival Estimation: Array-based Ambiguities Ambiguities can introduced to

the estimation by the array itself

Linear array has infinite ambiguities

Planar array has two

Limitations in Angle of Arrival Estimation: Atmospheric Turbulence Generally small (a few

microradians)

Can be significant depending on the application

Guided missiles

Estimation Algorithms

Correlation

Maximum Likelihood Estimation

MUSIC: Multiple Signal Classification

ESPIRIT: Estimation of Signal Parameters using Rotational Invariance Techniques

Matrix Pencil

Estimation Algorithms: Correlation

Non-adaptive estimation

Wish to estimate

The function has a maximum at

Optimal for single-user situation

Equivalent to DFT of x

Estimation Algorithms: Maximum Likelihood Estimation

Generalize n to an interference vector

Vector has property that

Both magnitude and AoA are unknown parameters

MLE described by

AoA estimate is where maximum likelihood estimate of spectrum takes maximum

Observations Requires a priori knowledge of interference covariance matrix

Highly intensive

Impractical algorithm

Estimation Algorithms: MUSIC

Multiple Signal Classification

Adaptive technique based on orthogonality of uncorrelated signal covariance matrix

is N x M steering matrix of M steering vectors

All eigenvectors are orthogonal to the M signal steering vectors

Pseudo-spectrum

Estimation Algorithms: MUSIC

Estimation Algorithms: Root-MUSIC

Addresses problem of accuracy in MUSIC due to discretization and need for human interaction

Uses a model of the signal--

Algorithm First requires calculation of correlation matrix R

provides an estimation of R

Decompose R into Q by

Partition Q for smallest eigenvalues,

, sum diagonals of this matrix provides

;

Roots near unit circle provide , for

Estimation Algorithm: ESPRIT

Estimation of Signal Parameters using Rotational Invariance Techniques

Operates based on constant phase shift within S matrix

Algorithm First requires calculation of correlation matrix R

provides an estimation of R

Decompose R into Q by

Partition to find , M largest eigenvalues of Q.

Matrix C defined by

Estimate

Calculate AoA with , for is provided as mth element of diagonal matrix

Estimation Algorithms: Matrix Pencil

Non-statistical technique

Time based signal

Again,

Estimate poles using multiple samples of x

Use X matrices (as shown) to calculate the system roots

, for

Summary of Methods Discussed

MUSIC/Root-MUSIC Requires assumption of N > M, resolving up to N-1 signals.

Large number of signals

ESPRIT Requires assumption that N > M as well

Large number of signals

Pencil Matrix Maximum value N/2 for even N, (N+1)/2 for odd

Does not require large number of samples

½ time of Root-MUSIC, less computation

If coherent detector is present, same accuracy as Root-MUSIC

Passive Radar for Detection of Ground Moving Objects

Recently developed for border security

Utilizes AoA MUSIC technique alongside range-Doppler technique for target location

Test operation at 1 GHz using a cell phone antenna emitting a BPSK signal

Passive Radar for Detection of Ground Moving Objects

References

http://www.comm.utoronto.ca/~rsadve/Notes/DOA.pdf

http://soma.mcmaster.ca/papers/Paper_112.pdf

http://www4.ncsu.edu/~mlsichit/Research/Publications/aoaLocalizationSecon06.pdf

Combined Use of Various Passive Radar Techniques and Angle of Arrival using MUSIC for the Detection of Ground Moving Objects. Chan et al. http://ieeexplore.ieee.org.www2.lib.ku.edu:2048/stamp/stamp.jsp?tp=&arnumber=5997047

Angle-of-Arrival of a Radar Beam in Atmospheric Turbulence. McMillan et al. http://ieeexplore.ieee.org.www2.lib.ku.edu:2048/stamp/stamp.jsp?tp=&arnumber=999728

Questions?