Angle of Arrival ( AoA )

1. Angle of Arrival (AoA) Calen Carabajal EECS 823

2. Introduction to Angle of Arrival Physics • “Angle between propagation direction of an incident wave and some reference direction” (orientation) • Plane wave impinging upon array

3. 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

4. Wave Propagation and Antenna: Specific Case • Constant amplitude assumed • Received signal for each antenna is • Summing signals together results in • Observations • – broadside vsboresight • Cancellation k*r • Frequency dependence

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. Limitations in Angle of Arrival Estimation: Atmospheric Turbulence • Generally small (a few microradians) • Can be significant depending on the application • Guided missiles

12. Estimation Algorithms • Correlation • Maximum Likelihood Estimation • MUSIC: Multiple Signal Classification • ESPIRIT: Estimation of Signal Parameters using Rotational Invariance Techniques • Matrix Pencil

13. 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

14. 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

15. 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

16. Estimation Algorithms: MUSIC

17. 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

18. 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

19. 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

20. 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

21. 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

22. Passive Radar for Detection of Ground Moving Objects

23. 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

24. Questions?