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## Angle of Arrival ( AoA )

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**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 vsboresight • 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: 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**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