Eng The University of Texas at Austin brPage 2br Introduction A sensor array is a group of sensors located at spatially separated points Sensor array processing focuses on data collected at the sensors to carry out a given estimation task Applicatio ID: 36479 Download Pdf

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Eng The University of Texas at Austin brPage 2br Introduction A sensor array is a group of sensors located at spatially separated points Sensor array processing focuses on data collected at the sensors to carry out a given estimation task Applicatio

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Spatial Array Processing Signal and Image Processing Seminar Murat Torlak Telecommunications & Information Sys. Eng. The University of Texas at Austin

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Introduction A sensor array is a group of sensors located at spatially separated points Sensor array processing focuses on data collected at the sensors to carry out a given estimation task Application Areas Radar Sonar Seismic exploration Anti-jamming communications YES! Wireless communications

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Problem Statement Find 1. Number of sources 2. Their direction-of-arrivals (DOAs) 3. Signal Waveforms

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Assumptions Isotropic and nondispersive medium Uniform propagation in all directions Far-Field Radius of propogation >> size of array Plane wave propogation Zero mean white noise and signal, uncorrelated No coupling and perfect calibration

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Antenna Array 12 3 45 Source Array Response Vector–Far-Field Assumption Delay Na rro wband Assumption Phase Shift [1 ;e f sin =c ;::: ;e f sin =c Single Source Case 1) f f 1) where sin =c

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General Model By superposition, for signals, )+ =1 Noise =1 )+ AS )+ where ;::: )] and ;::: ;s )]

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Low-Resolution Approach:Beamforming Basic Idea =1 1)( f sin =c =1 jw 1) where sin =c and ;::: ;M Use DFT (or FFT) to ﬁnd the frequencies )] jw jw jw 1) 1) 1) Look for the peaks in jF )) To smooth out noise =1

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Beamforming Algorithm Algorithm 1. Estimate =1 2. Calculate 3. Find peaks of for all possible ’s. 4. Calculate ;::: ;d Advantage - Simple and easy to understand Disadvantage - Low resolution

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Number of Sources Detection of number of signals for As )+ {z {z |{z} |{z} |{z} where is the noise power. No noise and rank of is

Eigenvalues of AR will be ;::: ; ; ::: Real positive eigenvalues because is real, Hermition-symmetric rank Check the rank of or its nonzero eigenvalues to detect the number of signals Noise eigenvalues are shifted by ;::: ; ; ;::: ; where ::: and >> Detect the number of principal (distinct) eigenvalues

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MUSIC Subspace decomposition by performing eigenvalue decomposition AR =1 where is the eigenvector of the eigenvalue span span ;::: span Check which span or or , where is a projection matrix Search for all possible such that After EVD of where the noise eigenvector matrix

+1 ;::: 10

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Root-MUSIC For a true f sin =c is a root of +1 [1 ;z;::: ;z [1 ;z ;::: ;z 1) After eigenvalue decomposition, - Obtain =1 -Form - Obtain roots by rooting -Pick roots lying on the unit circle - Solve for 11

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Estimation of Signal Parameters via Rotationally Invariant Techniques (ESPRIT) Decompose a uniform linear array of sensors into two subarrays with sensors Note the shift invariance property (2) jw 1) jw 1) jw (1) jw General form relating subarray (1) to subarray (2) (2) (1) jw jw (1) contains sufﬁcient information of 12

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ESPRIT span span and is a nonsingular unitary matrix comes from a Grahm-Schmit orthogonalization of Ab in (2) (2) and (1) (1) (2) (2) (1) (1) Multiply both sides by the pseudo inverse of (1) (1)# (2) (1) (1) (1) (1) where means the pseudo-inverse sH sH Eigenvalues of are those of 13

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Superresolution Algorithms 1. Calculate =1 2. Perform eigenvalue decomposition 3. Based on the distribution of , determine 4. Use your favorite diraction-of-arrival estimation algorithm: (a) MUSIC: Find the peaks of for from to 180 - Find =1 corresponding the peaks of (b) Root-MUSIC: Root

the polynomial - Pick the roots that are closest to the unit circle =1 and sin f (c) ESPRIT: Find the eigenvalues of (1)# (2) sin f 14

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Signal Waveform Estimation Given , recover from Deterministic Method No noise case: ﬁnd such that ;i k; 6? can do the job As With noise, Disadvantage increased noise 15

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Subspace Framework for Sinusoid Detection =1 j! Let us select a window of i.e., ;::: ;x +1)] Then 1) +1) =1 j! j! )( 1) j! )( +1) =1 j! j! )( +1) {z j! {z =1 As where is the window size, the number of sinusoids, and j! 17

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Subspace

Framework for Sinusoid Detection Therefore, the subspace methods can be applied to ﬁnd j! Recall =1 j! Then ﬁnding is a simple least squares problem. 18

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Wireless Communications Personal Communications Services (PCS) Cellular Telephony Wireless LAN Multipaths Direct Path co-channel interference To Networks Direct Path Multipath Direct Path Residential Area Outdoors Office Building Increasing Demand for Wireless Services Unique Problems compared to Wired communications 19

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Problems in Wireless Communications Scarce Radio Spectrum and Co-channel

Interference Multipath Base Station Multipath Direct Path Multipath Desired Signal Reflected Signal Time Coverage/Range 20

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Smart Antenna Systems Employ more than one antenna element and exploit the spatial dimension in signal processing to improve some system operating parameter(s): Capacity, Quality, Coverage, and Cost. User One User Two Multiple RF Module Conventional Communication Module Advanced Signal Processing Algorithms 21

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Experimental Validation of Smart Uplink Algorithm Comparison of constellation before (upper) and after smart uplink processing

(middle and lower) imaginary axis imaginary axis imaginary axis real axis Equalized Signal 2 real axis Equalized Signal 1 real axis Antenna Output 22

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Selective Transmission Using DOAs Beamforming results for two sources separated by 20 0.5 1.5 x 10 0.2 0.4 0.6 0.8 Power Spectrum Frequency [Hz], User #1 0.5 1.5 x 10 0.2 0.4 0.6 0.8 Power Spectrum Frequency [Hz], User #2 23

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Selective Transmission Using DOAs Beamforming results for two sources separated by 0.5 1.5 x 10 0.2 0.4 0.6 0.8 Power Spectrum Frequency [Hz], User #1 0.5 1.5 x 10 0.2 0.4 0.6 0.8 Power

Spectrum Frequency [Hz], User #2 24

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Future Directions Adapt the theoretical methods to ﬁt the particular demands in speciﬁc applications Smart Antennas Synthetic aperture radar Underwater acoustic imaging Chemical sensor arrays Bridge the gap between theoretical methods and real-time applications 25

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