Array processing: Difference between revisions

Revision as of 05:17, 19 May 2020

Revision as of 15:52, 14 September 2020

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<math>\textstyle 4.\ Calculate\ \theta_{k},\ i=1, .... q.</math><br>

<br>

Where '''Rx''' is the sample [[covariance matrix]]. Different beamforming approaches correspond to different choices of the weighting vector '''F'''. The advantages of using beamforming technique are the simplicity, easy to use and understand. While the disadvantage of using this technique is the low resolution.

==== Subspace-based technique ====

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<math>\textstyle 5.\ After\ EVD\ of\ R_{x}:</math><br>

<math>\textstyle P_{A}^{\perp}=I-E_{s}E_{s}^{*}=E_{n}E_{n}^{*}</math><br>

<math>\textstyle where\ the\ noise\ [[eigenvector\ matrix\]] <math>E_{n}=[e_{d}+1, .... , e_{M}]</math>

MUSIC spectrum approaches use a single realization of the stochastic process that is represent by the snapshots x (t), t=1, 2 ...M. MUSIC estimates are consistent and they converge to true source bearings as the number of snapshots grows to infinity. A basic drawback of MUSIC approach is its sensitivity to model errors. A costly procedure of calibration is required in MUSIC and it is very sensitive to errors in the calibration procedure. The cost of calibration increases as the number of parameters that define the array manifold increases.