Array processing
Wave propagation means there is a systemic relationship between the signal received on spatially separated sensors.
In addition to the information that can be extracted from the collected data the framework uses the advantage prior knowledge about the geometry of the sensor array to perform the estimation task.
The problems associated with array processing include the number of sources used, their direction of arrivals, and their signal waveforms.
[1] The ultimate goal of sensor array signal processing is to estimate the values of parameters by using available temporal and spatial information, collected through sampling a wavefield with a set of antennas that have a precise geometry description.
The antenna array is used in these systems to determine location(s) of source(s), cancel interference, suppress ground clutter.
By using the returns, the estimation of parameters such as velocity, range and DOAs (direction of arrival) of target of interest become possible.
Despite all these limitations and difficulties, sonar system remains a reliable technique for range, distance, position and other parameters estimation for underwater applications.
[6] They are currently working on an International Monitoring System which will comprise 50 primary and 120 auxiliary seismic stations around the world.
This success is a result of advances in communication theory and low power dissipation design process.
Base stations use an antenna array of several elements to achieve higher selectivity, so called beamforming.
In addition to these external sources, the strength of the desired signal is reduced due to the relatively distance between speaker and microphones.
In other words what we are interested in is estimating the DOA’s of emitter signals impinging on receiving array, when given a finite data set {x(t)} observed over t=1, 2 … M. This will be done basically by using the second-order statistics of data”[5][8] In order to solve this problem (to guarantee that there is a valid solution) do we have to add conditions or assumptions on the operational environment and\or the used model?
Toward this goal we want to make the following assumptions:[1][3][5] Throughout this survey, it will be assumed that the number of underlying signals, q, in the observed process is considered known.
The idea behind beamforming is very simple: steer the array in one direction at a time and measure the output power.
A breakthrough came about when the eigen-structure of the covariance matrix was explicitly invoked, and its intrinsic properties were directly used to provide a solution to an underlying estimation problem for a given observed process.
The rationale behind this approach is that one wants to emphasize the choices for the steering vector a(θ) which correspond to signal directions.
The tremendous interest in the subspace based methods is mainly due to the introduction of the MUSIC (Multiple Signal Classification) algorithm.
MUSIC was originally presented as a DOA estimator, then it has been successfully brought back to the spectral analysis/system identification problem with its later development.
While the spectral-based methods presented in the previous section are computationally attractive, they do not always yield sufficient accuracy.
An alternative is to more fully exploit the underlying data model, leading to so-called parametric array processing methods.
The cost of using such methods to increase the efficiency is that the algorithms typically require a multidimensional search to find the estimates.
The most common used model based approach in signal processing is the maximum likelihood (ML) technique.
When applying the ML technique to the array processing problem, two main methods have been considered depending on the signal data model assumption.
It therefore appears natural to model the noise as a stationary Gaussian white random process whereas the signal waveforms are deterministic (arbitrary) and unknown.
[3][4] The problem of computing pairwise correlation as a function of frequency can be solved by two mathematically equivalent but distinct ways.
The second approach "FX" takes advantage of the fact that convolution is equivalent to multiplication in Fourier domain.
In radio astronomy, RF interference must be mitigated to detect and observe any meaningful objects and events in the night sky.
that is not a known function of the direction of interference and its time variance, the signal covariance matrix takes the form:
The disadvantages to this approach include altering the visibilities covariance matrix and coloring the white noise term.
We briefly describe the different classifications of array processing, spectral and parametric based approaches.
