channel. Array Processing in Astronomy Applications Astronomical environment contains a mix of external signals and noises that affect the quality of the desired signals. Most of the arrays processing applications in astronomy are related to image processing. The array used to achieve a higher quality that is not achievable by using a single channel. The high image quality facilitates quantitative analysis and comparison with images at other wavelengths. In general, astronomy arrays can be divided into two classes: the beamforming class and the correlation class. Beamforming is a signal processing techniques that produce summed array beams from a direction of interest – used basically in directional signal transmission or reception- the basic idea is to combine elements in a phased array such that some signals experience destructive inference and other experience constructive inference. Correlation arrays provide images over the entire single-element primary beam pattern, computed off-line from records of all the possible correlations between the antennas, pairwise. Other applications In addition to these applications, many applications have been developed based on array processing techniques: Acoustic Beamforming for Hearing Aid Applications, Under-determined Blind Source Separation Using Acoustic Arrays, Digital 3D/4D Ultrasound Imaging Array, Smart Antennas, Synthetic aperture radar, underwater acoustic imaging, and Chemical sensor arrays...etc. General model and problem formulation Consider a system that consists of array of r arbitrary sensors that have arbitrary locations and arbitrary directions (directional characteristics) which receive signals that generated by q narrow band sources of known center frequency ω and locations θ1, θ2, θ3, θ4 ... θq. since the signals are narrow band the propagation delay across the array is much smaller than the reciprocal of the signal bandwidth and it follows that by using a complex envelop representation the array output can be expressed (by the sense of superposition) as : Where: is the vector of the signals received by the array sensors, is the signal emitted by the kth source as received at the frequency sensor 1 of the array, is the steering vector of the array toward direction (), τi(θk): is the propagation delay between the first and the ith sensor for a waveform coming from direction (θk), is the noise vector. The same equation can be also expressed in the form of vectors: If we assume now that M snapshots are taken at time instants t1, t2 ... tM, the data can be expressed as: Where X and N are the