Power estimation in Array Signal Processing: Case study

Abstract

Characterizing radiating source by an array of sensors is an important process in many scientific and civil applications such optical interferometry, telecommunications, seismology and submarine acoustics. When the collected echoes by the array are a mixture of several sources, processing data needs to take into account the interactions between the individual components such as spatial coherence or correlation between primary sources, interferences from secondary sources as perturbing noise and power level of each wavefront. In the case of single emitter, the problem of source characterization becomes easy, because a simple treatment of second order statistics of received data is sufficient to identify the parameters of the source such as the angle of incidence, the shape of the waveform and its variance or power. In this paper, we propose an alternative approach of power estimation of single source using an array of isotropic sensors, the conditions used are those of the far field radiation making the approximation of planar wave front valid and the narrowband spectrum where the bandwidth of waveform is negligible against the carrier frequency. We propose the combination of the standard beam forming spectrum and the information that diagonal elements of spatial covariance matrix contains, the solution of Signal to Noise Ratio estimation is based on two dimensional linear system. Some numerical simulations are carried out to compare the performance of the proposed solution with the method based on eigenvalues computation.