Adaptive beamforming methods are known to degrade if some of underlying assumptions on the environment, sources, or sensor array become violated. In particular, if the desired signal is present in training snapshots, the adaptive array performance may be quite sensitive even to slight mismatches between the presumed and actual signal steering vectors (spatial signatures). Such mismatches can occur as a result of environmental nonstationarities, look direction errors, imperfect array calibration, distorted antenna shape, as well as distortions caused by medium inhomogeneities, near-far mismatch, source spreading, and local scattering. The similar type of performance degradation can occur when the signal steering vector is known exactly but the training sample size is small. In this paper, we develop a new approach to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch. Our approach is based on the optimization of worst-case performance. It turns out that the natural formulation of this adaptive beamforming problem involves minimization of a quadratic function subject to infinitely many nonconvex quadratic constraints. We show that this (originally intractable) problem can be reformulated in a convex form as the so-called second-order cone (SOC) program and solved efficiently (in polynomial time) using the well-established interior point method. It is also shown that the proposed technique can be interpreted in terms of diagonal loading where the optimal value of the diagonal loading factor is computed based on the known level of uncertainty of the signal steering vector. Computer simulations with several frequently encountered types of signal steering vector mismatches show better performance of our robust beamformer as compared with existing adaptive beamforming algorithms.

http://www.ece.ualberta.ca/~vorobyov/RobBeamformer.pdf

Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem

Publisher Summary This chapter describes the techniques and applications of computer-generated holograms. “Computer-generated holograms,” “synthetic holograms,” and “computer holograms” are terms used to refer to a class of holograms that are produced as graphical output from a digital computer. Given a mathematical description of a wavefront or an object represented by an array of points, the computer can calculate the amplitude transmittance of the hologram and display the result on a CRT or plot it on paper. Using photoreduced copy of the graphical output from a computer as holograms is only one of the many things that distinguish computer generated holograms from conventional ones. The computer-generated holograms have their greatest potential in the area of interferometry. They have been shown to be useful in supplementing existing methods of optical testing. Laser beam scanning is another promising area for computer-generated holograms. Holographic grating scanners are in many ways better than other mechanical mirror scanners.

III Computer-Generated Holograms: Techniques and Applications

Since Gabor's first hologram, the meanings of that term have grown with increased use of the invention. Computers expanded applications further, and this paper surveys the methods and techniques of computer generated holograms.

Computer generated holograms: an historical review

Shallow Curie‐point isotherm depths, indicated by the analysis of magnetic anomalies, young silicic volcanism, hot springs, and high heat flow mark the Cascade Range of central Oregon as a potentially important geothermal resource area. Aeromagnetic measurements in the central Cascades between 43°00′ and 44°15′N latitude and 121°00′ and 122°30′W longitude exhibit predominant northwest‐southeast lineations and less prominent north‐northeast by south‐southeast lineations. Longer wavelength components of the magnetic anomalies (greater than 25 km), possibly related to deeper sources, trend approximately north‐south parallel to the Cascade Range. Magnetic anomalies show a right‐lateral offset of the High Cascades Volcanism at 43°30′N latitude, which is consistent with the tectonic structures of the Basin and Range province southeast of the area. Magnetic source depth calculations show that the High Cascades occupy a structural depression or graben on the eastern side of the Western Cascades. Spectral analysis...

Analysis of aeromagnetic measurements from the Cascade Range in central Oregon

The spatialization of the sound field in a room is studied, in particular the evolution of room impulse responses as a function of their spatial positions. It was observed that the multidimensional spectrum of the solution of the wave equation has an almost bandlimited character. Therefore, sampling and interpolation can easily be applied using signals on an array. The decay of the spectrum is studied on both temporal and spatial frequency axes. The influence of the decay on the performance of the interpolation is analyzed. Based on the support of the spectrum, the number and the spacing between the microphones is determined for the reconstruction of the sound pressure field up to a certain temporal frequency and with a certain reconstruction quality. The optimal sampling pattern for the microphone positions is given for the linear, planar and three-dimensional case. Existing techniques usually make use of room models to recreate the sound field present at some point in the space. The presented technique simply starts from the measurements of the sound pressure field in a finite number of positions and with this information the sound pressure field can be recreated at any spatial position. Finally, simulations and experimental results are presented and compared with the theory

/pdf/the-plenacoustic-function-and-its-sampling-4sab1ik208.pdf

The Plenacoustic Function and Its Sampling

From the Publisher:
Sensors arrays are used in diverse applications across a broadrange of disciplines. Regardless of the application, however, the tools of sensor array signal processing remain the same. Furthermore, whether your interest is in acoustic, seismic, mechanical, or electromagnetic wavefields, they all have a common mathematical framework. Mastering this framework and those tools lays a strong foundation for more specialized study and research.

Sensor Array Signal Processing helps build that foundation. It unravels the underlying principles of the subject without reference to any particular application. Instead, the author focuses on the common threads that exist in wavefield analysis. After introducing the basic equations governing different wavefields, the treatment includes topics from simple beamformation, spatial filtering, and high resolution DOA estimation to imaging and reflector mapping.
It studies different types of sensor configurations, but focuses on the uniform linear and circular arrays-the most useful configurations for understanding array systems in practice.

Unique in its approach, depth, and quantitative focus, Sensor Array Signal Processing offers the ideal starting point and an outstanding reference for those working or interested in medical imaging, astronomy, radar, communications, sonar, seismology-any field that studies propagating wavefields.
Its clear exposition, numerical examples, exercises, and wide applicability impart a broad picture of array signal processing unmatched by any other text on the market.

Sensor Array Signal Processing

A study of probability distribution function and spectrum of the Airborne Total Intensity Map for an area of 3000 Squ. miles covered by the Bundelkhand granite in India has revealed a close correlation between the Gaussian or non-Gaussian nature of distribution and the shape of unite value contour on the spectrum plot. Further studies of radial spectrum plots suggest that the surface magnetic sources are mainly responsible for the non-Gaussian character of the distribution function and as well as for irregular spectrum shape. The histogram of depth values for magnetic sources obtained from radial spectrum plots show three horizons, namely (i) surface (ii) 410 m(1400′) and (iii) 1000 m (3400′). Based on these informations blocks with ferromagnetic composition at the surface can be identified from those which are non magnetic at the surface.

Prabhakar S. Naidu

Papers

Sensor Array Signal Processing

Two‐dimensional power spectral analysis of aeromagnetic fields *

Circular array and estimation of direction of arrival of a broadband source

Quantization noise in binary holograms

Digital analysis of aeromagnetic maps: Detection of a fault