Over the last decade of the 20th century, the emerging ultrawide-band (UWB) impulse technology has found numerous applications in the commercial as well as the military sectors. The rapid technological advances have made it possible to implement (cost-effective, short-range) impulse radar and impulse-radio communication and localization systems. Array beamforming and space-time processing techniques promise further advancement in the operational capabilities of impulse radar and impulse-radio communications to achieve long-range coverage, high capacity, and interference-free quality of reception. In this paper, we introduce a realistic signal model for UWB impulse waveforms and develop the principles of space-time array processing based on the signal model. A space-time resolution function (STRF), a space-frequency distribution function (SFDF), and a monopulse-tracking signal are derived for impulse waveforms received by a self-steering array beamforming system. The directivity peak-power pattern and energy pattern of the beamformer are also derived. Computer plots of the STRF, SFDF, and the beam patterns are obtained too. The directivity beam patterns of impulse waveforms are sidelobe-free and, therefore, there is no need for sidelobe suppression via amplitude weighting of the array elements. Also, the resolution angle for the beam patterns is derived as a decreasing function of array size and frequency bandwidth. Electronic beamsteering based on slope processing of monopulse waveforms is described too.
Abstract-The Sumudu transform is derived from the classical Fourier integral. Based on the mathematical simplicity of the Sumudu transform and its fundamental properties, Maxwell's equations are solved for transient electromagnetic waves propagating in lossy conducting media. The Sumudu transform of Maxwell's differential equations yields a solution directly in the time domain, which neutralizes the need to perform inverse Sumudu transform. Two sets of computer plots are generated for the solution of Maxwell's equations for transient electric field strength in lossy medium. A set of plots presents the Sumudu transform of the transient solution and another one presents inverse Sumudu transform. Both sets of plots reveal similar characteristics and convey equal information. Such property is referred to as the Sumudu reciprocity.
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