Malek G. M. Hussain

Principles of space-time array processing for ultrawide-band impulse radar and radio communications

The emerging ultrawide-band (UWB) impulse technology has found numerous applications in the commercial as well as the military sector. 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. 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. 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.

TRANSIENT SOLUTIONS OF MAXWELL'S EQUATIONS BASED ON SUMUDU TRANSFORM

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.

Antenna patterns of nonsinusoidal waves with the time variation of a Gaussian pulse. III

The development of antenna theory for nonsinusoidal electromagnetic waves has been based on the idealized rectangular pulse. In practice, an antenna that is designed to operate in the mode of an electric hertzian dipole would radiate a pulse that best approximates a Gaussian one when the driving current consists of a linear transient. The principle of radiation of nonsinusoidal electromagnetic waves with the time variation of Gaussian pulses is discussed. The properties of the Gaussian pulse are presented, i.e., the autocorrelation function, energy spectral density, and spectrum. Antenna patterns, such as peak-amplitude pattern, peak-power pattern, energy pattern, and slope pattern are derived for a Gaussian pulse received (or radiated) by a linear array antenna. Computer plots of the derived antenna patterns are presented that show a considerable improvement in the angular resolution capability over that of the antenna patterns that have been derived for a rectangular pulse. >

Principles of high-resolution radar based on nonsinusoidal waves. II. Generalized ambiguity function

For pt.I see ibid., vol.31, no.4, p.359-68 (1989). A generalized ambiguity function for nonsinusoidal coded waveforms that are represented as a train of properly weighted Gaussian pulses is derived and analyzed to study its properties. Computer plots of generalized ambiguity functions of different binary codes, e.g. Barker, complementary, and pseudorandom codes, are presented. The various computer plots show that the desired thumbtack ambiguity function is achievable by nonsinusoidal coded waveforms. >

Theory and analysis of adaptive cylindrical array antenna for ultrawideband wireless communications

In this paper, the principle of cylindrical array beamforming based on ultrawideband impulse (UWBI) signals is introduced. A cylindrical array antenna is composed of a number of vertically aligned and concentric circular subarrays of equal radius and equal number of array elements. Theory, analysis, and computer simulation of the cylindrical array antenna are presented based on UWBI signals with the time variation of a generalized Gaussian pulse (GGP). The radiation pattern of the cylindrical array antenna is derived in terms of the inverse Fourier transform of the radiated far-zone GGP signal. The radiation pattern results in different azimuth and elevation beam patterns such as peak amplitude pattern, peak power pattern, and energy pattern. Computer plots of these antenna patterns are generated for different design parameters such as array radius, interelement spacing distance, frequency bandwidth, and steering angle. The phenomenon of beamwidth broadening associated with electronic beamsteering is analyzed, and the resolution angle for the cylindrical array antenna is derived too. Beamforming based on UWBI signals provides a tradeoff between array dimensions, frequency bandwidth, and steering angle for achieving a high angular resolution capability in the azimuth plane as well as in the elevation plane. Such a tradeoff is attractive in practice for UWBI communications, indoor (multimedia) communications, radar, and localization systems.

Propagation of Electromagnetic Signals

Electric field strength due to electric step excitation electric exponential ramp function excitation magnetic step and ramp function excitation sinusoidal pulse excitation. Appendix.

Aperture-Sparsity Analysis of Ultrawideband Two-Dimensional Focused Array

We investigate the effects of aperture sparsity on the focusing performance and the angular-resolution capability of a two-dimensional focused array antenna excited by ultrawideband (UWB) impulse waveforms. The UWB-focusing array is characterized by a planar square aperture and a design parameter referred to as array spatial bandwidth. Spatial bandwidth is a function of the number of array elements, inter-element spacing, and frequency bandwidth. Performance analysis is carried out by generating computer plots of three-dimensional and two-dimensional antenna patterns for different values of array spatial bandwidth that hold for large aperture sparsity and large aperture density. The antenna patterns are peak-amplitude pattern, peak-power pattern, and energy pattern, whose narrow beamwidth and low sidelobe level are robust against aperture sparsity that may be caused by removed or failed elements. The half-power beamwidth (HPBW) of the antenna patterns, the focal distance, and the far-field distance of the UWB-focused array are expressed in terms of array spatial bandwidth. Computer simulation results show that UWB-focused-array beamforming based on impulse waveforms achieves efficient focusing of the radiation energy in the radiation-near-field region and beyond, and yields improvement in focusing performance and angular resolution for increased values of array spatial bandwidth. Such practical advantages are achieved without encountering grating lobes, large sidelobe level, or distortion of the radiation beam pattern that often limit the performance of the conventional narrowband phased array antennas.

Line-Array Beam-Forming And Monopulse Techniques Based on Slope Patterns of Nonsinusoidal Waveforms

Nonsinusoidal waveforms with the time variation of a rectangular pulse, received (or radiated) by a line array of sensors (or emitters), yield various antenna patterns which are very attractive for achieving good angular resolution. These antenna patterns, such as peakamplitude, peak-power, energy, and slope patterns, have been derived for various array lengths under a noiseless assumption. The slope patterns are the most attractive for angular resolution. In this paper, line-array beamforming techniques are developed to provide slope patterns for nonsinusoidal signals. The techniques employ sliding correlators (SCs) for suppressing the additive Gaussian noise present with the received signal, and pulse-shaping processors for determining the slope pattern. Computer simulation is done for deriving peak-amplitude and slope patterns for various array lengths. Also, a method for obtaining monopulse peakamplitude and slope patterns is presented.

Active-array beamforming for ultra-wideband impulse radar

Ultra-wideband electromagnetic impulses have found numerous applications for radar and radio communications due to the recent technological advances in electronic and opto-electronic devices. This paper presents the principle of active-array beamforming for ultra-wideband impulse radar. The theory and analysis are based on a realizable signal model representing the impulse-type waveforms used in radar applications. The signal model is referred to as the generalized Gaussian pulse. Impulse waveforms radiated and received by an active-array beamforming system suffer a directional distortion that can be regarded as useful information for direction finding and automatic beam steering. The directional distortion associated with the energy density spectrum of the generalized Gaussian pulse is derived and plotted for different values of the angle of incidence. Also, the directivity pattern of the array beamforming system is expressed in terms of the energy of the radiated and received impulse waveforms. Computer plots of the sidelobe-free directivity-energy pattern are presented too. The energy pattern yields high angular-resolution capability that improves by increasing the spatial frequency bandwidth. The spatial frequency bandwidth is an important design parameter that allows a trade-off between effective bandwidth and array length to achieve a small resolution angle.

Response to a letter by J.R. Wait about electromagnetic waves in seawater

In response to a series of letters by J.R. Wait, and in place of a rebuttal, the authors challenge Wait to solve a never-before-published transient problem without a magnetic current density term added to Maxwells equations. In particular, they ask for the excited electric and the associated magnetic field strength of a planar wave due to an electric step function as excitation force in seawater, taking the ionic conductance into account by allowing the charge carriers to have a mass. >