Wavelet-Based Adaptive Antenna Systems


TECHNOLOGY AREA(S): Sensors, Electronics 

OBJECTIVE: Create a mathematical/numerical framework for the design, analysis and optimization of performance of multi-frequency antenna systems that can radiate vastly different frequency bands/waveforms and so simultaneously address diverse tasks, such as radar imaging and telecoms. Develop algorithms/software that implements these capabilities in military/commercial simulation applications and demonstrates feasibility of a small multi-frequency antenna by designing and building a hardware prototype. 

DESCRIPTION: Use of multi-frequency antennas for emitting radio waves has obvious practical benefits as the same hardware can be used to accomplish different missions. Such systems have received substantial attention in recent years. They include various multiband antennas [1], antennas that allow different tasks to share the same frequency bandwidth by projecting signals onto the null space of an interference channel [2], and antennas that exploit signal fragmentation (e.g., wavelets) to create the desired waveform [3]. Compact multi-freq antennas offer the additional benefit of being easily mounted on a small vehicle or UAV. Wavelet-based antenna systems show promise of providing the unifying design, analysis, and optimization needed for these operationally useful multifunction antennas. Wavelet-based antenna systems radiate short EM pulses that are by nature wideband. But if a linear combination of such pulses is used to form the desired signal, then both long and short wave signals can be radiated from the same modest array of individual antenna elements since each pulse has finite duration so that a given array element can be reused. A linear combination of short pulses can yield a low-freq signal, which may be useful, e.g., for AM or FM communication, or other digital modulation formats (e.g. FSK, PSK, QAM), or longer wavelength radar applications (e.g. P-band SAR [4]). At the same time, these short pulses can also be combined into signals of much higher frequency that may be useful, e.g., for L-band SAR. This project seeks computational methods to obtain the desired signal as a linear combination of pulses of various shapes in order to enable new multifunction antennas. For example, compactly supported wavelets are well known [5, pp. 215-287], being defined on finite intervals, having zero mean, and obeying an orthogonality relationship. Each wavelet, since it has zero mean, can in principle be radiated by an antenna. The use of multiple antennas radiating the properly selected wavelets (dilated and translated) can be combined to form the prescribed signal in the far field. A quasi-interpolation approach [6] or an approximate wavelet approach [7] can provide a simpler antenna structure. In the quasi-interpolation method, the desired function is expressed as a linear combination of translated, but otherwise identical, basis functions, each with zero mean. At a greater level of complexity, one can employ both translation and dilation for exact or approximate reconstruction. Applications of wavelets to radiation of the predetermined electromagnetic signals are discussed in [8] and [9]. We seek advances that leverage these tools from mathematical/numerical analysis. While operational requirements and system parameters are application-specific, the problems of designing small adaptive antennas have much in common. Foremost are considerations of energy efficiency. Radiation of long waves by small-size antennas will necessarily involve some destructive interference since generating a long wave composed of a sequence of short pulses will require that the spectral tails of those individual pulses cancel out. So there is a fundamental mathematical question of how to design constituent pulses to minimize power loss. Answering this will require ideas from Fourier analysis, wavelets, optimization, and other areas. Mathematical insight is needed for questions in antenna radiation patterns, i.e., in directivity. Achieving the ability to reduce or minimize power losses for both omnidirectional and direction-specific multi-freq antennas will lead to both theoretical advances for design tools, and will reduce the amount of required prototyping. 

PHASE I: a) Survey existing designs and approaches for constructing multi-frequency antennas, review typical applications and regimes of interest, and identify relevant settings and parameters to demonstrate the feasibility of a universal analytic and engineering structure for their design and fabrication. One candidate is the use of wavelets and filters. b) Analyze and identify useful families of basis functions that can reconstruct a given signal (wavelets, truncated derivatives of the sinc function, etc) and that show promise of optimization. c) Develop a scheme for producing optimal linear combinations from the basis, assuming nearly isotropic (nondirectional) small antennas (small ratio of dipole to wavelength) are used in the far field. An appropriate figure of merit may be the ratio of total far field power divided by the input power. d) Implement the foregoing optimization scheme numerically and conduct the appropriate proof-of-concept computations. e) After the optimization scheme has been demonstrated, use to fabricate a prototype omnidirectional multi-frequency antenna. 

PHASE II: a) The optimization technique from Phase I will be tested, validated, and implemented as a documented software package that can be shared or distributed. b) In the numerical work that seeks the best basis functions, demonstrate that the selected linear combinations reconstruct the square wave modulated sinusoids and square wave modulated chirps with minimal mean square error both computationally and in device tests. c) Since the basis functions are wideband, they may be radiated by directional antennas, and so a directional beam can be formed. Develop a computational scheme to optimize the basis function-antenna transfer function combination to maximize peak power radiation. First conduct the analysis for continuous wave (CW) operation. d) Incorporate the methodology of item c) into the software package of item a). e) Generalize the methodology described in item c) to other waveforms beyond CW, for example, frequency modulated continuous waves (FMCW) or linear chirps. f) Fabricate the nondirectional prototype antenna. Only a small number of antenna elements should be used (e.g., dipoles no more than 10 cm in length radiating pulses of approximately 1 ns in duration). Government is very interested in seeing the analysis and design package developed for fabrication. g) Develop optimal basis functions for directional antennas (eg, involving Vivaldi elements) using the computational methods of (a) and (d) above. Demonstrate success and utility of these methods, such as by fabricating a directional antenna, ideally with full width of 2-4 degrees when at half power. h) Prepare and make available software documentation of the developed package. i) Make available the software from items a) and d) to interested users in academia and industry under appropriate licensing agreements. 

PHASE III: Results will be corroborated by prototype fabrication. This work will lead to significant speedups in the design time of military detection, imaging, surveillance, and communication systems, and will be equally useful in similar commercial applications. The analysis and numerical techniques developed under this topic will be made available as an aid in further advancement of this important new technology of multi-frequency antennas, e.g. to ARL-SEDD-Antenna Branch, CERDEC-STCD, Electronic-Warfare-oriented businesses, and others. 


1: C. T. P. Song, Peter S. Hall, and H. Ghafouri-Shiraz, Multi-band Multiple Ring Monopole Antennas. IEEE Transactions on Antennas and Propagation, Vol. 51, No. 4, April 2003, pp. 722-72

2:  A. Khawar, A. Abdel-Hadi, T. Clancy, and R. McGwier, "Beampattern Analysis for MIMO Radar and Telecommunication System Coexistence," in Proceedings of the 2014 International Conference on Computing, Networking and Communications (ICNC), Honolulu, HI, USA, February 2014, pp. 534-53

3:  R. Albanese, Signal Segmentation as an Alternative Approach to Antenna Signal Configuration, Air Force Research Laboratory Report # AFRL-RH-BR-TR-2011-0001, May 201

4:  Mikhail Gilman, Erick Smith, and Semyon Tsynkov, Transionospheric Synthetic Aperture Imaging, Applied and Numerical Harmonic Analysis Series, Bikrhauser, Basel, 201

5:  Ingrid Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 61, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 199

6:  Robert Schaback and Zongmin Wu, Construction techniques for highly accurate quasi-interpolation operators, J. Approx. Theory, 91 (1997) pp. 320-33

7:  Vladimir Maz'ya and Gunther Schmidt, Approximate Approximations, Mathematical Surveys and Monographs, Vol. 141, American Mathematical Society (AMS), Providence, RI, 200

8:  Anthony Devaney, Gerald Kaiser, Edwin A. Marengo, Richard Albanese, and Grant Erdmann, The Inverse Source Problem for Wavelet Fields, IEEE Transactions on Antennas and Propagation, Vol. 56, No. 10, October 2008, pp. 3179-318

9:  Kaili Eldridge, Andres Fierro, James Dickens, and Andreas Neuber, A Take on Arbitrary Transient Electric Field Reconstruction using Wavelet Decomposition Theory Coupled with Particle Swarm Optimization, IEEE Transactions on Antennas and Propagation, Vol. 64, No. 7, July 2016, pp. 3151-315

KEYWORDS: Basis Function, Signal Fragmentation, Wavelet, Linear Combination 


Joseph Myers 

(919) 549-4245 


Joe Qui 

(919) 549-4297 

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