Table of Contents
Antenna arrays have been employed in wireless communications and radars to synthesize beampatterns with the smallest BW and PSLL achievable. When evaluating the performance of different types of arrays, half-power beamwidth (HPBW) and PSLL are the main metrics to consider. Directivity, or the ratio of energy delivered in the intended direction to total energy communicated, is another key performance characteristic. Traditionally, linear arrays with consistent inter-element spacing have been commonly used. ULAs with uniform excitation-current amplitudes or weights have a short BW but a large PSLL.
We propose a NULA with non-uniform weights in this work. The weights were calculated using a normal window function and the logarithmic function was used for inter-element spacing. A variety of window functions are available in the literature, but only the Bartlett-Hanning window function was employed for this proof of concept.
Major frameworks/libraries used in this project:
1. INTRODUCTION
- What is the array Half Power Beam Width (HPBW)?
- What is the array Directivity?
2. MODEL OF THE SYSTEM
Fig.1 Geometry and notations used for non-uniform linear array.
- Problem1:
First, regarding the window that is used for weighting we can see this resulting figure that describes the Beam patterns for various windows for N = 16;
- Problem2:
Second, to clarify the relationship between HPBW, BW, and directivity as we mentioned before we consider a standard 16-element linear array pointed at the broadside.Fist we find the Dolph-Chebychev weightings for sidelobes of -20dB, -30dB, and -40dB. After that, we plot the resulting beam pattern and we compute the HPBW. BW, and the directivity.
- Problem3:
By using the technique introduced in the reference “Optimum Array Processing” by Harry L. Van Trees [2] we design a beam pattern that maximizes the directivity subject to a -35 dB constraint of the sidelobe; considering a standard linear array with 16 elements. After that, we compare the resulting BW with that of a 16 element SLA using DolphChebychev weighting.
3. SUGGESTED METHOD
The non-uniform distribution of the 16-element linear array was found using a random search approach in the work of an investigator developing a portable radar [5]. MATLAB is used to analyze 100,000 random non-uniform distributions using the convex optimization software CVX [6], which can take more than 3 hours. But in our case, we just want to explain this approach for this we just show how its work.
Fig.2 Results from code [LA_random_spacing.m]
Fig.3 Distribution of the array elements(related to Fig.2)
Distributed under the MIT License. See LICENSE.txt for more information.
🔎
[1] C. A. Balanis, Antenna Theory, and Design. John Wiley&Sons, 1997.
[2] H. L. V. Trees, Optimum Array Processing. Wiley, 2002.
[3] K. L. Bell, H. L . Van Trees, and L. J . Griffiths, Adaptive beampattern control using quadratic constraints for circular array STAP. 8th Annual Workshop on Adaptive Sensor Array Processing ( ASAP 2000), M.I.T. Lincoln Laboratory, Lexington, Massachusetts, pp. 43-48, March 2000.
[4] C. A. Olen and R. T. Compton, Jr. A numerical pattern synthesis algorithm for arrays. IEEE Trans. Antennas Propag., vol.AP-38, pp. 1666- 1676, October 1990.
[5] Z. Peng, P. Nallabolu and C. Li, "Design and Calibration of a Portable 24-GHz 3-D MIMO FMCW Radar with a Non-uniformly Spaced Array and RF Front-End Coexisting on the Same PCB Layer," 2018 IEEE 13th Dallas Circuits and Systems Conference (DCAS), 2018, pp. 1-4, DOI: 10.1109/DCAS.2018.8620117.
[6] M. Grant, and S. Boyd "CVX: Matlab software for disciplined convex programming. http://cvxr.com/cvx
Rabih ND - @RabihND
Project Link: https://github.com/RabihND/NonUniformAntennaArray
- Fist Commit
- Next step ?!
Amirkabir University of Technology
(Tehran Polytechnic)