Fibonacci Sparse Antenna Array for Grating Lobe Suppression
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Solution Overview
Problem
Current radar systems, particularly submillimeter radars, face challenges in efficiently generating, transporting, and distributing signal power due to high losses and costly waveguide components, and lack effective design techniques for non-redundant planar arrays that can control grating lobes and sidelobes across a broad range of frequencies.
Innovation Solution
The use of a Fibonacci sequence for spacing antenna elements, which reduces the number of elements required while maintaining beam forming capability and resolution, allowing for more efficient aperture filling and cost-effective design by optimizing element placement and spacing, particularly using Fibonacci spacings in one-dimensional and two-dimensional arrays.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a regular array with equally spaced elements is used to avoid grating lobes, then the array can maintain beam forming capability, but the number of elements required increases significantly and costs increase
Solution Approach 1:
The patent applies asymmetric spacing of antenna elements according to a Fibonacci sequence, where the distance between adjacent elements follows the pattern F(n) = F(n-1) + F(n-2). This asymmetric, non-uniform spacing eliminates the periodicity that causes grating lobes while maintaining the array's beam forming capability, thereby reducing the total number of elements required compared to regular equally-spaced arrays
Solution Approach 2:
The patent changes the spacing parameter from a constant value (regular array) to a sequence following Fibonacci numbers. This parameter transformation allows the array to achieve grating lobe-free operation with fewer elements by creating a non-redundant, aperiodic element distribution that maintains spatial diversity for beam synthesis
2Ease of manufacture
If the number of antenna elements is reduced to lower costs, then the system becomes more cost-effective, but grating lobes and sidelobes become harder to control
Solution Approach 1:
By implementing asymmetric Fibonacci-based spacing, the patent creates a non-periodic element distribution that inherently suppresses grating lobes. The irrational ratio between successive spacings prevents the formation of repetitive interference patterns, allowing cost-effective reduction in element count while maintaining control over harmful lobes
Solution Approach 2:
The patent uses the mathematical Fibonacci sequence as a template to determine element positions. This mathematical copying approach provides a systematic method to generate optimal sparse array configurations that control sidelobes and grating lobes without requiring expensive dense element distributions
3Measurement precision
If more antenna elements are used to improve resolution, then the baseline length and aperture filling increase, but the system complexity and cost increase
Solution Approach 1:
The patent pre-determines the optimal positions of antenna elements using Fibonacci spacing calculations before physical deployment. This preliminary mathematical optimization ensures that the sparse array achieves maximum resolution capability with minimum elements, eliminating the need for complex post-deployment adjustments or additional elements
Solution Approach 2:
The patent transitions from uniform one-dimensional spacing to a two-dimensional Fibonacci spiral or grid arrangement. This dimensional transformation allows the array to achieve equivalent or superior resolution with fewer elements by utilizing both radial and angular dimensions for spatial sampling
Data Source
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AI summary
An antenna (80,90) has a one dimensional or multidimensional array of elements (20,40), wherein spacings between successive elements of at least part of the array are non periodic and correspond to a series of multiples of a unit spacing, the multiples following a Fibonacci sequence. Two dimensional arrays can be arranged as a Fibonacci grid or as a Fibonacci square tiling. The number of elements can be reduced for a given measure of resolution, while still enabling the signal being transmitted or received to have a peak in a single unique direction and thus form a beam. Furthermore, since there will be some elements clustered close together and a few which are well spaced, it can be more suitable for vehicles (30) than a regularly spaced array. It can be used as a transmit antenna or as a receive antenna for a submillimeter radar system.