Pixelated Antenna Design

XGBoost surrogate–assisted 2-D GA for pixelated antennas

The Pixelated Antenna Design project shows how an XGBoost surrogate plus a 2-D, submatrix-crossover GA speeds up pixelated antenna design. XGBoost learns the 0/1s → performance mapping, then spend EM time only on candidates that look promising. This surrogate-assisted optimization approach makes topology-free antenna design a practical tool for discovering unconventional, high-performance structures.

Pixelated antenna (hero demo)

Motivation

Pixelization (digitally coded geometry) turns an antenna into an $m \times n$ binary grid (1 = metal, 0 = empty). That invites wild, high-performance shapes—but also thousands of bits and expensive EM runs. We propose:

  • XGBoost as a fast, accurate surrogate for binary inputs and continuous EM metrics.
  • A 2-D GA with submatrix crossover that swaps rectangular pixel blocks—so useful geometric motifs survive recombination.
  • Surrogate-aware model management (SMAS) to simulate only the most promising designs.

Methodology

The takeaway is that, instead of the popular convolution neural networks with tons of samples, we use a tree-based model to predict one antenna’s performance with few samples, then iteratively searches over the binary design space and updates the model to refine its accuracy.

1) Geometry encoding
An $m \times n$ 0/1 matrix defines the pixel mask over the design area.

2) Surrogate modeling
XGBoost drives the loop; CART and GBDT are shown only to explain the idea (single tree → boosted trees → XGBoost). Training updates online as new EM-validated samples arrive.

CART (background concept)
GBDT (background concept)

3) 2-D GA with submatrix crossover
Pick parent pairs and a random rectangle; swap the submatrices to recombine 2-D features. Then apply light mutation (rate $\approx 1/d$, with $d$ = number of pixels). Selection respects performance + diversity using a Z-scored Hamming distance to the current best—keeping the search curious, not myopic.

2-D GA: submatrix crossover & mutation

Outcomes

Example 1 — Full-pixel UWB design (1920 pixels)

  • Target: match or beat state-of-the-art UWB at the same footprint.
  • Result: 2.9–13.6 GHz with $\lvert S_{11}\rvert \le -10\,\text{dB}$; min gain ≈ 2.64 dBi, min efficiency ≈ 80.7%; simulation and measurement align.
UWB baseline (demo)

Example 2 — 5G outdoor base-station (hybrid: conventional + pixelated feeds)

  • Pixelization only on the dual feeds (total 1496 pixels) to sharpen matching and isolation.
  • Result: over 3.3–3.8 GHz and 4.8–5.0 GHz: $\max \lvert S_{11}\rvert, \max \lvert S_{22}\rvert \le -14\,\text{dB}$ and $\max \lvert S_{21}\rvert \le -25\,\text{dB}$, with stable patterns and gain.
OB feeding structure (demo)

Example 3 — Low-resolution ESA (270 pixels) study

  • Specs: 1 GHz center, $\lvert S_{11}(1\,\text{GHz})\rvert \le -12\,\text{dB}$, efficiency $\ge 6\%$, maximize bandwidth.
  • Result: 95 MHz $(-3\,\text{dB})$ bandwidth, ≈ 6.38% efficiency.
  • Compute win: feasible design in ~1623 EM sims on average; standard GA needed 8910 for feasibility and 72,900 to reach a comparable bandwidth.
Pixelated antenna (demo)

Highlights

  • XGBoost + 2-D GA scales to high-res binary design while preserving spatial patterns.
  • Big EM savings vs. brute-force GA+EM; strong results on UWB, base-station feeds, and ESA.
  • Drop-in workflow for fully pixelated antennas or hybrid pixelated substructures across bands and specs.