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phased-array-systems 0.9.0: validated physics and multi-objective trade studies

2026-07-22

Version 0.9.0 of phased-array-systems is on PyPI, capping a run of three releases that changed what the package is. v0.7.0 made the digital beamforming models accurate (digitization levels, ADC jitter, exact Swerling statistics). v0.8.0 replaced every hand-fit physics approximation with the published model it was imitating, and added a validation suite that proves it. v0.9.0 adds the optimization layer: true multi-objective search, global sensitivity, and constraint-aware design of experiments.

The package is the trade-study layer of the toolchain I wrote about in modeling phased arrays in Python: it consumes phased-array-modeling for antenna patterns and answers system questions (detection range, link margin, cost, power, reliability) against explicit requirements. It installs as pip install "phased-array-systems[mdao]", imports as phased_array_systems, and ships a pasys CLI. Docs are at jman4162.github.io/phased-array-systems.

Physics you can check

The v0.8.0 release notes read like a confession, which is the point. Atmospheric and rain losses previously came from two-line and polynomial fits; they now come from ITU-R P.676-13 Annex 1 line-by-line gaseous attenuation (79 vendored oxygen and water-vapor spectroscopic lines) and ITU-R P.838-3 rain coefficients for both polarizations, with no new dependencies. Sea clutter follows the NRL model fitted to the Nathanson tables, ground clutter the constant-gamma model. Required radar SNR comes from the exact Marcum-Q inversion instead of Albersheim’s approximation, which moved the golden regression case from 13.115 to 13.183 dB. One noise convention now applies everywhere: rx_noise_temp_k is antenna temperature and T_sys = T_ant + 290(F-1), identical at 290 K and correct for low-sky-temperature satcom cases, and the radar equation honors the cascaded noise figure the same way the comms path does.

Each of these models is asserted against its published source in a 35-test validation suite, with the references and tolerances documented in the theory section of the docs. The documented approximations that remain are listed as approximations: slant paths use equivalent-height columns rather than layered integration, effective rain path length applies the ITU-R P.530 factor directly, and the CFAR variants beyond cell-averaging use published deltas on the universal curve. A model you can check beats a model that flatters the design.

Optimization joins the loop

Through v0.8, trade studies worked by sampling: generate a design of experiments, evaluate every case, filter to feasible, extract the Pareto front. v0.9.0 adds the direct route. optimize_pareto() (in phased_array_systems.trades.moo) runs mixed-variable NSGA-II via pymoo and returns the nondominated set with full metrics. The constraint handling is the part I care about: must-severity requirements become normalized inequality constraints, so the requirement set you already wrote is the constraint set the optimizer respects.

pasys optimize config.yaml --method nsga2 \
  --objective detection_range_m --objective2 cost_total_usd:minimize
pasys sensitivity config.yaml --sens-method sobol --samples 256

Sobol global sensitivity (first-order and total indices, with confidence intervals) answers which variables move the answer before you spend optimizer iterations on them, and the DOE generator can now rejection-sample against architecture construction, so batch studies no longer waste cases on configurations that fail to build. All of it lives behind an [mdao] extra (pymoo, SALib); the core install is unchanged.

Case study: detection range against cost

The repository’s radar example is a complete requirements-driven study, and everything below comes from running it as shipped (examples/03_radar_detection_trade.py). The scenario: an X-band radar at 10 GHz, a 10 dBsm target at 20 km, Pd = 0.9 at Pfa = 1e-6, 16-pulse noncoherent integration, four requirements defined. The baseline 16x16 array (2560 W peak, 29.1 dB gain) integrates to 16.0 dB SNR against 13.2 dB required, a 2.9 dB margin and 23.6 km of range at $178,000, and still fails the requirement set.

So the study sweeps: a 15-variable design space (array sizes from 8x8 to 32x32, per-element transmit power from 5 to 20 W, PA efficiency, cost per element), sampled with a 100-case Latin hypercube and evaluated in 0.6 seconds. 49 of 100 designs are feasible, and 8 are Pareto-optimal:

The front is the deliverable. At the cheap end, a 16x16 array meets the requirements at 27.2 km and $158,931; the knee sits around 16x32 designs in the mid-40s of kilometers for roughly $225,000; and the 32x32 corner buys 76.5 km and 23.3 dB of margin for $396,945. Every point carries its full metrics dict, so the argument between the $159k and $397k answers happens over named requirements and margins instead of taste.

With v0.9.0, the same study runs through NSGA-II instead of sample-and-filter. The two paths are complementary: the DOE view maps the landscape and feeds Sobol sensitivity, and the optimizer pushes the front itself once you know which variables matter.

Digital beamforming trades

The v0.7.0 layer deserves a mention because it changed what the cost and power numbers mean. digitization_level (element, subarray, or analog) drives the ADC count, beamformer data rate, compute load, and DC power from the digitized channel count instead of assuming one ADC per element. An aperture-jitter model combines with quantization noise into effective ADC SNR, the system dynamic-range metric includes the array processing gain, and v0.9.0’s thermal-reliability coupling estimates junction temperature from dissipated power and feeds the Arrhenius MTBF derating. A dedicated example and tutorial notebook run the element-versus-subarray-versus-analog architecture trade end to end.

Upgrade notes

• v0.8.0 shifts numeric results by design: real ITU-R losses, Marcum-Q required SNR, one noise convention, and cascaded noise figure in the radar equation.
• Removed: compute_cost_per_db and the empirical Swerling/CFAR adjustment tables (superseded by exact statistics and the universal curve).
• friis_noise_figure now reports per-stage contribution percentages that sum to 100; the cascade_analysis key is renamed stage_nf_contribution_pct.
• Python 3.10+ required; the test suite is at roughly 487 tests with mypy at zero errors as a blocking CI step.

Try it

pip install "phased-array-systems[mdao]"

The docs site has the user guide, CLI reference, tutorials, and the theory pages including the validation tables. A Streamlit app wraps the single-case, trade-study, RF-cascade, and radar calculators for browser use:

The repository has the examples used above and Colab-ready tutorial notebooks for the trade-study, DBF-architecture, and MDAO workflows.

phased-array-systems is an independent project I build on my own time. The views are my own and do not represent any current or former employer.