rf-compute

_{A 4-second loop. It plays once and rests, and shows a still frame if you prefer reduced motion. Watch it on repeat.}

Radio Frequency as a computational substrate — not a transmission medium.

A research-and-education surface for wave-domain computation. The waveform is the operand. Interference isn't noise to cancel — it's the multiply-accumulate operation. The medium is the math.

The one-sentence version

Instead of using RF to carry bits to a digital chip that does the math, you make the RF waveform be the math — interference performs the operation, the channel is the adder, the medium is the algorithm.

This is not a new idea. It's been hiding in plain sight across four separate research communities for ~18 years. rf-compute is the bridge that makes it legible to builders.

Why this exists

There is no unified developer surface for RF-as-compute. The field is real, peer-reviewed, and active — but it's scattered across four communities that don't share vocabulary, tooling, or a "hello world":

They all share one thing: the waveform is the operand. Nobody has built the bridge between them. That's the gap this project fills.

The $350 hello world

You don't need a fab, a clean room, or a metamaterial. You need two transmit SDRs, one receive SDR, and a laptop — clone-tier hardware gets you there around $350; official units run ~$725. Either way, the simulation kernel runs free on NumPy alone.

Tx1 ──┐
       ├── air ──→ Rx ──→ f(x1 + x2)  ← the channel computed the sum
Tx2 ──┘

Two transmitters send pre-coded signals simultaneously. The receiver reads their sum from the superposed waveform — without decoding either signal individually. Interference is the operation. This is the Nazer & Gastpar 2007 result, made legible.

This is the simplest wave-compute primitive that exists. If you can run this, you understand the field.

📖 Full walkthrough: docs/hello-world-aircomp.md — hardware, code, what to expect, troubleshooting

Budget option: One HackRF + one RTL-SDR (clone-tier ~$190, official ~$380). You transmit x1, x2, and x1+x2 sequentially and compare captures in post-processing. You lose the simultaneity that makes AirComp profound, but you learn the signal-processing structure for half the cost. Details in the walkthrough.

Quick start (60 seconds, no hardware)

git clone https://github.com/LE-VAI/rf-compute.git
cd rf-compute
pip install -e .
python examples/tier1_aircomp_kernel.py    # AirComp: 3+5=8
python examples/tier1_5_lattice_aircomp_kernel.py  # exact lattice sums, $0
python examples/tier1_6_fading_coefficients.py     # coefficient selection on fading, $0
python examples/tier2_convolution_kernel.py # 4 operators
python examples/tier3_inversion_kernel.py   # solves Ax=b
python examples/tier4_ota_federated_learning.py  # federated learning over the air, $0

The simulation kernel runs the same API as the hardware kernel — switch backend="sim" to backend="sdr" when you have SDRs. See docs/INSTALL.md for the SDR driver install (the one friction point when you're ready for hardware).

The hello-world ladder

Six reproducible experiments, escalating in cost. Each maps to a peer-reviewed result.

Tier 3 has three modes (simulation free, software-in-the-loop ~$200 clone / ~$395 official, analog feedback ~$350 clone / ~$480 official) — see the walkthrough for the trade-off.

📖 Full ladder walkthroughs: Tier 1 · Tier 1.5 · Tier 1.6 · Tier 2 · Tier 3 · Tier 4 — each with parts lists, code, and troubleshooting

What this is NOT

This is a research and education surface, not a product. We build the map, the vocabulary, and the reproducible "hello world." The community builds the future.

We are explicitly not building:

• ❌ Deep-learning-scale matrices (SOTA is 5×5; NN layers are 1024×1024 — that's a hardware physics problem)
• ❌ Phone-form-factor integration (45 MHz ≈ 6.7m wavelength — subwavelength resonator design at phone scale is unsolved)
• ❌ Noise-resilient analog compute for hostile EM environments (lab results won't hold in a pocket)
• ❌ 6G standards integration (AirComp is a 6G research candidate, not yet in 3GPP standardization; that's a multi-year institutional process)
• ❌ Commercial fabrication (Lightmatter is pursuing the optical frontier; pure-RF commercial compute is not this project)

These are real, important problems. They belong to the metamaterials physics community, the antenna engineers, the RF circuit designers, the standards bodies, and industry — not to a research-and-education surface. We name them clearly so builders know where the open frontier lives.

📖 Full deferral table: docs/field-map.md

The field map

The complete lineage-to-primitive map lives in docs/field-map.md. It covers:

• Each of the four lineages with origin papers, SOTA devices, key labs, and SDR-mappable primitives
• The SDR bridge: why software-defined radio is the unified developer surface
• The "hello world" ladder with cost estimates and parts lists
• Field maturity at a glance
• Full provenance and citation list

If you read one document, read the field map.

Hardware you'll need

Prices verified 2026-08-31, re-checked 2026-09-30. HackRF One official retail is ~$340 (SparkFun/Adafruit have retired the unit; GSG's successor HackRF Pro is ~$400). AliExpress clones run ~$100–150 but degrade above 1 GHz per Great Scott Gadgets' own clone test — fine for sub-GHz learning experiments, not for precision work. RTL-SDR Blog V4 is end-of-line (May 2026); current official units are the V3 or V4L at ~$35–40 (the V4L is itself a limited edition with roughly a year of chip stock).

Total entry cost: free (Tier 3 sim) / clone-tier ~$200–350 / official ~$390–725 depending on tier. No fab. No clean room. No metamaterial. Tier 3 Mode A is pure simulation and costs nothing — start there to see the math before buying hardware. If you buy clones, know what you're buying: they work for learning, they drift for precision.

Who this is for

• Builders who want to touch wave-domain compute without a physics PhD
• Researchers who want a shared vocabulary across the four lineages
• Educators who want reproducible experiments with real citations
• Curious engineers who read "the channel is the adder" and want to see it work

If you've never heard of RF-as-compute and want to understand it: start with the $350 hello world. If you're already in one of the four lineages: the field map is the bridge to the other three.

The key papers (start here)

📖 Annotated bibliography: docs/bibliography.md — every citation, reading order, how to use it

Status

Pre-release. The spine is complete: field map, six-tier hello-world ladder, annotated bibliography, contribution guide, and the SDR kernel abstraction. The simulation kernel is fully reproducible (every run seed-deterministic; 116 tests).

• ✅ Field map — the spine document
• ✅ Tier 1: AirComp sum — the $350 hello world
• ✅ Tier 1.5: Lattice-coded AirComp — the $0 exact-computation primitive (nested-lattice kernel)
• ✅ Tier 1.6: Fading-channel coefficients — the $0 coefficient-selection tier (computation-rate maximization, MMSE α, LLL + norm-bound search)
• ✅ Tier 2: Wave-domain convolution — the $200 linear-operator primitive
• ✅ Tier 3: Matrix inversion via feedback — the wave-domain capstone (free / $200 / $350)
• ✅ Tier 4: Over-the-air federated learning — the AirComp capstone ($0): aggregation over the air, misalignment, and a pilot-aided equalizer
• ✅ Annotated bibliography — every citation, reading order, how to use it
• ✅ Installation guide — pip install, SDR drivers, troubleshooting
• ✅ Contributing guide — the reproducibility + provenance + honesty bar
• ✅ LICENSE — MIT
• ✅ SDR kernel abstraction — one API across all four lineages
  • ✅ examples/tier1_aircomp_kernel.py — Tier 1 with the kernel
  • ✅ examples/tier1_5_lattice_aircomp_kernel.py — Tier 1.5 with the kernel
  • ✅ examples/tier1_6_fading_coefficients.py — Tier 1.6 with the kernel
  • ✅ examples/tier2_convolution_kernel.py — Tier 2 with the kernel
  • ✅ examples/tier3_inversion_kernel.py — Tier 3 with the kernel
  • ✅ examples/tier4_ota_federated_learning.py — Tier 4 with the kernel
• ⏳ Community contributions (see CONTRIBUTING.md)

License

MIT — see LICENSE.

Provenance

This project is a research-and-education surface synthesized from peer-reviewed literature. The underlying research was conducted 2026-07-31 via a multi-source academic search across Science, Nature, Nature Photonics, IEEE Trans. Inf. Theory, Journal of Lightwave Technology, and arXiv. Full provenance and citation verification in docs/field-map.md.

All citations are peer-reviewed unless marked [preprint] or [vendor]. Lightmatter performance figures are vendor-sourced. AirComp surveys are preprints. The spin-torque SDR mapping is approximate, not a hardware equivalent.

This surface does not claim authorship of the underlying physics. It claims only the bridge — the map, the vocabulary, and the reproducible "hello world."