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.
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.
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":
| Lineage | Where it publishes | What it does |
|---|---|---|
| Computational metamaterials | Science, Nature | Passive materials that perform math on wavefields |
| Over-the-air computation (AirComp) | IEEE Trans. Inf. Theory | The wireless channel is the computation |
| Microwave photonics | Nature Photonics | RF signals on optical carriers doing NN inference |
| Spin-torque neuromorphic | Nature Electronics | Microwave nano-oscillators as neurons |
They all share one thing: the waveform is the operand. Nobody has built the bridge between them. That's the gap this project fills.
You don't need a fab, a clean room, or a metamaterial. You need two transmit SDRs, one receive SDR, and a laptop. But you can also start for free — the simulation kernel runs 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 (~$190): One HackRF + one RTL-SDR. 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.
git clone https://github.com/rf-compute/rf-compute.git
cd rf-compute
pip install -e .
python examples/tier1_aircomp_kernel.py # AirComp: 3+5=8
python examples/tier2_convolution_kernel.py # 4 operators
python examples/tier3_inversion_kernel.py # solves Ax=bThe 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).
Three reproducible experiments, escalating in cost. Each maps to a peer-reviewed result.
| Tier | Experiment | Cost | Proves | Citation |
|---|---|---|---|---|
| 1 | AirComp sum | ~$350 | Interference IS computation | Nazer & Gastpar, IEEE TIT (2011) |
| 2 | Wave-domain convolution | ~$200 | Linear operators are native to wave physics | Silva et al., Science (2014) |
| 3 | Matrix inversion via feedback | free / ~$200 / ~$350 | The wave domain solves equations; settling, not iterating | Nature Communications (2025) |
Tier 3 has three modes (simulation free, software-in-the-loop ~$200, analog feedback ~$350) — see the walkthrough for the trade-off.
📖 Full ladder walkthroughs: Tier 1 · Tier 2 · Tier 3 — each with parts lists, code, and troubleshooting
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 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.
| Item | Tier 1 | Tier 2 | Tier 3 (Mode B/C) | Est. cost |
|---|---|---|---|---|
| HackRF One SDR (Tx) | ×2 | ×1 | ×1 | ~$150 each |
| RTL-SDR (Rx, receive-only) | ×1 | ×1 | ×1 | ~$30 |
| 10 MHz clock sync cable (BNC) | ✓ | ~$5 | ||
| Laptop (any OS) | ✓ | ✓ | ✓ | you have one |
| Passive scatterer / reflector | ✓ (Mode B) | ~$10–20 | ||
| RF circulator (one-way loop) | ✓ (Mode C) | ~$40 | ||
| Programmable attenuator (loop gain) | ✓ (Mode C) | ~$30 | ||
| RF splitter/combiner | ✓ (Mode C) | ~$15 |
Total entry cost: free (Tier 3 sim) / ~$200 (Tier 2 or Tier 3 Mode B) / ~$350 (Tier 1 or Tier 3 Mode C). 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.
- 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.
| Paper | Year | Why it matters |
|---|---|---|
| Nazer & Gastpar, "Computation over multiple-access channels," IEEE Trans. Inf. Theory | 2007 | The founding result. Interference computes functions. |
| Silva et al., "Performing mathematical operations with metamaterials," Science | 2014 | Passive materials do math on wavefields. |
| Torrejon et al., "Neuromorphic computing with spintronic oscillators," Nature | 2017 | Microwave nano-oscillators as neurons. 99.6% spoken-digit. |
| Zangeneh-Nejad et al., "Analogue computing with metamaterials," Nature Reviews Materials | 2021 | The canonical review. "Wave-based analog computing." |
| Li et al., "Performing calculus with ENZ metamaterials," Science Advances | 2022 | Differentiation + integration in the material. |
| "Programmable wave-based analog computing metastructure," Nature Communications | 2025 | The SOTA. Matrix inversion, Newton's method, Lagrangian optimization at 45 MHz. |
| Guan & Yao, "Microwave photonic neural network," J. Lightwave Technology | 2025 | RF photonic MVM. 55×10⁶ MAC/s. |
📖 Annotated bibliography: docs/bibliography.md — every citation, reading order, how to use it
Pre-release. The spine is complete: field map, three-tier hello-world ladder, annotated bibliography, contribution guide, and the SDR kernel abstraction.
- ✅ Field map — the spine document
- ✅ Tier 1: AirComp sum — the $350 hello world
- ✅ Tier 2: Wave-domain convolution — the $200 linear-operator primitive
- ✅ Tier 3: Matrix inversion via feedback — the capstone (free / $200 / $350)
- ✅ 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/tier2_convolution_kernel.py— Tier 2 with the kernel - ✅
examples/tier3_inversion_kernel.py— Tier 3 with the kernel
- ✅
- ⏳ Community contributions (see
CONTRIBUTING.md)
MIT — see LICENSE.
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."