NeuralRFIC

Build a real radio frequency chain, measure it properly, then build a numerical model that reproduces its behaviour, defects included.

• Status: architecture research and feasibility study
• Last reviewed: 2026-08-21

Nothing is built yet: no board, no measurement bench, no identified model. This repository is a public lab notebook. No component has been ordered and no operating frequency has been chosen, because that choice depends on an instrument audit that has not happened yet.

The point is not to put machine learning on an RF circuit so that it can be said to be there. The point is to answer one question:

Does a learned model beat a properly chosen classical model on a real RF system, and at what cost?

If the answer is no, it gets published as it stands. That is a useful answer.

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One honest remark before anything else

The project name contains "RFIC", meaning radio frequency integrated circuit. No integrated circuit will be fabricated here. The project works with commercial parts on a printed circuit board.

That is an important difference, not a vocabulary detail. Designing an RF integrated circuit requires access to a fabrication technology, specific design tools, and lead times measured in months. The name will therefore be revisited, see decisions/0002-project-name.md.

What the project actually does is still substantial: design an RF chain, characterise it with real instruments, and build a numerical model validated against measurement.

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Why the subject is interesting

An RF amplifier is easy to describe and hard to model.

At low power it behaves like a multiplier: the output is the input times a gain. As power rises that stops being true. The gain drops, new frequencies appear, and the response starts depending on what happened just before. That last property, called memory effect, is what makes the problem interesting.

It also poses a real engineering problem: an amplifier gives its best energy efficiency close to its non linear region, which is exactly where it distorts the signal. The trade-off is direct:

Operating point	Efficiency	Distortion
Well below saturation	poor	low
Close to saturation	good	strong

The answer used in every modern base station is digital predistortion: deliberately distort the signal before the amplifier so that the amplifier's own distortion cancels the first one.

   clean      +---------------+      +-----------+      nearly clean
   signal --> | predistortion | -->  | amplifier | -->  signal
              +---------------+      +-----------+
                      ^                    |
                      |                    |
                      +--- model identified from measurement ---+

For that to work you need a faithful model of the amplifier. That is exactly the problem this project attacks.

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The classical model, explained

The most widely used model in industry is the memory polynomial:

$$y[n] = \sum_{k=1}^{K} \sum_{m=0}^{M} a_{k,m} x[n-m] \bigl|x[n-m]\bigr|^{\,k-1}$$

Let us take it apart, because it looks worse than it is.

• $x[n] \in \mathbb{C}$ is the input sample at instant $n$. Its real and imaginary parts represent the two signal components, which together describe amplitude and phase.
• $\bigl|x[n-m]\bigr|$ is the signal amplitude $m$ samples earlier.
• The term $x[n-m],\bigl|x[n-m]\bigr|^{k-1}$ says the output depends on the past input, multiplied by a power of its amplitude. That is what describes the non linearity: the stronger the signal, the more that term weighs.
• $K$ is the non linear order. $K = 1$ gives a linear system. The larger $K$, the more kinds of distortion you can describe.
• $M$ is the memory depth. $M = 0$ means the output depends only on the present instant. $M > 0$ describes the fact that the circuit remembers.
• $a_{k,m} \in \mathbb{C}$ are the coefficients to identify from measurements. Being complex, they carry both a magnitude and a phase shift.

The model has $K(M+1)$ complex coefficients, which is where its cost comes from.

The remarkable property of this model is that it is linear in its coefficients. Collecting the measured terms into a matrix $\mathbf{U}$ and the coefficients into a vector $\mathbf{a}$, the model is simply $\mathbf{y} = \mathbf{U}\mathbf{a}$, so identification is a least squares solve that takes a fraction of a second and gives a reproducible answer.

That is why it is a serious reference. A learned model has to beat it, on data it has not seen, to justify its cost.

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The question the project has to settle

Model family	Coefficients	Identification	Interpretable	Compute cost
Memoryless polynomial	a handful	least squares	yes	very low
Memory polynomial	a few dozen	least squares	partly	low
Full Volterra	very many	least squares, but ill conditioned	hardly	high
Wiener, Hammerstein	few	non convex optimisation	yes, physical structure	low
State space	depends on order	system identification	yes	low
Neural network	hundreds to thousands	gradient descent	no	medium to high

The questions to answer, in this order:

1. How far does a well tuned classical model get on our measurements?
2. Under what conditions does it fail (high power, wide bandwidth, temperature change)?
3. Are those the conditions where a learned model actually helps?
4. Does the gain justify the cost, given that a predistortion model has to run in real time?

That last question is often skipped in the literature. A model that cuts the error by 2 dB but costs fifty times the compute is not usable in a real system.

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What will be measured, and with what

The project rests entirely on measurement quality. A model fitted to doubtful measurements is an arithmetic exercise, not engineering.

Quantity	What it describes	Instrument needed	Available
S parameters	how the circuit transmits and reflects, in magnitude and phase	vector network analyser	yes, characteristics to confirm
Gain compression	at what power the gain starts to fall	variable power source and power measurement	to establish
Intermodulation products	spurious frequencies created by the non linearity	two sources and a spectrum analyser	to establish
Noise figure	noise added by the circuit	specific equipment	probably not
Complex dynamic behaviour	what you need to identify a memory model	synchronised vector transmitter and receiver	to establish, and this is the critical one
Temperature drift	model stability over time	thermal chamber or controlled heating	to establish

The critical row is the second to last. A vector network analyser measures a linear system very well, but it is not built to send a wideband modulated signal and record the output sample by sample. That is exactly what identifying a memory model requires.

Routes under consideration, none chosen:

Route	Principle	Cost	Caveat
Software defined radio	a digital transceiver acts as source and analyser	low	limited bandwidth, self calibration required
Arbitrary generator and oscilloscope	generate and record directly	none if the hardware suits	oscilloscope bandwidth, limits the working frequency
Remotely accessible measurement benches	some labs publish benches usable over the internet	none	depends on availability, to verify
Public amplifier datasets	work from measurements taken by others	none	we do not control the measurement, but we can compare against the literature

The last route is particularly attractive to start with: it lets the whole modelling side be developed and validated before a bench exists, then repeated on our own measurements. That decouples two risks instead of chaining them.

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Simulation and measurement never get mixed

The project will produce three kinds of result, and they are always labelled:

Label	Origin	What it is worth
[simulated]	circuit or electromagnetic simulator	depends entirely on the quality of the device model
[measured]	real instrument, real circuit	this is the truth, with its uncertainty
[modelled]	output of the identified numerical model	to be compared against the other two

A simulation result that disagrees with measurement is not automatically a measurement error. Often it is the opposite: the vendor supplied device model is valid in a limited range, the board adds parasitics, and the connectors matter. Understanding that gap is a result in itself, and probably one of the most instructive in the project.

The simulation stack available here is unusually complete for a personal lab: circuit simulation, 3D electromagnetic simulation, and scripting for both. That makes a genuine comparison across levels possible:

  analytical model -> numerical model -> circuit simulation -> 3D electromagnetic
                                              simulation -> fabricated board -> measurement

Most projects stop at one or two of those levels. Walking several of them, and publishing where they diverge, is a realistic contribution.

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What is still open

1. The working frequency. It follows directly from what the available instruments cover, which is not yet established.
2. The chain architecture: a single gain stage, a full chain with filtering, or a deliberately non linear stage built for the study.
3. Component selection. Nothing gets ordered before the instrument audit.
4. The means of wideband vector measurement.
5. The model family, and the protocol that will settle it.
6. Whether predistortion is done in real time, which is a project of its own.

What already exists, briefly

Source	What you find there	What you do not
Academic	behavioural amplifier models, digital predistortion, neural models for the same problem	a comparison at comparable parameter count and compute cost, on the same measurements
Industry	application notes on non linear characterisation, deployed predistortion architectures	the real uncertainty of a modest lab bench
Open source	S parameter processing, instrument control, public amplifier datasets	thermal drift of an identified model, measured over hours

Details in research/state-of-the-art.md. Two resources are strategic: public datasets and remotely accessible benches. They let the modelling side start without owning a bench, which decouples two risks instead of adding them together.

How the project will be evaluated

Criterion	Threshold
Evaluation on data never used for identification	mandatory
Comparison at comparable parameter count, or a curve of error against parameter count	mandatory
Measurement repeatability quantified before any comparison	mandatory, it sets the significance threshold
Compute cost per sample measured	mandatory, a predistortion model has to run in real time
Systematic labelling of simulated, measured and modelled	mandatory
Amplitude error and phase error reported separately	mandatory, their physical causes differ

No conclusion is drawn from a gap smaller than the measurement repeatability.

How to read this repository

You want to	Go to
the scope and the questions	docs/scope.md
the equations, explained	docs/mathematics/formulation.md
the instrument audit and what is missing	docs/hardware/inventory-and-needs.md
the candidate chain architectures	docs/architecture/options.md
the model comparison method	benchmarks/methodology.md and benchmarks/specification.md
what already exists	research/state-of-the-art.md

Licence

Undecided at this stage. The repository will contain code, measurements and possibly board design files, which do not call for the same licence. Analysis in LICENSE-NOTES.md.