Waveform evaluation profiles (plan S15) — `ofdm-lte20-v1` and `ofdm-lte20-evm-v1`¶

Status: proposed, pending science review and cross-validation. The waveform, the measurement procedure, the reference-vector package and the tests below exist in the repository; the numbers of this profile become citable only after the cross-validation in §6 has been run by a maintainer and the error budget in §5 has been approved. Until then the profile is computed and stored like every other profile but is hidden in the GUI (MetricProfile.validation = pending_cross_validation) and every result it produces carries the limitation "profile pending cross-validation".

1. Scope¶

One waveform configuration, chosen because the lab's own captures (DPA_200MHz, DPA_160MHz) are LTE 20 MHz carriers:

Item	Value	Source
Waveform id	`ofdm-lte20-v1`	this document
Numerology	CP-OFDM, 15 kHz subcarrier spacing, 2048-point FFT at 30.72 MS/s, normal cyclic prefix (160, 144 × 6 samples per 0.5 ms slot), 14 symbols per 1 ms subframe	3GPP TS 36.211 §6.12 (OFDM baseband signal generation); standard version to be fixed at cross-validation
Occupied subcarriers	1200 (100 resource blocks × 12) at k = −600 … −1, +1 … +600; the DC subcarrier is empty	same
Modulation	64QAM on every occupied subcarrier of every symbol, unit average power, points (±1, ±3, ±5, ±7)/√42 in I and Q, drawn uniformly from a seeded generator (`numpy.random.default_rng(seed)`)	`opendpd/core/waveforms/ofdm.py`
Length	`n_subframes` × 30 720 samples (default 10 = one 10 ms frame); instruments play it in a loop	spec
What it is	a test waveform with known symbols: no synchronisation signals, reference signals, control or shared channels, no resource mapping, no filtering or windowing	—
What it is not	a conformance test signal (E-TM), a 3GPP-compliant transmitter, or evidence of standard compliance; the name "LTE 20 MHz" refers to the numerology only	—

Everything is regenerated from the specification (WaveformSpec: id, version, seed, n_subframes); the reference-vector package (§4) is a convenience for instruments and for cross-validation, never the source of truth.

2. Measurement procedure of `ofdm-lte20-evm-v1`¶

Input: the evaluated I/Q signal (a PA model output, a simulated or measured PA output with or without DPD) at its capture rate fs, and the dataset's binding to the waveform (§3). Every step is deterministic and recorded in MetricProfile.parameters.

Rate conversion. If fs ≠ 30.72 MS/s, the signal is converted with a polyphase resampler (scipy.signal.resample_poly, Kaiser-windowed FIR) using the exact rational ratio; fs below 30.72 MS/s or without a small rational ratio (denominator ≤ 10 000) gives not_applicable.
Timing. Circular cross-correlation with the regenerated waveform (one period) gives the integer offset and the normalised peak; a peak below 0.3 means the signal is not (a distorted copy of) the bound waveform → missing_reference.
Coarse frequency offset from the cyclic-prefix correlation of every complete symbol, skipping the first 32 prefix samples (channel memory of the previous symbol).
Equaliser. One complex gain per subcarrier, least squares over all complete symbols in the capture, from the known symbols (data aided).
Fine frequency offset from the slope of the per-symbol residual phase (known symbols) against time; steps 4–5 iterate at most three times until the update is below 1 mHz. No per-symbol phase tracking: whatever remains counts as error.
EVM. RMS over every occupied subcarrier of every complete symbol, EVM_RMS = 100 · sqrt(Σ|Ŝ − S|² / Σ|S|²) in percent, also reported in dB (20·log10). Symbols are demodulated at the nominal FFT position (end of the cyclic prefix).
ACLR at the capture rate: Welch PSD (Hann, nperseg of the dataset, 50 % overlap), main channel = [−9, +9] MHz (the 18 MHz transmission bandwidth configuration), first adjacent channels centred at ±20 MHz with the same 18 MHz rectangular measurement bandwidth, ACLR = 10·log10(P_adjacent / P_main) (leakage, negative dBc, lower is better, the repository's convention). Requires fs ≥ 58 MS/s; otherwise not_applicable with the reason. Definition after 3GPP TS 36.104 §6.6.2 (E-UTRA ACLR); version to be fixed at cross-validation.

Deviations from a standard EVM procedure (stated, to be quantified)¶

Standard procedure (TS 36.104 Annex E principles)	This profile	Why
Channel estimate from reference signals with time/frequency averaging	least-squares gain per subcarrier from all known symbols	data-aided test waveform; no reference signals exist
EVM evaluated at two FFT timing positions (window edges), maximum reported	one position: end of the cyclic prefix	first version; the two-position rule is a candidate for v2 after cross-validation
Frequency offset estimated per standard procedure	cyclic-prefix coarse estimate + data-aided fine estimate	same numbers expected for a static offset; drift within the window is not tracked
Measurement over specific subframes/slots and physical channels	every complete symbol in the capture	no physical channels

The data-aided equaliser over L symbols removes 1/L of the noise power from the reported EVM (bias sqrt(1 − 1/L)); with L ≥ 28 this is below 2 % relative and is part of the error budget.

3. Binding a dataset to the waveform¶

opendpd datasets import … --waveform <package>/waveform.json regenerates the waveform and cross-correlates it with the imported input column: the offset and the normalised peak are stored as signal.waveform (WaveformBinding) next to the package hash. The binding says which symbols were sent; the captured data is untouched. Without a binding, or when the input does not correlate with the waveform, the profile reports missing_reference for the EVM metrics and never falls back to another definition under the same name. Multi-carrier captures (the built-in DPA_200MHz, ten carriers at 800 MS/s) are therefore reported as not applicable to this profile, which is the correct answer.

4. Reference-vector package¶

opendpd waveforms generate --seed S --subframes N --out DIR writes

File	Content
`waveform.json`	the `WaveformSpec`, the package hash (spec + symbols), sample count, formats
`x.npy`	float32 `(n, 2)` I/Q at 30.72 MS/s, unit average power, to be played in a loop
`symbols.npy`	complex64 `(n_symbols, 1200)` reference symbols in subcarrier order

Expected results on the ideal signal (self-evaluation, recorded by the tests in tests/unit/test_waveform_ofdm.py): EVM below 1e-9 % at 30.72 MS/s; EVM floor 0.037 % after rate conversion from 122.88 MS/s or 800 MS/s (polyphase filter ripple); a frequency offset of ±350 Hz and a linear channel shorter than the cyclic prefix are removed exactly; white noise of SNR 30 dB gives EVM = 100/√SNR · √(1200/2048) · √(1 − 1/L) within 0.03 percentage points.

5. Error budget (proposed, pending approval)¶

Contribution	Bound in this implementation	Evidence
Numerical floor (no rate conversion)	< 1e-9 % EVM	`test_ideal_signal_demodulates_to_zero_evm_with_exact_timing`
Rate conversion floor	0.037 % EVM (122.88 and 800 MS/s)	`test_resampling_from_a_capture_rate_has_a_small_recorded_floor`
Equaliser noise bias	factor √(1 − 1/L), L = complete symbols in the capture	`test_white_noise_of_known_power_gives_the_predicted_evm`
Frequency offset residual	estimate within 0.01 Hz of an injected static offset; drift not tracked	`test_frequency_offset_and_phase_are_estimated_and_removed`
Timing	integer sample; sub-sample delay absorbed by the equaliser as linear phase	`test_timing_offset_and_looped_playback_are_recovered`, `test_linear_channel_inside_the_cyclic_prefix_is_equalised_exactly`
ACLR PSD estimate	Welch with the dataset's `nperseg`; bias of a tone of known power below 0.05 dB (as for `general-spectral-v1`)	`tests/unit/test_metrics_general.py` conventions

Comparison targets against the cross-validation backend (plan S15, fixed before any model comparison, never relaxed afterwards): adjacent-channel ratio within 0.1 dB, RMS EVM within 0.05 percentage points on the same digital reference signal. Values below the measurement floor are reported with the floor stated, not scored.

6. Cross-validation protocol (maintainer step; MATLAB not required for users)¶

Generate a package (--seed 1 --subframes 10) and, in MATLAB LTE Toolbox, build the same resource grid from symbols.npy and modulate it (lteOFDMModulate with a 20 MHz, normal-CP configuration); the time-domain signals must agree to numerical precision after scaling.
Pass the same distorted signals through both chains: the package played through a PA capture (or the synthetic PA of tests/fixtures/synthetic.py), scored here and by the toolbox's EVM/ACLR functions with their default procedure; record both numbers, the differences and the toolbox version.
Record the outcome in this document (§7), set validation = cross_validated in opendpd/core/metrics/ofdm_evm_v1.py (protected path, science review) and fix the standard versions cited above.

Users never need MATLAB: the reference vectors and the evaluation run in Python; MATLAB is the independent backend that checks them.

7. Validation record¶

Date	Backend and version	Signals	ACLR difference	EVM difference	Outcome
2026-10-08	MATLAB R2026a Update 5 on Linux; LTE Toolbox, Communications Toolbox and Signal Processing Toolbox 26.1	`ofdm-lte20-v1` waveform, synthetic memory-polynomial PA at four drive levels (1 % to 11 % EVM), a gain/delay/noise variant and a 245.76 MS/s variant (S0 to S9, plus S6b and S9b at +30 Hz)	7 of 84 scored values against `comm.ACPR` are outside the 0.1 dB budget, at most 0.21 dB, all on the two lowest-distortion signals	at most 2.1·10⁻⁹ percentage points from an independent MathWorks-blocks chain on the ten evaluable signals (budget 0.05)	not passed as registered: 102 of 115 scored items within budget, 7 outside, 6 not evaluable (the +350 Hz signals, which both tools refuse)

The outcome above is the record of the registered cross-validation, not an approval: the ACLR differences come from how the two tools integrate a band whose edge is not a bin centre (a pwelch PSD integrated with comm.ACPR's rule reproduces comm.ACPR to 2.5·10⁻⁴ dB), and the EVM chain, the waveform (lteOFDMModulate, 2.9·10⁻⁸ relative RMS) and the Welch estimator agree. validation in opendpd/core/metrics/ofdm_evm_v1.py is therefore not changed by this record. Whether to keep the band rule and document the expected difference (up to 0.2 dB at 60 kHz resolution and coarser), to state the carrier-offset capture range (the timing peak falls below the 0.3 rule at about 75 Hz for a 10 ms waveform) and the waveform's own ACLR floor (about -42 dBc), is a decision for the maintainers. Rules, signals, budgets, every number and the diagnostics: OpenDPD ↔ MATLAB parity.

8. Effect on existing results¶

Nothing changes for legacy-opendpd-v1 (frozen) or general-spectral-v1: the new profile is an additional file under runs/<id>/results/ and reports explicit statuses on every existing dataset (tests/unit/test_metrics_ofdm_evm.py).

Versioned follow-up (2026-10-11)¶

The v1 record above remains a failed-as-registered comparison, and ofdm-lte20-evm-v1 remains pending_cross_validation. The separately registered v2 profiles distinguish the two PSD configurations and add frequency-tolerant acquisition. Both real v2 runs passed all 115 scored items at the original tolerances and signal hashes; see the complete evidence. This does not promote v1 or alter the legacy/general/carrier profiles, and is not a 3GPP conformance claim.

Waveform evaluation profiles (plan S15) — ofdm-lte20-v1 and ofdm-lte20-evm-v1¶