Modulated Transmitter & Receiver Measurements

01 / 10

Two EVM numbers may measure different things

Lab A reports 6.98% EVM. Lab B reports zero. Which instrument is wrong?

Start with the fictional 2.450 GHz condition-monitoring node. Its transmitter has a known 4° common rotation in an exact four-symbol example. Lab A compares the observed symbols directly with the transmitted reference. Lab B removes that rotation first. Both calculations are correct; the word “EVM” did not capture their different measurands.

Think about itDoes removing the rotation prove that the transmitter has no phase error?

Answer

No. It demonstrates that this specified correction removes a common rotation. It does not establish a raw phase requirement, residual hardware floor or the performance of a synchronization estimator.

\begin{aligned}e &= \sqrt{\frac{\sum |\hat{S}_{k} - S_{k}|^{2}}{\sum |S_{k}|^{2}}} \\ \mathrm{EVM}\% &= 100e \qquad \mathrm{EVMdB} = 20 \log _{10}(e)\end{aligned}

EVM is a dimensionless RMS ratio at R3, the detected-symbol boundary. S is the reference and Ŝ the aligned observation. The denominator is total reference energy, not received energy or an average of pointwise percentages. Here N=4 and Σ|S|²=4.

Two reference contracts · identical raw observation
Processing	RMS EVM	What the number answers
Raw: Ŝ = S exp(j4°)	6.9798993405%	Error relative to the fixed reference, including common rotation.
Exactly known phase removed	0% · −∞ dB exact limit	Residual after fixture-truth correction; no estimator or hardware noise.

Instrument methods can use different reference normalizations and processing. Record them before comparing a percentage. [EVM-DEF] This module extends measurement definitions and uncertainty, lab integrity, spectral estimators and qualified RF planes. Every numerical fixture here is Illustrative / Derived, frozen on 2026-09-09; none is a hardware capture or a wireless qualification limit.

Common misconceptionLower EVM always means a better transmitter.

A more permissive reference receiver can remove more of the impairment. Keep the raw record and ask whether the selected processing answers the declared requirement.

Engineering decision → record update

Create TX record M08-05-TX-C and RX record M08-05-RX-C. Open three competing explanations: DUT change, reference-processing change and setup contamination. Preserve raw observations before applying any correction.

02 / 10

Freeze the waveform and test population

What must match before two waveform files represent the same experiment?

A modulation name is too small a definition. Keep the bits, mapping, pulse shape, sample rate, scaling, selected population and burst timing together. The inherited Path 02.7 baseline is generic QPSK; the short R3 vector witness and the local framed RX count contract are explicitly different variants.

Inherited baseline · WAVE-P02-QPSK-v1, unimpeded D3 reference
Identity item	Frozen definition
Carrier / rate	2.450 GHz; 10 ksymbol/s; 8 samples/symbol = 80 ksample/s; 256 symbols.
Bits / reset	PRBS-9, seed 0x1FF, output LSB; feedback bit0 XOR bit4, shift right into bit8. b[k+9]=b[k+4] XOR b[k]. Reset once per 512-bit record.
First 32 bits	11111111100000111101111100010111
Gray mapping / scaling	00→(+1,+1), 01→(−1,+1), 11→(−1,−1), 10→(+1,−1), each divided by √2. Unit symbol energy; complex baseband, e^(+jωt).
Pulse / transient removal	RRC α=0.35; span 8 symbols; 65 unit-energy taps; 32-sample group delay per filter. Frozen no-echo D3 crop [128,1984): 1856 samples; selected symbol centers 12…243, 232 symbols.
Finite D3 power / PAPR	Mean \|x\|²=0.125112532483; peak=0.299125509866; PAPR=3.785526369 dB on that crop. Neither is dBm until a physical voltage/power scaling is calibrated.

\mathrm{PAPR}=10\log_{10}\left(\frac{\max|x_n|^2}{\operatorname{mean}|x_n|^2}\right)

Mean and maximum refer to the same declared sample gate. Samples are complex envelope amplitudes; the normalization must be calibrated before mapping to watts at a real 50 Ω RF port. Finite sampled PAPR is not an intersample peak guarantee.

Think about itCan you add a header and CRC, then reuse the baseline PAPR unchanged?

Answer

No. The new sequence, boundary transitions and gate can change the envelope. Name a new variant and calculate or measure its statistics; retain an unknown if they have not been supplied.

A separate, explicit receiver population

WAVE-RX-COUNT-C/1.0: local synthetic frame, 280 Gray-QPSK symbols at 10 ksymbol/s; 8 alternating 00/11 preamble symbols, 8 header symbols (16-bit trial ID modulo 65536, MSB first), 256 PRBS-9 body symbols, 8 CRC symbols. CRC-16 polynomial 0x1021, initial 0xFFFF, no reflection/xor-out, covers header then body bits MSB first. Unit symbol energy; TX/RX 65-tap unit-energy RRC, α=.35, 8 sps; 2.450 GHz. 28 ms symbol allocation + .8 ms TX filter tail; 11.2 ms response/guard/settle budget. Minimum cycle 40 ms. This frame is specified, not synthesized or a standard packet; its PAPR and hardware scaling remain unknown.

Each externally scheduled frame is one attempt, even if no packet is detected. Accept exactly one complete frame with expected ID, matching body and correct CRC before the 10 ms post-waveform timeout. Any CRC/header/payload failure, loss or timeout counts as one error, never several. Duplicates do not add successes or attempts. Retries are disabled. Trial ID wrap is disambiguated by the external acquisition sequence. Fixed n is declared in advance. One failed frame is not a count of bad bits.

The four-symbol EVM fixture uses S = [1, j, −1, −j] at R3 with no pulse shaping or timing transient. The RX frame is specified for reproducible synthetic count interpretation, but its packet synthesizer is not implemented. Its count table is supplied evidence, not a Monte Carlo demodulation result.

Common misconceptionA thousand received packets means a thousand trials.

A receiver that fails to detect a frame must not erase that attempt. Use the external schedule as the denominator and include timeouts; a packet error count cannot be converted into a bit error count without bit-level observations.

Engineering decision → record update

Attach waveform ID, bit seed, mapping, filter, record boundaries, physical scaling, gate, CRC definition, retries and timeout to the method. Mark the framed variant’s unsupplied PAPR unknown.

03 / 10

Characterize the source and level path

Is the receiver seeing −110 dBm, or is that merely a generator setting?

The wanted source’s M-W setting is upstream of 65 dB branch attenuation and 5 dB combiner/common-path loss. The DUT’s conducted input is R1-RX. R2 is the antenna feed; S0 is the spatial OTA boundary. R3 is after detection and is never an RF power-input plane.

P(R_{1}-\mathrm{RX}) = -40 - 65 - 5 = -110 \mathrm{dBm}

Positive losses are measured along the wanted forward path, once each. Scalar power subtraction assumes a calibrated operating configuration; mismatches, drift and interactions belong in the uncertainty and validity evidence.

p08-m05-level-ledger-v1. Every forward loss is counted once. The blocker path entry includes its common-path loss; the reverse M-B→M-W isolation is a separate end-to-end characterization.

Think about itCan the same generator residual be assigned to every TX measurement?

Answer

No. A standalone transmitter generates its own modulation; an external wanted generator is absent. A source-driven PA includes the stimulus generator. A loopback includes both sides and the intervening path, so it cannot isolate a DUT mechanism by itself.

Source-quality and level evidence before acquisition
Topology / check	Required evidence	Failure consequence
Standalone TX	DUT waveform and output; analyzer residual at actual input level; pads/cable calibration.	Do not add a nonexistent external generator term.
Source-driven PA / loopback	Stimulus EVM/noise/spurs under actual level and crest factor; DUT operating state; analyzer residual.	Source and DUT errors may interact; do not assume independent floors.
Receiver wanted path	Calibrate at R1-RX, actual branch terminations, gain/AGC state and power statistic; inspect source noise and leakage.	Set-point arithmetic alone does not establish the available signal.
Protection and headroom	Conditional DC, peak, average and frequency ratings; source off for connections; verify total power, attenuation and overload indicators.	Acquisition validity precedes any statistical claim. Unknown ratings remain unknown.

Common misconceptionA cleaner-looking trace proves the source is negligible.

A source can be quiet near its carrier yet inject broadband noise in the wanted channel. Characterize the quantity and offset range that can affect this receiver.

Engineering decision → record update

Record calibration date/state, source and analyzer serial/firmware, forward losses, total and peak levels, instrument residuals and separate reverse isolation. Reuse the lab connection and abort plan, with this waveform’s envelope conditions.

04 / 10

Make synchronization and equalization part of the method

Which part of the error does the reference receiver permit itself to remove?

Synchronization is part of measurement processing. A frequency estimate can remove a phase ramp; a common phase correction removes one rotation; timing acquisition chooses sample instants. Equalization can compensate a channel or transmitter response, so its allowed degrees of freedom determine what remains visible.

Processing contract · record both permission and fitted value
Operation	Definition to freeze	What can disappear
Sample / symbol timing	Clock ratio; timing estimator, interpolation, lock criteria, reference delay and analysis crop.	Timing offset or part of pulse-shape distortion.
Carrier / common phase	Frequency search/estimate; pilot/data population; constant phase versus per-symbol tracking.	Carrier offset, static rotation or tracked phase variation.
Gain / DC / IQ	Fixed scaling versus fitted gain; DC removal; IQ correction; training/reference population.	Amplitude error, carrier leakage or IQ imbalance.
Equalizer	Off or tap count, span, training, update rate, constraints and transient exclusion.	Frequency-selective channel and some DUT linear distortion.
Decisions / reference	Known transmitted symbols versus detected decisions; errors included or excluded.	Wrong decisions can bias a decision-directed reference.

\begin{aligned}e_{\mathrm{phase}}&=|e^{j\phi}-1|=2|\sin(\phi/2)|\\\phi&=4^\circ\quad\Rightarrow\quad6.979899340500\,\%\end{aligned}

For an exactly known common φ and unit-energy S, the raw error is the chord between S and S exp(jφ). At φ=4°, this gives the pinned result. Multiplication by exp(−jφ) is truth-based phase removal, not an adaptive equalizer.

p08-m05-evm-reference-v1. Four algebraic points at R3; not a synthesized RF constellation or measured instrument capture. Lines represent vector differences; axis scale is fixed.

Phase witness · complete raw R3 population
k	S	Ŝ = S exp(j4°)
1	1 + j0	0.99756405 + j0.069756474
2	0 + j1	-0.069756474 + j0.99756405
3	-1 + j0	-0.99756405 − j0.069756474
4	0 − j1	0.069756474 − j0.99756405

Think about itIf a raw-EVM limit is 5%, does the corrected zero close it?

Answer

No. Raw 6.979899340500% exceeds this exact local threshold. Corrected zero answers REQ-EVM-PHASE-C instead. The planner marks a selected/required processing mismatch unresolved.

Common misconceptionAutomatic synchronization settings need not be recorded.

Automatic choices can change the reference fit, capture acceptance and reported population. Export the applied values and preserve the rejected captures as well as accepted ones.

Engineering decision → record update

Freeze REQ-EVM-RAW-C or REQ-EVM-PHASE-C before reading the answer. Both use a local 5% teaching criterion with different processing; neither imports a wireless-standard limit.

05 / 10

Read EVM together with error structure and floor

How much of 3.74% measured EVM belongs to the DUT?

An RMS value compresses the error structure. Plot error against symbol, time, frequency and amplitude before assigning causes. Static IQ imbalance can produce structured constellation distortion; compression can make error amplitude dependent; phase noise and clock error can vary with time. These are diagnostic hypotheses, not unique signatures. Measurement residuals can limit what is observable. [EVM-FLOOR]

\begin{aligned}\Vert d+s+a\Vert ^{2} &= \Vert d\Vert ^{2} + \Vert s\Vert ^{2} + \Vert a\Vert ^{2} \\ &+ 2 \operatorname{Re}(\langle d,s\rangle + \langle d,a\rangle + \langle s,a\rangle)\end{aligned}

Error vectors d, s and a are DUT, external-source and analyzer contributions, normalized by the same reference energy. The real cross terms are not generally zero. The source term is absent for standalone TX.

Use vD = [1, −j, −1, j], vS = [1, 1, 1, 1] and vA = [1, −1, 1, −1]. Each has energy 4; every pairwise inner product is zero. With d=0.03vD, s=0.01vS and a=0.02vA, finite-vector quadrature is exact. That algebra does not establish random independence in a real bench.

Residual witnesses · same nominal component magnitudes
Fixture	Observed / setup	Conditional DUT interpretation
Orthogonal source-driven	3.741657386774% / 2.2360679775%	3% recovered; all cross terms zero.
Collinear: all along vD	6% / nominal quadrature 2.2360679775%	Subtraction invalid. Naive quadrature gives 5.56776436283%, not 3%.
Standalone: d + a	3.605551275464% / 2%	No external source contribution; separate analyzer characterization still required.
Exact reference equals observation	0% / no error	−∞ dB semantic limit; do not replace zero with an arbitrary numerical epsilon.

Think about itCould correlated errors cancel and make a faulty DUT look better?

Answer

Yes. Opposite vectors can reduce the observed norm. Neither a small total nor a quadrature subtraction identifies the individual contribution without a justified relationship.

\begin{aligned}c_{\mathrm{obs}}&=\frac{e_{\mathrm{obs}}}{e_D},\quad c_{\mathrm{setup}}=-\frac{e_{\mathrm{setup}}}{e_D}\\e_{\mathrm{obs}}&\le e_{\mathrm{setup}}\Rightarrow\text{subtraction unresolved}\end{aligned}

Only with compatible zero-cross-term evidence: eD=√(eobs²−esetup²). First-order propagation includes covariance: uD² = cobs²uobs² + csetup²usetup² + 2 cobs csetup cov(obs,setup). The planner's supplied-uncertainty branch assumes that covariance is zero, explicitly.

At the subtraction boundary the sensitivity coefficients diverge. A negative radicand is evidence of an unresolved model/floor relationship, not a zero DUT. Near the boundary, the planner withholds a first-order interval if the separate ±2u ranges meet it. Obtain joint uncertainty evidence or reduce the setup residual. The GUM treatment includes covariance; the 2026 amendment emphasizes adequate treatment of significant nonlinearity. [GUM] [GUM-AMD]

Common misconceptionSubtract the generator EVM from a measured PER curve.

PER is a counted outcome of a receiver and waveform. It has no general EVM-subtraction rule. Improve or independently characterize the source, then acquire comparable counts.

Engineering decision → record update

Keep residual-floor adequacy, correlation evidence, numerical EVM and uncertainty as separate fields. Exact fixture arithmetic is eligible only as illustrative algebra; unknown physical uncertainty leaves a DUT decision open.

06 / 10

Keep spectral metrics and gates consistent

Can the transmitter meet an EVM target while putting too much energy into the next channel?

EVM uses a defined symbol reference. Spectral metrics integrate power over frequency and time. They answer complementary questions: a good in-band fit does not bound adjacent emissions, and a clean-looking average spectrum can hide a burst edge. Reuse the estimator, linear-power integration and capture validity rules from Module 08.3.

\begin{aligned}P_{\mathrm{channel}}&=\int G(f)\,\mathrm df\\P_{\mathrm{adj/main}}&=10\log_{10}\left(\frac{P_{\mathrm{adj}}}{P_{\mathrm{main}}}\right)\end{aligned}

Integrate PSD in W/Hz over explicit boundaries, then take a logarithm. This lesson defines adjacent/main as negative dBc; an instrument's positive ACLR convention may use the reciprocal. Identify the convention before comparing.

Inherited channel-PSD witness · complete ±30 kHz span
Band / estimator	Pinned value	Definition
Main −10…+10 kHz	-36.98970004336 dBm	−80 dBm/Hz ×20 kHz; linear rectangular integration.
Lower −30…−10 / upper +10…+30 kHz	-66.98970004336 dBm each; −30 dBc each	−110 dBm/Hz ×20 kHz; same statistic and gate.
99% occupied bandwidth	19839.6 Hz	Equal-tail cumulative-power boundaries 0.5% and 99.5% of complete supplied spectrum.
Missing outer span	OBW and adjacent ratio unavailable	Do not silently normalize only the visible portion.
Flat burst variant, on-time gate	+20 dBm on; 10% duty; +10 dBm period average	Zero off-power, no ramps in this ideal calculation.

Think about itShould a 10% duty cycle reduce on-burst power by 10 dB?

Answer

No. It reduces full-period average power in this flat, zero-off-power model. The on-time gate still measures +20 dBm. Ramps, leakage and a different gate change the actual integrated energy.

For a physical TX method retain channel center and bandwidth, RBW/ENBW, detector, averaging domain, window, record length, reference level, attenuation, overload checks, trigger and exact gate. For bursts add turn-on/off behavior, settling exclusions and missed-event/dead-time evidence. Spectral-mask limits need the actual applicable test definition; none is synthesized here.

Common misconceptionA narrow RBW makes adjacent-channel power more accurate automatically.

RBW changes selectivity and collected noise. The final quantity still requires consistent integration, a valid capture, known residuals and the method’s bandwidth convention.

Engineering decision → record update

Attach power, adjacent-channel, OBW and burst-time results to their own estimators and gates. Preserve raw IQ plus the unnormalized spectrum; do not reuse an EVM crop as a spectral gate without declaring it.

07 / 10

Sensitivity is a curve with a counting rule

How much confidence does an error-free minute buy?

“Zero errors” reports what happened in a finite population. Under a fixed-n IID binomial model, inversion of the binomial tail gives an upper bound on the unknown error probability. Correlated packets, a drifting channel or stopping when the result first looks favorable do not inherit that coverage. [STAT-EXACT]

\begin{aligned}p_U(k=0)&=1-\alpha^{1/n}\\n_{\mathrm{zero}}&=\left\lceil\frac{\log\alpha}{\log(1-p_0)}\right\rceil\end{aligned}

C=1−α. For 0≤k<n, pU=BetaInv(1−α;k+1,n−k); k=n gives pU=1. For k=0 use the stable closed form −expm1(log(α)/n). Equal-tail two-sided endpoints allocate α/2 to each tail instead.

Fixed-n confidence witnesses · one-sided 95%
Record / plan	Upper probability	Decision
0 / 1000	0.002991249545095 = 0.299124954510%	Supports 1%; does not support 0.1%.
5 / 1000	0.010484076911416 = 1.048407691142%	Observed 0.5% is below 1%; statistical target still inconclusive.
0 / 2995	0.000999744420901 = 0.099974442090%	Supports 0.1%, conditional on the planned zero-error outcome.
Zero-error target 1%	299 required attempts	Check n−1 and n; do not round a fractional trial count down.

Think about itCan you run 1000 trials, add more only after seeing zero errors, and call the result the same fixed plan?

Answer

No. The stopping/extension rule uses the observed outcome. Predeclare the new experiment or use a justified sequential procedure. This planner implements fixed-n intervals only.

p08-m05-rx-counts-v1. Pointwise intervals; 1 dB grid, no continuous sensitivity estimate. Enlarged circle marks the selected point. Ineligible metadata suppresses the confidence markers, while supplied counts remain visible.

RX-CURVE-C · one-sided 95% at each point
R1-RX wanted	Errors / attempts	Observed PER	Eligible upper bound	Local target decision
-112 dBm	180 / 1000	18%	20.117565801%	Above-target evidence
-111 dBm	35 / 1000	3.5%	4.613833609%	Above-target evidence
-110 dBm	5 / 1000	0.5%	1.048407691%	Inconclusive at this count
-109 dBm	0 / 1000	0%	0.299124955%	Upper target supported
-108 dBm	0 / 1000	0%	0.299124955%	Upper target supported

The first supported supplied point is −109 dBm. Keep the 1 dB grid and separately chosen illustrative level uncertainty ±0.4 dB, k=2. Searching five points does not create a simultaneous 95% threshold statement. No continuous fit or interpolation is implemented.

\begin{aligned}T &= n \Delta t + T_{\mathrm{fixed}} \\ 1000 \times 100 \mathrm{ms} &= 100 s \qquad 2995 \times 100 \mathrm{ms} = 299.5 s \\ 5 \times 1000 \times 100 \mathrm{ms} &= 500 s\end{aligned}

Trial duration includes the scheduled waveform/response cycle; fixed overhead is added once per level. The 100 ms default exceeds this frame's 40 ms minimum. These are planning times, not actual capture timestamps.

Lesson workbench · illustrative / derived

TX/RX Test & Confidence Planner

tx-rx-test-confidence-planner/2.0. One bounded planner for finite error vectors, fixed-n counts and a calibrated level ledger. No instrument connection, storage or generated hardware result.

JavaScript is off. The committed default below and all seven worked cases in the lesson remain readable. Custom controls require JavaScript; native evidence and checkpoint disclosures still open.[data-planner] form,[data-planner] [data-cursor]{display:none}

Load a complete presetLoading a preset atomically replaces all inputs and evidence assumptions.

InvestigationClosed choices. Reset default: PER / BER confidence.

Population, confidence and acquisition time

Trial populationClosed choices. Reset default: Packets · local framed variant.

Error counting ruleClosed choices. Reset default: CRC, payload, ID or timeout error.

Attempt count ninteger trials · 10…10000000 · step 1. Reset default: 1000.

Error count kinteger errors · 0…10000000 · step 1. Reset default: 0.

Confidence levelClosed choices. Reset default: 95%.

Interval displayClosed choices. Reset default: One-sided upper.

Upper error-probability targetfraction (1 = 100%) · 0.000001…0.2 · step 0.000001. Reset default: 0.01.

Trial intervalms · 1…1000 · step 1. Reset default: 100.

Fixed overhead per levels · 0…600 · step 1. Reset default: 0.

Calibrated level expanded uncertaintydB, illustrative k = 2 · 0…5 · step 0.1. Reset default: 0.4.

Independence and stationarityClosed choices. Reset default: IID / stationary synthetic trials.

Stopping ruleClosed choices. Reset default: Fixed n declared before acquisition.

RX-CURVE-C retains its supplied 1000 packet attempts at each of five levels. A custom bit record samples one prespecified payload bit per scheduled frame; each timeout counts as an error. It is a separate trial population, not a conversion of PER. Trial minimum is 40 ms for this local frame contract.

Eligibility before numerical inference

Waveform compatibilityClosed choices. Reset default: Complete synthetic waveform identity.

Reference receiver compatibilityClosed choices. Reset default: Compatible synthetic reference processing.

Plane and calibration compatibilityClosed choices. Reset default: Compatible calibrated synthetic plane.

Acquisition validityClosed choices. Reset default: Synthetic acquisition conditions verified.

Default synthetic record committed.

Inspect supplied curve point-110 dBm · 5/1000 packet errors. Use arrow keys; cursor does not alter counts or decisions.

Committed result · PER confidence

What does this count support?

Upper target supported

0/1000 packets errors is descriptive. The decision uses the 95% one-sided upper bound; a separately labelled one-sided lower bound can support above-target evidence.

The declared synthetic compatibility and acquisition gates are complete. This is conditional model evidence; real hardware verification remains unknown.

Observed PER: 0%
Eligible one-sided 95% upper: 0.299124955%

Selected interval display · one-sided bounds, each separately at 95%
Endpoint / meaning	Eligible probability
Separate one-sided lower bound (not a joint interval)	0%
One-sided upper bound	0.299124955%
Target / observed description	1%; observed proportion at or below target

Changing the interval display does not replace the declared one-sided decision rule. These fixed-n bounds describe repeated-procedure coverage under IID assumptions, not the posterior probability of the unknown error rate.

Plan before the next acquisition · zero-error condition
Plan quantity	Value / condition
Total trials required if zero errors	299 packets
Conditional bound at that count	0.996914679%
Time for current record	100 s; 100 ms/trial; 0 s overhead per level
Time for planned zero-error record	29.9 s
Eligibility of the plan	Conditional IID fixed-n planning only; zero errors are not guaranteed.

RX-CURVE-C · one-sided 95% at each point
R1-RX wanted	Errors / attempts	Observed PER	Eligible upper bound	Local target decision
-112 dBm	180 / 1000	18%	20.117565801%	Above-target evidence
-111 dBm	35 / 1000	3.5%	4.613833609%	Above-target evidence
-110 dBm	5 / 1000	0.5%	1.048407691%	Inconclusive at this count
-109 dBm	0 / 1000	0%	0.299124955%	Upper target supported
-108 dBm	0 / 1000	0%	0.299124955%	Upper target supported

Curve counts always use packets, n = 1000 per point. Calibrated level uncertainty is a separately chosen illustrative ±0.4 dB expanded interval at k = 2. There is no interpolated threshold, simultaneous confidence guarantee, or level uncertainty inside the binomial interval.

Current derived measurement record · full snapshot

p08-measurement-record-v1 · tx-rx-test-confidence-planner/2.0. Earlier raw fixture IDs remain immutable. This complete local snapshot needs no previous visit.

Current derived method and decision
Record field	Committed value
id	M08-05-CURRENT-DERIVED
parentIds	M08-05-RX-C · p08-m05-rx-counts-v1 · p08-m05-level-ledger-v1
owner	08.5 · fictional radio verification engineer
question	Which supplied sensitivity grid point supports the packet target, and can a blocker test isolate DUT behavior?
hypotheses	H-DUT: waveform distortion; H-REF: reference processing mismatch; H-SETUP: residual, level or clock contamination.
requirement	Error target 1%; population packets; packet-errors.
decisionRule	p08-m05-decision-rules/1.0: one-sided pU≤.01 (inclusive), pointwise only; choose the first supported supplied grid point. Setup/compatibility precedes this conditional screen. No interpolation or sequential stopping.
specimen	SYN-GATEWAY-C / p08-m05-rx-counts-v1; supplied counts RX-CURVE-C, not a channel simulation or hardware acquisition.
configuration	PER confidence; local hypothetical edits of retained fixtures. No new measured raw data.
state	Method plan: 3.300 V supply, 298.15 K steady state, fixed bench board, antenna removed, cable strain relieved. Real state evidence unknown.
timestamp	Synthetic configuration frozen 2026-09-09T10:00:00Z. No real acquisition timestamp.
environment	Illustrative 25 °C indoor screened bench; humidity and actual ambient coupling unknown.
stimulus	WAVE-RX-COUNT-C/1.0: local synthetic frame, 280 Gray-QPSK symbols at 10 ksymbol/s; 8 alternating 00/11 preamble symbols, 8 header symbols (16-bit trial ID modulo 65536, MSB first), 256 PRBS-9 body symbols, 8 CRC symbols. CRC-16 polynomial 0x1021, initial 0xFFFF, no reflection/xor-out, covers header then body bits MSB first. Unit symbol energy; TX/RX 65-tap unit-energy RRC, α=.35, 8 sps; 2.450 GHz. 28 ms symbol allocation + .8 ms TX filter tail; 11.2 ms response/guard/settle budget. Minimum cycle 40 ms. This frame is specified, not synthesized or a standard packet; its PAPR and hardware scaling remain unknown.
statistic	packets; packet-errors; 0/1000; fixed-n stopping fixed; IID evidence declared.
population	1000 independent identically distributed packet attempts per level within one frozen configuration. Five prescribed levels −112…−108 dB m in 1 dB steps. No pooling of levels. BER unavailable from these counts.
acquisition	Trial interval 100ms; per-level overhead0s; 100s. Acquisition evidence verified.
planes	M-W wanted source; M-B blocker source; combiner branches → R1-RX component RF input, real 50 Ω. R3 is decoded packet/bit decision boundary. Conducted only; no S0 inference.
chain	M-W-40dB m−65dB−5dB=-110dB m R1-RX; M-B-10dB m−5dB=-15dB m R1-RX; reverse-70dB m M-W.
instrument	SYN-VSG-W / SIM-W005, SYN-VSG-B / SIM-B005, firmware SIM-1; SYN-COMB-C; receiver counter SIM-R3. Source quality, reverse behavior and actual safety ratings are unknown outside these synthetic entries.
settings	Generic framed QPSK 2.450 GHz, RRC reference frozen; blocker CW 2.460 GHz for local ledger. RX matched filtering/timing acquisition and gain state recorded; no post-count reference fit. Source noise density −160 dB m/Hz already at R1-RX over 20 kHz ENBW in a separate noise fixture.
calibration	Waveform complete; reference complete; plane complete. Illustrative expanded levelU=0.4dB,k = 2; actual calibration evidence unknown.
rawEvidence	SYN-RX-C-COUNTS-001: k=[180,35,5,0,0],n=1000 at[−112,−111,−110,−109,−108]dB m. Separate SYN-BLOCK-PAIR-C-001 at−109 dB m: quiet 0/1000, blocker-on 35/1000 with−15 dB m blocker. Pair is supplied illustrative data; ledger changes do not synthesize new counts.
processing	tx-rx-test-confidence-planner/2.0; p08-m05-decision-rules/1.0; one display at95%; decision uses separately labelled one-sided bounds.
uncertainty	95% fixed-n confidence only if eligible; independent level uncertainty remains separate.
result	Upper target supported; observed 0%; eligible one-sided upper 0.299124955%.
inference	Upper target supported. Synthetic/model scope only; see every eligibility reason.
unresolved	Actual hardware acquisition, independent review and complete physical uncertainty remain unknown.
next	Counterfactual: add characterized isolation, recalibrate both forward paths to hold wanted/blocker levels fixed, and repeat the quiet/blocked count pair. If the error excess persists within declared uncertainty/confidence, reverse source coupling alone is falsified. Preserve both raw versions.
review	08.5 verification owner: recheck after waveform/firmware/cable/clock/level/gate/equalizer or thermal change; send immutable records to 08.6.

Go deeperA guided sequence through the seven presets

Start at PER confidence. Change the target from 0.01 to 0.001; inspect the stale banner before applying. Then set n=2995, k=0 and compare the bound and acquisition time.
Load RX-CURVE-C. Use the keyboard slider to inspect 5/1000 at −110 dBm and 0/1000 at −109 dBm. The supplied counts stay fixed.
Load Phase-only EVM. Select known phase removal, apply and observe the processing mismatch; then select the corrected requirement explicitly.
Compare Orthogonal error chain with Collinear error chain. A reported total remains visible when residual subtraction is unjustified.
Compare RX-LEVEL-C with Improved isolation. Reverse incidence improves, but source-noise and missing-count flags remain. Change an eligibility field to unknown to see which inference is withheld.

Common misconceptionA confidence bound is the probability that this DUT meets its limit.

Coverage describes the repeated sampling procedure under the model. It is not a posterior probability, a calibration uncertainty interval or a guarantee for future changing conditions.

Engineering decision → record update

Save n, k, confidence, sidedness, target, fixed stopping rule, trial definition and timing with each level. Preserve observed proportions when eligibility fails, but withhold confidence claims.

08 / 10

Build wanted-plus-blocker tests with isolation

When a blocker raises PER, did it disturb the receiver or the wanted generator?

A combiner joins forward paths and can couple sources in reverse. In RX-LEVEL-C the blocker is −10 dBm at M-B. With 60 dB end-to-end reverse isolation, −70 dBm reaches M-W. That is 10 dB above the supplied local −80 dBm source-interference ceiling. This ceiling is an illustrative interference criterion, not a connector damage rating.

Calibrated forward and reverse ledger · synthetic
Path / statistic	Calculation and level	Evidence consequence
Wanted at R1-RX	-40 − 65 − 5 = -110 dBm	Nominal path; mismatch/calibration verification required.
Blocker at R1-RX	-10 − 5 = -15 dBm	Complete forward path includes combiner/common loss.
Reverse at M-W	-10 − 60 = -70 dBm	-10 dB margin to local −80 dBm interference ceiling; not a damage rating.
Blocker-source noise, separate fixture	-116.98970004336 dBm; 4.771212547197 dB rise	−160 dBm/Hz at R1-RX ×20 kHz ENBW; independent baseline −120 dBm. Not a PER shift.
Two distinct CW blockers, separate fixture	−40 dBm each → -36.98970004336 dBm total	Linear average powers add; per-tone IP3 and coherent peak are different.
RX-WEAK-B coherent bypass	−40 −70 = −110 dBm intended; −40 −90 = −130 dBm bypass	Relative received-power error -0.915149811214…+0.827853703165 dB; phase dependent, not AWGN.

\begin{aligned}N_{\mathrm{source}} &= -160 + 10 \log _{10}(20000) = -116.989700043360 \mathrm{dBm} \\ \Delta N &= 10 \log _{10}(\frac{N_{\mathrm{source}} + N_{\mathrm{baseline}}}{N_{\mathrm{baseline}}}) = 4.771212547197 \mathrm{dB}\end{aligned}

The source noise density is already referred to R1-RX; do not subtract forward loss again. Add its integrated noise to the independent −120 dBm baseline in linear watts. This predicts a noise-power ratio, not an error-rate threshold shift.

Think about itDoes increasing reverse isolation to 80 dB remove every blocker-induced artifact?

Answer

No. Reverse incidence becomes −90 dBm, giving 10 dB margin, but the blocker source can still put noise or spurs directly in the wanted band. A physical isolation change also needs new forward-path calibration.

Two distinct CW blockers at −40 dBm each have −36.989700043360 dBm total average power. Receiver intermodulation depends on per-tone levels, frequencies, operating state and products such as 2f₁−f₂; total power is also needed for headroom. Verify source/combiner-generated products before attributing them to the DUT.

The inherited RX-WEAK-B bypass has −110 dBm intended and −130 dBm coherent leakage, an amplitude ratio of 0.1. Their relative power error ranges from 20log₁₀(0.9)=−0.915149811214 dB to 20log₁₀(1.1)=+0.827853703165 dB. Phase determines the sign. Treating this coherent path as independent noise loses the cancellation mechanism.

Separate supplied blocked comparison · RX-BLOCK-PAIR-C
Condition	Same frozen population	What remains unresolved
Wanted −109 dBm; blocker off	0/1000; upper 0.299124954510%	Different wanted state from RX-LEVEL-C’s −110 dBm.
Wanted −109 dBm; blocker −15 dBm	35/1000; upper 4.613833609365%	Source coupling and noise remain competing causes.
Edited planner level ledger	New paired counts unknown	No fabricated desense or blocking result follows a slider edit.

Common misconceptionA 4.77 dB noise rise is a measured 4.77 dB sensitivity loss.

The receiver’s error curve depends on waveform, processing and operating state. Acquire comparable quiet/blocked threshold curves; propagate shared calibration covariance when comparing their level difference.

Engineering decision → record update

Falsifier: add characterized isolation, recalibrate wanted and blocker levels at R1-RX, hold all other conditions fixed, and repeat the count pair. If the error excess persists within the declared evidence limits, reverse coupling alone cannot explain it.

09 / 10

Declare the channel and conducted/OTA boundary

Which channel did your conducted sensitivity result actually sample?

A cable experiment bounds the receiver at its RF input. A fading test adds a time-varying channel population. OTA includes the antenna and spatial environment. Each additional boundary requires its own reference definition; a conducted result cannot silently become a field-performance claim.

Channel and boundary contract
Method	Minimum declaration	Meaning of repeated trials
Conducted baseline	R1-RX level, source quality, reference filtering, calibrated cable/combiner path.	Fixed waveform and state; IID is an explicit model assumption.
AWGN variant	Noise density plane, bandwidth/ENBW, injection location, seed and reference SNR definition.	Independent draws only if generation and observation support that model.
Fading / multipath	Tap delays/powers/phases, Doppler/speed, spectrum, seed, realization count, reset and settling.	Packets within one fade may be correlated; count independent realizations or use a justified model.
OTA at S0	Frequency, antenna/enclosure state, orientation/polarization grid, chamber/site calibration, field/path loss, channel population.	Spatial and temporal sampling determine the claim; R2 feed and R1 input are distinct boundaries.

y(t) = \int h(t,\tau)x(t-\tau) d\tau + n(t)

This notation distinguishes an RF port level from an added channel response and noise. It is a method description, not an implemented fading simulator. h(t,τ), n(t), their units/scaling and sampling population must be supplied.

Think about itCan one thousand packets in a single deep fade supply one thousand independent channel trials?

Answer

Not automatically. They may share nearly the same channel state. Preserve the counts descriptively and mark independence unknown or correlated until the sampling design is justified.

A real test definition has a narrower scope

The pinned Bluetooth Core 6.2, Vol 6 Part A, §§4.3 and 4.6 specifies a blocking arrangement and reference signal; its LE reference uses GFSK, with PHY-specific conditions. The examined LE 1M reference has BT=0.5 and modulation index 0.5. Those definitions do not describe our QPSK frame. [BT-METHOD]

For that scope example, the DUT’s actual LE receiver supplies the decision process; an arbitrary QPSK equalizer is not a substitute. The executed packet population, applicable RFPHY test-suite revision and required-update details remain unresolved because the linked suite body was gated. No Bluetooth limits are assigned to this planner. Core 6.2 is retained for Path 07 continuity, not asserted to be the newest release. [BT-STATUS]

Common misconceptionA standards name on the waveform file makes this a conformance result.

A claim also needs the applicable revision, test case, complete method, population and required updates. A partially accessible reference cannot supply missing execution rules.

Engineering decision → record update

Keep the conducted result at R1-RX. Open a new record for each AWGN, fading or OTA population. Record unresolved test-suite applicability explicitly instead of borrowing a familiar threshold.

10 / 10

Publish repeatable TX and RX methods

Could another engineer reproduce both methods without asking what “the usual settings” meant?

The completed illustrative records below bind the question, specimen, waveform, processing, plane, calibration, acquisition, raw evidence, uncertainty and next test. Synthetic equipment IDs and chosen uncertainty values are plainly marked. Earlier raw fixtures remain immutable; changed processing produces a derived record with parent IDs.

Think about itWhat would falsify the claim that analyzer residual alone explains the TX result?

Answer

Use an independently characterized lower-residual analyzer at a calibrated input level, retain the same raw-reference contract and repeat the acquisition. If the error structure and magnitude persist beyond the declared uncertainty, analyzer residual alone is insufficient.

M08-05-TX-C · Complete standalone TX method

p08-measurement-record-v1 · M08-05-TX-C
Field	Completed illustrative entry
id	M08-05-TX-C
parentIds	M08-01-RAW-A · TX-BURST-B · p08-m03-analyzer-fixtures-v1
owner	08.5 · fictional radio verification engineer
question	Can the node TX method distinguish DUT modulation error from reference/analyzer residuals?
hypotheses	H-DUT: waveform distortion; H-REF: reference processing mismatch; H-SETUP: residual, level or clock contamination.
requirement	REQ-EVM-RAW-C: raw RMS reference-energy EVM ≤5%, four-symbol population at R3. Local illustrative criterion only.
decisionRule	p08-m05-decision-rules/1.0: resolve schema, waveform/processing/plane and acquisition first; local interval containment e+2u≤.05. Exact synthetic arithmetic does not approve a product.
specimen	SYN-NODE-TX-C / p08-m05-evm-reference-v1; finite algebraic decision vectors, not RF captures.
configuration	SYN-HW-C1, SYN-FW-TX-1, fixture SYN-TX-FIX-C1. This is a local method variant; earlier TX-PWR-A and TX-BURST-B are unchanged.
state	Method plan: 3.300 V supply, 298.15 K steady state, fixed bench board, antenna removed, cable strain relieved. Real state evidence unknown.
timestamp	Synthetic configuration frozen 2026-09-09T10:00:00Z. No real acquisition timestamp.
environment	Illustrative 25 °C indoor screened bench; humidity and actual ambient coupling unknown.
stimulus	Standalone DUT generates WAVE-P02-QPSK-v1: 2.450 GHz; Gray QPSK, 10 ksymbol/s, 80 ksample/s, RRC α=.35, span 8, 256-symbol teaching burst, PRBS-9 0x1FF. Four R3 symbols S=[1,j,−1,−j] are a separate algebraic fixture, not output of that waveform.
statistic	RMS fractional error normalized by total reference energy; raw policy, four unit-energy R3 symbols, no excluded symbols or fitted parameters. Peak per-symbol normalized error separately defined.
population	Four exact R3 vector samples. RF plan separately uses the inherited 232 selected decision symbols (12 excluded per burst edge); no measured RF EVM supplied.
acquisition	Acquire full 26.4 ms TX waveform including finite-filter tail at 100 ms cadence. Gate stable EVM symbols 12…243; retain raw time record including ramps for spectral assessment. No continuous-time peak guaranteed.
planes	R1-TX component RF output → M-A analyzer RF connector; real positive 50 Ω interfaces. Reference receiver produces R3 decision vectors. R2 feed, S0 OTA excluded.
chain	R1-TX → SYN-PAD-TX-C 20 dB → SYN-CABLE-TX-C 2 dB → M-A 50 Ω. +20 dB m local on-time plan becomes −2 dB m at M-A. These nominal levels do not establish PEP/DC safety; actual ratings unknown.
instrument	SYN-VSA-C / SIM-A005 / firmware SIM-1 / vector option SIM-QPSK; fictional. Source generator not present in standalone TX topology.
settings	Method plan: fc 2.450 GHz; complex acquisition 80 ksample/s; matched RRC 65 taps; known symbol clock/sequence; raw gain/phase policy; no equalizer, fitting, carrier-offset or timing correction. Record any real receiver tracking as a different contract.
calibration	SYN-LEVEL-C and SYN-REF-C are fictional evidence IDs. Verify external loss/mismatch and analyzer residual at the actual bandwidth/level; internal correction stored in acquisition metadata and never added as external loss. Recheck before/after run.
rawEvidence	SYN-TX-C-R3-RAW-001: S+.03vD+.02vA, exact four-symbol standalone observation. No external source vector. Earlier raw evidence is retained by parent ID.
processing	tx-rx-test-confidence-planner/2.0; p08-m05-evm-reference-v1; no correction applied. Separately computed conditional floor removal requires the exact zero cross terms and is not the raw requirement.
uncertainty	Exact vector fixture has no stochastic parameter uncertainty. Physical RF EVM uncertainty, analyzer residual distribution and traceability are unknown; no real pass follows from the algebraic screen.
result	Standalone raw EVM = √(.03²+.02²) = 3.605551275464%; algebraic analyzer floor 2%; conditional DUT 3% only for the orthogonal construction.
inference	Exact algebraic raw EVM is inside the local 5% criterion. Real TX inference unresolved until the physical method is acquired, verified and assigned uncertainty.
unresolved	Real source-free analyzer floor, correlation/clock policy, calibrated bandwidth/levels, PEP/DC limits, acquisition settings, reference-estimator bias and spectral/ramp evidence.
next	Counterfactual: substitute a characterized lower-residual analyzer/reference path at the same R1-TX level and processing. If EVM remains unchanged within the difference uncertainty, the original analyzer-limited explanation is weakened.
review	08.5 verification owner: recheck after waveform/firmware/cable/clock/level/gate/equalizer or thermal change; send immutable records to 08.6.

M08-05-RX-C · Complete conducted RX and blocking method

p08-measurement-record-v1 · M08-05-RX-C
Field	Completed illustrative entry
id	M08-05-RX-C
parentIds	SYN-RX-C-COUNTS-001 · RX-LEVEL-C · RX-WEAK-B
owner	08.5 · fictional radio verification engineer
question	Which supplied sensitivity grid point supports the packet target, and can a blocker test isolate DUT behavior?
hypotheses	H-DUT: waveform distortion; H-REF: reference processing mismatch; H-SETUP: residual, level or clock contamination.
requirement	REQ-PER-C: packet error probability≤.01 at a calibrated R1-RX level, selected local mode, fixed n, one-sided95% upper bound. Not a technology limit.
decisionRule	p08-m05-decision-rules/1.0: one-sided pU≤.01 (inclusive), pointwise only; choose the first supported supplied grid point. Setup/compatibility precedes this conditional screen. No interpolation or sequential stopping.
specimen	SYN-GATEWAY-C / p08-m05-rx-counts-v1; supplied counts RX-CURVE-C, not a channel simulation or hardware acquisition.
configuration	SYN-HW-C1; SYN-FW-RX-1; fixed AGC state RX-GAIN-C; CRC and retry settings frozen. Separate blocked comparison RX-BLOCK-PAIR-C uses wanted −109 dB m, source M-W −39 dB m; not RX-LEVEL-C’s−110 dB m wanted state.
state	Method plan: 3.300 V supply, 298.15 K steady state, fixed bench board, antenna removed, cable strain relieved. Real state evidence unknown.
timestamp	Synthetic configuration frozen 2026-09-09T10:00:00Z. No real acquisition timestamp.
environment	Illustrative 25 °C indoor screened bench; humidity and actual ambient coupling unknown.
stimulus	WAVE-RX-COUNT-C/1.0: local synthetic frame, 280 Gray-QPSK symbols at 10 ksymbol/s; 8 alternating 00/11 preamble symbols, 8 header symbols (16-bit trial ID modulo 65536, MSB first), 256 PRBS-9 body symbols, 8 CRC symbols. CRC-16 polynomial 0x1021, initial 0xFFFF, no reflection/xor-out, covers header then body bits MSB first. Unit symbol energy; TX/RX 65-tap unit-energy RRC, α=.35, 8 sps; 2.450 GHz. 28 ms symbol allocation + .8 ms TX filter tail; 11.2 ms response/guard/settle budget. Minimum cycle 40 ms. This frame is specified, not synthesized or a standard packet; its PAPR and hardware scaling remain unknown.
statistic	Each externally scheduled frame is one attempt, even if no packet is detected. Accept exactly one complete frame with expected ID, matching body and correct CRC before the 10 ms post-waveform timeout. Any CRC/header/payload failure, loss or timeout counts as one error, never several. Duplicates do not add successes or attempts. Retries are disabled. Trial ID wrap is disambiguated by the external acquisition sequence. Fixed n is declared in advance. One failed frame is not a count of bad bits.
population	1000 independent identically distributed packet attempts per level within one frozen configuration. Five prescribed levels −112…−108 dB m in 1 dB steps. No pooling of levels. BER unavailable from these counts.
acquisition	Source off for connections; verify ratings/DC/protection, warm-up and terminated-port losses. Quiet baseline then five levels in fixed order;100 ms per attempt plus explicit per-level overhead 0s;100s/level,500s total. Stop only at 1000/level; log every timeout.
planes	M-W wanted source; M-B blocker source; combiner branches → R1-RX component RF input, real 50 Ω. R3 is decoded packet/bit decision boundary. Conducted only; no S0 inference.
chain	RX-LEVEL-C: M-W−40 dB m−65 dB branch−5 dB combiner/common=−110 dB m R1-RX. M-B−10 dB m−5 dB complete forward path=−15 dB m R1-RX. Reverse M-B→M-W isolation60 dB gives−70 dB m; separate local interference ceiling−80 dB m,10 dB short. No double common-path correction.
instrument	SYN-VSG-W / SIM-W005, SYN-VSG-B / SIM-B005, firmware SIM-1; SYN-COMB-C; receiver counter SIM-R3. Source quality, reverse behavior and actual safety ratings are unknown outside these synthetic entries.
settings	Generic framed QPSK 2.450 GHz, RRC reference frozen; blocker CW 2.460 GHz for local ledger. RX matched filtering/timing acquisition and gain state recorded; no post-count reference fit. Source noise density −160 dB m/Hz already at R1-RX over 20 kHz ENBW in a separate noise fixture.
calibration	Calibrate each source alone at R1-RX with the other branch terminated in its actual state; characterize combined operation, source-source isolation, noise/spurs and leakage. SYN-LEVEL-C-U adds illustrative expanded U=.4 dB,k = 2, assumed near-normal level model; not a damage tolerance or counting interval.
rawEvidence	SYN-RX-C-COUNTS-001: k=[180,35,5,0,0],n=1000 at[−112,−111,−110,−109,−108]dB m. Separate SYN-BLOCK-PAIR-C-001 at−109 dB m: quiet 0/1000, blocker-on 35/1000 with−15 dB m blocker. Pair is supplied illustrative data; ledger changes do not synthesize new counts.
processing	tx-rx-test-confidence-planner/2.0; p08-m05-rx-counts-v1; fixed-n exact binomial inversion. Upper probabilities[.201175658005886,.046138336093647,.010484076911416,.002991249545095,.002991249545095].
uncertainty	Pointwise one-sided95% binomial bounds require IID/fixed-n assumptions; calibrationU=.4 dB,k = 2 is a separately chosen synthetic uncertainty. No simultaneous95% crossing claim. Desense differences require compatible thresholds and shared calibration covariance.
result	First statistically supported grid point −109 dB m; illustrative level interval−109±.4 dB. −110 dB m observed PER=.5% does not support 1% at 95%. Paired blocker-on 35/1000 has upper 4.613833609365%; source contamination remains unresolved.
inference	Conditional supplied-grid evidence only. The 60 dB reverse-isolation ledger is setup-limited; current blocking counts are unknown for arbitrary edited levels. One paired count difference is not a measured sensitivity shift or DUT-only mechanism.
unresolved	Real IID/stationarity, calibration and source validity; actual packet implementation; reverse interference and source broadband noise; complete safe-level criteria; repeated threshold curves; OTA/chamber/site distribution.
next	Counterfactual: add characterized isolation, recalibrate both forward paths to hold wanted/blocker levels fixed, and repeat the quiet/blocked count pair. If the error excess persists within declared uncertainty/confidence, reverse source coupling alone is falsified. Preserve both raw versions.
review	08.5 verification owner: recheck after waveform/firmware/cable/clock/level/gate/equalizer or thermal change; send immutable records to 08.6.

Use a two-stage review: first compatibility and acquisition validity, then the numerical decision rule and its uncertainty/confidence. The planner lists every failed gate in that order. A physically unsafe or incompatible acquisition cannot be rescued by a favorable percentage.

Go deeperModel contract and numerical boundaries

tx-rx-test-confidence-planner/2.0; p08-m05-evm-reference-v1; p08-m05-rx-counts-v1; p08-m05-level-ledger-v1; p08-m05-decision-rules/1.0. This lesson-scoped Class 1 workbench may inform a future Class 3 tool, but is not a Tools product. Binomial inversion uses a bounded continued fraction (4096 iterations) and bisection (128 iterations, bracket width ≤10⁻¹²); failure returns unavailable. Inputs bound attempts to 10…10⁷, errors to 0…n, confidence to 90/95/99/99.9%, and probability targets to 10⁻⁶…0.2. Independent oracle tolerances are 10⁻¹⁰ fractional EVM/probability, 10⁻⁸ percentage points and 10⁻⁹ dB for levels; trial counts and millisecond timing are exact. These tolerances are numerical checks, not physical uncertainty.

Common misconceptionA complete record must finish with pass or fail.

“Unknown,” “inconclusive,” “setup-limited” and “incompatible” are useful engineering outcomes when they identify the missing evidence and a discriminating next measurement.

Engineering decision → record update

Publish M08-05-TX-C and M08-05-RX-C as illustrative methods. Carry their unresolved hypotheses and counterfactual tests into Module 08.6, Systematic Debugging & Pre-Compliance.

Ungraded review

Check your understanding

Answer each question in your own words, then reveal the model answer.

01Why can 6.98% and 0% both describe the phase fixture?
Model answer
The first is raw RMS error against the fixed unit-energy reference. The second removes an exactly known 4° common rotation. They answer different processing contracts. The zero is an algebraic limit, not measured hardware accuracy, and a corrected result cannot close a raw-EVM requirement.
02When does quadrature residual subtraction recover the 3% DUT term?
Model answer
For the supplied orthogonal four-symbol vectors, all pairwise inner-product cross terms vanish, and √(3.741657386774%² − 2.236067977500%²) = 3%. That finite-vector fact does not establish stochastic independence in a bench. The collinear 6% case cannot use the same subtraction. At or below the floor, report unresolved; near it, uncertainty propagation becomes ill-conditioned.
03Does 0/1000 support a 0.1% target at one-sided 95% confidence?
Model answer
No. The exact upper bound is 0.299124954510%. A fixed plan of 2995 independent attempts supports 0.1% only if all are error free. At 100 ms per attempt and no overhead, that takes 299.5 s; stopping opportunistically invalidates this fixed-n coverage.
04Why is −110 dBm not the supported 1% curve point?
Model answer
Its observed proportion is 5/1000 = 0.5%, but the one-sided 95% upper bound is 1.048407691142%. The first supported supplied point is −109 dBm. This is pointwise evidence on a 1 dB grid; calibration uncertainty is separate and no interpolated or simultaneous 95% threshold is claimed.
05Improved isolation fixes reverse incidence. Has the DUT passed blocking?
Model answer
No. Moving reverse incidence from −70 to −90 dBm meets the local source-interference ceiling with 10 dB margin, but source noise, spurs, leakage, forward calibration and comparable quiet/blocked counts remain necessary. Noise-rise arithmetic is not a measured sensitivity shift.
06Can conducted R1-RX sensitivity establish OTA performance at S0?
Model answer
No. Antenna pattern, polarization, orientation, efficiency, enclosure, chamber/site calibration and channel statistics enter the spatial result. Define and acquire that separate population; retain conducted evidence as a component boundary condition.

References and further study

Primary-source access: 2026-09-09. Fixture freeze: 2026-09-09. Recheck before physical use or publication, and on method, waveform, firmware, instrument or source revision change. Informative method references and the scoped normative example are distinguished below. The Keysight asset URL exposed an excerpt, and the Bluetooth suite was gated; neither unavailable body is represented as fully reviewed.

EVM-DEF · Keysight Technologies. Making and Interpreting EVM Measurements. 5989-3144; current public asset-page excerpt. Publication date not exposed in excerpt; checked 2026-09-09. Consulted: Introduction; Defining EVM. Informative first-party excerpt read. Reference-dependent normalization and related error views. URL serves an HTML excerpt. Full PDF edition not verified; no unseen page, limit or proprietary figure reproduced.
EVM-FLOOR · Keysight Technologies. How to Measure Accurate EVM for a DUT in 5G NR Systems. Living use-case page. No publication date shown; accessed 2026-09-09. Consulted: Measuring Accurate EVM by Suppressing System Noise; Receiver Test Solution. Informative instrument-method context. Residual measurement noise can limit EVM; the described cross-correlated method uses two analysis paths. No ccEVM implementation, instrument rating, NR waveform or standards limit is imported. Our algebraic subtraction is not that instrument method.
STAT-EXACT · NIST/SEMATECH. e-Handbook §7.2.4.1 Confidence intervals. Live web handbook; exact-binomial subsection. No revision date displayed; accessed 2026-09-09. Consulted: Exact Intervals for Small Numbers of Failures and/or Small Sample Sizes; binomial tail equations and 4/20 example. Informative metrology/statistics reference. Fixed-n binomial tail inversion. One-sided adaptation allocates α to one tail; equal-tail uses α/2. The earlier Wilson section is not this implementation. No posterior probability, sequential coverage, independence test or familywise guarantee.
GUM · JCGM / BIPM. Evaluation of measurement data — Guide to the expression of uncertainty in measurement. JCGM 100:2008. 2008; current guide listing checked 2026-09-09. Consulted: §§5.1–5.2, especially 5.2.1–5.2.4; equation 13. Informative metrology method, full body consulted. Sensitivity coefficients, covariance, and shared-reference uncertainty. No complete hardware uncertainty budget or universal k=2 coverage is supplied.
GUM-AMD · JCGM / BIPM. Nonlinearity in measurement models. JCGM 100:2008/Amd.1:2026. 2026; guide list and actual amendment text checked 2026-09-09. Consulted: Amendments to 4.1.4 and 5.1.2; final page. Published metrology amendment read. Significant nonlinearity requires more than unexamined first-order propagation. No Monte Carlo residual estimator implemented here. Near-boundary propagation is explicitly withheld.
BT-METHOD · Bluetooth SIG. Core Specification — Radio Physical Layer Specification. Pinned legacy Core 6.2, Vol 6 Part A. Adopted listing checked 2026-09-09; selected for continuity with Path 07.2. Consulted: §§4, 4.1, 4.3 and 4.6; receiver criteria, blocking topology and reference signal. Normative body read; scope example only. A real test definition fixes the PHY/reference signal, error criterion and wanted/interfering stimulus. LE uses GFSK, not this generic QPSK. No masks/tables or thresholds imported into local decisions. Exact execution population and applicable RFPHY test-suite/update chain are unresolved.
BT-STATUS · Bluetooth SIG. Core Specification 6.2 catalogue and test-suite chain. Core 6.2; Erratum 28108 listing; RFPHY test-suite download. Status checked 2026-09-09. Consulted: Core catalogue, required-update notice and RFPHY Test Suite link. Catalogue/access evidence. Pins the reviewed body separately from tests and updates. RFPHY destination returned a download gate; complete suite and update body unread. Current applicability/qualification requires review; 6.2 is not asserted to be the newest Core.

Modulated Transmitter &Receiver Measurements

Two EVM numbers may measure different things

Freeze the waveform and test population

A separate, explicit receiver population

Characterize the source and level path

Make synchronization and equalization part of the method

Read EVM together with error structure and floor

Keep spectral metrics and gates consistent

Sensitivity is a curve with a counting rule

TX/RX Test & Confidence Planner

What does this count support?

Build wanted-plus-blocker tests with isolation

Declare the channel and conducted/OTA boundary

A real test definition has a narrower scope

Publish repeatable TX and RX methods

Check your understanding

References and further study

Modulated Transmitter &
Receiver Measurements