Antenna Measurement & Link Reality

Before you begin

Bring Modules 06.1–06.5: antenna quantities, family selection, product integration, arrays and diversity, and conditional link distributions. You will specify a measurand, reconcile apparently conflicting results, and write a validation request with a discriminating next test.

This lesson owns evidence architecture. Detailed VNA calibration, de-embedding, receiver operation and uncertainty execution belong to Path 08; exact normative OTA procedures, legal acceptance and product lifecycle work remain outside this lesson. No instrument is operated and no product is certified.

Local conventions: SI units, e^(+jωt), explicit real 50 Ω R1/R2 references, linear powers before dB conversion, and stated time/angle/polarization averages. No loss is assigned twice.

01 / 10

Failure: VNA success and chamber failure look contradictory

Which report is wrong: the VNA, the chamber, or the gateway?

The illustrative engineering case is an enclosed 2.45 GHz telemetry node. Its corrected port comparison looks nominal, yet its reported radiation efficiency is low. A pattern has a notch in a useful direction, and cable-attached chamber repeats disagree. The gateway link also misses a quality target. The team is tempted to keep the clean S11 plot and dismiss the rest as bad testing.

There is no contradiction until two results claim the same measurand under compatible conditions. A VNA observes the feed boundary. A radiation measurement observes power or field in space under its method. A packet trial also includes the channel, receiver, interference and traffic. Even perfectly repeatable instruments can answer different questions.

Think about itCan a matched, lossy antenna produce both a good S11 plot and low radiated power?

Answer

Yes. The port can accept energy that is then dissipated. At 0 dBm incident, −10 dB S11 and 20% radiation efficiency, 90% is accepted but only 18% is radiated. Those are compatible statements with different denominators.

The first evidence triage · all case observations are Illustrative
Domain	What it can support	What remains unknown
Simulation	Behavior of its geometry, materials, ports, excitation and solver model	Whether mesh convergence and real mechanics/materials/cables are represented
Bench / R2	Corrected reflection and accepted-power boundary	Dissipation versus radiation; 3D coverage
Chamber / S0	Defined angular or integrated radiation/receive behavior	Setup bias, mode comparability and intended-use population unless controlled
Field / R3	Link outcomes for the recorded site, state and traffic	Antenna efficiency, universal range and untested populations

Common misconceptionGood S11 and poor chamber performance are inherently contradictory.

They usually concern different parts of the chain. Align planes, states and definitions before deciding whether disagreement is physical or methodological. Discarding the inconvenient result can conceal a real loss or coverage problem.

Go deeperEvidence labels are part of the claim

Definition names a convention; Derived follows from stated inputs; Simulated names a numerical model; Illustrative is a teaching fixture. Measured requires an actual DUT, method, settings and uncertainty. Normative belongs to an accessed, pinned requirement; Informative explains principles. None of this node’s invented observations is Measured or Normative.

The next step is a complete measurement request, beginning with the quantity and its boundary.

02 / 10

Define the measurand and complete configuration

Would two laboratories know they were measuring the same thing?

A measurand is the quantity intended to be measured. “Antenna performance” is too broad. “Co-polar realized gain at θ=90°, φ=0°, referenced to incident power at the real 50 Ω R2 feed, on unit U01 in enclosure revision M6-r1 at 2.450 GHz” begins to define one. Its operating mode, method and uncertainty still need to follow.

Plane map · conceptual, not measured. R2-TX and R2-RX both map to R2. Each antenna’s mismatch and dissipation enter once; R3 remains the detector/decision boundary.

Information that travels with every result
Required field	Completed local example / effect on the decision
DUT and revision	U01, M6-r1 enclosure, battery, shield, adhesive and fastener drawing; tune T0; no substitution by a vendor evaluation board
State and frequency	ENC-test, 2.450 GHz, 25 °C, fixture F6-r1, cable A; compare against its specified ENC-ref pair, not an unlabelled open board
Plane and included losses	R2 incident for realized gain; accepted R2 power for radiation efficiency; upstream R1 feed loss accounted once
Coordinates and polarization	Specimen θ from +z, φ from +x toward +y; co eθ/cross eφ; O1 upright versus O2 +90° about +y
Mode and method	Passive fixed source, TX-N on-time waveform, or RX-N quality criterion; name gain-transfer, sphere integration or receive-threshold method
Population, uncertainty, decision	Per-unit/state result, repeats and grid; distinguish standard u from expanded U; predeclare threshold and boundary rule

R2-TX and R2-RX are local names for the two antenna feeds; both map to portfolio R2. Receive available power refers to compatible conjugate loading. Receive delivered power names the actual load. Neither is an EIRP. S0 requires distance/direction/polarization; R3 remains the detector/decision boundary. Calibration at a connector stays at that connector until a documented transformation reaches the feed.

Think about itA report gives −2.15 dBi with no uncertainty. Can you apply a −3 dBi minimum requirement?

Answer

You can compare nominal values, but you cannot apply a rule involving an uncertainty bound. Missing uncertainty is unknown. It is not 0 dB, and an unexplained vendor tolerance is not automatically a standard uncertainty.

A small uncertainty budget that changes the decision

$\begin{aligned}u_c^2&=a^2+b^2+2\rho ab\\a&=.3\,\mathrm{dB},\quad b=.4\,\mathrm{dB},\quad\rho=0\Rightarrow u_c=.5\,\mathrm{dB}\\U&=ku_c=2\times.5=1.0\,\mathrm{dB}\end{aligned}$ Derived teaching example for an additive-dB measurand. a and b are standard uncertainties in dB; ρ is their correlation coefficient.

With perfect positive correlation, u_c=0.7 dB, not 0.5 dB. For a difference A−B, a shared reference offset can cancel if the same error enters both results with the same sensitivity; drift, changed references or different sensitivities leave residual covariance. Do not apply root-sum-square to every number on a list. NIST TN 1297 §5 and Appendix A explain the standard-uncertainty and covariance framework.

Our hypothetical conservative rule is “measured gain minus expanded U must clear the minimum.” For −2.15 dBi and U=1.0 dB, the lower bound is −3.15 dBi. It does not clear −3 dBi under that rule. It also does not prove the actual gain is below −3 dBi. The choice of rule matters when an interval overlaps the threshold.

Common misconceptionk=2 always means exactly 95% confidence.

A coverage interpretation needs distribution and effective-degrees-of-freedom justification. Here k=2 is a stated expansion factor, and the uncertainty contributions are assumed teaching values. They are not a chamber capability claim. See NIST TN 1297 §6.

Go deeperA tolerance, a bound, and a standard deviation are different

A bounded ±a tolerance needs an explicit probability/model treatment before becoming standard uncertainty. For example, a justified rectangular model gives a/√3; the interval alone does not justify that distribution. Nonlinear transformations may require a fuller propagation model. The JCGM 100:2008 Amendment 1:2026 addresses nonlinear measurement models; it is not a license to use a linear approximation without checking its domain.

With the quantity fixed, a port measurement can now be interpreted precisely—and only as far as its boundary permits.

03 / 10

S11 is boundary evidence, not radiation evidence

Where does the accepted power go?

At a declared real 50 Ω port, signed S11 in dB is 20 log₁₀|Γ|. The reflected fraction is |Γ|² = 10^S11/10. Return loss uses the opposite sign. A nominal port comparison in the diagnostic fixture means no detectable change under its supplied rule; it is not a complete bandwidth or impedance qualification.

$\begin{aligned}P_{\mathrm{ref}} &= P_{\mathrm{inc}}|\Gamma|^{2} \\ P_{\mathrm{acc}} &= P_{\mathrm{inc}} - P_{\mathrm{ref}} \\ P_{\mathrm{rad}} &= \eta _{\mathrm{rad}}P_{\mathrm{acc}} \\ \eta _{\mathrm{tot}} &= (1-|\Gamma|^{2})\eta _{\mathrm{rad}}\end{aligned}$ Definition and derived conservation: watts at R2 and S0. The passive one-port antenna includes all radiator losses; no upstream feed loss is supplied.

p06-m06-measurement-examples-v1 · good match, poor radiation · M01-B-LOSS arithmetic preserved
Quantity / denominator	Value	Interpretation
R2 incident	1.000 mW = 0 dBm	Specified incoming feed power
R2 reflected	0.100 mW	10% returns through the port
R2 accepted	0.900 mW	Available to radiation plus dissipation inside this antenna
Dissipated	0.720 mW	80% of accepted power becomes loss
S0 radiated / TRP	0.180 mW = -7.447274949 dBm	20% of accepted, 18% of incident

The two conservation checks are 1 = 0.1 + 0.72 + 0.18 mW and 0.9 = 0.72 + 0.18 mW. Do not add accepted power again as another destination. These numbers reuse M01-B-LOSS, not a newly measured enclosure. The numerical example and the later categorical fault model have separate versions and do not predict each other’s numeric outputs.

Think about itRetune the antenna until reflection falls. Must its radiation efficiency or useful-direction gain recover?

Answer

No. Reduced reflection increases acceptance but does not remove dissipation, restore a damaged current distribution, or fill a direction null. A lossy structure may even appear broadly matched because energy is absorbed rather than returned.

Common misconceptionS11 measures radiation efficiency.

A matched termination is the limiting counterexample: it accepts power without functioning as an efficient antenna. Cable current and fixtures can also change the radiating structure. Pair the port evidence with independent radiation and setup controls before changing the matching network.

Go deeperKeep gain denominators consistent

Under the declared passive definitions, G=ηradD uses accepted feed power, and Greal=ηtotD uses incident power at the specified real impedance. Realized gain already includes antenna mismatch. If a measurement includes a feed or support loss, state that reference explicitly before combining it with a separate link-budget term. Removing mismatch a second time understates performance.

Even a correct total radiated power says little about the direction that reaches the gateway. That requires spatial evidence.

04 / 10

Patterns and polarization need more than one cut

What did the unmeasured directions do?

A cut is a slice through an angular function. An azimuth sweep fixes θ; a meridian fixes φ. A dipole-like equatorial cut can be uniform while the poles are nulls. A peak-normalized pattern discards the absolute power scale, so its 0 dB peak supplies no absolute gain or efficiency.

Coordinate sketch · not a measured radiation pattern. O1 keeps specimen +z upright; O2 rotates the specimen +90° about +y. Transform both the direction and polarization basis when registering a result.

Declare absolute EIRP, gain, realized gain, field amplitude, or relative power before plotting. In a complete local transverse basis, orthogonal eθ/eφ power components add linearly. “Co” and “cross” require a declared reference convention and coordinate transform; they are not intrinsic labels that survive every rotation unchanged. The scalar teaching pattern below specifies total power only and does not invent a vector polarization pattern.

$\mathrm{TRP}=\frac{1}{4\pi}\int_0^{2\pi}\int_0^\pi \mathrm{EIRP}(\theta,\phi)\sin\theta\,\mathrm{d}\theta\,\mathrm{d}\phi$ Full-sphere linear-power integration, θ∈[0,π], φ∈[0,2π). dΩ is solid angle in steradians; EIRP is watts, not dBm.

For D=1.5 sin²θ and TRP=0.18 mW, EIRP=0.27 sin²θ mW. Integration gives (0.27/4π) × (2π) × (4/3) = 0.180 mW. The equator is 0.27 mW everywhere. Calling that cut the sphere mean overstates TRP by 1.760912591 dB.

Analytic total-power samples · all φ · not measured data
Polar angle θ	D · linear	EIRP · mW
0	0	0 (analytic null)
30	0.375	0.0675
60	1.125	0.2025
90	1.5	0.2700
120	1.125	0.2025
150	0.375	0.0675
180	0	0 (analytic null)

Think about itCan averaging the dBm values repair an incomplete angular scan?

Answer

No. Integrated power requires linear values and solid-angle weights; dBm averaging computes a different statistic. Missing angular coverage remains missing. At an ideal null dBm has no finite value, while a real receiver floor provides censored data rather than an exact zero.

Common misconceptionOne azimuth cut proves spherical coverage and absolute efficiency.

It supplies neither the unsampled directions nor an absolute reference. The engineering consequence is a possible gateway outage hidden behind a reassuring normalized ring.

Go deeperSampling is an uncertainty contribution

Use an angular grid fine enough for the narrowest beam/null relevant to the claim, refine it and demonstrate convergence. Avoid duplicate 0°/360° samples and unintended pole weighting. A 5° grid is a local request, not a universal adequate spacing. At coordinate poles use a continuous limiting convention for vector fields; total power is basis invariant. Truncated scans and imperfect cross-polar isolation require explicit bounds or method corrections.

The scan is meaningful only if the range itself supports the claimed angular accuracy.

05 / 10

Far field, quiet zone, reflections, positioning, and dynamic range

Is five metres enough—or merely far enough to start checking?

The conventional direct-range screen R ≳ 2D²/λ limits an aperture phase-curvature effect under an assumed geometry. D is a relevant maximum radiating dimension, not automatically the length of a convenient PCB feature. Both the antenna under test (AUT) and the source/reference antenna, their separation convention and the required accuracy matter.

$\begin{aligned}\lambda&=\frac cf=0.122364268571\,\mathrm m\\\frac{2D^2}{\lambda}&=4.086160166\,\mathrm m\end{aligned}$ Derived screening example: vacuum c=299792458 m/s exactly, f=2.450 GHz, maximum dimension D=.50 m. This is a conventional starting criterion, not a universal far-field guarantee.

Range geometry · schematic only, not a measured quiet-zone map. The source/reference dimension and AUT dimension, amplitude/phase variation across the occupied volume, reflections and noise floor all remain separate checks.

Same direct-range example, two separations
Separation	Starting screen	Remaining decision
3 m	Not met: 3 < 4.086160166 m	Do not claim this direct-range screen is satisfied; change range or use a separately valid method
5 m	Met: 5 > 4.086160166 m	Verify both antenna dimensions, quiet zone, reflections, alignment, dynamic range and uncertainty

A quiet zone is a specified volume with sufficiently controlled field amplitude, phase and polarization for the intended test. An anechoic lining does not establish its quality. Probe taper, residual reflections, AUT/support loading and positioning errors can reshape a measured beam or fill a null. The Rohde & Schwarz OTA white paper, version 01.00, §§2.1.5 and 3 gives useful first-party orientation; its historical conformance examples are not adopted as current requirements here.

Check dynamic range at the weakest direction and polarization, not just at the peak. If the receiver can only establish EIRP below −40 dBm, report “<−40 dBm under this setup,” with its detection/uncertainty basis. A trace drawn at the floor is not an antenna value of exactly −40 dBm and does not establish a physical zero. Saturation at the other end can flatten the peak and corrupt normalization.

Common misconceptionAnechoic means zero uncertainty, and 2D²/λ guarantees every accuracy target.

Neither is true. Position, alignment, reference, floor and residual fields still enter the measurement model. A smaller geometric phase error may be needed for a deep-null or high-gain claim.

Go deeperA short chamber can use a different valid model

A compact antenna test range creates a controlled plane-wave region through a reflector or other field transformation. Near-field methods sample complex fields with probe and geometry corrections, then transform them to far field. Their finite scan area, sampling, phase stability and truncation errors require their own validation. Applying the direct-distance formula blindly to every short chamber rejects methods it does not describe.

Once the range is qualified for the quantity, choose a method that can establish its absolute scale.

06 / 10

Gain and efficiency method families

Where does the absolute gain reference enter?

Gain comparison substitutes an antenna with a supplied calibrated gain into the same compatible range and compares receiver readings. The source level, polarization, alignment, range geometry and loading must remain equivalent or be corrected explicitly. A difference in receive cable loss is part of the measurement equation, not an optional cosmetic offset.

$\begin{aligned}G_{\mathrm{real,DUT}} &= G_{\mathrm{real,ref}} \\ &+ (P_{\mathrm{DUT}}-P_{\mathrm{ref}}) + (L_{\mathrm{DUT}}-L_{\mathrm{ref}})\end{aligned}$ Derived local realized-gain substitution. P is the receiver reading in dBm after its receive cable; L is positive cable loss in dB. Reference gain and DUT gain both include mismatch at real 50 Ω R2.

p06-m06-measurement-examples-v1 · corrected gain-transfer ledger, 2.450 GHz
Term	Reference	DUT / difference
Supplied reference realized gain	2.15 dBi	Same direction and co-polar basis
Receiver reading after cable	-50 dBm	-55 dBm; difference −5.0 dB
Positive receive-cable loss	0.5 dB	1.2 dB; correction +0.7 dB
Without differential correction	2.15 − 5.00	-2.85 dBi (incorrect for this setup)
Corrected DUT realized gain	2.15 − 5.00 + 0.70	-2.15 dBi

The reference’s +2.15 dBi is a supplied realized-gain value, not a deduction from its family name. The range planes run from the fixed transmitting reference to each substituted receive antenna’s R2 plane; receiver readings are downstream of the listed cable. Cable mismatch and connector corrections must either be negligible under the stated compatible matched setup or included in a fuller model. Do not remove antenna mismatch again, and do not rename this result directivity.

Think about itCan a normalized pattern alone turn the −2.15 dBi result into radiation efficiency?

Answer

Only with sufficient full-sphere pattern information to establish directivity and compatible definitions. A single cut cannot supply D. Given true same-direction G and D, ηrad=G/D; using realized gain gives ηtot instead. All ratios are linear before conversion to dB.

Method families · choose by measurand and validity
Family	What it can establish	What must be controlled
Gain transfer / substitution	Absolute directional gain using a reference	Reference calibration and definition, cable corrections, alignment, polarization and range
Three-antenna relations	Compatible pairwise gains without one preassigned gain	Reciprocity, all three range/plane definitions, polarization and stable conditions
Full-sphere integration + feed power	Radiated total, directivity and efficiency denominators	Absolute scale, both polarizations, angular weights/sampling, accepted versus incident power
Reverberation method	Statistical chamber power/efficiency estimate under its model	Stirring, loading, chamber calibration, losses and ensemble adequacy; no directional cut from an integrated result
Wheeler-cap / related suppression methods	Radiation/loss separation for compatible antenna structures	Cap and cavity modes, antenna loading, assumed loss invariance and method domain; not a universal enclosure recipe

Common misconceptionA gain number and a normalized plot automatically prove efficiency.

The absolute reference and complete integration model matter. A method can also be precise while systematically biased by a fixture it failed to represent.

Go deeperThree compatible relations, three unknown gains

For the simplified reciprocal, aligned, polarization-matched far-field model, let Aab be each pair’s corrected dB transfer plus free-space loss, using accepted TX and available RX powers. Then Aab=Ga+Gb, Aac=Ga+Gc, Abc=Gb+Gc. Hence Ga=(Aab+Aac−Abc)/2, with cyclic expressions for Gb and Gc. Mismatch and cable corrections must match this gain definition; a realized-gain variant uses its own consistent port powers. See NBS TN 1311 (1987), §2.2 for the basic pairwise idea and its generalizations. This is method orientation, not a calibration procedure.

Before believing a small gain difference, deliberately perturb the parts of the setup that are supposed to be irrelevant.

07 / 10

Cable, common mode, fixture, chamber loading, and references

Did the antenna change, or did the measurement become a different antenna?

A cable transports a desired guided signal, but its exterior can also carry common-mode current and couple to the product. Changing the route, ground contact or a choke can alter that current, the feed impedance and the radiating structure. A feed correction removes the modeled guided response at a specified plane; it does not erase radiation from the outside of the cable.

Competing setup explanations and discriminating controls
Observed dependence	Compatible explanation	Next controlled comparison
Pattern moves when cable route changes	Common mode / cable scattering; possibly changed loading	Same unit, tune and R2 correction; paired cable A/B, choke and cable-free states; record reference and outer-current evidence
Feature follows support or fixture	Support scattering, loss, incorrect fixture correction	Independent low-scattering support/fixture, registered position; verify port plane separately
Reference and DUT both vary spatially	Range ripple or alignment; reference drift can imitate it	T-H: reference-antenna spatial/range repeat with cable and polarization controlled
Gain changes after a reconnect	Connector repeatability, reference shift or calibration drift	Reconnect repeat and start/end reference; retain covariance rather than counting shared errors twice
Passive result stable; active RX worsens	Receiver mode, platform noise or desense	T-R: conducted receiver comparison under the same clocks/display/charger state

Think about itA cable-free repeat improves efficiency. Does that prove added radiator dissipation is absent?

Answer

No. It removes or changes one setup contribution. In the supplied diagnostic model, E2 depends on L OR C, so confirming C still leaves L possible. Use an independent efficiency method with controlled setup to discriminate L.

Keep a known reference interleaved with DUT measurements. A slow source drift can look like a spatial pattern when scan order follows position. An extra absorber, battery lead or support changes chamber loading. Record fixture drawings, reference-antenna ID/calibration, cable route/choke location, alignment, source level and scan order with the result. An “unchanged chamber” is a configuration claim to verify.

Common misconceptionThe cable only carries the wanted signal and cannot radiate.

The outer-surface current is outside the ideal guided-port model. A good connector correction cannot make the cable electromagnetically invisible. Ignoring this can send the team into repeated antenna retuning while the test setup remains the cause.

Go deeperA counterfactual changes one specified factor

“Remove the cable” may also change power supply, firmware mode or source reference. A discriminating pair must preserve those conditions or explicitly model the differences. Choke tests need insertion/loading checks and repeatability; they are not perfect isolators by definition. If the comparison is inconclusive, keep the hypotheses rather than forcing a yes/no outcome.

Active OTA adds the transceiver and its operating state to this already configuration-sensitive measurement.

08 / 10

Active OTA, TRP, TIS, and operating modes

Does the same device behave the same way while transmitting and receiving?

Total radiated power (TRP) is transmitted radiated power integrated over direction and polarization for a declared frequency and operating state. Specify waveform, drive, port state and time averaging: on-time mean and wall-clock mean can differ greatly for a telemetry node. Peak EIRP emphasizes one direction; it is not the sphere total.

Total isotropic sensitivity (TIS) concerns radiated receive sensitivity under a defined signal and receiver quality criterion with a specified angular/polarization treatment. It includes the receive system’s interaction with its noise environment. It is not an emission, noise figure, efficiency, arithmetic average of dBm sensitivities, or negative TRP. The exact applicable procedure and normalization must be obtained before a normative test.

Active OTA comparison · separate mode definitions and evidence
Metric / boundary	State that must accompany it	Supported decision / limitation
TRP · S0 transmitted W or dBm	TX-N, 2.450 GHz, QPSK/RRC .35; 20 kbit/s uncoded, 10 ksymbol/s; 256-symbol burst; source at R2; receiver idle; on-time mean	Compare emitted totals for matched drive/configurations; cannot establish RX sensitivity or all directional coverage
Directional EIRP · S0 W or dBm	Same TX state plus θ, φ, polarization and absolute gain reference	Link coupling in that direction under valid range assumptions; cannot replace sphere integration
TIS / radiated RX sensitivity · S0	RX-N, signal/waveform/bandwidth, ≤1% PER local criterion, angular/basis treatment, clocks/display/charger noise, TX state	Assess radiated receive performance for that method/mode; cannot infer from TRP alone
Conducted sensitivity · R1-RX to R3	Calibrated delivered signal, real 50 Ω, same RX waveform/criterion and platform mode	Separates receiver-chain impairment from the antenna/channel; does not measure installed radiation

Think about itCan a receiver-noise fault worsen TIS while leaving TRP and S11 unchanged?

Answer

Yes. A platform noise source or receiver-chain issue may impair RX without changing passive match or TX radiation. The training model represents that possibility with R in E5/E6 but not E1/E4. That is a deliberate signature choice, not a universal physical transfer function.

TX and RX may use different frequencies, switches, matching states or power configurations. Receiver desense can also depend on whether the transmitter or digital subsystem is active. Passive reciprocal antenna behavior under identical conditions does not make the entire active TX and RX chains reciprocal. The historical R&S LTE UE receiver paper, 01.00 (September 2017), §4 is used for this conceptual distinction; its legacy standard references and shorthand averaging are not adopted as current normative algorithms.

Common misconceptionTRP, EIRP, gain, total efficiency and TIS are interchangeable.

They have different dimensions, references, integrations or receiver criteria. Replacing one with another can falsely approve a low-coverage direction or conceal desense.

Go deeperTime averages need a denominator too

The local validation request uses 256 symbols at 10 ksymbol/s: 25.6 ms on-time every 1 s. If radiated power is constant during the burst and zero otherwise, wall-clock mean is 0.0256 times on-time power, a −15.917600347 dB change. This is a local traffic definition, not a change to the earlier antenna fixture. State detector, bandwidth, integration window and treatment of ramps or idle emission before applying the approximation.

Once the node is taken outside, the antenna and receiver meet a changing channel. Packet statistics need an equally explicit population.

09 / 10

Field and packet trials are channel/system evidence

What population do 100 successful packets represent?

A site survey records environmental and geometric conditions. A packet trial records an end-to-end result. Site, route, distance, antenna height/orientation/mounting, traffic, waveform, retries, receiver mode, interferers and repetitions all determine what the statistic means. Keep failures, censored RSSI values and rejected records, with their reasons.

RSSI is a receiver-specific estimate at a defined measurement point, bandwidth and gain state; interference can increase it while packets get worse. PER depends on decoding, timing and traffic as well as RF signal quality. Neither is a calibrated antenna-efficiency measurement. The three 06.5 scenarios—outdoor LOS, office corridor and machine hall/on-metal—remain separate illustrative channel models. Their synthetic draw counts are not measured field confidence.

$\begin{aligned}\Pr(0\text{ failures}\mid p)&=(1-p)^n\\(1-p_{\mathrm{upper}})^n&=\alpha\\p_{\mathrm{upper}}&=1-\alpha^{1/n}\end{aligned}$ Derived exact zero-failure bound for n independent, identically distributed Bernoulli packet trials with constant unknown failure probability p. One-sided tail probability α=.05.

For n=100, p_upper=0.029513050, about 2.951305% failure probability. Zero observed failures is not zero failure probability. The bound has a repeated-sampling interpretation under the IID model; it is not a posterior probability for this device.

Think about itDo 100 consecutive packets in one favorable orientation certify the machine-hall population?

Answer

No. Correlation, selected orientations, changing routes or nonstationary interferers violate that simple population interpretation. Define independent route/time blocks, include required mounting states, and justify effective sample size or a method that handles dependence.

Field design choices that change the inference
Record / control	Reason to retain it
Node/gateway IDs, mechanics, O1/O2 and heights	A population of places is not a population of manufactured units or orientations
Route, timestamps, speed, machine/door state	Multipath, blockage and temporal correlation can cluster failures
Interferer channel/mode and receiver bandwidth	Signal, additive power and structured blocking have different receiver consequences
Payload, spacing, retries, power-saving state	Count original attempts and final delivery separately; do not silently count successful retries as first-attempt success
Independent hold-out blocks and uncertainty method	Fitting and validating on the same selected records can conceal model error

Common misconceptionPacket success or a strong RSSI measures antenna efficiency.

Those are channel/system observations. Inferring a radiator loss from one field metric confuses multiple unknowns and can trigger an unnecessary antenna redesign. The TI range-debugging note, SWRA603A, §§2–5 supports separating conducted receiver/transmitter checks from antenna questions; its product-specific examples are not thresholds here.

Go deeperConfidence and uncertainty answer related but different questions

The binomial bound addresses finite sampling of one specified packet population. It does not include receiver level calibration, mechanical uncertainty, route representativeness or future interferer changes. More correlated packets cannot repair a biased population. Use pilot data to plan independent blocks and report per-state results before a justified use-weighted aggregate.

Now the evidence domains can be reconciled without promoting the most convenient plot into the whole answer.

10 / 10

Reconcile simulation, bench, chamber, and use-case evidence

Which next observation would remove a competing explanation?

The node’s nominal port, low efficiency estimate, notch and field failure admit several explanations. We use a finite Boolean training universe to make that ambiguity inspectable. It is a model of evidence logic, not a posterior probability model or a quantitative inverse solver. The OR signatures do not add dB losses or synthesize measured curves.

antenna-evidence-reconciler/2.0 · exact bit order; every one of the 64 subsets is permitted
Fault / bit	Meaning
D · bit 0	Detectable detune
L · bit 1	Radiator dissipation
O · bit 2	Product-direction null
C · bit 3	Cable / common mode
H · bit 4	Chamber / reference ripple
R · bit 5	Receiver issue

In these supplied signatures, cable and chamber faults contaminate chamber observations. The field trial is cable-free. A product-direction null O can damage coverage without reducing whole-sphere TRP; a receiver issue R can damage reception without changing port or TX evidence. These choices deliberately simplify real electromagnetics and exclude many actual mechanisms.

p06-m06-signatures-v1 · supplied categorical forward model, not measured physics
Observation / test	Adverse means	Boolean flag / duration
E1-port	Corrected S11 / impedance changed from the port reference	D
E2-efficiency	Radiation-efficiency estimate low; attached-cable bias unresolved	L OR C
E3-pattern	Directional notch; product null and range ripple not separated	O OR H
E4-trp	TRP lower than its matched operating / reference configuration	D OR L OR C OR H
E5-tis	Radiated receive sensitivity worse in the specified mode	D OR L OR C OR H OR R
E6-field	Representative teaching link trial misses its stated quality target	D OR L OR O OR R
T-D	Repeat corrected port comparison at the same plane/state	D; 10 min supplied
T-L	Independent efficiency method with controlled cable/setup	L; 40 min supplied
T-O	Product rotation in a verified reference range	O; 35 min supplied
T-C	Paired cable route/choke or cable-free comparison	C; 10 min supplied
T-H	Reference-antenna spatial/range repeat for ripple	H; 25 min supplied
T-R	Conducted receiver sensitivity with controlled operating state	R; 15 min supplied

Read E1=false and name the 32 alternatives it leaves. Predict whether E2 can separate L from C.
Reveal E2, E3, E4, E5 and E6. Inspect eligibility before using each row. E5’s incomplete “poor TIS” note does not count as true.
At 17 sets, compare both partitions of every test. Predict and select T-R before revealing its outcome.
Continue with T-C, T-H and T-L. Inspect every remaining alternative and the observation that eliminates it.
Undo or hide an observation, then try the port-only, contradictory and stale-configuration bundles. Restore metadata separately from acquiring a result.

Interactive · choose discriminating evidence

Antenna Evidence Reconciler

Start with the nominal port result. Reveal evidence one row at a time, inspect the surviving alternatives, then predict and choose a controlled test. This is an Illustrative six-fault training model; it cannot diagnose a physical product.

Evidence bundleEach bundle restores its own complete case, visibility, metadata and test history.

1. Reveal or hide observations

Default path: E2 → E3 → E4 → E5 → E6. E5 is incomplete. Hidden evidence is available to reveal; unavailable evidence cannot be revealed.

E1-port

Corrected S11 / impedance changed from the port reference

Normal (false)eligible · Visible, compatible conditions and an explicit binary result

E2-efficiency

Radiation-efficiency estimate low; attached-cable bias unresolved