Math Bridge: Reciprocal Antenna Loss in NB-IoT Access

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Math BridgeCellular IoTStruggle-friendly runway

Why does one detuned antenna tax both access directions?

Follow one 4 dB installed loss through uplink EIRP, downlink aperture, and an ideal repetition estimate.

Radio Remi, the guideRadio Remi guides
The one targetApply passive-antenna reciprocity without double-counting or overclaiming.
The chapter case23 dBm; 0 dBi nominal; 4 dB loss; eight baseline repeats.
What it buys youBudget both listening and sending before reading a current trace.

A field team faces an unresolved physical question: Why does one detuned antenna tax both access directions? They must answer it before changing installed antenna detuning loss on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is installed antenna detuning loss. The middle card applies this page's relationship. The green card is uplink eirp. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

Installed antenna detuning loss changes uplink eirp An input card leads through the page relationship to the uplink eirp result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. The same installed gain term enters both directions, but real downlink waiting and uplink repetitions are separate events controlled by the network and modem.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for installed antenna detuning loss is 4.

  2. 2

    Name the relationship. G=G0-L; EIRP=Pt+G; A/A0=10^(-L/10); Nideal=N0·10^(L/10)

  3. 3

    Substitute the chapter fixture. Set installed antenna detuning loss to 4. The page ledger gives uplink eirp as 19.00 dBm.

  4. 4

    Read the result. Keep dBm beside the value. Use it only inside the technical boundary on this page.

Predict, then change installed antenna detuning loss

Try Predict the direction of uplink eirp. Move one control, calculate, then check your prediction.

4
Chapter baseline
Uplink EIRP

Observe The same installed gain term enters both directions, but real downlink waiting and uplink repetitions are separate events controlled by the network and modem. Reset the control to 4 and compare uplink eirp.

Explain Only installed antenna detuning loss moves here. The other chapter fixtures remain fixed.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only installed antenna detuning loss moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only installed antenna detuning loss. It replays the chapter fixture; it is not a field prediction.

1. Follow the access sequence

An NB-IoT device listens for timing and control, sends a request, listens for a grant, and sends data. A passive antenna's installed gain applies on both the receive and transmit legs.

Radio Remi: Reciprocity shares the antenna property, not the network workload.

2. Name the algebra moves

1

Subtract installed lossGinstalled=G0−L.

2

Add uplink powerEIRP=Pt+Ginstalled.

3

Undo the receive lossA/A0=10^(−L/10).

4

Form an ideal multiplierM=10^(L/10).

5

Choose a stated step modelNstep=2^ceil(log2(N0M)).

3. Reproduce the 4 dB case

Ginstalled=0−4=−4 dBi; EIRP=23−4=19 dBm; M=10^(4/10)=2.51×

The receive aperture is 39.8% of the nominal case. Eight repeats become 20.1 ideally; a deliberately assumed power-of-two step model selects 32.

4. Try one controlled change

G=G0−L; EIRP=Pt+G; A/A0=10^(−L/10); Nideal=N0·10^(L/10)

TryChange only the installed antenna loss. The radio power, nominal gain, baseline count, and illustrative step model stay fixed.

Installed gain
Uplink EIRP
Receive aperture left
Ideal multiplier
Ideal repetitions
Power-of-two model

ObserveAt 4.00 dB loss, installed gain is −4.00 dBi, uplink EIRP is 19.0 dBm, receive aperture is 39.8%, and the ideal count is 20.10.

ExplainThe same installed gain term enters both directions, but real downlink waiting and uplink repetitions are separate events controlled by the network and modem.

Technical boundaries.

Reciprocity is a component relation, not an energy-accounting shortcut.

Passive
The gain relation assumes a passive reciprocal antenna path
Steps
The power-of-two rule is an explicit teaching model, not a universal grant table
Energy
Listening, access, sending, retries, and sleep have different current states

Confirm supported repetition values and measure the whole access trace on the target network.

5. Do not multiply both legs together

A 4 dB antenna loss does not become an 8 dB link loss merely because the device both listens and sends. Apply 4 dB to each separate leg, then count the time and energy spent in each state.

6. Carry the evidence forward

Record installed gain or efficiency, NPSS and NPDCCH acquisition time, NPRACH attempts, granted repetitions, NPUSCH duration, downlink windows, failures, RSRP, SINR, and current by state.

7. Check yourself

Why does the receive aperture fall to 39.8%?
Answer: A 4 dB loss is a linear power factor of 10^(−4/10)=0.398.
Is 32 a guaranteed NB-IoT grant?
Answer: No. It is the result of the page's stated power-of-two step model.
Should the uplink and downlink losses be added into one 8 dB number?
Answer: No. Apply the shared 4 dB antenna property to each separate link event.
Honesty boundary.

The page exposes one reciprocal loss without pretending to simulate NB-IoT access scheduling.

4 dB
Illustrative installed detuning loss
20.1
Ideal combining count
32
Assumed step-model result

Go deeper into the chapter's access sequence, then validate the actual modem, operator profile, and installed antenna.

Return to NB-IoT Channel Access with the maths unpacked →