When an Antenna Is Worth 200 Repetitions

When an Antenna Is Worth 200 Repetitions

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

When an Antenna Is Worth 200 Repetitions

In this chapter’s metering rollout, 20% of the meters sit in basements at an RSRP of −123 dBm — deep enough that NB-IoT must repeat every message many times just to be heard, draining airtime and battery. An external antenna at street level lifts that same basement signal to −100 dBm, a 23 dB gain bought once in hardware. This audit asks what that antenna is really worth: how many repetitions of airtime does its 23 dB replace?

Companion to the chapter Lab: Coverage Planning — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is repetitions. The middle card applies the page rule. The green card is repetition gain. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

Repetitions changes repetition gain An input card leads through the rule gain = 10 x log10(repetitions) to the repetition gain result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Coverage bought with repetitions is paid again in airtime and battery.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 32 repeats.

  2. 2

    Name the relationship. gain = 10 x log10(repetitions)

  3. 3

    Substitute with units. 10 x log10(32) = 15.05 dB

  4. 4

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

Predict, then change repetitions

Try Predict the direction of gain = 10 x log10(repetitions). Test another repetitions, then compare repetition gain.

32 repeats
Chapter baseline
Repetition gain

Observe Coverage bought with repetitions is paid again in airtime and battery. Reset repetitions to 32 and compare repetition gain.

Explain Coverage bought with repetitions is paid again in airtime and battery.

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 repetitions moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only repetitions. It is not a field prediction.

TryUse Check derivation to compare 32, 64, and 128 repetitions with the antenna's 23 dB measured gain.
ObserveRepetition gain rises from about 15 to 21 dB, so the fixed antenna improvement exceeds even the 128-repeat arithmetic.
ExplainCoherent energy accumulation grows as 10 log10 of repetition count, while raising the antenna changes every transmission without multiplying airtime.

Ready: use the stated baseline inputs, then compare each displayed result.

Ada: The section’s whole argument is that coverage and capacity are the same lever, and it hangs on the repetition-gain rule ~10 x log10(N) dB. Let me verify that rule on the chapter’s own numbers and then price the basement fix in repetitions.

  • The stated case: 10 x log10(32) = 15.0515 dB, matching the chapter’s ~15 dB for 32 repeats.
  • The deep-coverage band it quotes (64-128 repeats): 10 x log10(64) = 18.0618 dB up to 10 x log10(128) = 21.0721 dB – roughly 18-21 dB bought purely by repeating in time.

Now the worked fix. The external antenna lifts the basement from -123 dBm to -100 dBm, a gain of -100 - (-123) = 23 dB. How many repetitions would buy that same 23 dB instead? Invert the rule: N = 10^(23 / 10) = 10^2.3 = 199.5, about 200 repeats.

That is the equivalence the chapter is pointing at: 23 dB of hardware antenna gain replaces roughly 200 repetitions of airtime per message. The design meaning is that the link-budget lever and the capacity lever are literally the same decibels – spend 23 dB once in an antenna, or pay it forever in ~200x the airtime and battery, which is why good planning attacks the deep-coverage minority first.

Every number above is taken from the chapter’s own material and re-derived step by step.

Technical boundaries. Spatial fading, interference, cell loading, combining loss, battery current, and antenna-installation variability are outside this dB equivalence comparison.