Wireless 101
M12 · L02
Module 12 · Lesson 2
Every Promise Has a Price in Decibels
Sub-terahertz, satellites, reflecting surfaces, radios that sense, learned air interfaces. Not one of them repeals Friis, Shannon, kTB or Doppler. Each spends a resource you can already count — so count it.
01 / 11
Wireless 101
M12 · L02
6G, before the marketing
A Terabit Is a Spectrum Claim
Shannon, run backwards
B = \frac{C}{\eta} = \frac{10^{12}}{20} = 50\ \text{GHz} \quad\text{or}\quad \frac{10^{12}}{4} = 250\ \text{GHz}
- IMT-2030 is a targets document — no standard, no chipset, no channel
- At a generous 20 b/s/Hz: 50 GHz of bandwidth
- At a sober 4 b/s/Hz: 250 GHz
- Nothing that wide exists below 100 GHz
So it is not a modulation claim. It is a claim about going above 100 GHz.
02 / 11
Wireless 101
M12 · L02
28 → 300 GHz, priced in full
Thirty Gigabits, Across a Room
The whole sub-THz proposition
C = 10\ \text{GHz}\cdot\log_2(1+10) = 34.6\ \text{Gbit/s} \;\text{at}\; d = 15.3\ \text{m}
- +20.6 dB of path loss, cancelled by an 11×11 array at 20.83 dB
- That panel is 5.5 mm square — area was never the problem
- What you bought is a 5.1° beam you must keep re-aiming
- Reaching 100 m needs 784 elements, each with an amplifier
Both halves are true. Quoting either one alone is the dishonesty.
03 / 11
Wireless 101
M12 · L02
The misquoted one
Absorption Is Linear. Spreading Is Not.
- Spreading: 20 dB per decade of distance. Absorption: dB per km
- 10 dB/km near 300 GHz over 15.3 m = 0.15 dB. Invisible
- 60 GHz oxygen band, 15 dB/km, across 100 m = 1.5 dB — WiGig works
- Over a kilometre it is 10 dB, and that is the wall
Absorption is not what limits a short link. It is what forbids a coverage layer — every 10 dB of new gain buys only 1 more km.
04 / 11
Wireless 101
M12 · L02
LEO — 550 km up
Buying Latency, Paying Doppler
RTT LEO
7.3 ms
RTT GEO
477 ms
FSPL saved
36.3 dB
- 7.59 km/s gives ±256 kHz at 11 GHz — 213% of a 120 kHz subcarrier
- Too big to track, so it is pre-compensated from ephemeris
- A pass lasts 4.5 minutes. Handover forever, even standing still
- 185 satellites tile the Earth; thousands fly. The gap is capacity
05 / 11
Wireless 101
M12 · L02
Try it — climb the spectrum
Why the Industry Keeps Climbing
B = 171 MHz
FSPL@100m = 83.1 dB
array 43.9 cm
C = 4.6 Gbit/s
range 60 km
Throughput peaks near 100 GHz, then falls. Bandwidth keeps growing; power and range do not.
06 / 11
Wireless 101
M12 · L02
RIS — the most oversold one
A Mirror, Not an Amplifier
Distances multiply; they do not add
\frac{P_r}{P_t} \;\propto\; \frac{N^2}{d_1^2\,d_2^2} \quad\Longleftrightarrow\quad L = \text{FSPL}(d_1) + \text{FSPL}(d_2) - 2G_s
- 256 elements, 0.69 m panel, 29.05 dBi counted twice
- Midway on a clear 100 m path: 96.5 dB — 13.2 dB worse than nothing
- A relay takes the worse hop; a surface adds both. That is the difference
- Break-even needs 1168 elements and a 1.46 m panel
The midpoint is the worst place to mount one. It wins only where the direct path is blocked.
07 / 11
Wireless 101
M12 · L02
ISAC — sensing on the comms radio
The Echo Pays d⁴
Two-way loss, and resolution
\frac{P_r}{P_t} = \frac{G^2\lambda^2\sigma}{(4\pi)^3 d^4}, \qquad \Delta r = \frac{c}{2B}
- Comms spreads once (d²); an echo spreads twice — 40 dB per decade
- A 10 m² car at 100 m is 41 dB weaker than a phone standing there
- 97 dB of budget reaches 369 m for a car, 207 m for a person
- Δr = c/2B: 1.5 m at 100 MHz, 3.7 cm at 4 GHz
Comms donates beams and symbols; sensing donates its waveform to OFDM’s 8–12 dB of back-off.
08 / 11
Wireless 101
M12 · L02
“AI-native” — say precisely what is new
The Radio Has Been Adaptive Since 3G
- LTE picks a modulation from a 4-bit report every 1 ms (M6-L4). Not new
- Real: learned channel-feedback compression — it attacks overhead
- Real: beam prediction — turns a search into an inference. Buys latency
- Not real: learned decoders. LDPC is already within a fraction of a dB of Shannon
The test: name the resource spent. More throughput with no bandwidth, power or antennas is a claim to beat Shannon.
10 / 11
Wireless 101
M12 · L02
Recap
What you learned
- Sub-THz: 34.6 Gbit/s at 15.3 m, and 784 amplifiers to reach 100 m
- LEO: 36.3 dB and 7.3 ms, paid in ±256 kHz and a 4.5-minute pass
- RIS: a product of distances — 13.2 dB worse than an empty street
- ISAC: d⁴, 41 dB down, and Δr = c/2B
- AI: buys overhead, never capacity
Next in Module 12
Price the promise, or it is not engineering yet. Module 12 closes with career paths →
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