Wireless 101
M11 · L04
Module 11 · Lesson 4

Twenty Bytes an Hour, for Ten Years

Modules 5 and 6 chased bits per hertz. These radios chase joules per bit and cents per node. A door sensor on a coin cell is a harder problem than a gigabit over 10 m — money solves the gigabit.

01 / 11
Wireless 101
M11 · L04
The design inversion, costed

The Radio Is 1.3% of It

A CR2032, divided by a decade
I_{avg} \le \frac{220\ \text{mAh}}{87\,660\ \text{h}} = 2.51\ \mathrm{\mu A}
  • One hourly BLE report ≈ 8 mA × 15 ms = 33.3 nAh
  • × 87 660 events = 2.92 mAh of the 220 mAh cell
  • So sleep gets 217 mAh → allowed 2.48 µA asleep

Nothing here is short of hertz. Everything is short of joules and cents.

02 / 11
Wireless 101
M11 · L04
Bluetooth — two radios, one logo

Classic Hops, BLE Sips

  • Classic: 79 × 1 MHz, FHSS at 1600 hops/s → 625 µs dwell
  • Pure TDD on one hop sequence (M10-L4) — a switch, no duplexer
  • BLE: 40 × 2 MHz, 2402 + 2k MHz; 37 data channels
  • GFSK at 1 Msym/s — M5-L2’s constant envelope, collected
  • 0.5 bit/s/Hz is wasteful and irrelevant; a cheap class-C amplifier is not

2.4 GHz is shared with WiFi (M11-L1), so both are designed against interference, not just noise (M9-L3).

03 / 11
Wireless 101
M11 · L04
Marketing, meet M8-L4

“4× Range” Needs 12 dB

Coded PHY S = 8, against the claim
10\log_{10}8 = 9.03\ \text{dB} \;<\; 20\log_{10}4 = 12.04\ \text{dB}
  • Eight symbols per bit → 8× the energy per bit = 9.03 dB
  • 4× range costs 10n log₁₀4 — that is 12.04 dB only at n = 2
  • Real silicon measures ~10 dB → 1010/20 = 3.16× in free space
  • Indoors at n = 3: 1010/30 = 2.15×. At n = 4: 1.78×

A range claim with no path-loss exponent is quoting its best case. Price: 125 kbit/s, so 8× the airtime.

04 / 11
Wireless 101
M11 · L04
Zigbee — 802.15.4

Mesh Buys 14 dB for Free

  • 250 kbit/s, O-QPSK; 32 chips per 4 bits = 2 Mchip/s
  • Processing gain 2×10⁶/250×10³ = 8 = 9.03 dB (M10-L1)
  • 0 dBm to −100 dBm, less 16.1 dB margin → 29 m per hop
  • 3 hops reach 87 m; one hop would need 14.4 dB more
  • Charged in latency, 10 log₁₀3 = 4.8 dB of throughput, and complexity

Routers cannot sleep. A mesh of nothing but batteries is not buildable.

05 / 11
Wireless 101
M11 · L04
Try it — name your constraint

Which One Survives?

Rate 1.0 kbit/s
Range 100 m
Battery 5 yr
LoRa SF SF12
fits: LoRa, NB-IoT out: WiFi rate ok, battery fails SF12: 30.5 sym/s, 293 bit/s, 151 dB
06 / 11
Wireless 101
M11 · L04
LoRa — the best link in the lesson

CDMA’s Trick, With a Chirp

Spreading factor, and the same Gₚ as M10-L1
R_s = \frac{B}{2^{SF}},\quad R_b = SF\cdot R_s\cdot CR,\quad G_p = \frac{B}{R_b}
  • SF12: 125 000/4096 = 30.52 sym/s → 12 × 30.52 × 4/5 = 293 bit/s
  • SF7: 125 000/128 = 976.6 sym/s → 5469 bit/s, a span of 18.7×
  • Gₚ = 125 000/366.2 = 341 = 25.3 dB, against IS-95’s 21.07 dB
  • −137 dBm sensitivity vs a −117 dBm floor = 20 dB below the noise

Per bit it is ordinary: Eₖ/N₀ = −20 + 25.3 = +5.3 dB (M9-L1). The chirp supplies the rest.

07 / 11
Wireless 101
M11 · L04
151 dB, and what really caps it

Two Minutes of Silence

Budget
151 dB
On air
1155 ms
Then off
114 s
  • 14 dBm − (−137) = 151 dB, vs WiFi’s low-rate 110 dB
  • The 41 dB = +22.0 narrower + 25 relaxed SNR − 6 power ✓
  • Paid with 10 log₁₀(6×10⁶/293) = 43.1 dB of rate
  • 1% duty cycle → 31 msg/h at SF12, 873/h at SF7 (28×)
  • Class A is uplink-biased: two brief windows, then unreachable
08 / 11
Wireless 101
M11 · L04
Cellular IoT — licensed spectrum

One Resource Block, Nothing More

NB-IoT’s carrier, and its extra 21 dB
12 \times 15\ \text{kHz} = 180\ \text{kHz},\quad 10\log_{10}128 = 21.07\ \text{dB}
  • 180 kHz is exactly one LTE resource block (M10-L2) — drops into a live carrier
  • ~164 dB coupling loss: 23 − 164 = −141 dBm needed, and 128 repeats give 21.07 dB
  • LTE-M: 6 blocks = 1.08 MHz, ~1 Mbit/s, ~156 dB, handover + VoLTE
  • PSM and eDRX — not the modulation — are what buy the decade

164 vs LoRa’s 151 dB, but 9 dB of it is just transmit power. On sensitivity the gap is 4 dB.

09 / 11
Wireless 101
Knowledge Check

Check whatstuck

Four questions on low-power IoT radios — the energy budget, BLE range, Zigbee mesh, and LoRa.

Question 1 of 0
Score 0/0

10 / 11
Wireless 101
M11 · L04
Recap

What you learned

  • A decade on 220 mAh means 2.51 µA; the radio is 1.3% of it
  • BLE Coded S=8 gives 9.03 dB, not the 12.04 dB “4×” implies
  • Zigbee mesh: 29 m per hop, and routers that cannot sleep
  • LoRa SF12: 293 bit/s, 151 dB, 31 messages an hour
  • NB-IoT = one 180 kHz resource block; LTE-M adds mobility and voice
Next: Module 12, the capstone
Putting It All Together →
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