Wireless 101
M12 · L01
Module 12 · Lesson 1
Forty-Three Pieces, One Link
Every lesson worked its own numbers to make its own point. This one fixes one parameter set and carries it from the amplifier to a delivered megabit — so the power on line 1 is why the cell is 336 m, and the constellation on line 4 is why you need three times the sites.
01 / 11
Wireless 101
M12 · L01
The chain, and its mirror
Every Block Buys and Bills
- Coding: bandwidth out, 5–8 dB of gain back (M6-L4, M9-L2)
- Mapping: +2 bits per symbol costs about 6 dB (M6-L4)
- OFDM: a cyclic prefix and 8–12 dB of PAPR, for a flat channel (M10-L2)
- Antenna: aperture out, dBi back — gain is geometry (M7-L2)
- LNA first, because the Friis cascade makes stage 1 the whole NF (M9-L1)
Source coding is in the diagram and nowhere in this course — the codec, not the radio, usually sets the rate.
02 / 11
Wireless 101
M12 · L01
3.5 GHz · 100 MHz · 64-QAM r=3/4 · 2 layers
Fix It, Then Never Move It
Sensitivity — four terms, M9-L1
S = -174 + 80 + 7 + 20.0 = -67.0\ \text{dBm}
- 10 log₁₀(10⁸) = 80.00 dB → floor −94.0 dBm, the figure M9-L1 states
- Plus NF 7 dB → effective floor −87.0 dBm
- 80 dB of that sensitivity is bandwidth: the same silicon in 200 kHz reads 27.0 dB better
A sensitivity without a bandwidth beside it is meaningless (M9-L4).
03 / 11
Wireless 101
M12 · L01
The required SNR, derived not asserted
The Ledger Closes at Zero
M6-L4’s Eₖ/N₀, a stated coding gain, M9-L1’s conversion
\mathrm{SNR}_{req} = 18.8 - 5.3 + 10\log_{10}4.5 = 20.0\ \text{dB}
- EIRP 46 − 2 + 17 = 61.0 dBm; Pₕₓ = 56.0 − PL
- Margins 8.0 + 10.2 + 3.0 = 21.2 dB (M8-L3, M8-L4, M9-L3)
- Allowed PL 101.8 dB → at n = 3.5 from 83.33 dB, d = 336 m
- SNR arriving 41.2 dB − 21.2 reserved = 20.0 dB = exactly what it needed
04 / 11
Wireless 101
M12 · L01
From hertz to delivered bits
100 MHz Becomes 710 Mbit/s
Six factors, none of them optional
R_b = L\cdot N_{sc}\cdot R_{sym}\cdot U\cdot \log_2 M\cdot R_c
- 273 blocks × 12 = 3276 subcarriers = 98.28 MHz of 100
- 14 symbols per 0.5 ms = 28 000 sym/s, 93.33% useful (M10-L2)
- 3276 × 28 000 = 91.73×10⁶ RE/s; less 14% control → U = 78.89%
- × 4.5 bits × 2 layers = 710 Mbit/s, η = 7.10 b/s/Hz
21.1% total overhead — inside M6-L3’s 20–30% ✓. M6-L3 gives LTE 2×2 about 7.5.
05 / 11
Wireless 101
M12 · L01
Try it — build the whole link
Does It Close?
closes — margin 0.0 dB
710 Mbit/s · 7.10 b/s/Hz
max range 336 m
06 / 11
Wireless 101
M12 · L01
The gap to Shannon, fully spent
2.73 dB, and Nothing Left Over
Ceiling 1331.6 Mbit/s, delivered 710
10\log_{10}\frac{6.658}{4.5} + 10\log_{10}\frac{1}{0.789} = 1.70 + 1.03 = 2.73\ \text{dB}
- log₂(1 + 100) = 6.658 b/s/Hz per layer at 20 dB (M6-L3)
- × 2 layers × 100 MHz = 1331.6 Mbit/s ceiling (M10-L3)
- 1.70 dB is the implementation gap: 4.5 of the 6.658 permitted
- 1.03 dB is the 21.1% overhead — small in dB, so nobody hides it
Datasheet minus delivered, accounted for line by line. That is what a capstone is for.
07 / 11
Wireless 101
M12 · L01
Change one thing, move three
5.95 dB Paid for 1.25 dB
64-QAM
336 m
256-QAM
227 m
+ 3 dB I
187 m
- 8 bits instead of 6 → 946.6 Mbit/s, +1.25 dB of rate
- Costs 4.7 dB of Eₖ/N₀ plus 1.25 dB of η = 5.95 dB of link
- Cell area falls to 45.7%, so 2.19× the sites
- Capacity density 2002 → 5847 Mbit/s/km² = 1.333 × 2.188 ✓
- More sites → interference 3 → 6 dB → 187 m → 3.23× the sites
08 / 11
Wireless 101
M12 · L01
What the model cannot tell you
The Weakest Row Is the Exponent
- n = 2.7 instead of 3.5 turns 336 m into 483 m — 2.1× the area, from one plausible fit (M8-L4)
- 8 dB of coding gain instead of 5.3 gives 403 m: one row, 20%
- 710 Mbit/s is one user holding the whole carrier
- TDD at a 75% downlink share charges rate, not decibels: 532 Mbit/s, still 336 m (M10-L4)
- 10.2 dB of shadowing margin means one edge user in ten misses out
A budget is a model. Its real use is telling you which row to go and measure first.
10 / 11
Wireless 101
M12 · L01
Recap
What you learned
- One parameter set, nine modules, sixteen rows — none optional
- 41.2 dB arrives, 21.2 is reserved, 20.0 dB reaches the demodulator
- 336 m at 64-QAM, 892 m at QPSK — 7.0× the area
- 710 Mbit/s, η = 7.10, and a Shannon gap of 2.73 dB fully split
- Denser cells cause part of their own cost; beams, not power, break the loop
Next in Module 12
11 / 11