The Noise Floor Was Never the Problem
M9-L2 warned you about a BER curve that flattens and stops responding to power. Here is why: in almost every deployed system the limit is not thermal noise but other transmitters.
Twenty-One dB Becomes Nine
S = −80 dBm, thermal N = −101 dBm, a co-channel cell at I = −90 dBm. Convert and add: 1.000×10−9 + 0.0794×10−9 = 1.0794×10−9 mW = −89.67 dBm.
The noise term is a rounding error once interference sits 11 dB above it. Shaving a decibel off the noise figure buys you nothing here.
Power Helps Nobody
Turn every transmitter up by 10 dB: S = −70, I = −80, N unchanged. SINR goes 9.67 → 9.97 dB. Ten decibels bought 0.30 dB, because everyone rose together.
No Filter Can Save You
CCI is on your own frequency, so there is no frequency difference to filter. Cellular fixes it geometrically: split channels into N groups and space the repeats by D/R = √(3N).
Only certain N tile a hexagonal plane — 1, 3, 4, 7, 9, 12, 13 — which is why you never meet a reuse factor of 5.
Where 18 dB Came From
- N = 7, n = 4: 21² = 441, /6 = 73.5 → 18.66 dB
- N = 12: 1296/6 = 216 → 23.34 dB
- Cost of that 4.68 dB: 48 channels per cell → 28, a 42% cut
- At n = 3, nothing in the table reaches 18 dB
SINR and Reuse Explorer
Move I past N and watch the weaker term stop mattering. The lower panel is C/I against reuse factor at your exponent.
A Ratio Problem, Not a Leak
An ACLR of 45 dBc puts the leakage 45 dB below its own carrier. Arriving 30 dB stronger than your wanted signal, that leakage lands 45 − 30 = 15 dB below it. Harmless.
- Same transmitter, 50 dB stronger: leakage +5 dB above — link dead
- 500 m vs 20 m at n = 3.5: 35 log₁₀25 = 48.93 dB imbalance
- So the leakage sits 3.93 dB above what you wanted
- The near-far problem is a power-control problem
Five Symbols Deep
Urban στ = 1 µs (M8-L3) at 5 MBd gives Ts = 200 ns, so the spread covers 5 symbols. ISI is made of your own signal, so more power moves it not at all.
Impulses Are Not Gaussian
- Noise σ for 99% of the time, 10σ for 1%
- Q(4) predicts 3.17×10−5; the truth is 3.48×10−3
- 110× worse, while average noise power rose only 2.99 dB
- Buying it back with power would take 16.7 dB
- Ovens at 2.45 GHz, LED drivers, power lines, IP3 products
Averaged noise power is the wrong statistic, and so is the independent-bit assumption behind PER.
What you learned
- SINR = S/(I+N); add powers, never decibels
- I ≫ N makes transmit power worth 0.30 dB
- D/R = √(3N); N = 7 at n = 4 gives 18.66 dB
- ACI is a power ratio; ISI is your own signal
- Filtering cannot touch CCI — geometry and control can