Pick Two
A radio link has three currencies: bandwidth, power, and the errors you tolerate. You can improve any two — by spending the third.
The Communication Triangle
- Bandwidth — more hertz, more rate; but spectrum is auctioned for billions
- Power — more watts, better SNR, fewer errors; but batteries and amplifiers are finite
- Error rate — tolerate more and everything else gets cheaper
Fix any two targets and physics fixes the third for you.
Bandwidth Cuts Both Ways
A wider receiver also lets in more noise, so B helps outside the log and hurts inside it. Push B to infinity and capacity stalls at P/(N₀ ln 2).
Which Wall Are You Hitting?
Power-limited (η < 2 b/s/Hz): spectrum to spare, no signal. Spread out, code hard, drop the constellation. Bandwidth-limited (η > 2): plenty of signal, no hertz. Go denser, code lighter, add antennas.
Squeezing Hertz Costs Energy
2 b/s/Hz needs 1.76 dB; 4 needs 5.74; 8 needs 15.03. As η → 0 it falls to ln 2 — the −1.59 dB floor of M6-L1.
Design the Link
Buy bandwidth, buy SNR, and watch which modulation the channel will carry — and which wall you end up against.
Coding Gain: Errors Paid For in Hertz
A rate-1/2 code doubles the bandwidth and hands back 5–8 dB of transmit power at the same BER. Bandwidth in, error-rate performance out — the amplifier never moves.
Adaptive Modulation and Coding
Walk across a room and your SNR can swing 20 dB. Design for the worst case and everyone crawls; for the best case and most people lose the link. So measure the channel, then pick the densest scheme it supports — over and over.
Every Millisecond
The handset reports a CQI (1–15) as often as every 1 ms subframe; the scheduler picks an MCS from the ladder QPSK → 16-QAM → 64-QAM (→ 256-QAM in LTE-A Pro). It aims at ~10% first-try block error, and HARQ retransmits with extra parity when it misses.
What you learned
- Bandwidth, power, error rate: improve two, spend the third
- Eb/N₀ ≥ (2η−1)/η — 1.76 dB at 2 b/s/Hz, 15.03 dB at 8
- Power-limited below ~2 b/s/Hz, bandwidth-limited above — opposite fixes
- Coding buys error performance with hertz; AMC re-decides every millisecond