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Shannon-Hartley and spectral efficiency
The Shannon-Hartley theorem is a ceiling: it connects bandwidth and signal-to-noise ratio to an ideal channel capacity.
Question
What does signal quality imply about the maximum possible data rate?
Inputs
- Channel bandwidth B
- Signal-to-noise ratio expressed as a linear ratio
Answer
Working
Convert SNR from dB before substituting: S/N = 10^(SNR_dB/10). Spectral efficiency is C/B = log2(1 + S/N) bits/s/Hz. Real systems operate below this ceiling because they need coding margin, pilots, framing, retransmissions, and robust behavior in a changing channel.
Visual explanation
- More SNR
- Smaller incremental capacity
- More bandwidth
- Linear capacity opportunity
Interpretation
The theorem explains why a clean narrow channel can outperform a noisy wide one, and why ever-higher power produces diminishing returns once another link term dominates.