About the Shannon Channel Capacity Simulator
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So, in plain English, what is Shannon capacity? Is it just the maximum Wi-Fi speed?
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Close. Claude Shannon proved in 1948 that, given bandwidth B and SNR S/N, no scheme can move information faster than C = B·log2(1+S/N) with vanishing error. With B = 1 MHz and SNR = 20 dB (S/N = 100), the cap is about 6.66 Mbps. Real Wi-Fi/5G systems get within a couple of dB of that bound using strong coding and MIMO.
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If noise rises, capacity collapses quickly when I drag the slider!
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Right. A 10x increase in noise removes 10 dB of SNR, which costs you about 3.3 bit/s/Hz of efficiency. That is why satellite and mmWave radar systems pour engineering effort into low-noise amplifiers and cryogenic front-ends — every dB of noise temperature buys real link distance. Hit Noise sweep and watch the capacity track the SNR.
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And spectral efficiency is just capacity per Hz of bandwidth? I have seen 10 b/s/Hz quoted for Wi-Fi 6.
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Exactly: η = C/B. Wi-Fi 6 uses 1024-QAM plus MU-MIMO to push η past 10, and 5G NR targets 20. Inverting Shannon, η = 10 needs SNR around 30 dB — which is why 5G/6G base stations rely on beamforming to lift the local SNR rather than the raw transmit power.
What is Shannon channel capacity?
The Shannon channel capacity is the maximum rate at which information can be transmitted with vanishing error probability over a noisy channel of bandwidth B and signal-to-noise ratio S/N. Derived by Claude Shannon in 1948, it underlies every modern wireless, wireline, satellite and optical communication system: every link budget is benchmarked against this bound.
Physical model and key formulas
For a continuous AWGN channel the capacity is:
$$C = B\,\log_2\!\left(1 + \frac{S}{N}\right)$$
where B is the bandwidth in Hz, S the received signal power in W and N = N0·B the noise power in W. SNR in dB is SNR_dB = 10·log10(S/N) and spectral efficiency is η = C/B in bits/s/Hz. The bandwidth required to meet a target rate R is B_need = R/η.
Real-world applications
Wi-Fi standards: Wi-Fi 6/6E/7 combine 1024-QAM or 4096-QAM with 160/320 MHz channels and MIMO to approach the Shannon limit. Designers use exactly this calculation to budget the SNR margin needed for each modulation step.
5G and 6G cellular: 5G NR aims for 20 b/s/Hz peak spectral efficiency in mmWave bands by combining wide bandwidth with massive MIMO beamforming. 6G research targets 100 b/s/Hz, which can only be reached with extreme cell densification and reconfigurable surfaces.
Satellite and deep-space links: With receive power often below the noise floor, modern codes (turbo, LDPC) approach within 0.5 dB of the Shannon bound. CCSDS standards rely on this to push data rates from Mars rovers and outer-planet probes.
Optical fibre: Long-haul fibres deal with a nonlinear Shannon limit, and DWDM systems combine coherent detection with 16-QAM/64-QAM modulation to reach Tbit/s per fibre.
Common pitfalls
Doubling bandwidth does not double capacity: it doubles the noise N = kTB as well, so SNR drops and the log2(1+SNR) term shrinks. Going wideband always implies more antenna gain or more transmit power somewhere.
No product can exceed Shannon: marketing peak rates usually come from channel bonding or instantaneous values with non-zero error rate. The "% of Shannon" figure is the honest efficiency metric.
Mind dB versus linear ratios: SNR 20 dB equals a linear ratio of 100, not 20. Shannon's log2 takes the linear value: log2(1+100)=6.66 versus log2(1+1000)=9.97, so 10 dB of extra SNR adds only 1–3 bit/s/Hz, not ten times more capacity.