The Capacity Formula

Claude Shannon proved that the capacity $C$ of a channel is limited by two primary physical factors: the Bandwidth (frequency range) and the Signal-to-Noise Ratio (SNR).

Where:

• C: Channel Capacity (bits per second).
• B: Bandwidth (Hz).
• S/N: Signal-to-Noise Power Ratio (linear, not dB).

Converting dB to Linear

In the field, we measure SNR in decibels (dB). To use the Shannon formula, we must convert the log-scale dB back to the linear power ratio:

Example: An SNR of 30dB corresponds to a linear ratio of 1000. Under these conditions, a 20MHz Wi-Fi channel has a theoretical limit of roughly $20 \times \log_2(1001) \approx 200 \text{ Mbps}$.

Increasing Capacity: MIMO and MCS

How do we bypass these limits in modern hardware?

• MIMO: Multiple-Input Multiple-Output uses spatial multiplexing to create multiple "virtual channels," effectively multiplying the capacity by the number of spatial streams.
• High-Order Modulation (QAM): Encoding more bits per symbol allows us to pack more information into the same bandwidth, but requires a significantly cleaner SNR (lower noise floor).

The Future: Terahertz and Beyond

As we reach the peak of SNR efficiency in the Gigahertz range, the only path forward for 6G and beyond is moving into higher frequency bands (Terahertz), where vast amounts of Bandwidth (B) are still available, even if the SNR remains challenging at those ranges.