Calculate channel capacity, spectral efficiency, and Nyquist bandwidth from bandwidth, SNR, and modulation levels with common presets.

Ideal band-limited AWGN channel. SNR is signal power divided by noise power.

Channel Capacity Formula

The following formula is used to calculate the channel capacity.

C = B ร— log2(1 + SNR)

Variables:

  • C is the channel capacity (bps)
  • B is the bandwidth of the channel (Hz)
  • SNR is the signal-to-noise ratio (dimensionless)

To calculate the channel capacity, multiply the bandwidth of the channel by the logarithm base 2 of 1 plus the signal-to-noise ratio. This gives the theoretical capacity of an ideal band-limited additive white Gaussian noise (AWGN) channel. With suitable coding, rates below capacity can have arbitrarily low error probability; this is not a measured throughput or zero-error guarantee.

What is a Channel Capacity?

Channel capacity, in information theory, is a theoretical rate limit under a specified channel model. Reliable communication with arbitrarily low error probability is possible below that limit under the coding theoremโ€™s assumptions. It is typically measured in bits per second (bps) and depends on the bandwidth of the channel and the signal-to-noise ratio. The concept of channel capacity was introduced by Claude Shannon in his foundational work on information theory.

How to Calculate Channel Capacity?

The following steps outline how to calculate the Channel Capacity using the given formula:

  1. First, determine the bandwidth of the channel (B) in Hz.
  2. Next, determine the linear signal-to-noise power ratio (SNR), or choose the dB method, which converts SNRdB using S/N = 10^(SNRdB/10).
  3. Next, use the formula C = B * log2(1 + SNR) to calculate the channel capacity (C) in bps.
  4. Select the required solve mode and Calculate. Spectral efficiency is log2(1 + S/N) bits/s/Hz; the ideal noiseless real-baseband Nyquist model uses C = 2B log2(M), with integer M โ‰ฅ 2.
  5. After inserting the values of B and SNR into the formula and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Bandwidth of the channel (B) = 1000 Hz

Signal-to-noise ratio (SNR) = 10