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komm.AWGNChannel

Additive white Gaussian noise (AWGN) channel. It is defined by $$ Y_n = X_n + Z_n, $$ where $X_n$ is the channel input signal, $Y_n$ is the channel output signal, and $Z_n$ is the noise, which is iid according to a Gaussian distribution with zero mean. The channel signal-to-noise ratio is calculated by $$ \snr = \frac{P}{N}, $$ where $P = \mathrm{E}[X^2_n]$ is the average power of the input signal, and $N = \mathrm{E}[Z^2_n]$ is the average power (and variance) of the noise. For more details, see CT06, Ch. 9.

Attributes:

  • signal_power (float | Literal['measured']) –

    The input signal power $P$. If equal to the string 'measured', then every time the channel is invoked the input signal power will be computed from the input itself (i.e., its squared Euclidean norm).

  • snr (float) –

    The channel signal-to-noise ratio $\snr$ (linear, not decibel). The default value is np.inf, which corresponds to a noiseless channel.

noise_power: float property

The noise power $N$.

capacity

Returns the channel capacity $C$. It is given by $C = \frac{1}{2}\log_2(1 + \snr)$, in bits per dimension.

Examples:

>>> awgn = komm.AWGNChannel(signal_power=1.0, snr=63.0)
>>> awgn.capacity()
np.float64(3.0)

__call__

Transmits the input signal through the channel and returns the output signal.

Parameters:

  • input (ArrayLike) –

    The input signal $X_n$.

Returns:

  • output (NDArray[floating]) –

    The output signal $Y_n$.

Examples:

>>> rng = np.random.default_rng(seed=42)
>>> awgn = komm.AWGNChannel(signal_power=5.0, snr=200.0, rng=rng)
>>> x = [1.0, 3.0, -3.0, -1.0, -1.0, 1.0, 3.0, 1.0, -1.0, 3.0]
>>> awgn(x).round(2)
array([ 1.05,  2.84, -2.88, -0.85, -1.31,  0.79,  3.02,  0.95, -1.  ,  2.87])