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 | str) –

  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 (Optional[float]) –

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

Input:

• in0 (Array1D[float]) –

  The input signal $X_n$.

Output:

• out0 (Array1D[float]) –

  The output signal $Y_n$.

Examples:

>>> np.random.seed(1)
>>> awgn = komm.AWGNChannel(signal_power=5.0, snr=200.0)
>>> 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([ 1.26,  2.9 , -3.08, -1.17, -0.86,  0.64,  3.28,  0.88, -0.95,  2.96])

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)