komm.GaussianChannel

Gaussian 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 is characterized by the noise power (variance) $$ \sigma_Z^2 = \mathrm{E}[Z_n^2]. $$

The channel supports real- and complex-valued signals. In the complex case, the noise is circularly symmetric complex Gaussian, with the noise power equally divided between the real and imaginary parts.

For more details, see CT06, Ch. 9.

Parameters:

• noise_power (float) –

  The noise power (variance) $\sigma_Z^2$. The default value is 0.0, which corresponds to a noiseless channel.

transmit()

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

The input signal may be real- or complex-valued. If the input is real, the noise is real-valued Gaussian with variance equal to the noise power $\sigma_Z^2$. If the input is complex, the noise is circularly symmetric complex Gaussian, with the noise power equally divided between the real and imaginary parts, i.e., $\mathrm{E}[\mathrm{Re}\{Z_n\}^2] = \mathrm{E}[\mathrm{Im}\{Z_n\}^2] = \sigma_Z^2/2$.

Parameters:

• input (ArrayLike) –

  The input signal $X_n$.

Returns:

• output (NDArray[floating | complexfloating]) –

  The output signal $Y_n$.

Examples:

>>> rng = np.random.default_rng(seed=42)
>>> ch = komm.GaussianChannel(noise_power=0.025, rng=rng)
>>> ch.transmit([1, 3, -3, -1, -1, 1, 3, 1, -1, 3]).round(2)
array([ 1.05,  2.84, -2.88, -0.85, -1.31,  0.79,  3.02,  0.95, -1.  ,  2.87])

>>> rng = np.random.default_rng(seed=42)
>>> ch = komm.GaussianChannel(noise_power=0.05, rng=rng)
>>> ch.transmit([1 + 3j, -3 - 1j, -1 + 1j, 3 + 1j, -1 + 3j]).round(2)
array([ 1.05+2.84j, -2.88-0.85j, -1.31+0.79j,  3.02+0.95j, -1.  +2.87j])