Digital Demodulation

Until now, we haven’t included the impact of noise. The symbols sent as $-1$ and $+1$ have been received at the same amplitude. Let’s include the additive white Gaussian noise and see how bits can be obtained from the equalized samples.

Additive white Gaussian noise

Additive white Gaussian noise (AGWN) results from the random motion of electrons in the receiver frontend.

• This noise is added to the received signal.
• White light consists of all seven colors with equal intensity. Similarly, white noise implies a power spectral density that is equally spread across all frequencies.
• The noise amplitude is Gaussian distributed. This implies that the values close to the mean (the received signal itself) are more probable than values away from the mean.

Minimum distance rule

When AWGN is added to the received samples, the equalized samples do not exactly map to the symbols $-1$ ...