## Impact of Multipath on the Received Signal

In this article, we describe the impact of multipath caused by the wireless channel on the signal arriving at the receiver from a constellation viewpoint. Recall that an eye diagram, a transition diagram and a scatter plot are the stethoscopes of a communication system and hence it is imperative to bring in that perspective for a Tx signal convolved with the channel impulse response. This is because a wireless channel can be seen as a Finite Impulse Response (FIR) filter with the result that the sampled Rx signal is a convolution between taps of this FIR filter and the Tx

## Additive White Gaussian Noise (AWGN)

The performance of a digital communication system is quantified by the probability of bit detection errors in the presence of thermal noise. In the context of wireless communications, the main source of thermal noise is addition of random signals arising from the vibration of atoms in the receiver electronics. You can also watch the video below. The term additive white Gaussian noise (AWGN) originates due to the following reasons: [Additive] The noise is additive, i.e., the received signal is equal to the transmitted signal plus noise. This gives the most widely used equality in communication systems. \label{eqIntroductionAWGNadditive} r(t) = s(t)

Remember that in the article on correlation, we discussed that correlation of a signal with proper normalization is maximum with itself and lesser for all other signals. Since the number of possible signals is limited in a digital communication system, we can use the correlation between incoming signal $r(nT_S)$ and possible choices $s_0(nT_S)$ and $s_1(nT_S)$ in a digital receiver. Consequently, a decision can be made in favor of the one with higher correlation. It turns out that the theory of maximum likelihood detection formalizes this conclusion that it is the optimum receiver in terms of minimizing the probability of error.