Probability Theory
Haesik Kim · 2015
The reason why many wireless communication books start from probability theory is that wireless communications deal with uncertainty. If there are no channel impairments by nature, we can receive the transmitted messages without any distortion and do not need to care about probability theory. A random signal cannot be predicted but we may forecast future values from previous events using probability theory. When we consider a signal over time, we find the energy spectral density (ESD) and power spectral density (PSD). A correlation function is used to know the relationship between random variables. When we face a noise that the nature has made electrical component noises or thermal noises, we assume it follows Gaussian distribution because of central limit theorems. This theorem means that the sample average and sum have Gaussian distribution regardless of distribution of each random variable.