Additive White Gaussian Noise (AWGN)
AWGN's PSD and its iDFT
In words, each noise sample in a sequence is uncorrelated with every other noise sample in the same sequence. Both positive and negative value can be acquired with equal probablity, therefore, mean value of a white noise is zero.
AWGN's instant value distribution
The probability distribution of the noise samples is Gaussian with a zero mean, i.e., in time domain, the samples can acquire both positive and negative values and in addition, the values close to zero have a higher chance of occurrence while the values far away from zero are less likely to appear. This is shown in Figure below. As a result, the time domain average of a large number of noise samples is equal to zero.
AWGN's Power
As with all densities, the value is the amount of noise power
per unit bandwidth
.
For the case of real sampling, we can plug in the above equation and the noise power in a sampled bandlimited system is given as
Thus, the noise power is directly proportional to the system bandwidth at the sampling stage.
PS: 功率 的计算
- 单边功率谱密度
，对应单边带宽宽度
- 双边功率谱密度
，对应双边带宽宽度
通信系统中常见的热噪声近似为白噪声（功率谱密度符合均匀分布，为一常数），且热噪声的取值恰好服从高斯分布（幅度瞬时值的取值分布符合高斯分布，即在均值两边对称分布）
