What does the expression 'exponentially distributed fading power' means? I am trying to understand a research article which states the following, $h_{t,u}^v \sim exp(1)$ denotes the exponentially distributed fading power from transmitter $t$ to the receiver $u$ over Rayleigh fading channel. Can anyone help me to understand what it means? Also, what does $exp(1)$ mean here? For detail relevant to the question image is attached below. * * * $ here. In case someone is curious, $P_M$ is Power by the transmitter, $l_{\alpha N}(m,u)$ is the distance-dependent fading for the channel and $u$ is the receiver.

The notation $X\sim\text{exp}(1)$ means that $X$ is a random variable that has the exponential distribution with parameter $1$. Thus $X$ randomly takes on a value in the interval $[0,\infty)$, but small values are more likely than large values.

The parameter $\lambda$ governs the exact shape of the distribution. For a distribution with parameter $\lambda$, the mean is $\lambda^{-1}$ and the variance is $\lambda^{-2}$.