1. The simplest channel model just scales the input signal by a real number between 0 and 1 e.g. if the signal at the transmitter is s(t) then at the receiver it becomes a*s(t). The effect of channel is multiplicative (the receiver noise on the other hand is additive).
2. The above channel model ignores the phase shift introduced by the channel. A more realistic channel model is one that scales the input signal as well rotates it by a certain angle e.g. if s(t) is the transmitted signal then the received signal becomes a*exp(jθ)*s(t).
3. In a realistic channel the transmitter, receiver and/or the environment is in motion therefore the scaling factor and phase shift are a function of time e.g. if s(t) is the transmitted signal then the received signal is a(t)*exp(jθ(t))*s(t). Typically in simulation of wireless communication systems a(t) has a Rayleigh distribution and θ(t) has a uniform distribution.
4. Although the above model is quite popular, it can be further improved by introducing temporal correlation in the fading envelope. This can be achieved by the Smith’s simulator which uses a frequency domain approach to characterize the channel. The behavior of the channel is controlled by the Doppler frequency fd. Higher the Doppler frequency greater is the variation in the channel and vice versa .
5. Finally the most advanced wireless channel model is one that considers the channel to be an FIR filter where each tap is defined by the process outlined in (4). The channel thus performs convolution on the signal that passes through it. In the context of LTE there are three channel models that are defined namely Extended Pedestrian A (EPA), Extended Vehicular A (EVA) and Extended Typical Urban (UTU) .
Note: As an after thought I have realized that this channel model becomes even more complicated with the introduction of spatial correlation between the antennas of a MIMO system .