What is multipath fading and how can it be modeled in cellular networks?

1 Rayleigh fading

Rayleigh fading is a simple and widely used model for multipath fading, especially when there is no dominant line-of-sight path between the transmitter and the receiver. It assumes that the signal components arriving from different directions are randomly distributed and have equal average power. The resulting signal envelope follows a Rayleigh distribution, which describes the probability of a certain signal amplitude. Rayleigh fading can cause severe signal degradation and requires robust modulation and coding schemes to overcome it.

2 Rician fading

Rician fading is a more general model for multipath fading, which accounts for the presence of a dominant line-of-sight path along with other scattered paths. It assumes that the signal components arriving from different directions have different average powers, depending on their angle and distance. The resulting signal envelope follows a Rician distribution, which describes the probability of a certain signal amplitude relative to the dominant component. Rician fading can vary from mild to severe, depending on the ratio of the dominant component to the scattered components, known as the Rician factor.

3 Nakagami fading

Nakagami fading is another general model for multipath fading, which can capture a wide range of fading scenarios and channel conditions. It assumes that the signal components arriving from different directions have different average powers, depending on their shape and dispersion. The resulting signal envelope follows a Nakagami distribution, which describes the probability of a certain signal amplitude relative to the mean. Nakagami fading can be characterized by a parameter called the Nakagami parameter, which indicates the degree of fading and the shape of the distribution.

4 Fading parameters

Besides the type of distribution, there are other parameters that can be used to model multipath fading in cellular networks. The coherence bandwidth indicates how much the channel varies with frequency and how much frequency diversity is available, while the coherence time indicates how much the channel varies with time and how much time diversity is available. Doppler spread reveals the range of Doppler shifts caused by the relative motion of the transmitter and the receiver, and it indicates how quickly the channel changes and how much Doppler diversity is available. Delay spread, on the other hand, provides insight into the range of delays caused by different paths between the transmitter and receiver, indicating how much the channel disperses the signal and inter-symbol interference present.

5 Fading mitigation

Multipath fading can be mitigated through the implementation of various techniques and strategies in wireless communication systems, such as diversity, equalization, channel coding, and adaptive modulation. Diversity involves the use of multiple antennas, frequencies, or codes to provide multiple independent paths for the signal, reducing the probability of deep fades and improving the signal-to-noise ratio. Equalization involves the use of filters or algorithms to compensate for channel distortion and interference. Channel coding involves the use of redundancy or error correction codes to protect the signal from noise and fading, increasing its reliability and robustness. Lastly, adaptive modulation involves the use of variable modulation schemes to adjust the signal rate and complexity according to the channel conditions, optimizing its spectral efficiency and throughput.