What is WSSUS Wide Sense Stationary Uncorrelated Scattering

WSSUS: Wide-Sense Stationary Uncorrelated Scattering

Understanding WSSUS

Wide-Sense Stationary Uncorrelated Scattering (WSSUS) is a statistical model used to characterize the behavior of wireless communication channels. It simplifies the complex multipath propagation environment by making specific assumptions about the channel's statistical properties.

Key Assumptions of WSSUS

1. Wide-Sense Stationarity (WSS): This implies that the statistical properties of the channel, such as the mean and autocorrelation function, do not change over time. In other words, the channel's behavior is stationary in a statistical sense.
2. Uncorrelated Scattering (US): This assumes that the scatterers in the environment are independent and their contributions to the received signal are uncorrelated. This means that the multipath components arriving at different delay times are statistically independent.

Mathematical Representation

The WSSUS channel is characterized by its impulse response, h(t, τ), where:

• t is the absolute time
• τ is the delay spread

The WSSUS assumption implies that the autocorrelation function of the channel impulse response depends only on the time difference τ, and not on the absolute time t:

• R_h(τ, Δt) = E[h*(t, τ)h(t + Δt, τ + Δτ)] = R_h(τ)

Implications of WSSUS

• Channel Characterization: The WSSUS model simplifies channel characterization by focusing on the statistical properties rather than the detailed behavior of individual scatterers.
• Channel Modeling: It enables the development of mathematical models for channel simulation and performance analysis.
• System Design: WSSUS is used to design communication systems that are robust to the effects of multipath fading.

Limitations of WSSUS

• Idealization: The WSSUS model is an idealization and may not accurately represent all real-world channel conditions.
• Time-Varying Channels: While WSSUS assumes stationarity, real channels can exhibit non-stationary behavior due to factors like user mobility and environmental changes.

Applications of WSSUS

• Channel Modeling: WSSUS is widely used to create realistic channel models for simulation and performance evaluation of wireless communication systems.
• Equalization: Channel equalization techniques often rely on the WSSUS assumption to design effective equalizers.
• Diversity Techniques: WSSUS is used to analyze the performance of diversity techniques, such as space-time coding and frequency diversity.

Conclusion

The WSSUS model provides a valuable framework for understanding and analyzing wireless communication channels. While it simplifies the complex channel behavior, it offers a reasonable approximation for many practical scenarios. By understanding the WSSUS assumptions and limitations, engineers can design more robust and efficient wireless communication systems.