WSSUS Wide Sense Stationary Uncorrelated Scattering

Wide Sense Stationary Uncorrelated Scattering (WSSUS) is a fundamental assumption in wireless communication system analysis and modeling, particularly in the context of multiple-input multiple-output (MIMO) systems. It is a simplified and widely used scattering model that simplifies the analysis of the effects of scattering in wireless communication channels.

In wireless communication, when a signal is transmitted from a transmitter to a receiver, it propagates through the wireless channel. The channel can be thought of as a complex environment with various objects, obstacles, and reflecting surfaces. As the signal interacts with these objects, it gets scattered and arrives at the receiver through multiple paths, each with different time delays and phases.

WSSUS makes specific assumptions about the characteristics of the scattering process:

1. Stationarity: The scattering process is considered stationary, meaning that its statistical properties remain constant over time. In other words, the scattering environment is assumed to be roughly the same during the transmission of a signal. This assumption simplifies the channel modeling and allows for the use of statistical methods to describe the channel behavior.
2. Uncorrelated Scattering: WSSUS assumes that the scattered signals arriving at the receiver from different paths are uncorrelated. In other words, the signal scattered by one object or surface does not depend on or influence the scattering from other objects or surfaces. The uncorrelated scattering assumption simplifies the analysis by allowing each scattering path to be treated independently.
3. Wide Sense: The term "wide sense" in WSSUS refers to the statistical second-order moment of the scattering process. It implies that the scattering process is characterized by a mean value (expected value) and a covariance matrix that describes the correlation between different scattering paths.

Based on the WSSUS assumption, the wireless channel can be represented as a linear time-invariant system with a finite number of propagation paths. Each propagation path is associated with a complex gain, representing the attenuation and phase shift experienced by the signal along that path. These gains are assumed to be independent and identically distributed random variables.

In a MIMO system, WSSUS is often used to model the channel matrix, which represents the multiple antennas at the transmitter and receiver and their interaction with the wireless channel. The channel matrix is crucial for MIMO system analysis, including capacity estimation, beamforming, and diversity techniques.

While WSSUS provides a simplified and tractable model for the wireless channel, it is essential to recognize its limitations. In real-world scenarios, wireless channels can exhibit time-varying and frequency-selective characteristics, leading to more complex and dynamic channel models. Moreover, in scenarios with strong line-of-sight (LOS) components or when the scattering environment is highly correlated, the WSSUS assumption may not hold, and more sophisticated channel models are required.

In summary, Wide Sense Stationary Uncorrelated Scattering (WSSUS) is a simplified scattering model used in wireless communication systems to facilitate channel analysis and modeling. It assumes that the scattering process is stationary, uncorrelated, and characterized by a mean value and covariance matrix. While it provides a convenient framework for MIMO system analysis, it is essential to consider more complex channel models when dealing with real-world wireless communication scenarios.