TWDP fading

Two-Wave with Diffuse Power or TWDP fading is a stochastic model for radio propagation fading. This type of fading is caused by the constructive-destructive interference of two strong radio waves and numerous smaller, diffuse waves. TWDP fading is a generalized form of physics-based wave fading distributions, which include Rayleigh fading and Rician fading as special cases.

For signal analysis, mathematicians and scientists had long sought envelope statistics for the problem of two sinusoids in the presence of Gaussian noise. The application of this scenario for radio wave propagation, including the name two-wave with diffuse power (TWDP) fading and its popular KΔ parameterization, was first presented by Durgin, Rappaport, and de Wolf. Frolik was the first to measure TWDP fading (in a plane fuselage), coining the term Hyper-Rayleigh to denote this and other fading scenarios that result in worse-than-Rayleigh received power outages for a radio link. Subsequently, other researchers have developed alternate, improved expressions for the TWDP distribution and its statistics.

TWDP fading arises in a radio channel characterized by two constant-amplitude waves and numerous, smaller radio waves that are randomly phased with respect to one another. A TWDP-distributed envelope R follows from the following combination of elementary random variables:

where ${\displaystyle U_{1}}$ and ${\displaystyle U_{2}}$ are independent uniform random variables over the interval [0,1); ${\displaystyle X}$ and ${\displaystyle Y}$ are independent, zero-mean Gaussian random variables with standard deviation ${\displaystyle \sigma }$. The two constant amplitude components are referred to as the specular components of the fading model. The ${\displaystyle X+jY}$ term represents the sum of numerous amplitudes and phases of smaller waves, which by the law of large numbers follows a complex Gaussian distribution.

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