JPL's Wireless Communication Reference Website Slide Show

Envelope Correlation (Amplitudes)

Amplitude R₁² = I₁² + Q₁²

Conversion from (I₁, Q₁, I₂, Q₂) to (R₁, f₁, R₂, f₂).

n Jacobian is ½J½ = R₁ R₂

n so the PDF is

f(r₁,f₁,r₂,f₂) =

r₁r₂ f(i₁=r₁cos f₁, q₁=r₁sinf₁, i₂=r₂cosf₂, q₂=r₂sinf₂).

Integrating over f₁ and f₂ gives

where

the Bessel function I₀ occurs due to ò exp{cosf} df

 

the normalized correlation coefficient r is

JPL's Wireless Communication Reference Website © Jean-Paul M.G. Linnartz, 1993, 1995.