Obtaining power distribution of faded signal

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SUMMARY

To obtain the power distribution from an amplitude fading distribution, such as Ricean, Rayleigh, or Nagakami fading, one must establish the relationship between power and amplitude, typically expressed as p = r². The process involves deriving the expression for power, dp/dr = 2r, and then integrating the envelope probability density function (pdf) over dp using dp = 2rdr. Additionally, the discussion highlights the importance of considering non-stationary signals and the application of the Jacobian and variable transformation in signal processing algorithms.

PREREQUISITES
  • Understanding of amplitude fading distributions (Ricean, Rayleigh, Nagakami)
  • Knowledge of signal power and envelope relationships
  • Familiarity with integration techniques in probability
  • Basic concepts of signal processing algorithms and non-stationary signals
NEXT STEPS
  • Study the mathematical foundations of Ricean, Rayleigh, and Nagakami fading distributions
  • Learn about the Jacobian transformation in signal processing
  • Explore the implications of non-stationary signals in communication systems
  • Investigate antenna diversity techniques for enhancing signal processing
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Signal processing engineers, telecommunications professionals, and researchers focused on fading signal analysis and power distribution optimization.

JamesGoh
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If I want to obtain the power distribution from an amplitude fading distribution (whether it is Ricean, Rayleigh or Nagakami fading), do I simply do the following ?

1. Find the mathematical relation between the power and amplitude (which in most cases is p=r^2 where p=signal power, r= signal envelope/amplitude)

2. Derive the expression for p, i.e. dp/dr = 2r

3. Make dp the subject, i.e. dp = 2rdr

4. Integrate the envelope pdf over dp, using dp=2rdr

regards
James
 
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First, fading is not a stationary signal. Lots of signal processing algorithms first presume you have stationary or at least cyclostationary signals. The latter can be used with antenna diversity (multiple antenna) to extract enough information.
 
my problem is resolved. it was actually a case of using the Jacobian and variable transformation
 

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