Re: Prob 4.7

Ed Casas (edc@ece.ubc.ca) Tue, 8 Feb 2000 13:20:51 -0800 

Date: Tue, 8 Feb 2000 13:20:51 -0800
From: Ed Casas <edc@ece.ubc.ca>
Subject: Re: Prob 4.7



On Mon, Feb 07, 2000 at 06:46:22PM -0800, Maria Lei [4681] wrote:

> In problem 4.7, it listed "a signal level 10dB below the rms level..."
> 
> Does this refer to:
> 1) p = R/Rrms = -10 dB

Yes, rho is the threshold value relative to the rms value of the
envelope at which your are measuring the level crossing rate or
mean fade duration ("p" is "rho").

> 2) Pr[ r <= R ] = 1 - exp(-p^2) = 1 - exp(- (R^2)/(2*sigma^2) )
>    where R = 0.1 sigma

These are two expressions for the CDF of the Rayeleigh
distribution.  The first is in terms of rho (R/Rrms) and the
second in terms of sigma (the rms value of the two component
Gaussians) and R.  From these definitions you can derive the
relationship between rho, R and sigma:

	rho = R/(sqrt(2)*sigma)

Note that Rrms and R are voltages (use 20log(.) to convert
to/from dB).

-- 
Ed Casas   edc@ece.ubc.ca   http://casas.ece.ubc.ca   +1 604 822-2592