Ed Casas (edc@ece.ubc.ca) Thu, 3 Feb 2000 16:11:08 -0800
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Date: Thu, 3 Feb 2000 16:11:08 -0800 From: Ed Casas <edc@ece.ubc.ca> Subject: Re: prob 4.17On Thu, Feb 03, 2000 at 03:08:20PM -0500, Maria Lei wrote: > I values I got for sigma & A are extremely small, and the > resulting cdf does not addup to -80dBm. > > This is what I did: > > r_median = 1.177 sigma = 10^-7 (= -70dBm) This is true for the Rayleigh distribution but it's not the case for a Ricean distribution. For a Ricean distribution the median will be a function of both A and sigma (as noted in problem 4.16). For large values of K (A>>sigma), the Ricean distribution approaches a Gaussian distribution and the mean and median both approach A (you can use this, and the fact that A=0 corresponds to a Rayleigh distribution to check your results). You can find the median value from a CDF plot by finding the value for which the CDF is 0.5 (this is the definition of the median). If you move to a point 10 dB below the median you can read the CDF for a value 10 dB below the median. The CDF is the probability that the RV will be less than the given value (while the question asks for the probability that the signal will be *greater* than the given value). Note that the Ricean distribution is the distribution of the magnitude of the complex number (the voltage) not magnitude-squared (the power) so convert to/from dB accordingly. While the values along the abscissa of the CDF will be a function of the values you choose for sigma and A, the shape of the curve will be fixed for any given K, so it shouldn't matter what value you use for sigma as long as you scale A accordingly (I used sigma=1 to keep the numbers manageable). If you use a different sigma you'll have to do the integration over a different range of values to get an accurate plot. Also remember that you have to multiply the cumulative sum by the integration interval. But wait! You shouldn't need to compute anything (if you don't want to) you can read all the numbers you need off the curves that I put on the course web page. -- Ed Casas edc@ece.ubc.ca http://casas.ece.ubc.ca +1 604 822-2592
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