Could anyone please guide me to calculate the CDF for user's throughput in a wireless communication system? What are the factors used for assumption? Any recommendation would be appreciated. Thank you very much in advance.
Dear Moh.
welcome,
The cumulative distribution function CDF is the he probability to have the users with throughput smaller equal to certain value. Assume that the throughput is x then the CDF= F(x) = The fraction of the users having throughput smaller equal x.
We can express it further as CDF= N(x)/ N where N is the total number of users in the cell. So, the physical model is we have a cell with N users distributed in its area A. N(X) is the number of users in in an edge ring with outer radius Rc and inner radius R,
The number of users in the edge ring N(x)= Nd pi( Rc^2-R^2), (N(x)/ Nd pi Rc^2)=N(x)/ N= [1-(R/ Rc)^2] == CDF.........(1)
The throughput at the radius R is determined from the Shanon theory as
x==C= B log2( 1+S/N)= B log2(1+ K R^-n / N)..........(2)
with S is the received signal power at the radius R. According to the propagation model S= K R^-n , where K is the propagation constant and n is the exponent varying from 2 to 4
Then one can calculate C as a function of R, with C=x
Then one can calculate CDF as a function of x, which is the required curve.
This is my proposed model for the required function.
Please review it and assess numerically.
Best wishes
The CDF of the normalized throughputs with respect to the average user throughput for all users in the system is determined.
Brother, in matlab there is a builtin function name 'cdf' available to calculate the cumulative density function. It is very easy to use. Follow the link
https://www.mathworks.com/help/stats/prob.normaldistribution.cdf.html
Cheers! (Mostafa Zaman Sir ke amar salam janie dio vai)
Regards
Md. Asadur Rahman
BME, KUET
Dear ...you can see this paper " Fundamental Limits of CDF-Based Scheduling: Throughput, Fairness, and Feedback Overhead " is available online ...Regards
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