sniggerImp
Newbie level 3
I am having a little trouble with my Energy Detection simulation for spectrum sensing
expression 1 -> pf * gamma(u)= incomplete_gamma(u,lambda/2)
where pf = probab. of false alarm
u = Time-Bandwidth product
lambda = threshold
expression 2 -> pd = Q(sqrt(2*snr) , sqrt(threshold))
where Q() is the generalized marcum function
pd = probability of detection.
1. How do we set the threshold for the energy detector ?
in many papers i have read , they usually suggest deriving the threshold from expression 1 , by choosing a pf ( say 0.05) and then calculating lambda.
( i tried doing this , but got stuck - cause was unable to implement the inverse incomplete gamma function .......... any suggestions how i can calculate the lambda ? )
( I dont have the function gammaincinv in my MATLAB version , so please suggest some alternative way)
2. in expression 2 .. the probability of detection is a function of threshold and snr.
if assuming the Time-Bandwidth product , and snr is kept const .. and the amplitude of signal and noise is increased .................. then by expression 1 , the threshold would come out to be the same , and hence even pd would turn out to be the same.
Which is wrong , cause with change in noise value , lambda should change , but that doesn't happen here.
Am I missing something ??
Please help
expression 1 -> pf * gamma(u)= incomplete_gamma(u,lambda/2)
where pf = probab. of false alarm
u = Time-Bandwidth product
lambda = threshold
expression 2 -> pd = Q(sqrt(2*snr) , sqrt(threshold))
where Q() is the generalized marcum function
pd = probability of detection.
1. How do we set the threshold for the energy detector ?
in many papers i have read , they usually suggest deriving the threshold from expression 1 , by choosing a pf ( say 0.05) and then calculating lambda.
( i tried doing this , but got stuck - cause was unable to implement the inverse incomplete gamma function .......... any suggestions how i can calculate the lambda ? )
( I dont have the function gammaincinv in my MATLAB version , so please suggest some alternative way)
2. in expression 2 .. the probability of detection is a function of threshold and snr.
if assuming the Time-Bandwidth product , and snr is kept const .. and the amplitude of signal and noise is increased .................. then by expression 1 , the threshold would come out to be the same , and hence even pd would turn out to be the same.
Which is wrong , cause with change in noise value , lambda should change , but that doesn't happen here.
Am I missing something ??
Please help