Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronic Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

Register Log in

Probability Of error for a joint PDF

Status
Not open for further replies.

M_A

Newbie level 3
Joined
Feb 24, 2007
Messages
3
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,281
Activity points
1,297
If we want to compute the probablity of error for a 4-PAM for example assuming AWGN and ISI having discrete values then it's straightforward ,
But what if ISI is also gaussian, how can i get the pdf of such a function?

thanks i
 

bulx

Full Member level 4
Joined
Aug 7, 2004
Messages
225
Helped
47
Reputation
94
Reaction score
17
Trophy points
1,298
Activity points
1,520
Can you clarify what you mean by discrete ISI?
-b
 

M_A

Newbie level 3
Joined
Feb 24, 2007
Messages
3
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,281
Activity points
1,297
ISI takes certain values with given probabilties, which is stastical independent
with the Gaussian Noise .
 

Bhanumurthy

Full Member level 5
Joined
Jun 18, 2008
Messages
255
Helped
34
Reputation
68
Reaction score
20
Trophy points
1,298
Location
Subcontinent
Activity points
2,743
Hi,
A fundamental concept in probability theory is 'A Random variable X is called a normal or Gaussian Random Variable if its pdf is of the form

fX(x) = 1/√2Πσ exp[-(x-µ)]²/2σ².
Hence rewrite your ISI in terms of above equation and u'll be able to plot the pdf.And then u can proceed for calculation of probability of error in terms of the complementary error function Q(z).

Regards
Bhanumurthy.
 

bulx

Full Member level 4
Joined
Aug 7, 2004
Messages
225
Helped
47
Reputation
94
Reaction score
17
Trophy points
1,298
Activity points
1,520
Question would be: What is probablistic in ISI? The pulse shapes are deterministic. The channel transfer function could be taken to be determinstic (but may be unknown), the rx and tx filters are also deterministic. The only probablistic quantity is the data itself. So are you refering to the discrete nature of the data when you say ISI is discrete? If so, ISI cannot be gaussian (as it is a continous distribution) where as data is discrete. Of course, added noise is random.

secondly, does the result that the sum of 2 normal independent random variables is also normal provide some direction?
-b
 

Bhanumurthy

Full Member level 5
Joined
Jun 18, 2008
Messages
255
Helped
34
Reputation
68
Reaction score
20
Trophy points
1,298
Location
Subcontinent
Activity points
2,743
Hi Bulx,
Central Limit Theorem provides some insight to u'r second question.
Regards
Bhanumurthy.
 

Status
Not open for further replies.
Toggle Sidebar

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Top