Finding the Variance for Gaussian Channel.

[malaylah]

I am a new guy in digital communication. Is there anyone here can help me.
We know that:

Eb/No=(X^2)/(2*var^2*R)

Know that this is a general equation.While R is the rate and Var is the variance. Just wondering, what is X in this equation?Is it the energy for one symbol or one bit?

If let say I am using QPSK with +1 and -1. Then what is my X^2 here?Thanks a lot.

 

[joshuashi]

I am a new guy in digital communication. Is there anyone here can help me.
We know that:

Eb/No=(X^2)/(2*var^2*R)

Know that this is a general equation.While R is the rate and Var is the variance. Just wondering, what is X in this equation?Is it the energy for one symbol or one bit?

If let say I am using QPSK with +1 and -1. Then what is my X^2 here?Thanks a lot.

X^2 is the variance of the signal. It can be understood intuitively as the power of the signal (per bit or per symbol). For the QPSK case you mentioned, it should be 2.

I think the equation you mentioned should be understood as:

N0: noise power spectral density.
Eb: signal energy per bit.
var: noise variance. = N0*B (B:bandwidth).

So,

Eb/N0 = Eb/ (var/B)
= Pb*Tb/(var/B) % Pb: power per signal bit; Tb: bit duration
= E(Xb^2)*Tb/(var/B) % for zero mean signal. E(): expectation

Note B is not necessary equal to bit rate.

pls correct me if I am wrong.

 

[cwjcwjcwj]

I believe x^2 for QPSK is equal to 1 instead of 2.......Someone pls clarify it......

 

[joinfaisal]

Hello...
In QPSK you have symbol +1 -1 j or -j means all symbols have amplitude (lets call it) equal to 1.Now X^2 represent sysmbol energy so it will be always 1 because 1^2 will be 1.