1
$\begingroup$

I am having a doubt that why channel power gain is denoted by $|h|^2$. For example, if the signal received is $$y(n) = hx(n)+w(n)$$

where $x(n)$ is transmitted signal with power $P$ , $w(n)$ is AWGN with power $N$ and $h$ rayleigh fading channel.

The SNR from above equation is given as

$$\mathrm{SNR} = \frac{|h|^2P}{N}\tag{1}$$

My query is why $|h|^2$ is written in equation $(1)$?

Any help in this regard is highly appreciated.

Improve this question
$\endgroup$
2
  • $\begingroup$ SNR stands for signal to noise ratio, i.e., it is the ratio of the power of the input signal to the power of the noise. In this case, the signal power is given as $h \times x[n] \times x^*[n] \times h^*$, which is equal to $|h|^2 P$. The noise power is given as $N$. Take the ratio, and you get the SNR which includes the absolute value of $h$. $\endgroup$
    – Maxtron
    Commented Sep 2, 2021 at 6:52
  • $\begingroup$ Ok... Thank You so much... $\endgroup$
    – paru
    Commented Sep 2, 2021 at 8:35

1 Answer 1

Reset to default
0
$\begingroup$

In general, the channel coefficient $h$ is a complex number so it has magnitude and phase. Physically, $|h|^2$, is the attenuation/power-loss due to the channel and that is why you include it in the signal power calculation. The signal power is:

$$ \mathbb{E}\big[hx[n](hx[n])^* \big]=|h|^2\mathbb{E}\big[|x[n]|^2\big]=|h|^2P $$

Improve this answer
$\endgroup$
2
  • $\begingroup$ Thanks a lot for such a descriptive answer...... $\endgroup$
    – paru
    Commented Sep 2, 2021 at 9:46
  • $\begingroup$ The $|h|^2$ is taken out of Expectation because it is not depending on $n$. Is my understanding correct? $\endgroup$
    – paru
    Commented Sep 2, 2021 at 10:55

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.