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## Re: [Discuss-gnuradio] BER over air

 From: Mostafa Alizadeh Subject: Re: [Discuss-gnuradio] BER over air Date: Mon, 29 Dec 2014 19:42:25 +0330

Marcus you're right. This question is somehow out of GNURadio discussion. However, I've found something about different perspectives of SNR calculation at a receiver.

Thank you for participating in this discussion. If I find enough time, I will try to generate a code for SNR calculation regardless of type of modulation used and I will share it.

Best,
Mostafa

On Dec 29, 2014 4:53 PM, "Marcus Müller" <address@hidden> wrote:
Hi Mostafa,

On 12/29/2014 01:58 PM, Mostafa Alizadeh wrote:
I completely agree to the statement. But take a look at this simple model:

y(t) = h(t) * x(t) + n(t).
it's totally ok to use that model, but only if your application indicates that this is the right model to use. By the way, *all* components in your equation have time dependency (t), so this alone doesn't justify assuming time-invariance.
Estimation h is called gaining channel state information, to give you some hints on what to look for in literature.

'y' is the received signal, 'h' is the channel response (here I assumed that the channel is linear as a filter), 'x' is the desired signal and 'n' is noise and the sign '*' is the convolution. Hence, if we try to find signal (x) power to noise (n), it implies that the 'h' is somehow estimated.
convolution with the channel is exactly identical to "applying a filter". This implies your channel is not flat.

Again, consider that noise and channel are different both statistically and in nature.
If I understand you correctly, then you state exactly what I'm saying: everything you calculate is but an estimate, and the things you can say about SNR are thus only estimates. Whether or not that estimate is a good representation for the reality depends on the way you estimate, and how well your assumptions match reality. This demands a high level of understanding for the underlying concepts!

He said:

" In the case of an SNR estimator, though, I thought about this and had to come to the conclusion that the only way to handle this is to have an estimator that you can plug in variables for your channel model, which of course assumes that you have or can estimate these parameters."

So we need acquire 'h'.
There's two key words in this paragraph: 1. "channel model" and 2. "acquire".
1. "channel model": this implies you model the channel, ie. you make justified assumptions on what the channel is. in the y(t) = h(t)*x(t)+n(t), it's implied the channel is linear and might have a time dependence.
2. acquiring channel state information usually is done by transmitting something that you already know (e.g. a preamble) or using redundancy (ie. coding); if you're being honest, you would have to say "ok, now that I have information about h, I can actually transmit data, but since it took energy and time to get that information, I must account for this effort (==energy) when considering the effort I have sending the data (==bit energy)". That's a strong argument for not using SNR but E_b/N.

All in all, I think I should stop participating in this thread, since I feel that I'm repeating myself. I'd very very humble suggest that you take a few days with the appropriate theoretical literature on digital communications [1], as you seem to be about to write something with a very strong theoretical aspect. None of these mails related in any kind to GNU Radio or even SDR, just basic digital communication theory.

Best regards, and all the best,

Marcus